The Precipitation of Hydrides in Zirconium Alloys
T
HE
P
RECIPITATION OF
H
YDRIDES IN
Z
IRCONIUM
A
LLOYS
A thesis submitted to The University of Manchester for the degree of Doctor of
Philosophy, in the Faculty of Engineering and Physical Sciences
M ATTHEW S EBASTIAN B LACKMUR
2015 ◦ MMXV
M ATERIALS P ERFORMANCE C ENTRE
S CHOOL OF M ATERIALS
The Precipitation of Hydrides in Zirconium Alloys
Contents
Microstructure and Properties .................................................................. 26
The Synchrotron Accelerator and X-Ray Diffraction .................................. 59
Synchrotron Studies of the Zirconium-Hydrogen System .......................... 62
1 | Contents
The Precipitation of Hydrides in Zirconium Alloys
Non-Hydrogen-Charged Sample (S1)......................................................... 74
Hydrogen-Charged Sample (S2) ................................................................ 76
Deconvolution of Material Reflection Profiles ........................................... 78
Debye-Scherrer Ring Integration ............................................................... 83
Quantitative Analysis of Diffraction Patterns .................................................. 85
The Rietveld Method for Structural Model Refinement ............................ 87
Preparation for Rietveld Refinement of Structural Models ....................... 92
Application of the Rietveld Method for Refinement ................................. 93
The Le Bail Method for Structural Model Refinement .............................. 97
Application of the Le Bail Method for Refinement .................................... 98
Phase Weight Percentages ...................................................................... 100
Temperature Measurement .................................................................... 102
Hydrogen Concentration ......................................................................... 107
Contents | 2
The Precipitation of Hydrides in Zirconium Alloys
Annex – Transmission Electron Microscopy ................................................... 185
Non-Hydrogen-Charged Sample (S3) ............................................................. 230
Appendix I – Rietveld Refined Structural Model (TOPAS INP Format)........ 233
Appendix II – Le Bail Refined Structural Models (TOPAS INP Format) ........ 235
A thesis composed of 83043 words.
3 | Contents
The Precipitation of Hydrides in Zirconium Alloys
Table of Figures
Figure 5. Pure zirconium pressure-temperature phase diagram (reproduced from [40]). .......... 29
Figure 6. Weight gain as a function of oxidation time up to 100 days at 400 °C (reproduced from
Figure 9. Hydrogen evolution with temperature in Zircaloy-4 sheet (reproduced from [90]). .... 39
Figure 11. Three inter-granular hydride forms, (a) along both boundary sides, (b) cross boundary,
Figure 14. Effect of applied tensile stress on hydride orientation, (a) unstressed orientation,
(b) stress induced reorientation perpendicular to applied load (reproduced from [108]). ......... 46
Figure 15. The mechanical effect of hydriding [15] (reproduced from (a) [123] and (b) [122]). . 50
Figure 18. Schematic of the crack velocity to stress intensity factor relationship for DHC,
Figure 19. The interaction between scattered waves, showcasing (a) destructive and
Figure 20. Schematic representations of (a) Debye-Scherrer diffraction cones,
Figure 21. (a) Bragg-Brentano (reflection) and (b) Debye-Scherrer (transmission), and
Table of Figures | 4
The Precipitation of Hydrides in Zirconium Alloys
Figure 22. The European Synchrotron Radiation Facility, photograph reproduced from [151]. .. 62
Figure 26. ElectroThermal Mechanical Tester (ETMT) sample mounting schematic. .................. 74
Figure 29. Diffraction patterns from (a) cerium dioxide (a standard reference material), and
Figure 31. The experimental profile compared with the CuK
emission profile........................... 82
Figure 35. Schematic showing multiple solutions to reflection overlap during analysis of a single
Figure 39. Pyrometer temperature as a function of thermocouple temperature. .................... 103
5 | Table of Figures
The Precipitation of Hydrides in Zirconium Alloys
Figure 50. Zircaloy-4 TEM micrograph at 17,000x magnification, observed in the 0002𝛼 direction.
Figure 52. ‘Coffee-bean’ strain contrast features, thought to be hydrides, at (a) 350,000x,
Figure 56. Charged sample notch tip hydride mapping of sample S3 under applied load. ....... 232
Table of Figures | 6
The Precipitation of Hydrides in Zirconium Alloys
Table of Tables
Table 2. Standard compositions for zirconium alloys in weight percentages [27,29,32–34]. ...... 26
Table 5. Matrix-hydride interfacial strains (Barrow et al.)/stress free transformation strains
Table 9. Solubility temperatures and hydrogen concentration calculated from the offset method.
7 | Table of Tables
The Precipitation of Hydrides in Zirconium Alloys
Table of Equations
Table of Equations | 8
The Precipitation of Hydrides in Zirconium Alloys
Abstract
This alternative format thesis is submitted by Matthew Sebastian Blackmur to The
University of Manchester for the degree of Doctor of Philosophy in the year of 2015, entitled “The Precipitation of Hydrides in Zirconium Alloys”. The thesis first introduces the topic of nuclear energy and provides a brief section on plant familiarisation, after which zirconium nuclear fuel cladding is explained, and an in-depth literature review is presented on the in-service degradation of this component from hydriding. The concept of synchrotron X-ray diffraction is elucidated, and examples of its use are given, relevant to the topic of this work.
The experimental section discusses an initial quantification of the Zircaloy-4 material used throughout the present work, and documents in minutia the process of collecting and analysing in-situ synchrotron X-ray diffraction data. The experimental campaign discussed within involved a series of consecutive thermal cycles designed to investigate the redistribution of hydrogen as a function of thermal and concentration gradients; the kinetics of precipitation during isothermal dwells at reactor relevant temperatures; and the evolution of strain in the matrix and hydride during these dwells.
As an alternative style thesis, these three topics are separated into three independent proposed manuscripts, produced in a format ready for publication.
The diffusion and redistribution paper observes localised enrichment and depletion that occurs as a function of time and temperature, investigating the flux of hydrogen that results from concentration and thermal gradients, and introduces the concept of hydrogen trapping. The second manuscript documents evidence of the rate limiting kinetics for hydride precipitation seen at elevated temperatures, and describes a model for nucleation, developed to support the experimentally produced results. The final manuscript investigates the nature of the strains that evolve in the matrix and hydride phases during precipitation and growth, highlighting slow-strain rate relaxation in both phases and examining the constraining effect that the matrix has on the hydride precipitates.
Lastly, the themes from each of the three manuscripts are drawn together in a final conclusion, after which further experimental analysis that is to be performed as part of this experimental campaign is outlined.
9 | Abstract
The Precipitation of Hydrides in Zirconium Alloys
Declaration
The work presented herein has not been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning.
Copyright Statement
I.
The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the “Copyright”) and s/he has given
The University of Manchester certain rights to use such Copyright, including for administrative purposes.
II.
Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents
Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time.
This page must form part of any such copies made.
III.
The ownership of certain Copyright, patents, designs, trademarks and other intellectual property (the “Intellectual Property”) and any reproductions of copyright works in the thesis, for example graphs and tables (“Reproductions”), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions.
IV.
Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the University
IP Policy 1 , in any relevant Thesis restriction declarations deposited in the
University Library, The University Library’s regulations 2 and in The University’s policy on Presentation of Theses.
1 See http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487
2 See http://www.manchester.ac.uk/library/aboutus/regulations
Declaration & Copyright Statement | 10
The Precipitation of Hydrides in Zirconium Alloys
Dedicated to the memory of,
Leo Mac Harley
United States Army Air Corps
9 th August 1925 – 27 th January 2015
And,
Anthony George Blackmur
United Kingdom Royal Artillery
17 th February 1929 – 17 th November 2014
Loving and devoted grandparents.
Proud Servants of their respective countries during the second great war.
Truly, they were the greatest generation.
11 | Declaration
The Precipitation of Hydrides in Zirconium Alloys
Acknowledgements
The author would first like to acknowledge The University of Manchester for providing an exciting, dynamic environment in which to study, with facilities that are second to none. The infrastructural support of the University as a whole, The Faculty of
Engineering and Physical Sciences, and the Material Performance Centre is also recognised for providing assistance throughout this programme of study.
The Engineering and Physical Science Research Council is thanked for graciously providing the sponsorship funding for this project, as is Rolls-Royce PLC for providing an industrial case award. Appreciation is owed to Edward Darby, Aidan Cole-Baker, Andrew
Barrow, David Rugg and Robert Bentley of Rolls-Royce PLC for providing an industrial perspective and technical advice on various topics during this work.
The Institut de Radioprotection et de Sûreté Nucléaire is thanked for their incredible donation of beam time and experimental data, without which this thesis would not exist; furthermore, a debt of gratitude is owed to Olivier Zanellato for providing training, help and advice throughout the project. Similarly, thanks are given to Robert
Cernik for assistance with TOPAS and general crystallography, and to Susan Ortner for discussions on the behaviour of hydrogen in zirconium.
The author is grateful to San-Qiang Shi and the Hong Kong Polytechnic University for the incredible opportunity of an overseas secondment and collaboration on industry-leading modelling, as well as help with numerical studies. Thanks are also given to Jakob Blomqvist and Tuerdi Maimaitiyili for fruitful discussions pertaining to synchrotron studies of hydrides, the opportunity to visit the University of Malmö and allowing collaboration on their experiments.
The author is grateful beyond measure to Michael Preuss and Joseph Robson for all of their support, endless assistance and unfaltering patience provided during the programme of study; the author could not have asked for better supervisors, and enjoyed working with them greatly. To his family, the author is endlessly grateful for the love and support they have given throughout. Finally, eternal thanks are given to Sarah Connolly, without whom the motivation to finish this thesis would not have been possible. To each of these, I owe everything.
Acknowledgements | 12
The Precipitation of Hydrides in Zirconium Alloys
1.
Introduction
1.1.
The Nuclear Reactor
The birth of nuclear energy is intrinsically linked to the arms race that took part between
Nazi Germany and the United States of America during the Second World War. The first self-sustaining fission reaction was produced under the supervision of Fermi at the University of
Chicago in 1942, and gained significant interest from those wishing to develop advanced weapons to combat the Nazis [1]. The post-war emphasis, however, shifted the focus away from weaponisation, towards civil energy production, and in 1951 the first electricity was generated from nuclear energy in Breeder Reactor I [1]. Over fifty years later, civil nuclear power capacity has grown significantly and is on track to generate more than 400 GW e by 2030, supported by the entry of many more nations into the nuclear energy sector [2].
While many aspects of design may have changed to improve safety, efficiency and capacity in this time, the fundamental principle behind the functioning of a fission reactor complex has remained essentially the same. The heat energy released during the fission of atoms, triggered by neutrons in a controlled chain reaction, is used to heat a coolant medium in one or more loops, where the final medium is gaseous and drives a turbine, thus generating electricity.
In practice, the coolant medium used can take the form of light water, heavy water, liquid metal/molten salts or gas, depending on the design of specific reactors [3–7]. This thesis, however, explicitly considers reactors that utilise light water (H
2
O, as opposed to D
2
O) as a coolant.
Fundamentally, there are two derivatives of the light water reactor, the BWR (Boiling
Water Reactor) and PWR (Pressurised Water Reactor), which are shown schematically in Figure 1
and Figure 2. The BWR, being the earlier developed system, uses a single closed loop in which the
coolant is boiled in the reactor pressure vessel to produce steam. Unfortunately, this potentially leads to the contamination of the turbine, making it difficult to repair during service or dispose of during end of life decommissioning. The newer PWR design uses a sequence of loops, with the innermost pressurised to ≈15.5 MPa, keeping the coolant entirely fluidised within this first circuit
(with the exception of some within the pressuriser) [8].
The heat energy from the primary loop can then be used to boil water in a secondary loop, thus preventing the turbine from coming into contact with contaminated coolant. In both heavy and light water reactors, the water in the primary loop acts as both a coolant, conducting heat away from the reaction that takes place in the fuel, as well as a moderator. This crucial component of a reactor acts to slow fast neutrons, which are those produced during the process of fission, converting them to thermal neutrons. This deceleration subsequently increases the chance of the neutrons interacting with fissile atoms within the fuel, causing further fission.
13 | Introduction
The Precipitation of Hydrides in Zirconium Alloys
Reactor efficiency can also be improved through the use of a pressurised primary loop containing only fluidised coolant, as liquid water acts as a far superior moderator when compared with steam, thus improving the stability of the chain reaction [7]. In addition, the reactor is able to passively stabilise itself, as accidental rises in temperature lead to the localised boiling of the pressurised coolant, thus decreasing the moderating effect [7]. With fewer fast neutrons being slowed, there are fewer thermal neutrons to trigger fission, which then leads to a reduction in the rate of fission and subsequently diminishes the generation of thermal energy, lowering the temperature [7].
Introduction | 14
The Precipitation of Hydrides in Zirconium Alloys
15 | Introduction
Figure 1. Schematic of a Boiling Water Reactor (BWR) [9].
The Precipitation of Hydrides in Zirconium Alloys
Figure 2. Schematic of a Pressurised Water Reactor (PWR) [9].
Introduction | 16
The Precipitation of Hydrides in Zirconium Alloys
1.2.
The Reactor Core
At the heart of the plant lies the reactor pressure vessel, where the energy that is used to heat coolant, drive turbines and generate power, originates. As previously mentioned, the heat energy itself stems from thermal neutrons colliding with the atomic nuclei of a fissile fuel and causing them to decay, releasing fission products, fast neutrons and heat energy. The thermal energy is taken up by the coolant and ultimately generates electricity through the driving of a turbine, while the fission products remain in the fuel and are discarded as waste at the end of the fuel’s life [10,11]. The fast neutrons that are released by the decay of atoms are slowed by the moderator, collide with fissile atoms in other fuel, and create a cascading chain reaction [10].
In LWRs, the fuel itself usually takes the form of cylindrical pellets that are stacked and encased within a cladding material to form fuel rods or pins, which can measure more than
12 meters long [7]. These rods are then grouped together into bundles or assemblies, and many sets of these are inserted into the core of the reactor [7]. In addition to fuel, control rods are also present within the pressure vessel, allowing for the dynamic control of the fission reaction, through limiting the interaction of adjacent fuel rods [7]. By adjusting the level of insertion of these rods, the speed of the reaction can be manipulated, enabling precise control of a stable chain reaction [7]. The interaction of individual fuel rods in an assembly can be seen schematically
in Figure 3, along with the effect of control rod insertion.
17 | Introduction
The Precipitation of Hydrides in Zirconium Alloys
Figure 3. Schematic diagram of fuel rod, coolant and control rod interaction [7].
1.3.
Nuclear Fuel Cladding
The aforementioned cladding, which encapsulates oxide fuel pellets, plays a crucial part in the operability of the reactor. Primarily, the cladding material must function as a structural component, acting to fix large numbers of pellets in place, while conducting heat into the coolant that flows turbulently between rods [7]. In addition to this role, the cladding also serves as a buffer between the fuel and the surrounding reactor environment. By functioning as a sealed unit, cladding tubes can contain gaseous fission products that escape the fuel, preventing contamination of the coolant with high-level waste [7,12,13]. The importance of the mechanical stability of the cladding in-operando cannot be understated, as it is intrinsically linked to the operability, safety and efficiency of the reactor [12]. These conditions, however, impose a challenge when selecting a suitable material, as it is continuously exposed to a rapidly flowing,
Introduction | 18
The Precipitation of Hydrides in Zirconium Alloys hot aqueous environment [7,13]. In the case of PWRs, the temperature of the cladding can range between 280 °C and 400 °C, at coolant pressures of up to 15.5 MPa, creating a highly corrosive medium under normal reactor operating conditions [7,8,14,15]. As a result, the cladding tubes must be highly resistant to aqueous corrosion while preserving their mechanical properties at operational temperatures (and potentially those of accident conditions) in order to maintain structural integrity [7].
While there are a number of highly corrosion resistant materials that display mechanical stability in elevated-temperature environments, the basic operating principle of a fission reactor creates an additional limitation on the cladding [13]. The neutrons produced by one rod must be able to interact with the fuel present in other rods, so as to maintain a stable chain reaction. As such, they need to be able to pass through the cladding material, rather than being absorbed, in order for this interaction to take place. This feature of a material, to allow transmission rather than to absorb, is known as neutron transparency, and it is this that sets zirconium apart from other potential cladding materials [13,16].
Table 1 demonstrates the thermal-neutron cross section of a number of common
engineering materials with melting temperatures above the operating range of a nuclear reactor, which would be mechanically stable under normal operation. When looking at their neutron transparency, however, the majority of these are at least an order of magnitude poorer than the four materials demonstrating the lowest capture cross-section. Early work on beryllium, with the lowest cross section, deemed it too brittle, reactive and expensive for use in the applicable environment [13]. While these features were not true for aluminium and magnesium, they were also seen as unsuitable due to concerns over temperature range and reactivity [13]. More specifically, the comparatively low melting temperature of these two elements may have raised questions over their behaviour during potential accident situations, where temperatures could increase significantly within the reactor vessel. Ultimately, factors like the superior corrosion performance in aqueous environments, a high melting temperature (providing good thermal stability to mechanical properties), good wear resistance (resisting vibration induced abrasion from spacers) and low neutron capture cross section set zirconium apart as the strongest option for fuel pin cladding. Therefore, the use of zirconium as a cladding material is now ubiquitous in water-cooled reactors across the world.
19 | Introduction
The Precipitation of Hydrides in Zirconium Alloys
Table 1. Neutron capture cross sections for elements with relatively high melting temperatures [13].
Element
Beryllium
Magnesium
Zirconium
Aluminium
Columbium
Iron
Molybdenum
Chromium
Copper
Nickel
Vanadium
Titanium
2.4
2.9
3.6
4.5
4.7
5.6
Thermal-Neutron Capture
Cross-Section (σ a
)
0.009
0.059
0.18
0.22
1.1
2.4
Melting Temperature (°C)
1280
651
1845
660
2415
1539
2625
1890
1083
1455
1710
1725
1.4.
Structure, Justification and Aims of Thesis
What follows is a thesis composed around a synchrotron X-ray diffraction experimental campaign that contains a number of separate, but complimentary, components, aimed at elucidating certain aspects of the precipitation of hydrides in Zircaloy-4. As synchrotron studies provide a wealth of information, a number of papers were planned from this programme, namely:
The diffusion and redistribution of hydrogen.
The kinetics of hydride precipitation.
The evolution of strain during hydride precipitation.
The effect of tri-axial stress and a notch on the redistribution of hydrogen and hydrides.
Given the interest in the delayed hydride cracking, an investigation into tri-axial stress was seen as an important one, but given the complexity of such an experiment it was thought that a number of preceding tests would be useful to understand further the in-situ behaviour during experimentation. As a result, a broader experimental campaign was designed out of thoughts pertaining to the loading experiment. Each of the three other topics, however, was proposed as a standalone investigation, with findings thought to be both novel and industrially relevant. Furthermore, while the emphasis is on the experimental programme, each topic was also coupled with some form of computational assessment, aiming to support the results from each and to strengthen understanding.
To begin with, the selection of the heating and loading apparatus meant that the sample would be exposed to an axial thermal gradient, owing to the Joule heating process, and so an assessment of the migration of hydrogen under the Soret Effect (thermo-diffusion) was needed.
Introduction | 20
The Precipitation of Hydrides in Zirconium Alloys
This not only supports the current campaign, but also benefits the wider topic of hydrogen in zirconium, where the thermal redistribution of hydrogen and hydrides in service components is an observed effect. As temperature plays an important part in the precipitation of hydrides, it thus became important to quantify the precipitation kinetics of hydride formation and nucleation.
While there has been work of this nature published in the literature already, doing so under the conditions relevant to the broader programme was seen as a useful study. Finally, other authors have quantified the chemical and thermal strains that influence the hydride and matrix during precipitation, and so it was thought that an evaluation of the directional strain evolution during long dwells at temperature might prove interesting. Given the versatility of synchrotron X-ray diffraction, the strain and kinetics observations were rolled into a single set of operations, making concurrent observations of these phenomena possible.
The fourth experimental analysis is ongoing, but separate manuscripts have been produced documenting each of the first three topics, which are those included within this thesis.
In keeping with the style of a traditional thesis, a brief introduction to the context of the role of zirconium in nuclear power is given, a broad technical background to the zirconium-hydrogen system is presented, and an explanation of advanced X-ray diffraction techniques is provided.
While each paper contains a detailing of the experimental method, these are abridged through necessity, and so an in-depth chapter explains the precise experimental and analytical steps needed to replicate this work. Appendices are also be included containing the structural models employed in the simulating of diffraction patterns.
Each of the three papers is included in a pre-print format, whereby they have been read and approved by the various co-authors associated with the work. Each manuscript in the series is included with a foreword that details the precise contribution of each listed author to the related publication, and an annex that details any further scientific information relevant to the text, where necessary. The overall contribution of each author, and their institutional affiliations, are listed as follows:
Michael Preuss – The University of Manchester – Primary supervisor during this research, focusing on experimental studies, synchrotron X-ray diffraction and mechanical interactions, providing guidance and support on each of these topics.
Joseph Robson – The University of Manchester – Secondary supervisor during this research, specialising in modelling and thermodynamics, topics on which instruction and direction were provided.
21 | Introduction
The Precipitation of Hydrides in Zirconium Alloys
Olivier Zanellato – École Nationale Supérieure d'Arts et Métiers, formerly of Institut de
Radioprotection et de Sûreté Nucléaire – Instrumental in designing the experimental programme as an extension of his previous studies, providing the material utilised, collaborating on the experimentation and giving advice and support on data analysis. Further to this, Olivier provided the EBSD maps that are used to quantify the base metal.
San-Qiang Shi – The Hong Kong Polytechnic University – Provided the Phase Field
Modelling software used during this thesis and technical support on its use, along with further aid with other computational studies.
Robert Cernik – The University of Manchester – Provided training with specialist software and technical guidance on X-ray crystallography and its analysis.
Jérôme Andrieux – Université de Lyon, formerly of The European Synchrotron Radiation
Facility – The beamline scientist associated with the present experimental work, key to the successful execution of the experimental campaign.
Fabienne Ribiero – Institut de Radioprotection et de Sûreté Nucléaire – Supervisor to
Olivier Zanellato while he was a member of the IRSN and experimental collaborator.
Allan Harte – The University of Manchester – Provided the technical capability to electro-polish TEM samples of the material used in synchrotron studies.
Dimitris Tsivoulas – The University of Manchester – Provided the expertise needed to image hydrides and microstructures using TEM.
Additionally, technical discussions with individuals other than the listed authors have benefitted this thesis and the manuscripts contained herein, those persons are:
Sarah Connolly – The University of Oxford – General technical and editorial oversight.
Susan Ortner – National Nuclear Laboratory – Hydrogen redistribution and strains.
Andrew Barrow – Rolls-Royce PLC – Hydride precipitation kinetics.
Tuerdi Maimitiyili – Malmö University – Hydrides and synchrotron analysis.
Jakob Blomqvist – Malmö University – Hydrides and synchrotron analysis.
Introduction | 22
The Precipitation of Hydrides in Zirconium Alloys
2.
Literature Review
2.1.
Zirconium Fundamentals
2.1.1.
Origins
The transition metal zirconium is found abundantly around the world, contained primarily in the naturally occurring ore zircon [17]. This silicate ore, from which zirconium takes its name, has been in use in jewellery dating back to the ancient Egyptians and was thought to be a form of diamond at certain points in history [18,19]. In 1789 however, Martin Klaproth demonstrated through an oxidation experiment that the mineral zircon contained a previously undiscovered element [18]. While he was not able to separate the metal from the oxide, Klaproth was able to identify its existence and it was subsequently named zirconium [18]. While zircon is the most commonly occurring ore of zirconium, found naturally in granites and distributed throughout river and sea beds as a result of erosion, a second impure ore also exists that is known as baddeleyite [17]. As an element, zirconium is estimated to be as abundant on earth as carbon, and features 11 th on the list of prevailing elements in the earth’s crust, but it is only these two forms that are considered to be commercial ores [17,18,20].
It was not until 1824 that the metal was finally isolated from its ore in an impure form by the Swedish scientist Berzelius, through a chemical reaction that rendered a powder containing
93 % zirconium [18–20]. While this discovery was significant, production of ductile metal in bulk form was not possible until over one hundred years later, through a technique developed by van Arkel and de Boer [20]. Prior to the van Arkel method, those producing zirconium metal faced a problem in that while they were able to yield relatively high purity powders, the inclusion of just a small fraction of oxide, carbide or nitride caused significant embrittlement [20]. This meant that upon consolidation of the powder, no real degree of ductility existed in the resultant metal, rendering it unusable commercially [20]. With the development of the van Arkel process, it was finally possible to produce bulk zirconium metal of high purity [20]. The significant cost associated with its production, however, initially limited its viable applications [20]. This changed with the birth of the commercial nuclear energy industry at the end of the Second World War, where a great deal of industrial interest in zirconium was suddenly generated [20]. As a result, a second commercially viable process for producing zirconium on large scales was developed by Kroll to compete directly with the van Arkel method [20].
23 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys
2.1.2.
Non-Nuclear Uses
The considerable resistance to corrosion in a variety of environments makes zirconium and its alloys a very attractive material to a number of major industries. When competing against more traditional corrosion resistant engineering materials like stainless steel, however, the cost of zirconium is comparatively high [21]. While this may have prevented the widespread adoption of the metal, a combination of corrosion resistance and other advantageous properties does mean zirconium is still found in a number of highly demanding applications outside of the nuclear industry [22].
In light engineering, zirconium can be found as the getter in vacuum tubes, like those used in electron guns, where its high affinity for gasses, including oxygen and nitrogen, allows it to increase and maintain the level of vacuum [20,23]. Another niche area in which zirconium can be found is explosives, where zirconium is combined with potassium perchlorate to form a commercial grade primer, which is used to trigger the detonation of highly explosive compounds
[24]. Uses such as these are considerably smaller in consumed volume of material, when compared with heavy engineering applications. The chemical industry, for example, has been known to use commercial grade zirconium alloys in the manufacturing of valves, centrifugal pumps, pressure vessels, reactors, agitators, piping and heat exchangers [20,22]. Similarly, zirconium is extensively utilised as a structural component in the production of anhydride and acetic acid [25].
These adoptions can be easily attributed to the discussed resistance of zirconium to corrosive media, as well as the stability of mechanical properties demonstrated at elevated temperatures, which may be necessary during certain stages of chemical processing. Despite this, the largest consumer of zirconium by tonnage, however, remains the nuclear industry.
2.1.3.
Common Alloys
The widespread adoption of zirconium in the nuclear industry has led to the development of numerous alloying systems over the years since the Kroll and van Arkel methods were developed. The most commonly adopted early alloy developments took the form of Zircaloy-2,
Zircaloy-4 and a set of Russian systems containing niobium [26]. Despite their early adoption, the
Zircaloys still remain in use today, due in part to the wealth of research available on them, as well their advantageous properties for use in the nuclear sector [27]. As a result, these two families of alloy set the benchmark against which the advantages of contemporary alloys are measured [27].
The primary component in the Zircaloy systems is tin, added to prevent the detrimental effect of nitrogen on the corrosion rate of zirconium; this initial binary system became known as
Zircaloy-1 [28]. The development of the subsequent generations of Zircaloy came about initially as a result of the accidental contamination of zirconium with stainless steel [28]. The addition of
Literature Review | 24
The Precipitation of Hydrides in Zirconium Alloys iron, nickel and chromium was shown to dramatically increase the corrosion performance of the metal in its pure form, sparking an investigation into the effect of these impurities on the already existing tin-zirconium alloy [27,28]. The results of this research were positive, demonstrating an increase in nitrogen tolerance and a significant increase in corrosion resistance, especially in high temperature water [29]. This new alloy, later named Zircaloy-2, contained trace amounts of the constituents of stainless steel, as it was deemed that the presence of all three beneficial elements created the desired properties [28]. This generation of Zircaloy is still in use in 2015 in boiling water reactors (BWRs) and has seen a number of improvements over the years to overcome corrosion and irradiation induced defects [30].
As part of on-going research to improve the Zircaloy family, Zircaloy-3 was developed as a chromium and nickel free derivative, with reduced tin and increased iron contents, intended to improve upon the properties of the previous alloy [28,29]. The explored compositions, however, were not effective. While the corrosion resistance of the new alloy was similar to that of the previous alloy, a new corrosion product was generated, known as ‘stringers’ [28,29]. While the presence of these stringers could be controlled or eliminated with specific processing routes, ultimately, poorer mechanical properties limited the usefulness of Zircaloy-3 [28].
Zircaloy-4 was born out of the observation that nickel played an important role in the absorption of hydrogen, wherein increases in nickel content lead to an increase in hydrogen pick-up [27–29]. For reasons that will be explored later in this work, hydrogen pickup was deemed to be a detrimental effect, and so research was undertaken to develop a new alloy system with minimal absorption. Early work determined that simply removing the nickel component was deleterious to the corrosion performance of the alloy, so to compensate, an increase in iron content was made [29]. This new alloy, subsequently named Zircaloy-4, was demonstrated to pick up substantially less hydrogen than Zircaloy-2 in water, but not steam [29]. This derivative of
Zircaloy has seen extensive use in PWRs, and current development focuses on improving corrosion performance in these applications [30]. Typical compositions for the Zircaloys are
Concurrently to the western development of Zircaloy, the Soviet Union developed its own set of corrosion resistant alloys based on the addition of niobium to zirconium [31]. These alloys were employed by the Canadians in CANDU type reactors, and in recent years renewed research efforts, resulting from the limiting performance of Zircaloy-4 in certain conditions, has led to the development of newer niobium based alloys [29]. Most worthy of note are the alloy systems known as M5 and ZIRLO, which demonstrate a greater degree of corrosion resistance in pressurised water environments, when compared with Zircaloy-4, for example [27,29]. More recently, development of these alloys has focused on use with high burn-up fuels and increasing power densities in PWR conditions [30]. Both of these contemporary alloys are based on the
25 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys original research undertaken in what is now Russia, and while the M5 alloy is based around the simple addition of niobium, ZIRLO incorporates additional elements demonstrated to boost corrosion performance ahead of the classical Zircaloys [27,29]. The compositions for these alloys
Table 2. Standard compositions for zirconium alloys in weight percentages [27,29,32–34].
Alloy Sn Fe Cr Ni Nb Hf
Zircaloy-1 2.5 % - - - - 0.01 %
O
1000 to
1400 ppm
Zircaloy-2
Zircaloy-3
Zircaloy-4
1.2 % to
1.7 %
0.25 % to
0.5 %
1.2 % to
1.7 %
0.07 % to
0.2 %
0.20 % to
0.4 %
0.18 % to
0.24 %
0.05 % to
0.15 %
0 % to
0.2 %
0.07 % to
0.13 %
0.03 % to
0.08 %
-
-
-
-
-
0.01 %
0.01 %
0.01 %
1000 to
1400 ppm
1000 to
1400 ppm
1000 to
1400 ppm
Zr-Nb - - - -
2.4 % to
2.8 %
0.01 %
0.09 % to
0.13 %
ZIRLO ~1 % ~0.2 % - - ~1 % No Data No Data
M5 - - - - ~1 % No Data 0.125 %
2.1.4.
Microstructure and Properties
Commercially pure zirconium metal displays two allotropic modifications in its solid state at atmospheric pressure, meaning that atoms can be arranged in two distinct ways. The structuring of atoms under atmospheric conditions is determined by thermal energy, and can be separated into the low temperature alpha (α) and high temperature beta (β) phases. The α-phase
takes the form of a Hexagonal Close Packed (HCP) structure, shown in Figure 4 – (a), which is
stable up to a temperature of 862 °C in pure zirconium [20]. Above this temperature, the β-phase
is stable, a face centred cubic crystal structure (Figure 4 – (b)) that exists up to the melting
temperature for the metal, at approximately 1860 °C [20,35]. In each of the phases schematised
in Figure 4, the unit cells dimensions and atomic radii are to scale, and the number of atoms
present in each illustrates the number of whole atoms contained within each cell. The hydride structure present here is for comparison and will be discussed later.
Literature Review | 26
The Precipitation of Hydrides in Zirconium Alloys
The lattice parameters for both zirconium crystal structures are presented in Table 3,
along with the temperature ranges at which they are stable. Through a combination of electron microscopy and X-ray techniques, Burgers investigated the nature of the allotropic transformation between the two different phases, finding that on rapid cooling from β to α, the process closely resembled the formation of martensite needles in steels [36]. Under slower rates of cooling, the transformation takes place as nucleation and growth of lamellae, where coarser
α-lamellae are produced by lower cooling rates, and vice versa [37]. At high temperature, the microstructure appeared to be composed of roughly equiaxed β-crystallites, which were then replaced by varying regions of a lamellar α-structure, corresponding to where the β-crystallites had previously existed [36]. Subsequent reheating was then shown to reverse the transformation, producing crystallite regions corresponding approximately to the original structure [36]. This process, unlike diffusion controlled nucleation and growth of new phases, involves both shearing and dilatation of coherent regions of the lattice in specific crystallographic directions to convert from one structure to another [36].
27 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys
Figure 4. Scale schematics of (a) α-zirconium hexagonal close packed (b) β-zirconium body centered cubic and (c) δ-hydride face centered cubic crystal structures.
Table 3. Zirconium lattice parameters, crystal structure and stable temperatures [35].
Phase
Crystal Structure
Stable Temperature Range
Prismatic Lattice Parameter
Basal Lattice Parameter
Basal : Prismatic Ratio
Alpha (α)
Hexagonal Close Packed
Below 868 °C
3.23 Å
5.14 Å
1 : 1.592
Body Centered Cubic
868 °C – 1860 °C
3.62 Å
-
-
Beta (β)
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The Precipitation of Hydrides in Zirconium Alloys
The sequential phase transition following α → β → liquid at the temperatures given earlier in this section is that which occurs at atmospheric pressure. Above this pressure, an additional phase transformation into omega (ω) occurs, as described by the pressure-
temperature phase diagram in Figure 5 [35]. This phase exists at pressures in excess of 2 GPa and
produces a primitive hexagonal crystal structure with a higher density than the α-phase [35]. This figure also acts to demonstrate the α to β transformation temperature range, which decreases with increasing pressure. It should be noted that this pressure-temperature based assessments
of phase stability is for pure zirconium, and alloying in the way described in 2.1.3 will somewhat
change these transition temperatures. In Zircaloy-2, the cumulative effect of alloying elevates the
β transition temperature from 868 °C to ≈966 °C, while the melting temperature remains fairly constant at ≈1849 °C [38]. For Zircaloy-4, on the other hand, the change in composition results in a reported α + β phase temperature range of ≈845 °C to ≈1008 °C [39].
Figure 5. Pure zirconium pressure-temperature phase diagram (reproduced 3 from [40]).
Aside from these phases of zirconium, the alloying components that are added to create commercial alloys lead to the formation of a number of inter-metallic phases within the matrix.
In the Zircaloy family of alloys, the most widely reported of these is the Zr(Cr,Fe)
2
phase, occurring in both Zircaloy-2 and -4, while the Zr
2
(Ni,Fe) phase is commonly reported in -2 but only in -4 with a high level of nickel impurity [41]. These are based on the hexagonal close-packed ZrCr
2
and body centered tetragonal Zr
2
Ni phases, respectively, where Fe substitutes for Ni/Cr in quantities based
3 With permission from Elsevier Limited.
29 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys on alloy composition and component thermal history [41]; these being the phases that are also predicted by numerical studies [42]. Aside from these two significant inter-metallics, for
Zircaloy-4 there are also published reports of Zr
3
Fe precipitates (also predicted by [41]) and compounds based on corrosion products or impurities, typically involving Sn, Si, C, O, H, N or P
[41].
Neither the ω nor β phases are observed during the work presented in this thesis, or within Zircaloy-4 fuel cladding under normal PWR operating conditions, and those inter-metallic phases that do exist (Zr(Cr,Fe)
2, for example) are in a minority and are outside the scope of the discussion in this thesis, so only the α phase of zirconium will be discussed further.
Looking specifically at the α-zirconium phase, the c:a ratio given in Table 3 is below the
value quoted for an ideal packing of spheres, 𝑐 𝑎
⁄ , which would describe a perfect crystal in which all atoms would have an affinity for one another that was equal [43]. Given the packing of atoms in the zirconium unit cell, the basal plane is that which is closest packed, a feature that would normally determine the plane on which slip is most readily activated [44]. Instead,
α-zirconium is primarily subject to prismatic slip on the
{101̅0}
α
planes in the
⟨112̅0⟩
α
directions during deformation [44–47], owing to the type of interatomic binding within the crystal [48].
Pyramidal slip on the
{101̅1}
α
planes and basal slip on the
{0001}
α
planes, both in the
⟨112̅0⟩
α family of directions, are more difficult to activate and so contribute to plastic deformation to a lesser degree [44–47].
The occurrence of twinning is common in the HCP (that of α) lattice as a method for accommodating deformation, where a relatively small number of slip systems are available [44].
In the case of α-zirconium, the particular systems which are most active during twinning are
{112̅2}
α
⟨1̅1̅23⟩
α
and
{101̅1}
α
⟨101̅2⟩
α
during compression, as well as
{101̅2}
α
⟨101̅1⟩
α
and
{112̅1}
α
⟨1̅1̅26⟩
α
during tension, when stress is applied in
⟨0002⟩
α
[45,46,49]. While the overall contribution of twinning may be comparatively small when assessed against slip, its role is still significant in the deformation process of the α-phase [44]. This is due to the resulting crystallographic reorientations that occur, which may realign slip systems preferentially to the deformation direction, subsequently allowing the activation of previously dormant slip systems
[44].
The gross product of the availability and predominance of deformation mechanisms is that α-zirconium displays a high degree of mechanical anisotropy during plasticity [46]. For example, when examining yield strength as a function of loading direction, a ratio of approximately 3:2:1 has been observed between parallel compressive, parallel tensile and perpendicular tensile/compressive loading, relative to the
⟨0002⟩
α
direction [46]. This difference stems from the type and number of deformation systems activated during loading, ultimately
Literature Review | 30
The Precipitation of Hydrides in Zirconium Alloys having a pronounced effect on the mechanical properties of the material [46]. In the case of parallel compressive loading, only one twinning system acts to accommodate deformation, in conjunction with pyramidal <c+a> slip, thus producing the highest yield strength [46]. In parallel tensile loading, two twinning systems are active, producing a lower yield strength [46]. In the case of perpendicular loading, prismatic slip is the most easily activated system, and so the lowest yield strength is produced in directions where this system is most easily activated [46]. This anisotropy, however, is not necessarily a negative factor, as it allows zirconium to be used in both high strength roles and high ductility fabrication routes, through the tailoring of texture to suit specific situations [46].
Chemically, Zirconium demonstrates a significant degree of corrosion resistance in a wide range of highly aggressive mediums [50]. This property has been intrinsically linked to its widespread adoption in highly demanding industries, including the nuclear and chemical sectors
[50]. Evaluations of the performance of zirconium in marine, acidic and alkaline conditions carried out early in the history of the metal were quick to make comparisons with other corrosion resistant metals, such as tantalum [20]. The findings of these works highlighted its exceptional performance in alkalis and good performance in acids, where only exposure to hydrofluoric and highly concentrated solutions of sulphuric acid demonstrated corrosion [20]. Of most interest to both early and contemporary researchers, however, is the corrosion performance in water and steam, due to the significant interest in zirconium from the energy sector.
Initial observations of the behaviour of zirconium in hydrochloric acid led to the belief that an aqueous environment would have little or no effect on the metal, however, subsequent investigations quickly disproved this belief [20]. Of primary interest to later studies on the corrosion of zirconium are those alloys developed specifically for use in the nuclear field; the composition and function of which will be described in the following section. In the case of these alloys, the kinetics of corrosion are marked by a number of distinct and repeating periods, separated by points of transition [51]. An illustration of the oxidation process observed in a zirconium alloy with various processing histories, as investigated using weight gain
measurements, is presented in Figure 6.
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The Precipitation of Hydrides in Zirconium Alloys
Figure 6. Weight gain as a function of oxidation time up to 100 days at 400 °C (reproduced 4 from [52]).
In each of the samples, a clear cyclic behaviour can be observed, although the stress relieved series repeats faster than the others contained in this figure. Those series showing slower cycling can be split into two distinct regions, separated at ≈50 days by a transition point. The pre-transition region is characterised by the initially fast growth of the oxide layer (where the gradient is steep), which gradually slows up to the transition (where the gradient is shallow), where an increase in corrosion rate occurs suddenly [53]. After this point, the behaviour described initially by some was a region of linear corrosion behaviour, but more recently as a continued repetition of pre-transition and transitional behaviours [14].
Detailed studies into the precise nature of oxide formation during the repeating cycles has shown distinct regions of grain structure and phase to be evident within the developed oxide
[54,55]. This research suggested that initial rapid oxide growth occurs as small equiaxed grains composed of the tetragonal ZrO
2
phase [54,55]. From these, a large number were thought to develop further, eventually taking on a columnar morphology that consists of the monoclinic ZrO
2 phase, which develop at a declining speed to form a thicker layer up to the point of transition
[54,55]. The behaviour at transition, however, has raised conflicting views over the precise mechanisms involved. In the work undertaken by Anada et al., the data presented suggests that during transition the initial equiaxed tetragonal region disappears, to be replaced by an extension of the columnar monoclinic structure [55]. In contrast, the more recent work undertaken by
Yilmazbayhan et al. demonstrates a number of alternating layers of the two different structures
4 Reprinted, with permission, from ASTM STP1245 “How the Tetragonal Zirconia is Stabilized in the Oxide
Scale that is Formed on a Zirconium Alloy Corroded at 400°C in Steam”, copyright ASTM International, 100
Barr Harbor Drive, West Conshohocken, PA 19428.
Literature Review | 32
The Precipitation of Hydrides in Zirconium Alloys
[54]. Similarly, Garner et al. suggest that the transformation from tetragonal to monoclinic oxide is a continuous and progressive process that occurs with the growth of the oxide layer, as one or more of the constraints that stabilise the tetragonal phase are released [56]. Given that the tetragonal phase is thought to be stress stabilised by the large compressive residual stresses that are present within the oxide, the observation of significant lateral cracking in bands within the oxide may indicate a destabilisation of the tetragonal phase in those regions [57,58]. This relaxation is observed towards the end of each cycle, and so the phase transformation may be linked in some way to the return to rapid oxidation kinetics [54,57,58]. The precise mechanisms causing the transitional behaviour remain unclear at this time.
2.2.
In-Reactor Degradation of Zirconium
2.2.1.
Aqueous Corrosion
When exposed to an oxygen rich environment, such as air or oxygenated coolant, zirconium and zirconium alloys develop an oxide layer in the way summarised in the previous section. Once exposed to an aqueous environment, the corrosion process is fuelled by electrons generated from the oxidation reaction dissociating the coolant water, yielding oxygen and hydrogen [59]. The oxygen combines with zirconium atoms to form further oxide at the metaloxide interface. The hydrogen, produced as a product of this reduction, can go one of two ways; either, it will combine to form hydrogen molecules which are dissolved back into the coolant medium, or it will diffuse into the metal [59]. A simplified equation for the oxidation process is shown as Equation 1 [59,60], where hydrogen recombines to form the H
2
molecule.
𝑍𝑟 + 2𝐻
2
𝑂 → 𝑍𝑟𝑂
2
+ 2𝐻
2
Equation 1
The amount of hydrogen which is able to enter the metal when compared with the amount produced from the oxidation process is termed the ‘hydrogen pickup fraction’ [59]. It is this fraction that is significant, as any hydrogen entering the material is thought to do so as a result of this process, rather than being absorbed from hydrogen molecules in the coolant medium [61]. The exception to this, however, is if the nickel component of the alloy remains in metallic form within the developing oxide layer, as the result of a particularly low corrosion potential [61]. Where this is the case, the nickel within the oxide acts to take up hydrogen that is dissolved in the coolant [61].
The nature of the diffusion mechanism for hydrogen into the metal has been the subject of a number of differing interpretations in recent years [61]. Early work on the kinetics and
33 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys mechanisms behind the diffusion through the oxide layer undertaken by Smith suggested that two simultaneous diffusion processes took place [62]. A combination of positively charged vacancies allowing hydrogen to move between interstitial positions within the lattice, along with diffusion along line defects was believed to be responsible for the ingress of hydrogen into the metal [62]. An in-depth analysis of previous micro-mechanical models undertaken by Cox, however, refuted the idea of solid-state diffusion being responsible for the transportation of hydrogen through the oxide layer [63]. Cox calls on early work undertaken by Roy, which used tritium autoradiography to demonstrate that pre-oxidised zirconium exposed to a tritium atmosphere did not contain any tritium in the oxide layer [63,64]. This, Cox proposed, was indicative of zirconium in an aqueous environment, and demonstrated that the hydrogen found in oxide layers by other researchers was not linked to uptake by the base metal [63]. Instead, he believed that this hydrogen was either trapped during the corrosion process, rendering the atoms immobile, or came from hydroxides encased in pores within the porous regions of the oxide [63].
Ultimately, the work undertaken by Cox went on to suggest that hydrogen uptake occurs at very localised regions where flaws in the oxide penetrate to the metallic interface [63]. This was characterised by locating cathodic reaction sites on the surface of the alloys in question, which tended to be cracks where second phase particles existed or had previously existed [63].
Earlier work undertaken by the same author also suggested that an intermetallic bridging effect might take place, where alloying elements formed as inter-metallics at the metal-oxide interface behave as entry points for hydrogen [63,65]. This line of thought was picked up by Isobe and
Hatano, years after it was first proposed, whom investigated the concentrations of hydrogen in inter-metallics within the oxide, also using tritium autoradiography. A series of papers published by the two authors confirmed that inter-metallics dispersed within the oxide layer showed a marked increase in tritium content against the background oxide [66–68].
In addition to the flow of hydrogen through inter-metallics, the pair also suggested that diffusion through grain boundaries within the oxide may also be a contributing factor [66]. This, however, was thought to only be significant after the point where intermetallic precipitates became oxidised and the hydrogen was no longer able to use them to bridge the oxide layer [66].
Again, Cox disputes the relevance of inter-metallics in his later work, from reviewing the solubility and heats of solution for the precipitates [63]. He believed that the distribution of hydrogen seen by Isobe and Hatano in the particles likely occurred when the specimens were cooled, and suggested that near instant quenching would be the only way to verify the findings [63].
These ideas around the transport mechanisms responsible for the ingress of hydrogen into zirconium through the oxide layer are representative of the major theories behind the processes involved [61]. They are, however, still just hypotheses, and as of yet there has been no conclusive explanation of the discrepancies between data supporting each of the different
Literature Review | 34
The Precipitation of Hydrides in Zirconium Alloys possibilities [61]. As a result, research into the precise nature of the transport mechanisms through the oxide layer is still on-going [61]. More firmly identified are the factors influencing the pickup of hydrogen, which Strasser summarises as the nature and structure of the oxide, alloy composition and coolant medium [61]. More specifically, the microstructure, composition and dimensions of the alloy and protective oxide play a major part in determining the hydrogen pickup fraction, as does the inclusion of any second phase particles [61]. In addition, the chemistry of the coolant is also important in determining the rate of corrosion, and, by proxy, the rate of hydrogen absorption [61].
To give some context to this concept, the reviews of PWR operating conditions presented in the works by Billot et al. [69] and Weidinger et al. [70] provide an average burnup for a fuel assembly of between 44 and 55 GWd/t
U
over four to five cycles [69,70]. Figure 7 contains a
schematic curve for hydrogen pickup in Zicaloy-4 calculated from experimentally measured hydrogen contents over this range and up to an achievable burnup for PWR fuel assemblies [70].
In this figure, the green region indicates an average fuel burnup of 44 GWd/t
U
, the yellow indicates 55 GWd/t
U
(the target burnup of EDF), while the red marks that believed to be achievable [70].
Figure 7. Hydrogen pickup performance of zircaloy-4 with average burnup [70].
35 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys
2.2.2.
Hydriding of Zirconium
The hydrogen absorbed into the cladding tube during reactor operation will remain in solution, where it generally occupies tetrahedral sites within the HCP cell, until the solubility limit for the alloy and temperature is reached [71]. Past this limit, hydrogen will bond with zirconium atoms to precipitate into a number of allotropic forms, depending on the thermal history and concentration of hydrogen that has been taken up [72,73]. From hydrogen pickup, a concentration range for spent fuel of between 300 and 600 ppm wt.
, or 0.03 to 0.05 % wt.
hydrogen can be said to be contained within spent fuel cladding. This figure is verified by Wiesenack’s studies on fuel behaviour and by work undertaken by Kim on the effect of hydrogen and oxides on Loss Of Coolant Accidents (LOCA), both demonstrating values of 500 and 600 ppm wt.
respectively [74,75]. Taking a highly simplistic assessment of the solubility of hydrogen within fuel, based on the typical operating outlet temperature of a PWR reactor, 323 °C [76], a maximum solubility of 132.2 ppm wt.
can be calculated from the equations derived by McMinn [77]. This can
then be compared with the average hydrogen pickup curve, Figure 7, to indicate that in Zircaloy-4
cladding material at 323 °C, hydrogen could begin to precipitate after an average burnup of
23.3 GWd/t
U
, assuming the corrosion performance follows the literature curve [70].
This, of course, is not an accurate portrayal of the thermal state of the cladding, as a temperature gradient exists along the axial length of fuel assemblies (from the cooler bottom of the reactor core to the warmer top). Similarly, the cladding also experiences a radial thermal gradient between the inner and outer tube surfaces, as thermal energy is transferred into the cladding from the fuel inside, and removed by the coolant from the outer surface. Modelling, undertaken by Davis, predicts an axial thermal gradient ranging from 50 °C to 70 °C in magnitude, and a radial gradient of 10 °C to 35 °C, although these gradients are dynamic and will evolve with time [78,79]. This creates a complex three-dimensional thermal state, which leads to a similarly complicated set of solubilities local to different regions within cladding material. The solubility of hydrogen in zirconium is illustrated in the temperature-composition phase diagram summarised
by Tulk and reproduced in Figure 8, which describes the phases that are present as a function of
the concentration of hydrogen within the material and the temperature at which it exists.
At the lower end of the concentration axis in both subplots, the α and β phases of zirconium can be seen in separate, higher temperature regions of this diagram, while at lower temperatures in the same region exists a two-phase system of α-zirconium and δ-hydride, with metastable γ-hydride [80]. An alternative interpretation of this region is to split the lower central region it over a temperature range of 190-255 °C, where α+δ is stable above the transition, while
α + γ is stable below it and δ is only metastable [80]. Moving towards much higher concentrations of hydrogen (rightwards in the figure), δ-hydride becomes the sole stable phase, and as hydrogen saturates the material, it is thought that the ε-hydride phase becomes the stable allotrope. In
Literature Review | 36
The Precipitation of Hydrides in Zirconium Alloys comparison with δ-hydrides, however, the γ and ε phases are relatively uncommon under conditions relevant to PWR operation, though γ has been seen to coexist with δ on occasion [61].
Figure 8. Zirconium-hydrogen binary phase diagrams illustrating two alternative possibilities for the stability of the δ- and γ-phases (reproduced 5 from [80]).
The non-stoichiometric face centered cubic δ phase is a member of the Fm-3m space group [81], possessing an irrational number of hydrogen atoms per unit cell (based on the precise stoichiometry of the phase), which randomly occupy a varying number of the eight possible tetrahedral sites (≈⅚ sites for ZrH
1.66
, but given as 4 sites by some authors [81]). This structure
can be seen illustrated to scale in Figure 4 – (c). In the more uncommon γ-hydride phase,
hydrogen atoms sit on alternating
(110) 𝛾
planes in the associated tetrahedral sites [81]. The
compositions and structures for these phases are listed in Table 4.
Table 4. Zirconium hydride compositions & crystallographic structures [61,81].
Hydride Phase
Gamma (γ)
Delta (δ)
Epsilon (ε)
Crystal Structure
Body centered tetragonal
Face centered cubic
Body centered tetragonal
Typical
Composition
ZrH
ZrH
ZrH
1
1.66
2
Composition Range
ZrH
ZrH
ZrH
1.0
1.5
1.7
to ZrH
to ZrH
to ZrH
1.5
1.7
2
Extensive investigations into the precipitation, dissolution and morphology of hydrides in zirconium alloys have been undertaken as part of a push to enhance the irradiation lifespan of fuel assemblies [82]. Of early interest to researchers looking at the precipitation and dissolution of hydrides was the hysteresis seen between the Terminal Solid Solubility for Precipitation (TSSP)
5 With permission from Elsevier Limited.
37 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys and Dissolution (TSSD) [83]. This hysteresis is the path or history dependent behaviour in the precipitation and dissolution processes during thermal cycles. Experimentally, this phenomenon
can be seen clearly in work undertaken by Zanellato, represented in Figure 9. The clear difference
between the completion of dissolution on heating, at around 500 °C, and the initiation of precipitation during cooling, at approximately 440 °C, is an example of the hysteresis. It should be added that the horizontal region topping out the plot is the point at which all hydrides have been dissolved, leaving all hydrogen contained in solid solution.
Puls, as part of his work into metal-hydride systems, looked closely at the mechanisms involved in generating this hysteresis, summarising that the lower density of the hydride creates a corresponding volume misfit with the matrix [83]. The degree of misfit strain between these two phases was the work of much early research, with Kearns and Wood producing a value of approximately 14.3 % using a density to volumetric relationship [84,85]. Carpenter, however, disputed their methodology, stating that the density-volume relationship used by the pair was incorrect when considering the compositional change found when generating hydrides [85].
Instead, he gave a value of ≈17.2 %, which was calculated through examining the way in which the site of a zirconium atom effectively changed shape and size during the phase transformation
[85]. More contemporary literature, however, does not entirely agree with the isotropic transformation strain on the basal plane that Carpenter reports for δ, where Barrow et al. measured a clear anisotropy in the interfacial strains for this phase [85,86]. It should be noted, however, that these newer values correspond to the residual interfacial strains that exist after plastic deformation has occurred during hydride precipitation, rather than being the stress-free transformation strains. The values presented in that work would give a significantly lower total
misfit of ≈9.3 %; the values from both Carpenter and Barrow et al. are given in Table 5 [86].
Table 5. Matrix-hydride interfacial strains (Barrow et al.)/stress free transformation strains
(Carpenter) [85,86].
Direction
[0001] 𝛼
[112̅0] 𝛼
[1̅100] 𝛼
[111] 𝛿/𝛾
[11̅0] 𝛿/𝛾
7.2 %
4.6 %
4.6 %
–
–
δ – Carpenter
5.5 %
3.1 %
Hydride Allotrope
δ – Barrow
0.5 %
-1.3 %
-1.0 % –
γ – Carpenter
5.7 %
0.6 %
5.6 %
–
γ – Barrow
4.1 %
0.6 %
0.5 %
-1.1 %
0.0 %
In other relatively recent work, such as that published by Une, the range of misfit strain values derived theoretically and calculated experimentally is large, encompassing the figures from the early literature [87]. Values spanning 11 % to 19 % have all been reported by Une, however,
Literature Review | 38
The Precipitation of Hydrides in Zirconium Alloys figures in the mid to upper end of this range (mostly around 17 %) tend to be more commonly presented [87,88]. This, however, illustrates the complexity of the hydride system, as the values put forward by Barrow from experimental measurements are significantly lower than would be expected from earlier studies. Similarly, the simple reporting of a single misfit from a mismatch between two different phases is a gross simplification for a system that will experience a range of temperatures during reactor operation. For this reason, theoretical studies like that from Singh are important for describing the way in which misfit likely changes based on temperature [89].
Figure 9. Hydrogen evolution with temperature in Zircaloy-4 sheet (reproduced 6 from [90]).
When examining the effect of the lattice mismatch between metal and hydride, Puls suggests that as diffusion of metal atoms cannot accommodate the misfit at lower temperatures, a combination of elastic strain and misfit dislocations must be generated [83]. This explains the delay in precipitating hydrides on cooling, as a greater amount of energy is required to counteract the mismatch, generate elastic strain and plastic deformation, ultimately allowing for the formation of hydrides [83]. Later work published by Shek elaborates on this point by stating that it is specifically on cooling that the misfit strain is initially accommodated elastically, due to the small nature of the hydride nuclei, and then plastically as the precipitate grows [91]. During the heating cycle, however, Shek states that the hydrides dissolving with heating are of sufficient size that plastic deformation has already relieved the majority of misfit strains, and the energy lost to this relaxation is non-recoverable [91]. This supports the suggestion by Puls that the additional
6 With permission from Elsevier Limited.
39 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys energy required to precipitate hydrides is directly correlated to the elastic strain energy, as the dissolution behaviour is almost entirely stress free [83,91]. To further corroborate this theory, the accommodation of larger precipitated hydrides through plastic deformation is supported by the observation of large numbers of dislocations surrounding the hydrides [87,92,93]. This is corroborated in the Transmission Electron Microscopy (TEM) work by Zhao, where smaller intra-granular hydrides were accompanied by contrast lines, indicating the presence of elastic strain fields, while the larger inter-granular and trans-granular hydrides were haloed by misfit dislocations [94]. It should be noted that preparation of thin foils for study using TEM has a propensity for introducing additional hydrides into zirconium samples, generally on/close to the surface of foils, and so studies of these precipitates must be undertaken with care.
Recently, a number of authors have sought to understand better the precipitation kinetics during hydride formation. In earlier work, Kammenzind et al. used diffusion profiles for hydrogen in Zircaloy-4 to derive rates ranging from 1 to 4 ppm s -1 , as a function of temperature
[87,95]. McMinn et al., Kammenzind et al., Une et al. and Tang et al. have all stated that there is little difference in TSSP and TSSD when comparing various zirconium alloys, suggesting that alloy composition has little effect on the kinetics of hydride formation [77,87,88,95]. As such, the rates calculated by Une should be relatively similar, yet his DSC analysis produced values of 0.5 to 1.7 ppm s -1 [87]. Further work undertaken by Tang et al. [88], using a similar DSC analysis approach, agrees more closely with the values produced by Une et al. [87] than those produced by
Kammenzind et al. [95]. These differences, however, are most likely attributed to the different methodologies employed by the three authors, rather than properties of the materials being studied. That being said, a memory effect is reported for zirconium alloys containing hydrogen by
Cameron [96], whereby legacy matrix defect structures left behind by dissolved hydrides can act as heterogeneous nucleation sites for new hydrides to form. This makes the process of hydride precipitation very sensitive to the thermal history of any material being studied, and could possibly account for experimental deviations. Furthermore, the trapping of solute hydrogen within dislocations, observed by Cox, could further promote this mechanism, as an enriched hydrogen atmosphere present within these defects will influence the local solubility and promote rapid heterogeneous precipitation at those locations [97].
In addition to understanding the kinetics of hydride formation, a significant amount of research has been undertaken to characterise their morphology since the early days of zirconium utilisation in the nuclear industry [93]. Due to the unavailability of advanced analytical techniques early on, however, some conclusions made by these researchers were incorrect, such as
δ-hydrides possessing a face-centered tetragonal structure [93]. Nevertheless, what early researchers were able to observe was that even from low concentrations of hydrogen, hydrides formed either needle like precipitates or platelets, depending on cooling rates and alloy hydrogen
Literature Review | 40
The Precipitation of Hydrides in Zirconium Alloys
content [73]. The misfit associated with the δ and γ phases are given in Table 5, which act in
conjunction with the anisotropy of the parent lattice to control the geometry of hydride precipitates. Further to their geometry, these microscopic needles or platelets have a tendency to group or stack to form macroscopic hydride regions, which are commonly observed optically
[15,73,90,98–101]. An example of this phenomenon is given in Figure 10, from TEM observations
made by Bradbrook on Zircaloy-2 samples, along with a supporting schematic demonstrating the effect of micro-hydride stacking relationship to optically observed macro-hydride geometry [99].
These micro-hydrides can then also coalesce into larger hydrides through growth [102]. It should
be noted that the TEM micrograph presented in Figure 10 comes from an electro-polished
sample, and is thus susceptible to sample preparation induced hydriding. The specific methodology employed by Bradbrook et al. in preparing those samples for imaging aimed to prevent the formation of surface hydrides, by implementing a low temperature of -60 °C during the final thinning stage [99].
Cox suggests that this chaining effect may be due to a hydrogen atmosphere developing in dislocations created by the very first hydrides to precipitate in each chain [15,97]. The resulting lattice dilation has been shown to encourage a build-up of hydrogen within the cores of the dislocations punched out by growing hydrides, which may then encourage nucleation of a new hydride platelet neighbour/daughter [15,97]. Calculations by Perovic et al. indicated that the auto-catalytic process causing the formation of stacks of hydrides resulted from the tensile stresses induced in the matrix surrounding an initial hydride lowering the nucleation energy barrier in discrete locations close to the first precipitate [100–102].
41 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys
Figure 10. TEM observation of γ-phase micro-hydride stacking in Zircaloy-2, with a schematic diagram of the impact of stacking geometry on apparent macro-hydride trace (reproduced 7 from [99]).
Early work undertaken by Ells was quick to identify that hydrides prefer to nucleate at grain boundaries, although more recent research highlights the fact that cooling rate and grain size has a significant impact on precipitation location [15,73,82,98]. Where cooling rates are high or matrix grain size is large, intra-granular hydrides dominate precipitation, while at lower cooling rates and grain sizes, inter-granular, or grain boundary hydrides are dominant [15,82]. Kumar, in an EBSD study of hydrides, identified three derivatives of grain boundary hydrides in Zircaloy-4, two which span multiple grains, and one which inhabits only one grain [82]. The three types of hydride were categorised into the following categories; those which initiate at the boundary and grow simultaneously into two neighbouring grains, those which grow along a boundary in both neighbouring grains, and those which grow along a boundary, but only on one side of it [82].
These are illustrated in Figure 11, where red colouring indicates hydride precipitates and the
different matrix grains inhabited are lettered. In his texture analysis, Kumar looked extensively at the three mentioned inter-granular hydrides, as well as the intra-granular hydrides, finding that they all possessed the same orientation relationship relative to the matrix of
(0 0 0 1)
α
∥ (111)
δ
[82,98], pictured in Figure 12.
7 With permission from Elsevier Limited.
Literature Review | 42
The Precipitation of Hydrides in Zirconium Alloys
(a) (b)
(c)
Figure 11. Three inter-granular hydride forms, (a) along both boundary sides, (b) cross boundary, (c) along boundary one side (reproduced 8 from [82]).
Figure 12. Matrix-hydride crystallographic orientation relationship.
8 With permission from Elsevier Limited.
43 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys
Earlier work undertaken by Une on the analogously behaving alloy Zircaloy-2 revealed a similar orientation between matrix and hydride of
{0001}
α
∥ {111}
δ
for both inter- and intragranular types [103]. Where his work differed, however, is that he also identified some instances of
{101̅7}
α
∥ {111}
δ
occurring for radially oriented inter-granular hydrides [62]. An example of the high-resolution transmission electron micrograph and corresponding selected area
diffraction pattern used by Une to confirm this relationship are presented in Figure 13. Here the
lattice planes for the matrix
[0001] 𝛼
and hydride
[111]
δ
planes can be clearly seen either side of the interface between the two phases. Similarly, the diffraction spots for both of these planes are those that show greatest alignment. The directional relationship, determined by Northwood and Gilbert [104] was found to be
⟨110⟩ 𝛿
∥ ⟨112̅0⟩ 𝛼
for the δ-hydride phase.
Figure 13. TEM and SAD images of Zircaloy-2 showing both α and δ phases (reproduced 9 from [103]).
Results published by Singh, using a finite element modelling approach, mirror experimental observations of this relationship for both macro- and microscopic hydrides [105].
From this work, Singh suggests that where volume change occurs during phase transformation, strain energy plays an important part in determining precipitate orientation [105]. Taking both a fully elastic and an elasto-plastic volumetric misfit scenario, his model predicted the accommodation energy for the precipitation of δ in α, as a function of precipitate orientation
[105]. Plots of this energy for both cases showed clear minima where platelets formed on the
9 With permission from Elsevier Limited.
Literature Review | 44
The Precipitation of Hydrides in Zirconium Alloys basal plane of an α crystal, parallel to the
[112̅0]
α
direction [105]. Singh proposes that this factor is especially important in determining platelet orientation when the interfacial energy of the system is comparatively small next to strain energy [105]. Barrow compares a calculated chemical driving force for nucleation with the strain energy from Puls [106], stating that initially it would appear that the strain energy is the dominant contribution to the energy barrier to nucleation
[107]. Barrow, however, dismisses this as incorrect, proposing that the interfacial energy is the dominant barrier to nucleation, and that hydride misfit is thus less than assumed by Puls [107].
This is substantiated by the further work by Barrow in which he measures lower interfacial strains than the stress free transformation strains derived by Carpenter, the latter of which is used by
Puls; these values are given in Table 5 [106,107]. As observed by Kumar, grain boundary hydrides
tend to precipitate in grains which have basal planes oriented closely to grain boundaries [82]. As a result, this distribution minimises interfacial energy as well as grain boundary energy, demonstrating that strain energy is still significant in deciding the nature of hydride precipitation
[82]. Further to this, when nuclei coarsen, it seems likely there will be a size beyond which hydrides will be large enough that the strain energy associated with the misfit between precipitate and matrix becomes more dominant than the energy associated with the changing size of the interface. These factors together could well account for the preferential habit plane occupied by hydride platelets, as well as their heterogeneous distribution within specimens [82].
While micro-hydrides precipitate on a preferential plane, the orientation of macro-hydrides can also be influenced by applied stresses during thermal operations, as observed initially in a report published by the Savannah River Laboratory [3,73]. Ells summarises the effects for both sheet and tube material by demonstrating that areas exposed to compressive stresses breed hydride platelets oriented parallel to the axis of stress, while tensile forces generate perpendicular hydrides [73,85]. An example of the reorientation phenomenon is demonstrated
Carpenter justifies these observations by explaining that a precipitating phase with a large directional misfit will nucleate such that the tensile stress is in the direction of most significant mismatch [85]. This seems plausible, as any strain generated by the induced tensile stress in the matrix would serve to reduce the elastic accommodation energy required in the direction of greatest misfit, when forming the hydride. This would then make it most energetically viable for hydride platelets to form normal to tensile stresses, as the bulk of volume misfit is accommodated in a direction normal to the platelet [100].
Given that the micro-hydrides have a preferential habit plane on which they precipitate, a crystallographic reorientation would seem unlikely. Instead, the reorientation phenomenon would be the result of a change in the strain fields around an initial hydride causing a shift in the
‘sweet-spot’ at which the accommodation contribution to the nucleation energy barrier is at a
45 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys minimum [102]. This, coupled with a sequence of successive nucleation events could then lead to a change in the stacking geometry of the micro-hydrides, producing macro-hydrides with their
apparent normals significantly reoriented [102]; see Figure 10.
Figure 14. Effect of applied tensile stress on hydride orientation, (a) unstressed orientation,
(b) stress induced reorientation perpendicular to applied load (reproduced 10 from [108]).
In the case of light water reactor fuel cladding, where internally pressurised tubes of zirconium alloys are used (thus establishing a tri-axial stress state), Ells summarises a significant reorientation effect, wherein hydrides would be precipitated with their major axis oriented in a radial direction [73]. This was drawn from the work of Marshall, whose studies of Zircaloy-2 and
Zircaloy-4 led him to conclude that fabrication was the key decider for stress reorientation of hydrides [73,109]. More specifically, the largest amount of stress reorientation occurred in directions where compression occurred during fabrication, rather than being a function of local texture [73,109]. Newer studies, like that undertaken by Colas, elaborate on this principle, explaining that the texture developed from the major compression axis during thermo-mechanical processing (tube pilgering or plate rolling) is the controlling factor for orientation during hydride precipitation [108]. Where alloys are subject to a stress field above a certain threshold, however, the reorientation phenomena occurs in the way already described, where the threshold value is determined by processing and microstructure [108]. Taking the work undertaken by Colas on Zircaloy-2 and -4 as an example, a value for uniaxial loading of 80 MPa was seen to be the threshold value for reorientation, which triggered a 25 % increase in radial hydrides [108].
In order for these reorientations to occur, hydrogen must be able to move freely within the α-matrix while in solid solution, so that it is able to re-precipitate in new locations. Early scientists, including Sawatzky and Kidson, looked into the diffusion behaviour of hydrogen in solid
10 With permission from Elsevier Limited.
Literature Review | 46
The Precipitation of Hydrides in Zirconium Alloys solution within zirconium alloys as a function of temperature, stress and concentration
[15,110,111]. Where a concentration or thermal gradient exists within a zirconium alloy, hydrogen will diffuse down the gradient towards areas of lower temperature or concentration
[15], following the Soret Effect [112,113] and Fick’s Law [113,114], respectively. Where a hydrostatic stress gradient exists, however, the inverse is true and hydrogen will migrate towards an area of increased tensile stress, such as the region around a crack tip, although this happens predominantly during thermal cycles or at elevated temperatures [15,115]. If there is a conflict between temperature and stress gradients, the temperature effect tends to be the stronger influence on hydrogen diffusion [115]. Together, temperature, stress and concentration determine the chemical potential for the hydrogen in solid solution, which acts as the overall driving force for diffusion, causing hydrogen to be drawn from regions of high chemical potential towards areas of low potential [116].
The equation, stated by Kammenzind et al. [115], to describe diffusion as a function of these three drivers predicts a high rate of transport down thermal and concentration gradients, however, there are certain stipulations for this to actually be the case [15]. When looking at thermal gradients, rapid diffusion will only occur where hydrides have precipitated in cold regions as a result of the local solubility limit being exceeded [15,111]. In the case that all hydrogen within the material remains in solution, the small difference in the heat of solution between the hot and cold regions of the sample will create a slow drift of hydrogen towards the colder areas [15,111].
This, in turn, creates a concentration gradient within the alloy, which also promotes a gradual migration of hydrogen in the opposite direction, creating an equilibrium state. A similar principle applies to diffusion across hydrostatic stress gradients, where hydrogen concentrations below the terminal solid solubility limit will only lead to a slow diffusion of hydrogen to stressed areas
[15,111]. Where hydrogen levels are above solubility and hydrides have precipitated, however, a rapid flow of hydrogen will occur up the stress gradient, allowing for near-continuous precipitation of hydrides in the region [15].
In practice, this means that where the outer surface of cladding is colder as a result of being in contact with the coolant medium, hydrides tend to precipitate close to this surface first
[15]. This is the result of the terminal solid solubility limit for precipitation being reached sooner in this region than in others, owing to thermo-diffusion of hydrogen to these regions of lower solubility [15]. Similarly, an increase in hydrostatic stress at a point will lead to an increase in local hydrogen concentration, which, in turn, results in the local solubility limit being reached first within the stress field [15]. This leads to hydrides precipitating preferentially within stress fields, which generally result from damage to or flaws in zirconium components [15].
Hydrogen diffusion is not, however, without obstacles, as there are a number of matrix features that can act as traps for hydrogen, binding it to the feature until sufficient driving forces
47 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys exist to liberate it [117]. Early work published by Cox reviews published experimental data, identifying interstitial oxygen and dislocations as traps for hydrogen, the latter being the stronger of the two [97]. This can be significant, as hydrides punch out dislocation structures in the surrounding matrix when they precipitate and these structures remain behind when they dissolve. As a result, the solute hydrogen could enter, and then become trapped in, these dislocation structures once dissolved into the matrix, preventing further diffusion.
More recently, ab-initio studies into the zirconium-hydrogen system, by Christensen et al., have shown vacancies of being capable of trapping up to 9 hydrogen, which will remain within the defect during vacancy migration [42,118]. Similarly, substitutional chromium is predicted to be able trap up to 2 atoms of hydrogen, nickel is thought to trap some unpublished number, and substitutional/interstitial iron is quoted as having a stronger binding energy than either of these
(although no comment is made in the text as to this) [42]. All of these features combined will mean that there will always be some population of hydrogen that is immobilised without significant driving forces for diffusion. Furthermore, the trapping of hydrogen in these features could also mean that the solubility of hydrogen is effectively increased, where some hydrogen remains distributed in these traps, rather than agglomerating to form a precipitate [118].
2.2.3.
The Impact of Hydrides
Zirconium hydride is thought to be inherently brittle in bulk and its presence as precipitates can deleteriously affect the mechanical properties of zirconium alloys [15,116,119–
121]. The degradation of fuel cladding as a result of hydrogenation can be a significant problem during normal service life, as well as accident conditions, reactor shutdown and intermediate fuel storage [15]. The overall mechanical effect of hydride inclusion within fuel cladding can be broken down into effects on tensile strength, yield strength, fracture toughness and ductility [15]. As with much zirconium research, a number of authors have examined a variety of different alloys using an assortment of conditions and tests. For example, Yeniscavich et al. and Lin et al. looked at the mechanical properties of Zircaloy-2 and -4, demonstrating that past a critical point, the increasing presence of hydrides leads to a decrease in ductility and tensile strength [15,122,123]. The work by Yeniscavich demonstrated that tensile strength remains constant with increasing concentration up to a point around 500 ppm wt.
, where further solute hydrogen causes a rapid drop in strength [15,123].
When reviewing this work, Whitmarsh proposed that this value of 500 ppm wt.
was a sensible limit for the hydrogen content in Zircaloy-2, which is a standard still in use by some fuel producers as a design limit for their zirconium components [15,38]. In the case of the work carried out by Lin et al., a nominal value of 300 ppm wt.
hydrogen was suggested as a maximum hydrogen content in Zircaloys, to prevent degradation of tensile strength [15,122]. This stems from the fact
Literature Review | 48
The Precipitation of Hydrides in Zirconium Alloys that up to around 400 ppm wt.
Lin observed an increase in ultimate tensile strength, after which the material rapidly weakened [15,122]. Unlike UTS, however, yield strength was shown by Lin to increase gradually with hydrogen content, although other authors have not observed this trend in their work [15,122].
As ductility and tensile strength are mechanical properties that depend on test temperatures, a number of authors including Arséne and Bai explored the effect of temperature on ductility [15,124]. While the work carried out by the pair agrees with the previously mentioned studies suggesting a critical hydrogen content after which ductility starts to drop, the actual value is more in line with Whitmarsh than Lin, with the most significant decrease seen above 800 ppm wt.
[15,124]. What the pair were able to observe, however, was that by increasing the temperature to a level analogous with reactor operating conditions, a large increase in ductility occurred
[15,124]. At 300 °C, an increase in the critical hydrogen content level from 500 ppm wt.
to
2000 ppm wt.
was recorded, but when irradiated the pair noted that this value more than halved, demonstrating the deleterious effect of radiation on ductility [15,124]. Finally, while examining the fracture toughness of Zircaloy-2, Grigoriev was able to identify a ductile to brittle transition above 600 ppm wt.
hydrogen content at room temperature [125,126]. At higher temperatures, this study demonstrated the expected increase in the Ductile to Brittle Transition Temperature (DBTT) expected from thermal softening of the matrix [125,126]. In contrast, the work carried out by
Kreyns on irradiated Zircaloy-4 highlighted a continuous decrease in fracture toughness with increasing hydrogen content up to a value of 1500 ppm wt.
, rather than a sudden ductile-brittle transition [126,127].
49 | Literature Review
(a)
The Precipitation of Hydrides in Zirconium Alloys
(b)
Figure 15. The mechanical effect of hydriding [15] (reproduced 11 from (a) [123] and (b) [122]).
In service life, this reduction in cladding ductility can lead to failure during thermal transients, where changes in reactor power output resulting from shutdown, accident conditions or turbine electrical load variations, lead to deviations in temperature [15]. When these fluctuations in temperature occur, thermal expansion of fuel pellets within fuel pins may lead to the introduction of stresses into the cladding material, in a phenomenon known as ‘Pellet
Cladding Mechanical Interaction’, or PCMI [15]. Where regions of high brittle hydride concentrations exist, cracks may nucleate and propagate, the degree of which being determined by the level of hydride concentration through the thickness of the cladding, as observed by
11 With permission from Elsevier Limited and The American Nuclear Society, respectively.
Literature Review | 50
The Precipitation of Hydrides in Zirconium Alloys
Rudling [15,126]. One such cause of hydride localisation is where spallation occurs in the protective oxide formed on the outer clad surface, leading to a greater thermal conductivity in a localised region where the oxide is thinner or entirely lost, as the exposed cladding metal possesses a higher thermal conductivity than the oxide [15]. Subsequently, the local temperature decreases due to the flow of coolant over exposed cladding, leading to a thermal gradient within the material, which collects hydrogen, and once the solubility limit is exceeded a region of high hydride concentration will evolve [15]. Ultimately, this may lead to cladding failure during significant power transients, releasing radioactive fission products into the primary coolant loop, making PCMI a serious consideration when examining cladding performance [15]. In practice, however, transients of significant enough scale to cause PCMI failures in PWRs are rare during normal service, thanks to advanced power regulation technologies [126]. As such, outside of accident conditions these types of failures are far more common in older BWR reactors [126].
Another cause of failures in earlier fuel rods was the phenomenon known as hydrogen blistering, occurring predominantly on the inner surface of cladding tubes [15,128]. These blisters consisted of highly concentrated regions of hydrides, which developed as the result of significant absorption of hydrogen from impurities within fuel pellets [38, 68]. The associated increase in volume of the hydride phase then induced stresses into the brittle blisters, leading to cracking and, in some cases, catastrophic fuel rod failure [38, 68]. In addition, where defects existed in the cladding through which coolant could pass, the tube could become filled with liquid or vaporised coolant, further supplying hydrogen to the blistering process [38, 68]. This problem is far less prevalent in newer fuel rods, owing to improvements in fabrication processes decreasing the amount of impurities within fuel pellets, as well as the introduction of oxide fuel drying steps [38,
68].
Aside from these mechanisms for failure, Simpson and Ells were quick to confirm that zirconium alloys also demonstrated a time-dependent cracking phenomenon related to hydrogen content [116,129]. In these experiments, the authors investigated cracks found in welds between
Zr-2.5Nb cladding and end-caps, which had been stored for an extended period of time at room temperature, before use in a reactor [116,120,129]. These cracks were attributed to hydrides found within the material, along with residual stresses produced by the welding process
[116,120,129]. Authors have since referred to the mechanism as Delayed Hydride Cracking, or
DHC, and while initial evidence was only produced for zirconium alloys containing niobium, the same process has since been demonstrated in Zircaloy family alloys [116,120,130].
In a review by Cox, it is highlighted that prior to its publication in 1990 the process of DHC had the greatest financial impact of any process of failure in zirconium alloys for chemical plant and CANDU reactor pressure vessels [120]. As the hydride content in fuel cladding is directly related to the length of exposure to in-operando corrosion, the concern over the risks of DHC to
51 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys fuel integrity increases with fuel assembly age [116]. As such, a great deal of research has been undertaken in order to predict the operational lifespan of fuel pins, to prevent the rupture of fuel rods and the subsequent release of fission products into coolants during operation or storage ponds/casks at end of life [116]. Models of the phenomena describe the crack growth as being sub-critical, in that failure occurs over an extended period of time under a continuously applied load that is below the yield strength of the matrix [116].
The fundamental process for DHC in zirconium alloys, as explained in a report on the subject by the IAEA, involves the fracture of brittle hydrides, which precipitate in hydrostatic stress raisers (such as crack tips), allowing gradual propagation through the thickness of the pressure tube over time [116]. As noted in publications by McRae et al. and Efsing et al., the initiation of the process relies on the pre-existence of a stress raiser, like the field arising from a crack, scratch or pore that may result from accidental damage or processing steps, like surface sand blasting [119,120,130]. At this stage of the process, however, there is a degree of conflict in the literature over the precise driving forces involved in DHC, where two competing models have been suggested to explain the formation of hydrides at the crack tip [119,131].
The first model, labelled as the Diffusion First Model (DFM), and championed by Puls, relies upon an increase in hydrogen concentration at the flaw tip occurring as a result of diffusion induced by a stress gradient [119,132,133]. As fuel pins are internally pressurised and may operate in a pressurised environment, the cladding is essentially uniformly stressed, however, the introduction of a flaw leads to a region of increased tensile stress and an intrinsic stress gradient around this area [130]. This tensile stress is thought to be hydrostatic, which subsequently lowers the chemical potential of hydrogen in the region, leading to diffusion up the stress gradient towards the crack tip, where it accumulates [116,131]. As the level of hydrogen in solid solution in the surrounding material is lowered due to diffusion towards this hydrogen sink, existing hydrides in regions away from the crack tip dissolve in order to maintain the local concentration of hydrogen in solid solution [116]. This dissolution of hydrides at some characteristic distance away from the crack tip or flaw provides the hydrogen feedstock required for diffusion to the region of heightened stress [116]. Once the build-up of hydrogen in the flaw region exceeds the terminal solid solubility limit for the local temperature, hydrides will precipitate at the crack tip [116,119]. Due to the stress field produced by the flaw, as well as the stresses applied to the material from the environment, the precipitating platelets develop at the point of highest stress, oriented in line with the flaw or advancing crack tip, and normal to the stress in the bulk material [116,130]. An image of hydride precipitates and orientation at the crack
tip is present in Figure 16. The hydride will then continue to grow, supplied by diffusion from
dissolving remote hydrides, up to a critical level that is defined by applied stress intensity and hydride size, after which the precipitate fails [116]. This fracture of the platelet allows the crack
Literature Review | 52
The Precipitation of Hydrides in Zirconium Alloys to advance up to the hydride-matrix interface, where a small amount of ductile failure in the matrix arrests the crack [116,119]. Once hydride fracture has occurred and the crack has ceased propagating, precipitation begins again at the crack tip, and the repetition of this cycle allows the crack to advance slowly through the material [116,119].
Figure 16. Micrograph of hydride reorientation and failure through DHC produced by notching a specimen (reproduced 12 from [131]).
The second model, known as the Precipitation First Model (PFM), which has been extensively documented by Kim, is based on stress-induced precipitation whereby the applied hydrostatic tensile stress causes the nucleation of a hydride platelet at the crack tip [119,131].
Thermodynamically, a strain effect stimulating nucleation would occur either through lowering the energy barrier to nucleation or by increasing the chemical driving force for precipitation, thus causing a nucleus to form from hydrogen already at the location. The resulting drop in the local concentration of dissolved hydrogen at the hydride-matrix interface establishes a concentration gradient around the crack tip, which further draws in hydrogen allowing the precipitate to grow
[119,131]. Subsequent steps in this model follow the same pathway of failure, re-precipitation
12 With permission from Elsevier Limited.
53 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys and growth as the DFM model [119,131]. Kim’s interpretation of this model stems from early models put forward by Dutton and Puls, as well as Simpson and Ells, which incorporated a combination of both PFM and DFM during DHC [119,129,134]. The flaw McRae highlights in this model, however, is that it makes the assumption that an applied hydrostatic tensile stress lowers the precipitation solvus in the region of the crack tip [119]. Past work undertaken by several authors indicates that this is not the case and that the effect of hydrostatic stress on the solubility of hydrogen is generally thought to be essentially negligible [119,120,135]. There is, however, evidence that stress may have some small effect on solubility, as in the work of Vizcaino et al.
[136] where applied stress was thought to change the solubility of hydrogen in a subset of grains, such that hydrides precipitated preferentially where they had not previously formed.
The DFM model was originally put forward in its earliest form in 1976 by Dutton and Puls, but since its conception, the model has evolved to include the hysteresis of hydrogen solubility seen in zirconium alloys [116,119]. In a recent work, Puls reviews his own model alongside Kim’s model, in order to correct for errors in understanding, which he sees as being the cause of conflict between the two models [133]. This work also acts as a good summary of the developmental history of both DHC models [133]. Puls reiterates that while numerically it is possible for a concentration difference to exist where a volume change occurs on transformation from matrix zirconium to hydride, the effect is not significant enough to drive DHC [133]. Instead, the driving force is shown entirely to be the result of the effect of the stress gradient on the chemical potential of hydrogen in solid solution, which Kim is believed to have erroneously discounted
[133]. While both Kim and Puls have published extensive articles debating the precise nature of the initial steps of DHC, neither author seems entirely satisfied with the other’s explanation
[133,137–139]. The DFM model put forward by Puls, however, has been regarded by other authors as the most thermodynamically sound, and forms the basis for common understanding of the DHC phenomenon [116,119].
The inclusion of the effect of hysteresis on DHC in Puls’ model is seen as particularly important, as variances in crack velocity were observed between cracking on heating and on cooling, which was explainable through the newer models [116]. More advanced modelling, using finite element methods have also sought to determine cracking rates during thermal transients, changes in flaw stress states during hydride precipitation, and the effect of load and thermal variations on hydride growth [116].
The importance of the hysteresis phenomenon to DHC stems from the fact that the primary driving force for hydrogen diffusion to the crack tip is the chemical potential gradient of hydrogen in solid solution [116]. In turn, this potential is governed by the fractional concentration of hydrogen within the material that is contained in solid solution, where a higher concentration of dissolved hydrogen leads to a higher chemical potential [116]. As this is the case, DHC rates
Literature Review | 54
The Precipitation of Hydrides in Zirconium Alloys are at their greatest when the temperature is such that all hydrogen is in solid solution, or if the thermal history is such that the concentration is at the precipitation solvus level, rather than the
dissolution solvus level [116]. Figure 17 demonstrates the dependence of DHC rate on thermal
history. During the heating cycle (moving right to left following T
1
, T
2
, T
3
, T
4
), the maximum velocity occurs at T
2
which may be the result of the rising temperature increasing the mobility and supply of hydrogen, and thus the rate of DHC. With further increasing temperature beyond
T
2
, the rate of DHC propagation drops to zero and remains unchanged up to the maximum temperature at T
4
, possibly the product of the diminished driving force for hydride precipitation.
On cooling (moving left to right following T
4
, T
5
, T
6
, T
2
), no DHC occurs until T
5
, where the driving force becomes sufficient to initiate DHC; thereafter, the decreasing temperature leads to a diminishing rate of DHC propagation, which may be the result of the decreasing mobility of hydrogen.
Figure 17. DHC rate as a function of thermal history (reproduced 13 from [140]).
This assessment makes it clear that thermal history and thermal operation pathways play a fundamental part in determining whether DHC will take place, and at what rate it will occur
[116]. Furthermore, the peak temperature that the specimen reaches, and the subsequent cooling rate, have also been demonstrated to influence chemical potential and subsequent DHC velocities [116,141].
13 Reprinted, with permission, from ASTM STP939 “Prevention of Delayed Hydride Cracking in Zirconium
Alloys”, copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428.
55 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys
One final point to address when reviewing the mechanism of DHC is the relationship between crack velocity and applied stress intensity factor, K
I
, which is the stress state at a crack/notch tip resulting from a long-range stress field or residual stresses. For failure of crack tip hydrides, a certain critical threshold stress intensity must be exceeded within the material, K
IH
, otherwise no DHC will occur [116]. Above this level, stable sub-critical crack growth occurs, the rate of which is relatively independent of the applied stress intensity factor up to the fracture toughness of the material, K
IC
[116]. Above the fracture toughness, unstable crack growth will occur [116]. The relationship between stress intensity factor and crack velocity is shown
Figure 18. Schematic of the crack velocity to stress intensity factor relationship for DHC
(reproduced 14 from [140]).
2.3.
X-Ray Diffraction
2.3.1.
Fundamentals
Electromagnetic radiation has been used to quantify materials for many hundreds of years, ranging from fundamental techniques like optical microscopy up to highly complex approaches involving particle accelerators. One of the early techniques responsible for quantifying atomic and molecular structures is X-ray diffraction, which, unlike X-ray imaging, is
14 Reprinted, with permission, from ASTM STP939 “Prevention of Delayed Hydride Cracking in Zirconium
Alloys”, copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428.
Literature Review | 56
The Precipitation of Hydrides in Zirconium Alloys capable of probing the nature of ordered structures with atomic resolution [142]. This is down to the short wavelength and high-energy exhibited by radiation for this range of the electromagnetic spectrum [142]. When X-rays are incident on an arrangement of atoms, the cloud of electrons associated with each will cause some amount of the photons to undergo omnidirectional scattering [142]. Both crystalline and amorphous structures of atoms will result in the scattering of X-rays, but the latter will only produce diffuse scattering, whereas the former will produce strong diffraction patterns indicative of the atomic structure. There are, however, two fundamental criteria that must be satisfied for diffraction to occur [142]:
The matter responsible must be capable of scattering the incident radiation.
The size of spacing between obstacles must be similar to the wavelength of the probing emission.
The scattered photonic waves then interact with one another to produce constructive
This difference leads to the waves being in phase and in antiphase, respectively, and so the resultant waves are bolstered and diminished by the differing degree of coherence between the two different θ angles considered. These two examples are the extremes of the process, and the pattern that is projected by diffraction will be the result of an interaction between in-phase and anti-phase waves, as well as all of those that are in between these two degrees of coherence.
(a) (b)
Figure 19. The interaction between scattered waves, showcasing (a) destructive and
(b) constructive interference [142].
The interaction of neighbouring rays form discrete regions that project outwards from
the crystal in cones comprised of regions of high amplitude and low amplitude, Figure 20 – (a),
known as Debye-Scherrer cones. By bisecting these cones with a two-dimensional area detector,
ring patterns can be recorded yielding diffraction patterns like that seen in Figure 20 – (b). These
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The Precipitation of Hydrides in Zirconium Alloys patterns can be integrated, either fully or partially, around their centre of symmetry to provide a two-dimensional diffractogram, which is a plot of intensity/arbitrary number of counts against a spatial term (2
, d – inter-planar spacing, or Q – reciprocal space). Here, the positions of greatest intensity in these plots correspond to the bands of constructive interference in the projected diffraction cones.
(a) (b)
(c)
Figure 20. Schematic representations of (a) Debye-Scherrer diffraction cones,
(b) a Debye-Scherrer ring pattern and (c) a diffractogram.
The position of the reflections in this signal can be described by Bragg’s Law, Equation 2,
where n is the order of the reflection (being an integer that does not cause 𝑠𝑖𝑛
to exceed unity), 𝜆 is the wavelength of the incident X-rays, 𝑑 ℎ𝑘𝑙
is the spacing between regular planes of atoms in a crystal (where the ℎ𝑘𝑙 subscript denotes the miller indices describing the plane), and
is a measure of the angle of the incident radiation from being parallel with the plane (visualised in
𝑛𝜆 = 2𝑑 ℎ𝑘𝑙 𝑠𝑖𝑛 𝜃 Equation 2
Where this equation is satisfied, the intensity of the resultant beam will be at its highest, owing to the degree of constructive interference that results from the phase synchronisation of interacting waves, producing the signature Bragg reflections seen above. This law, however, does not account for unit cells containing scattering atoms at positions other than corners, which, at certain Bragg angles, will generally produce out-of-phase scattering [142]. This destructive interference will act to remove certain Bragg reflections from diffraction patterns originating
Literature Review | 58
The Precipitation of Hydrides in Zirconium Alloys from non-primitive unit cells (Face-Centered Cubic, FCC, and Body-Centered Cubic, BCC, for example) [142]. These, so-called forbidden, reflections occur for planes where h + k + l is odd for BCC crystals, or where they are either not all odd or all even for FCC cells [142].
X-ray diffraction on a laboratory scale is performed using a diffractometer, a relatively compact device that is generally comprised of a source, stage and detector (either point or area).
These three principal components are generally motorised in some combination, such that the angular relationship between them can be precisely controlled, thus allowing precise measurement of the angle between the incident beam path and a point detector, or the beam and positions on an area detector. By varying θ while recording the X-ray intensity with mobile point detectors, or with knowledge of the relationship between points on an area detector and the direct beam, it becomes possible to construct a diffractogram of intensity against 2θ, similar
to that created from integrating the ring patterns recorded from an area detector, Figure 20 – (c).
21 – (c). The choice of which geometry to use is made based on experimental parameters. For
example, an area detector will allow the capturing of large segments of Debye-Scherrer cones simultaneously, Bragg-Brentano geometry allows sampling large volumes within materials in addition to being capable of analysing absorbent materials, while the Debye-Scherrer geometry allows good counting statistics to be achieved by rotating a cylindrical sample about its axis [143].
(a) (b) (c)
Figure 21. (a) Bragg-Brentano (reflection) and (b) Debye-Scherrer (transmission), and
(c) image plate diffraction geometries.
2.3.2.
The Synchrotron Accelerator and X-Ray Diffraction
While laboratory diffractometers are still a staple of materials research, X-ray sources for diffraction and crystallography have evolved significantly since their conception, in order to overcome the limitations faced by these small-scale experimental apparatus. With the advent of particle accelerators, a by-product was observed in the form of X-rays produced wherever beams
59 | Literature Review
The Precipitation of Hydrides in Zirconium Alloys of high-energy electrons were deflected within these instruments [144]. In the 1960s this emission was first harnessed for the purpose of X-ray crystallography as part of pre-existing accelerator facilities, but the 1980s saw the birth of the first purpose-built synchrotron light source designed to produce X-rays, the Synchrotron Radiation Source installed at the Daresbury
Laboratory [144]. The following decade saw the development of insertion devices (wigglers and undulators), which added several orders of magnitude to the brilliance of third generation light sources, bringing them to the current state-of-the-art for ring-based accelerator light sources
[144].
This brilliance is one of the significant features that set the synchrotron apart from laboratory scale light sources, being a description of the degree of collimation (or lack of divergence) and the photonic flux density of the resulting beam [145]. Third generation instruments generate X-rays that are highly collimated, minimising artificial instrument broadening to Bragg reflections, have a high flux, allowing rapid imaging of patterns, and can generate a wide range of wavelengths, making them ideal for probing atomic lattice-resolution features [144–146]. In addition to this, the high energies they are capable of producing allow them to penetrate far deeper into materials, allowing bulk measurements of large volumes of material to be made. Where laboratory diffractometers take minutes and hours to acquire good quality data, synchrotron detectors can take seconds to record clear patterns with high angular resolution. This enables users to not only image samples under static conditions, but to design dynamic, in-situ experiments to perform while recording patterns, allowing a study of crystal evolution to be undertaken. In recent years, however, the birth of the Free Electron Laser (FEL) has signalled the start of the next generation of X-ray diffraction and crystallography, owing to the significant increases in brilliance and temporal resolution that they afford [144].
The accelerator itself can be broken down schematically into a number of component
parts, pictured schematically in Figure 22 overlaying an aerial photograph of the European
Synchrotron Radiation Facility (ESRF). For the remainder of this section, an explanation of the workings of a synchrotron will be given based on the specific design for this facility, given that all experimental work presented in this thesis was performed there. The process starts in a similar way to the electron gun found in electron microscopes, where electrons are liberated from a heated cathode using a high-voltage field, with an initial energy of 100 x 10 3 eV [144,147]. These electrons are captured by the LINAC (Lear Accelerator), where Radiofrequency (RF) fields accelerate the particles up to 200 x 10 6 eV, while bunching them together into packets and focusing the resulting electron beam [144,147]. Next, bending magnets transfer the beam into the 300 m diameter booster ring, where a series of subsequent bending magnets guide the electrons in a 10 Hz looping circuit through magnetic optics and RF cavities that further accelerate the electrons up to an energy of 6 x 10 9 eV [144,147].
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The Precipitation of Hydrides in Zirconium Alloys
Once the target energy has been reached, a transfer line allows the beam to pass from the booster ring to the 844 metre circumference storage ring (a series of straight stretches, cornered by bending magnets) where further optics ensure the beam maintains its focus while
RF cavities mitigate against energy loss [147]. Insertion devices are embedded periodically in the straight sections of the ring and are comprised of a series of inverted polarity magnets, such that they cause the electrons to wiggle or undulate (hence their names), in order to tune the parameters of the resulting beam [144]. Where the beam is bent to continue its ‘circular’ path at the end of each straight section, a beam of photons is projected tangentially from the ring, which travels down a beamline, through a series of lenses and instruments, and ultimately being delivered to an experimental hutch [148]. Within each hutch, these streams of photons are then used to interact or illuminate material, primarily to characterise features with a similar size to the wavelength of photons used [148]. For example, high-energy X-rays from a synchrotron, when illuminating a crystalline material, can be diffracted in the way outlined previously, producing the characteristic Debye-Scherrer cones. These cones can be imaged in 2D using an area detector, allowing high quality diffraction patterns to be recorded rapidly.
Aside from X-ray diffraction, the range of experimental capabilities available within synchrotron facilities is expansive, where techniques like SXRD (Synchrotron X-Ray Diffraction) and GIXRD (Grazing Incidence X-Ray Diffraction) can be augmented with dynamic in-situ conditions like pressure and temperature, and so providing a comprehensive list does not benefit this work. Instead, a full technical description of the beamline pertinent to this thesis can be found in [149,150], highlighting various important features and capabilities of ID15B at the European
Synchrotron Radiation Facility.
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The Precipitation of Hydrides in Zirconium Alloys
Figure 22. The European Synchrotron Radiation Facility, photograph reproduced from [151].
2.3.3.
Synchrotron Studies of the Zirconium-Hydrogen System
The ability to perform diffraction experiments on samples exposed to dynamic in-situ conditions has led to a growing number of authors using synchrotron X-ray diffraction as a method for quantifying the zirconium-hydrogen system. This section seeks to provide an overview of some of the areas of research currently being performed using synchrotron radiation, and is by no means exhaustive.
At its most fundamental, synchrotron X-ray diffraction is used as a characterisation tool, and so an initial starting point for this discussion is work like that of Daum et al. whom used it to examine the regional population distribution of hydride phases in material [152]. Here, δ-hydride was that seen most commonly, although material with hydrogen levels in excess of 1250 ppm wt.
also showed evidence of γ-hydride precipitates [152]. Further enrichment to above 3000 ppm wt.
was seen to encourage the formation of the ε-hydride phase, although no threshold stability concentration was seen experimentally [152]. Another example of ambient hydride characterisation is found in the work from Tulk et al., where the impact of matrix yield strength on the phase stability of hydrides was investigated, indicating that this parameter has a strong influence over the stability of γ-hydrides [80]. Given the similarity between hydride phases, the overlap between reflections from each of these phases is significant, as can be the overlap with matrix reflections, and so these works each illustrate the importance of the high diffraction
(angular) resolution offered by this technique when studying similar crystal structures.
Given the temporal resolution of synchrotron X-ray diffraction, it is possible to perform in-situ experimentation while collecting diffraction patterns, and so a large number of authors
Literature Review | 62
The Precipitation of Hydrides in Zirconium Alloys have published studies of that nature. Tulk et al. went further than ambient conditions by implementing a heating programme whilst recording diffraction patterns, allowing a deeper investigation into the interchange between δ and γ [80]. No evidence of a δ to γ transformations was recorded, supporting the premise that the γ-hydride phase is metastable [80]. As well as examining phase stability with temperature, the kinetics of the processes of precipitation and dissolution can easily be followed, by tracking changes in the diffraction signal as a function of temperature. Other examples of temperature dependent synchrotron X-ray diffraction are studies of the solubilities and kinetics of hydrogen in various alloys of zirconium, undertaken by
Zanellato et al. [90], A.T.W. Barrow et al. [107] and L. Barrow et al. [153].
Zanellato et al. were able to demonstrate the significant impact that solute hydrogen has on matrix lattice strain, where even a small atom in great enough numbers can have a marked impact on matrix lattice spacing [90]. This is thought to be significant where lattice strains are used as an indicator of stress, as dissolved hydrogen could likely impact upon these measurements of stress [90]. A.T.W. Barrow et al. coupled thermodynamic modelling to X-ray diffraction studies to examine nucleation of hydrides in zirconium, showing that the kinetics of the transformation from α to α + δ (the process of precipitation) is rate limited above 287 °C, at the cooling rates used in that experiment [107]. Furthermore, an evaluation of solubility temperature, accurately measurable with synchrotron X-ray diffraction, was thought to show that an increase in the precipitation chemical driving force led to smaller, but more abundant, hydrides forming [107]. The work of L. Barrow et al. looked at the solubility of hydrogen in hexagonal (α) and cubic (β) matrix structures, finding that β is able to host far more solute hydrogen than α, thought to be the result of the quantity and size of tetrahedral interstices in the
β structure [153]. Additionally, studies of solubility were also able to provide equations for the precipitation and dissolution solvi for hydrogen in the β-phase of zirconium [153]. The importance of temperature in hydride related experiments cannot be understated, as service components will be subject to everything from ambient and operating temperatures, up to potentially extreme temperatures under accident conditions. Given that changes in temperature can lead to variations in mechanical properties, kinetics and thermodynamics, it is important that a full understanding of the behaviour of hydrogen in zirconium be developed, relevant to the life of fuel assemblages.
Temperature is not the only consideration that must be made, however, as hydrides formed at various temperatures are thought to impart stresses into both themselves and the surrounding matrix, as in the work by Santisteban et al. [154]. There, the precipitation of hydrides was thought to induce biaxial stresses of ≈360 MPa in the particles [154], a value that disagrees somewhat with those presented by Colas et al. [155] (although it is in closer agreement to the lower von Mises equivalent stress presented in the latter work). In both works, the ability to
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The Precipitation of Hydrides in Zirconium Alloys record complete Debye-Scherrer rings with good spatial and temporal resolution using synchrotron X-ray diffraction is a prerequisite of being able to measure directionally resolved stresses within material.
The stress developed from the formation of hydrides is not the only source that can be investigated, as complex loading occurs in cladding material, owing to the internal pressurisation of tubes. Given this fact, a number of works have investigated the effect of applied (albeit predominantly uniaxial) loads on hydride precipitates. Kerr et al. were successfully able to demonstrate the ability to calculate strains for hydrides in samples with hydrogen concentrations lower than 100 ppm wt.
, demonstrating the usefulness of high-energy monochromatic X-ray radiation and sampling large volumes of material when studying a minority phase [156]. This work led to an observation that the hydride has an elastic moduli similar to that of Zircaloy-2, with a value of approximately 100 GPa [156], a value that has been used to calculate stresses in other work [155]. Earlier work by Steuwer et al. was able to use energy-dispersive synchrotron X-ray diffraction to measure lattice strain evolution during in-situ loading experiments [81]. In this work, evidence of stress-induced ordering of tetrahedral interstitial hydrogen was seen, triggering a transformation from δ to γ hydride [81].
This is not the only work investigating the redistribution of hydrogen and hydrides with applied load, as Colas et al., for example, have undertaken extensive synchrotron campaigns into the impact of stress on the orientation of macro-hydrides [108,155,157]. In the earliest of these works, a threshold of 80 MPa was found to cause a 25 % increase in radially oriented hydrides during precipitation, and a signature in the hydride FWHM for the reorientation was documented
[108]. Next, these authors identified compressive strains in the TD and RD within the hydride, although the magnitude of these remained below the level required for plasticity [155].
Additionally, the broadening of hydride profiles was identified to be predominantly the effect of strain related broadening (as opposed to size), an observation necessary to support the broadening signature for reorientation [155]. In the final of these publications, the authors demonstrated that under a stress that is above the reorientation threshold, these reoriented hydrides formed at lower temperatures than normally oriented hydrides in unstressed samples
[157]. Interestingly, the radially oriented precipitates that form under stress were seen to exhibit tensile strains orthogonal to the platelet face [157]. It is thought [132,158] that the internal compressive stresses established from the misfit act to effectively ‘shield’ hydrides from some applied load, increasing the stress intensity required to initiate failure. Given the observations by
Colas et al. [157] that the strain state in reoriented hydrides may differ from normal precipitates, it seems possible that crack-tip hydrides, reoriented by local stress fields, may exhibit different strain states than those in the bulk metal, with diminished ‘shielding’.
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The Precipitation of Hydrides in Zirconium Alloys
Redistribution of hydrogen, on a grain-to-grain basis related to component texture, was also investigated by Vizcaíno during thermal cycling with, and without, applied loads [136]. In that work, two grain families were identified as containing the bulk of precipitated hydrides, those with the
⟨0002⟩ 𝛼
oriented along the hoop (circumferential) direction, and those with this axis oriented between the hoop and radial directions [136]. These families exhibited differing hydrogen solubilities during thermal transients [136], which may possibly speak of the variations in the internal stress state of these grains, owing to the polycrystalline thermal expansion mismatch. Significantly, the application of a tensile load was found to influence the dissolution and precipitation temperatures, with a net impact of reducing the hysteresis between the two
[136], an observation that may lend some merit to the PFM model for DHC [119]. A stress of
225 MPa was seen to be the interchange point above which hoop oriented grains were those where precipitation occurred first, as opposed to below this where grains tilted between the hoop and hoop directions were first [136]. Interestingly, the application of load in this work [136] was not seen to show any redistribution of solute hydrogen between the two families of grain being evaluated, perhaps countering those observations by Steuwer et al. [81].
One of the more complex issues surrounding hydrogen in zirconium is the prevalence and causation behind DHC, and so one of the ultimate aims of experimental work in this field is to characterise it in such a way that a full mechanistic understanding of the process is developed.
To that end, a number of works utilising synchrotron X-ray diffraction to investigate this phenomenon have been published in the literature. Kerr et al., for example, was able to map strain fields in the matrix and hydride phases present around a notch, under applied load [159].
This work demonstrated that not only could strain fields be resolved easily in two dimensions using this technique, but that it was also possible to detect hydride failure in-situ, where the peak stress transferred from the notch-tip hydride to the nearby matrix [159]. In later work, Kerr went on to combine thermal transients with applied load to precipitate these notch-tip hydrides, demonstrating that the transformation misfit associated with these precipitates serves to relax some of the matrix strain associated with the notch [160]. A final example of the probing of notch-tip hydrides is found in work published by Allen et al. [161], who expanded upon the Kerr et al.’s studies in the area [159,160]. As with the previous work, Allen et al. were able to document hydride failure through a change in the load distribution between the two phases, and by a change in the position of peak load in the matrix, thought to advance with the tip of the crack; a fact corroborated using electron microscopy [161]. In this study, deviations in strain observed between matrix and hydride were attributed to plasticity in the matrix lowering the effective stiffness of the parent lattice, given that the elasticity of both phases is considered to be similar
[161].
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The Precipitation of Hydrides in Zirconium Alloys
All of these are just a representative sample of the various works being published in the field of zirconium hydriding, studied with synchrotron X-ray diffraction, and while the time and monetary cost associated with this form of work is high, the wealth of information it can provide is beyond the capabilities of many other analytical solutions. One overriding theme in many of these works, however, is that while experimental methods are a good way of investigating the various phenomenon that govern hydrides, supporting these studies with modelling of various natures allows for a significantly deeper understanding of processes taking place. Combining physical and computational studies in this way will be key to developing the aforementioned mechanistic understanding of the system, which is needed to support the safety case for increasing the burnup of fuel assemblies.
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The Precipitation of Hydrides in Zirconium Alloys
3.
Methodology
Concise experimental methodologies for each investigation within the broader experimental campaign are provided in the proposed manuscript for each of the respective topics discussed in this thesis. Given the complex nature of the study in its entirety, the scope of details discussed in these works must be limited, and so this chapter contains the finer specifics of the experimental and analytical process used throughout. Young et al. have produced guidelines on the publication of Rietveld and pattern decomposition (i.e. Le Bail) studies [162], which will provide a structure for this section (albeit not quite in the order suggested by those authors).
3.1.
Sample Specifications
3.1.1.
Base Material
A number of samples were employed in this campaign, provided by the Institut de
Radioprotection et de Sûreté Nucléaire (IRSN), all being based on a single primary chemistry and processing history, like that found in the work by Zanellato et al. [90] and Krebs et al. [163]. To summarise, Zircaloy-4 was rolled to 0.4 mm and recrystallisation annealed, before being cut into coupons measuring 5 mm in the transverse direction (TD) and 50 mm in the rolling direction (RD),
Figure 23. Sample physical geometry.
Table 6. Zircaloy-4 chemical composition.
Source
Sn
Standard [32] 1.45
IRSN [163] 1.30
0.21
0.20
Fe
0.10
0.10
Element (
Cr wt.
%)
O
No Data
0.129
0.01
Hf H
No Data
No Data 0.0012
A number of Electron Backscatter Diffraction (EBSD) maps collected by IRSN were provided 15 , which were used to quantify the grain size and texture of the material, examples of
which are illustrated in Figure 24. All EBSD analysis was performed using the MTEX 4.0.12 toolbox
15 No details on sample preparation are available, unfortunately.
67 | Methodology
The Precipitation of Hydrides in Zirconium Alloys for Matlab 2014b, and maps at two scales are presented, each produced from the same sample.
The first EBSD map, Figure 24 – (a), measures 156.4
m x 71.8
m, with a 0.2
m step size, and
the second, Figure 24 – (b), has dimensions of 19.25 mm x 9 mm, and a step size of 50
m.
The high-resolution map allows individual grains to be resolved, allowing grain size statistics to be calculated, but with fewer crystals being sampled a meaningful measurement of texture cannot be performed. Additionally, the spiking and noise in the map precludes an automatic grain size assessment being performed by the software, as these small regions of noise are considered single pixel grains, and so a manual assessment of grain size was needed instead.
This process was performed by manually selecting grains and tabulating their major axis length
(calculated by the software), providing an average grain size between 8
m and 10
m, similar to those values presented by Zanellato et al. (10
m) and Krebs et al. (7.3
m) for similar material
[90,163].
The second map is substantially larger in dimensions, but has a step size that means it is not possible to resolve individual crystallites, instead allowing a large area of material to be sampled, providing good counting statistics for measuring texture within the sample. From this orientation set, the pictured pole figure can be constructed that shows the strong orientation of basal poles close to the ND, but offset by some small amount (typically 15° to 25° [164]) towards the TD. This, coupled with the
{11̅00} 𝛼
poles being oriented in the RD, is indicative of a hexagonal material with a c/a ratio below the ideal, which has been cold-rolled [164]. From the macroscopic
EBSD map, Kearns factors can be calculated, describing the fraction of poles from a plane oriented in a specific direction of the material [165]. The derived factors for the basal poles are 𝑓
𝑅𝐷
=
0.120
, 𝑓
𝑇𝐷
= 0.248
and 𝑓
𝑁𝐷
= 0.631
, while those for the
{11̅00} 𝛼
plane poles are 𝑓
𝑅𝐷
= 0.440
, 𝑓
𝑇𝐷
= 0.376
and 𝑓
𝑁𝐷
= 0.184
from the macroscopic map.
Once fabricated, the samples were separated such that some remained non-hydrogen-charged (containing ≈12 ppm wt.
from fabrication, Table 6), while others went on
to be charged with hydrogen to a range of concentrations. Those remaining non-charged required no further treatment, and were intended to allow a study of the response of the base zirconium metal to the experimental process, necessary to deconvolute the response of hydrides from that of the matrix during the broader programme. The method for hydrogen charging performed on the remaining samples is described in the following section.
Methodology | 68
The Precipitation of Hydrides in Zirconium Alloys
(a)
(b)
(0002)
TD
(11̅00)
TD
(112̅0)
TD
RD RD
Figure 24. Representative (a) high magnification grain map and (b) low magnification texture and orientation map, with associated pole figure.
69 | Methodology
The Precipitation of Hydrides in Zirconium Alloys
3.1.2.
Hydrogen Charging
Hydrogen was charged into the sample by F. Wheling at École Centrale Paris, using the methodology described in [90,163]. To summarise, samples were put under vacuum (to minimise the formation of oxide that would lower the pickup of hydrogen) and then heated to 450 °C, at which point hydrogen gas (H
2
) was introduced incrementally, to control the absorbed concentration [163]. The concentration and distribution of hydrogen within each sample was verified using gas fusion analysis, with a JUWE ON/H-mat 286 (a predecessor to the Bruker
Galileo) [163]. Concentration distributions were minimal, measured to be ≈3 ppm wt.
mm -1 [90], although the error in concentration measurements was thought to be ±8 ppm wt.
[163]. Given the geometry of the sample and the temperature at which charging took place, it was thought that a relatively uniform through-thickness distribution of hydrogen was created [163]. Finally, charging material with hydrogen was not observed to affect the matrix texture in any significant way [90].
Charging of samples was executed to the quantities listed in Table 7, which also contains
specific details of the samples used within the kinetics, strain, diffusion and loading portions of the experimental campaign. It is noted that the value given for S2 was the initial hydrogen content charged into the sample, but that the concentration at the time of experimentation was observed
to differ; further details are discussed in Section 3.8.3.
Table 7. Sample descriptions and as-charged hydrogen concentrations.
Sample Charged H (ppm wt.
)
S1
S2
0
550
S3
S4
0
200
Details
Standard sample.
Identical to S1, but charged with hydrogen.
Similar to S1, but with Ø1 mm notches.
Identical to S3, charged with hydrogen.
3.2.
Synchrotron X-Ray Diffraction
The entirety of the experimental campaign was undertaken at the European Synchrotron
Radiation Facility (ESRF), in Grenoble, France. The instrument used was beamline ID15B, a high-energy diffraction beamline described in technical detail by Tschentscher et al. and Suortti et al. [149,150]. The material was illuminated in Debye-Scherrer geometry (transmission), with the X-ray beam being parallel to the ND of the material, orthogonally incident to the flat surface,
shown in Figure 25 – (a). The beam geometry was chosen to be 300 μm x 300 μm, which combines
with the sample thickness to produce a gauge volume of approximately
300 μm x 300 μm x 400 μm. The choice of geometry and beam size allowed diffraction from a large number of crystallites within the material to be recorded, meaning that the presented measurements were representative of the bulk properties of the region being illuminated.
Methodology | 70
The Precipitation of Hydrides in Zirconium Alloys
The Debye-Scherrer diffraction cones originating from the gauge volume were bisected by a Trixell Pixium 4700 detector, an array of 2640 x 1920 pixels, each measuring
154
m x 154
m. This device was used to record patterns in 5 second acquisitions, followed by
4-5 second disk-write operations, producing a temporal resolution of 9-10 seconds per recorded pattern. While faster acquisitions would have been possible, thus improving temporal resolution, it was observed that shortening the imaging time would degrade the signal-to-noise ratio, affecting the line profile stability of the small hydride reflections and reducing data quality.
Furthermore, the disk-write time could not be reduced significantly, and so shortening from the total of 9-10 seconds by the small amount that could be gained from reducing the acquisition time was not seen as beneficial when considering the marked degradation in data quality that would result.
(a) (b)
(c)
Figure 25. (a) Diffraction geometry, (b) sample-detector distance variation and (c) geometry for calculating sample-detector distance.
Monochromatic X-rays were desired, granting high diffraction/angular (2θ) resolution, with a chosen energy of 87 keV for the experiment, and so the instrument was configured to meet this choice. Diffraction patterns from a Standard Reference Material (SRM), cerium dioxide
(CeO
2
) [166], were imaged at two different sample-detector distances, although at this point the precise distances were not known and only the motor encoder positions at D
1
and D
2
were available. These two positions were thus nominal values, with a known distance between the points, termed 𝛥𝐷
, illustrated in Figure 25 – (b).
71 | Methodology
The Precipitation of Hydrides in Zirconium Alloys
The software package Fit2D, provided by the ESRF, was subsequently used to find the beam centre and integrate both of the patterns in the way described by the software documentation [167]. At this stage, values used for sample-detector distance and wavelength were unknown, and so a nominal wavelength was entered in conjunction with the D
1
and D
2 motor positions for each of these two patterns. The MFIT functionality within Fit2D was then used to apply Voigtian peak profiles to the recorded reflections, by first using “INITIALISE” to designate approximate positions, and then “OPTIMISE” to refine the profiles, yielding values for the positions of reflections. Using this method, relative values for r
1
and r
2 were calculated for a chosen reflection within the SRM pattern, corresponding to the centroid positions of the
reflections relative to the direct beam, seen in Figure 25 – (b). From the geometry illustrated in
Figure 25 – (c) it was possible to construct Equation 3, which allowed D
1
to be calculated accurately, describing the sample-detector distance for the CeO
2
SRM.
𝐷
1
= 𝑟
2 𝑟
2
∙ ∆𝐷
− 𝑟
1
Equation 3
The SRM pattern acquired at D
1
was finally used with the “CALIBRANT” function (within the “POWDER DIFFRACTION (2D)” mode of Fit2D) to calculate the experimental wavelength, using the previously determined parameters for beam centre and the newly calculated sample-detector distance for this SRM. In the present campaign, a value of λ = 0.14223 Å was calculated for wavelength, with a corresponding energy of 87.17 keV.
3.3.
In-Situ Environment
Samples were successively mounted in the electrically conductive, water-cooled grips of an Instron ETMT8800 (ElectroThermal Mechanical Tester), which used direct current to induce
Joule (or resistive) heating in the metal. An S-Type thermocouple was spot-welded at the axial centre of each sample, close to where the gauge volume would be, from which local temperature could be measured. The reading from this sensor was used by the ETMT software to control the temperature by varying the current passed between the grips. The equipment was calibrated such that any heating current induced offset in the thermocouple reading was accounted for. As a secondary check of temperature, a FAR Associates FMPI multi-wavelength pyrometer was arranged such that the ≈3 mm spot was located close to the gauge volume. This device, however, was unable to give readings below ≈350 °C, and so could not be used as anything other than a supporting check at high temperature.
The grips themselves were contained within a sealable atmospheric chamber, which was purged with inert argon during the experiment to minimise further oxidation of the sample during
Methodology | 72
The Precipitation of Hydrides in Zirconium Alloys periods of elevated temperature. This continuous, slow flow of argon, in conjunction with the water-cooling in the grips, led to the loss of thermal energy from the sample through a combination of conduction, convection and radiation. As a result, the current in the ETMT was adjusted dynamically by the software to compensate for these effects. It should be noted, however, that heat loss to conduction would have affected material closest to the grips most strongly, as conduction could occur into both the cooled grips and the surrounding argon atmosphere.
The mounting within the ETMT was such that the samples were gripped at either end,
seen in Figure 26, and if these mounting points were static, then compressive stresses would have
developed within the material as a function of temperature, where thermal expansion of the sample would have been constrained. Instead, the position of the loading armature (used to apply force to samples in mechanical tests) was set to react dynamically to stresses within the sample, such that the load was always zero. Similarly, the thermal expansion of a sample mounted to a static point at one end would mean that the gauge volume would drift within the material during heating, where material closer to the fixed point (the static grip) would expand into the path of the beam. To compensate for this, the maximum linear thermal expansion 16 seen in the sample was measured using the ETMT strain gauge, and an effective thermal expansion coefficient for the axial direction was calculated. The motor controlling the lateral position (with respect to the direction of the beam) of the experimental table was then used to offset the ETMT in its entirety, as a function of the temperature of the sample. This was thought to keep the gauge volume in the same approximate point within the sample.
16 In HCP metals, two thermal expansion coefficients describe the anisotropic dilatation of the unit cell. To describe linear thermal expansion in a polycrystalline material, a single effective one dimensional coefficient will be an average between these two parameters, as a function of the texture of the material.
73 | Methodology
The Precipitation of Hydrides in Zirconium Alloys
Figure 26. ElectroThermal Mechanical Tester (ETMT) sample mounting schematic.
3.4.
Thermal Operations
The overall thermal profile of the experiment consists of a number of thermal cycles, spanning Cycle 0 (C0) to Cycle 8 (C8) for the diffusion, kinetics and strain portions of the experiment. Given that differences exist between the cycles employed for the hydrogen charged sample and those for the non-charged material, this section will be divided by sample condition.
Furthermore, as the minutia of the thermal operations is explained in each of the proposed manuscripts in a way that is relevant to the content of each, the following sections will instead give only an overview to the thermal programme, and include any details that were deemed unnecessary for journal publications.
3.4.1.
Non-Hydrogen-Charged Sample (S1)
The function of this sample was to act as a baseline for measurements made on the similar, but hydrogen charged, material, such that it was possible to deconvolute the influence of hydrogen from the natural behaviour of the base material. Key temperatures were determined from the exposure of S2 during the later experiments (C2-C8), and so the first cycle involved heating the sample to each of these temperatures and recording diffraction patterns.
At each ‘shelf’ temperature (a term used in later manuscripts), the gauge volume was
‘scanned’ axially within the material in a way that meant diffraction patterns were recorded in steps between the centre of the sample (0 mm) and the fixed armature at one end of the sample
(11 mm). Given that the thermocouple measured the temperature at a fixed point within the material, the axial scans were designed to allow a profile of matrix lattice strains to be calculated, from which the magnitude of the Joule heating temperature gradient could be defined. The scanning of the sample was performed by moving the position of the ETMT assemblage, using
Methodology | 74
The Precipitation of Hydrides in Zirconium Alloys the same lateral motor as was used for compensating for thermal gauge volume drift. As such, an algorithm was programmed into the experimental macro that calculated the motor position as a function of both the desired gauge volume position (relative to the axial centre) and the change in this position owing to thermal drift. What was not considered at the time, however, was that thermal expansion would also increase the distance between the desired points. As such, there exists some degree of error in the position of measurement points, although given that the total linear expansion of the sample was only recorded to be ≈50 μm, it would seem likely that the maximum drift in the position of the considered points was only ≈25 μm. With a lateral beam dimension of 300 μm (that parallel to the sample axial direction), it is thought that this error in measurement point should not affect results significantly.
After each axial scan, the gauge volume was returned to the primary position at the axial centre of the sample, where a series of consecutive measurements were made, before the temperature was changed again. These central measurements were performed to provide good counting statistics for calculating thermal expansion coefficients, by providing a large number of patterns from each temperature to average over. The overall temperature profile for the
non-charged sample is provided in Figure 27.
Figure 27. Thermal profile and gauge volume displacement relative to material axial centre as a function of time for the non-charged sample (S1).
75 | Methodology
The Precipitation of Hydrides in Zirconium Alloys
3.4.2.
Hydrogen-Charged Sample (S2)
The hydrogen charged material was subjected to a far more extensive thermal programme, designed to measure precipitation kinetics, strain evolution and hydrogen redistribution. It should be noted that prior to this part of the campaign sample S2 was exposed to a ‘dry run’ to test the responsiveness of the sample to the applied heating current, whereby the sample was heated to 570 °C and held for a short time, before being cooled again.
Unfortunately, the shutter was closed during this, and no log data or diffraction patterns exist to allow the operation to be fully quantified. For this reason, it is excluded from this section, although its impact is considered later.
The thermal profile that was implemented while recording diffraction from S2 consisted of a ramp-hold-ramp type operation (C1), followed by a series of seven heat-hold-quench-hold operations (C2-C8). The first cycle was implemented to allow the measurement of the dissolution and precipitation solubilities for the material, using a continuous heating/cooling rate of 1 °C s -1 .
Holds were implemented at 300 °C during both the heating and cooling segments of this cycle, during which further axial scans were made. The temperature at which to hold the sample to dissolve all hydrides in all subsequent cycles was determined from the point of hydride dissolution observed in this first cycle, a temperature termed the ‘soak’ henceforth.
The second cycle and onward then involved rapidly heating the material to the soak temperature and holding, both allowing hydrides to dissolve and potentially allowing matrix defects to recover, possibly mitigating against further heterogeneous nucleation of hydrides. This latter point is important, as hydrides are known to create large dislocation structures in the surrounding matrix that can trap hydrogen [97], and may act as preferential nucleation sites for hydrides [93], in what is known as a memory effect [96,168]. Although matrix recovery is thought to occur at a range of temperatures relevant to the experiment [169–171], these high-temperature soaks were deemed important in minimising any influence of the memory effect on the precipitation solubilities in this experiment seen from cycle to cycle. As a check against the memory effect, a 1 °C s -1 heating ramp was implemented prior to the soak in C7, from which the dissolution solubility curve could be measured and compared against that in C1, demonstrating little change in solubility between these two cycles (at the beginning and close to the end of the experiment.
After the soak, samples were quenched to a target temperature, which rose in increments of 50 °C with successive cycles; the temperature was then held for an extended period, known henceforth as the ‘dwell’. The quench was performed using a sudden reduction in heating current, and allowing conduction (into the grips and argon atmosphere), convection
(within the argon gas) and radiation to remove thermal energy and cool the sample. The limitations of this method precluded an instantaneous quench, and so a maximum cooling rate in
Methodology | 76
The Precipitation of Hydrides in Zirconium Alloys these cycles was observed to be ≈30 °C s -1 , giving a maximum time between soak and dwell of
≈13 seconds for the largest magnitude quench. Diffraction patterns were recorded throughout this process using the parameters outlined previously, and these acquisitions were used to investigate the kinetics and strain evolution associated with hydride precipitation.
Between each of the cycles, the sample was cooled to a base temperature of 40 °C and, at each of these points, axial scans were performed in the same way outlined for the non-charged sample, to study the distribution of hydrides in the material. Further to this, hydrogen depletion at the axial centre of the sample was monitored using observations of strain at 0 mm (the axial centre of the sample) during each of the high temperature soaks. When dissolving after rapid heating, the hydrogen released into the matrix then would diffuse away from the location of the dissolving precipitate, in order to form a homogenous concentration distribution. With a heterogeneous distribution of hydrogen, strain measurements would not be indicative of the true quantity of dissolved hydrogen, and so these strain measurements were performed once matrix lattice strain evolution had stabilised, suggesting homogenisation of hydrogen throughout the sample. This typically took ≈7 minutes out of the 15 minute soak, and so strain recordings were averaged over the remaining 8 minutes of this operation. The positions of these checks, along with a representation of the broader thermal profile for the hydrogen charged sample, are
Figure 28. Thermal profile and gauge volume displacement relative to material axial centre as a function of time for the hydrogen-charged sample (S2).
77 | Methodology
3.5.
Data Reduction and Pre-Analysis
The Precipitation of Hydrides in Zirconium Alloys
The diffraction patterns recorded from the synchrotron were written to European Data
Format (“.edf”) files, which can contain parameters pertaining to the file (time, date), the detector
(model, dimensions), and even the experiment (although this depends on the instrumental
configuration). Example patterns from the present experiment are given in Figure 29 for the
Standard Reference Material (SRM), (a), and S2, (b); illustrating the difference between diffraction from a crystalline powder with essentially perfect rings, and a textured polycrystalline material with spotty or incomplete rings. Note the presence of a white strip running diagonally from the centre towards the lower-right corner, which is the trace of a beam-stop that was used to protect the detector from the direct beam. This region was masked during data reduction to prevent it affecting the results.
(a) (b)
Figure 29. Diffraction patterns from (a) cerium dioxide (a standard reference material), and
(b) hydrogen charged Zircaloy-4 (S2).
3.5.1.
Deconvolution of Material Reflection Profiles
In order to interpret the patterns recorded from the material of interest, it was first necessary to quantify the contribution of the instrument to the observed line profile of Bragg reflections. As the observed line shape is the product of contributions from the source wavelength profile, the instrument profile and the sample profile [172], these effects can be deconvoluted to some extent using an SRM 17 . This provides an instrument resolution function
17 Unfortunately, it is not possible to fully deconvolute each of these effects entirely.
Methodology | 78
The Precipitation of Hydrides in Zirconium Alloys
(describing the emission and instrument profile), and separates the majority of scattering of the sample. Here, lanthanum hexaboride (LaB
6
) powder was used to determine the instrument resolution function (as a crystal containing minimal stacking faults), and so it was imaged under the same conditions as the sample. The resulting pattern was loaded into Fit2D, and the
“CALIBRANT” feature was used to refine the beam centre, ellipticity (from detector non-orthogonality) and sample-detector distance. This SRM was positioned such that the gauge volume occupied the same point in three dimensional space as the material to be investigated, such that the sample-detector distance of these samples can be determined from the LaB
6 calibrant 18 . For reference, if the positioning of either SRM is such that it is not a reliable measure of sample-detector distance for the material to be examined, it can be approximated by imaging
the material at two distances and applying Equation 13 to the positions measured from strong
and stable reflections in the resulting patterns. It is always preferable, however, to use a standard for accurately determining sample-detector distance.
With these parameters defined, the SRM pattern was then integrated using the known values for pixel size, sample-detector distance, wavelength, beam centre and ellipticity, which were all used on the first option page for the integration. On the second page, the scan type was set to 2
, intensity conservation (normalisation of the intensity at a point by the number of contributing pixels) was disabled, polarisation correction was disabled (as it was dealt with later), a geometrical correction to intensities (describing the change in the distance photons travel to reach the extremities of a flat plate detector) was applied, and appropriate maximum angles and bin numbers are chosen (based on the data in question). The patterns were integrated radially around the beam centre to provide a diffractogram; a two-dimensional plot of intensity
(measured in nominal counts) against a spatial term (interplanar spacing, 2θ, or Q), as illustrated
in Figure 30. This diffractogram was saved to an ASCII X-Y delimited text file (CHIPLOT “.chi”, for
example), for further use outside of Fit2D.
18 As the closest approximation that an external standard can give.
79 | Methodology
(a) (b)
The Precipitation of Hydrides in Zirconium Alloys
Figure 30. Lanthanum hexaboride (a) Debye-Scherrer rings, and (b) diffractogram.
From a crystallographic database (such as the STFC Chemical Database Service [173]), a structural model was obtained, describing details of the LaB
6
(or any other crystal) structure, including atomic positions, space group and lattice parameters. That used in this work is from
[174] (entry 659491 in the Inorganic Crystal Structure Database – ICSD), which provided a base model for the standard, and was downloaded in the Crystallographic Information File (“.cif”) format. At this point, the software package TOPAS Academic v5 [175] was implemented, whereby the LaB
6
diffractogram was imported, and the CIF file describing the crystal was added into the pattern. It should be noted that “.chi” files cannot be read by TOPAS, and so some conversion to a readable format must be performed. This is most easily done by removing the four header lines from the file (leaving just an X column and a Y column), and then changing the extension from
“.chi” to ‘.xy’.
All model refinements processed using TOPAS are first designed within input text files
(“.inp”) using jEdit 5.2 and the TOPAS integration plugins [176], after which they are passed to
TOPAS and the least squares regression is performed. Values from the SRM data sheet [177] for lattice parameter (4.15689 Å), strain-induced broadening (strains of 0
ε) and crystallite size-induced broadening (Lorentzian domain size of 0.7
m) were entered into the model for
LaB
6
, and the profile function was set to Fundamental Parameters (FP). All of these parameters are fixed to the given values, preventing them from being refined by TOPAS; this is important as they are known quantities from which other parameters relating to the instrument can be calculated. Additional corrections describing zero point error (positional error in 2θ), the Lorentz-
Polarisation factor, and peak asymmetry from axial divergence were also enabled.
Methodology | 80
The Precipitation of Hydrides in Zirconium Alloys
Zero point error correction allows the positions of reflections generated from the known lattice parameter of the SRM to be moved, such that they align with the reflection centroids recorded experimentally, meaning that instrument related deviances to the positions of reflections are removed. The polarisation correction accounts for the effect of the monochromator crystal polarising the incident X-rays, leading to regions of dissimilar intensity within the beam [178]. The Lorentz factor describes the change in intensity of reflections related to their angular spread from the direct beam (with increasing 2
) [178]. These two parameters together affect the intensity of reflections and depend on the angle of the monochromator, so they are combined into a single correction; for fully polarised radiation, like that from synchrotron
X-ray diffraction, the angle supplied is usually 0° [179], which is a fixed parameter.
Within the emission profile section for the LaB
6
model that is being constructed, the wavelength that was previously calculated from the CeO
2
SRM (described on in section 3.2) is
entered, and the area of this wavelength is set to 1, as the radiation is monochromatic and thus this one emission line makes up 100 % of the emission profile. The Gaussian and Lorentzian half-width parameters are both enabled and set to refine, bringing the total number of refinable parameters to five; one parameter for zero point error, two parameters from the Finger et al. correction for axial divergence induced asymmetry [180], and one parameter each for Gaussian and Lorentzian emission half-width. A least-squares regression is then performed, where a model of the LaB
6
SRM is refined by the software using the Rietveld method (explained in detail later) whereby the refinable parameters describing a simulated pattern are adjusted until it closely matches the observed pattern.
The optional functions within TOPAS of “Continue after Convergence” and “Randomise as a Function of Errors” can also be enabled, to improve the resulting model. These tell the software that once the regression has met the convergence criteria, whereby the process would normally terminate, to randomise the refinable parameters (based on the final errors in them) and then repeat the process of regression. This is performed iteratively, in a number of cycles, until a set number of repetitions is completed (or the user intervenes), after which the software reports those parameters that provided the best fit of the simulated pattern to the recorded one.
From the result of this process, the refined parameters for axial divergence correction, zero point error and emission profile half-widths are then fixed, and the values are recorded.
These parameters, along with the already known Lorentz-Polarisation factor and wavelength, are subsequently used in all further simulated patterns. In this way, aberrations from the instrument are corrected using models for axial divergence and zero point error, and the instrument resolution function is described using the emission half-width parameters. When studying patterns recorded from the materials of interest, the predetermination of corrections and an
81 | Methodology
The Precipitation of Hydrides in Zirconium Alloys instrument resolution function means that any changes in the recorded patterns from the material can be quantified in a way that relates to the microstructure of the specimen.
Similarly, with a known zero point error in positions in 2
it becomes possible to make accurate measurements of lattice parameters from the positions of Bragg reflections. The caveat to this, however, is that the zero point correction applies to a gauge volume centered in the SRM, and so any slight difference between the centroid of the SRM and that of the sample (from an external standard not being positioned quite where the sample diffracts from, for example) will lead to error in lattice parameters after applying the zero point correction. For studies requiring highly accurate calculations of lattice parameter, it is usual to include an internal standard for accurate calibration.
The instrument resolution function calculated from the LaB
6
31, along with the emission profile for CuK
α
[181], for reference. Note the multiple energies of the CuK
α
profile, which is actually composed of four separate emission lines in this example [181].
It should be known that while the synchrotron X-ray wavelength is considered monochromatic, the instrument itself will induce some geometric broadening in the profile [172], which is convolved with the wavelength profile.
Figure 31. The experimental profile compared with the CuK
α
emission profile.
Methodology | 82
The Precipitation of Hydrides in Zirconium Alloys
3.5.2.
Debye-Scherrer Ring Integration
From the SRM patterns used previously, values for the beam centre, sample-detector distance, wavelength and detector non-orthogonality are known, and it is with the use of these that the Zircaloy-4 data were prepared for analysis. This preparation, however, was done in two ways, based on the type of analysis that was to be performed, where either complete integrations
(a single =360° azimuthal segment) or partial integrations (multiple <360° azimuthal segments) were implemented. The former was used in this work for evaluating the precipitation of hydrides, as sampling diffraction from the full ring pattern would account for the maximum possible quantity of scattering crystals, giving statistical relevance to phase distributions calculated in this way. An evaluation of integration-induced broadening (from strain related ellipticity, for example) in the hydride reflections found that a full 360° integration produced up to a 9 % increase in the
FWHM, when compared with narrow partial integrations. This small amount of artificial broadening was considered acceptable, as only the intensity of hydride reflections were used from the full integration, and so the effect of this broadening would not have any significant on the results of that assessment.
For analyses of strain, full integrations were identified as not being suitable for describing any directionality to the mechanical effects taking place within the sample, and so a partial integration at the four compass point azimuths, ψ, was performed (N – 0°, E – 90°, S – 180°,
W – 270°), corresponding to the TD and RD of the material. For the matrix, producing the majority of diffraction, an integral of 15° (ψ ± 7.5°) was chosen, as a sensitivity study indicated that this range provided the best combination of counting statistics (improving the signal-to-noise ratio by sampling more crystals with a wider ψ range), without diluting the directionality too significantly.
The hydride, however, was seen to be more problematic given the low intensity of these reflections, and a larger range was needed to achieve sufficient counting statistics for this phase, totalling 45° (ψ ± 22.5°). A diagram indicating the integration sizes and directions is presented as
83 | Methodology
The Precipitation of Hydrides in Zirconium Alloys
Figure 32. Partial integration positions and ranges.
Fit2D was once again implemented to perform the process of integration, and a macro was created to allow rapid integration of all patterns (totalling over 4,000 in cycles C0 to C8); a description of the method for creating and using macros for file sequences is provided in the software documentation [182]. To create full integrations, patterns from the material were integrated in a similar way to the LaB
6
SRM, and “.chi” files were exported.
For the partial integrations, the “CAKE” option was instead implemented. Here a similar set of parameters was presented on the first option screen as similar to that of the full integration, and so the values were checked and accepted. On the next screen, a different set of options was provided, detailing the start and end azimuth, inner and outer radii, the number of azimuthal bins, and a number of corrections. The start and end azimuths were -7.5° and 352.5°, with a corresponding number of azimuthal bins of 24, producing a series of segments with centroids starting at 0°, increasing incrementally by 15° up to 345° (the bins not at the compass points were ignored in this analysis). Similarly, for a 45° integration, the starting azimuth was -22.5°, ending at 337.5°, with 8 bins in total. As with previous integrations, polarisation and intensity corrections were disabled, the geometrical correction was enabled and appropriate inner/outer radial limits
Methodology | 84
The Precipitation of Hydrides in Zirconium Alloys were chosen. Once integrated, the files were output as spreadsheet (“.spr”) files, and the azimuthal and 2θ axes were also exported as text (.chi”) files.
Next, a bespoke Matlab function was used first to automatically convert all “.chi” files into “.xy” files (two-columns of X and Y data) and remove the headers from each, providing a format that can be read by TOPAS. During this operation, the intensities of these patterns were scaled by a function of the beam intensity at the time each acquisition was made, to mitigate against storage ring current decay and the effect it had on the intensity of the incident beam,
using Equation 4. Here, each observed pattern,
𝑦 𝑜𝑏𝑠
, was divided by the beam intensity at the time of each pattern being image (recorded by a sensor in the path of the beam),
𝐼
, values that were stored in the experimental log file generated by the beamline software. The output was then multiplied by the mean value of all intensities recorded by this sensor throughout the experiment, 𝐼 𝑎𝑣𝑔
. 𝑦 𝑠𝑐𝑎𝑙𝑒𝑑
= 𝑦 𝑜𝑏𝑠
𝐼
∙ 𝐼 𝑎𝑣𝑔
Equation 4
A similar process was performed for the partial integrations stored in the “.spr” type files, except that the spreadsheet file contains a matrix of intensities for each azimuthal slice, with no
2θ axis (which is stored in an external file). As a result, the function that handles these data needed to first identify the four azimuthal ‘slices’ of interest, pair each up with a 2θ axis taken from the external file, normalise the pattern intensity against the beam intensity and then save files in a way that allowed their azimuth and acquisition number to be identified. Once these tasks are complete, a file structure exists consisting of a series of “.xy” files for the 360° integration, a series for each of the four compass points from the 15° partial integration, and each of the four from the 45° partial integration, all stored separately and readily identifiable for their integration size, azimuthal and temporal positions.
3.6.
Quantitative Analysis of Diffraction Patterns
Once diffraction patterns have been transformed into diffractograms, some method for quantifying the material that has been illuminated can be performed, by modelling the diffraction profile and relating the parameters used in the model to those describing some aspect of the material. There are three common methods for this; reflections can either be examined independently, using single line profiles; the full pattern can be simulated as a function of multiple structures, using the Rietveld method to refine a structural model relating Bragg reflections to one another; or it can also be decomposed into separate patterns for each structure, using the
Le Bail method, for example.
85 | Methodology
The Precipitation of Hydrides in Zirconium Alloys
3.6.1.
Single Reflection Analysis
While the single reflection analysis could be considered the simplest method for quantifying diffraction patterns, owing to each reflection being treated individually through having an independent profile function, this fact also makes it a highly versatile method for analysis. In this way, microstructurally induced profile changes affecting only a single reflection can be described, such as line broadening from irradiation-induced defects.
The profile of each reflection is defined by a mathematical function (e.g. Gaussian,
Lorentzian, Pearson VII, Pseudo-Voigt, etc.), which, at their most fundamental level, contain
terms for Full Width Half Maximum (FWHM), spatial positon and intensity, Figure 33. Because
each reflection is treated as independent of others within the pattern, it becomes easy to rapidly describe uncomplicated patterns using this approach, by simply identifying approximate maxima of reflections in the pattern and assigning a profile function to each of these spatial positions.
Structures possessing a high symmetry will show a relatively low number of unique Bragg reflections, instead manifesting singular large reflections composed of diffraction signal from families of equivalent planes, the contributing number of which is described by the term
“multiplicity”. In synchrotron X-ray diffraction patterns (where diffraction/angular resolution is high) that contain a single, high symmetry phase, reflections will often be well defined and isolated from one another, making the identification of the position of each simple. Applying a set of profile functions to describe these terms, in addition to a background function, becomes a trivial task, which can often be performed automatically by commercial software.
Difficulties arise, however, where either a number of structures are present within a diffractogram or crystal symmetry is low, and so significant overlap between reflections can exist.
This may then lead to some degree of uncertainty when developing a model for this type of pattern, through increasing the number of possible ways that profile functions could be arranged to form the composite profile, especially where it is unclear how many functions should be used in the first place. For situations like these, it becomes necessary to use alternative methods that link related Bragg reflections in a way that reduces the number of possible solutions to the regression performed on the pattern.
Methodology | 86
The Precipitation of Hydrides in Zirconium Alloys
Figure 33. A schematic of a single reflection (points) modelled with a profile function (solid line), with residuals plotted (undulating line at zero axis), Full Width Half Maximum (FWHM) and centroid marker (vertical line) added.
3.6.2.
The Rietveld Method for Structural Model Refinement
There exists a large amount of open literature explaining the mathematical bases and derivations for this method [183–187], as well as articles detailing guidelines for the technique
[188], and explanations of uncertainty and quality of Rietveld models [189]. There also exists a series of comprehensive studies on the software, experimental methodologies, Rietveld model refinement methodologies, and the accuracy of X-ray diffraction analysis using the Rietveld approach [190,191]. Explanations of advanced methods for refining the temporal evolution of parameters within a Rietveld structural model over successive X-ray diffraction patterns are also available in the literature [192]. Instead of replicating the discussion in these works, this section will instead provide a lay description of the fundamental principle of the Rietveld approach to structural model refinement.
The Rietveld method [186,193] for refining a structural model considers the entirety of a diffraction pattern from a crystal, using a variety of parameters relating to the structure itself, and the diffraction conditions it was recorded under, to mathematically describe the resulting profile. This simulated pattern can then be compared against experimentally recorded data, and using a least-squares regression 19 it becomes possible to refine these parameters such that the difference between the modelled and recorded patterns is minimised [193].
19 Where the sum of the squared residuals between points in the simulated and recorded patterns is minimised mathematically.
87 | Methodology
The Precipitation of Hydrides in Zirconium Alloys
𝑆 = ∑ 𝑤 𝑖 𝑖
∙ [𝑦 𝑖
− 𝑓 𝑖
] 2
Equation 5
The minimisation function, given in Equation 5 [194], contains the following, where
𝑖 is a position in 2
:
𝑆 – The sum of the weighted squares of residuals, the value to be 𝑤 𝑖 𝑦 𝑖 𝑓 𝑖 minimised.
– A weighting at 𝑖
, based on counting statistics.
– The observed intensity at
– The simulated intensity at 𝑖 𝑖
.
.
The equation describing the simulated intensity of a profile at point 𝑖
6; a more detailed description of the contained terms is given in [194].
𝑓 𝑖
= 𝑦 𝑏
+ 𝛷(𝑄 𝑖
) ∙ 𝐴(𝑄 𝑖
)
∙ 𝑆 ∙ ∑ [𝑚 𝑘 𝑘
∙ |𝐹 𝑘
| 2 ∙ 𝐸
𝐾
∙ 𝑃
𝐾
∙ 𝐿(𝑄 𝑘
) ∙ 𝜙(𝑄 𝑖
− 𝑄 𝑘
)]
Equation 6
The terms on the first line relate to the X-ray beam, where: 𝑓 𝑖 𝑦 𝑏
– The simulated intensity at point 𝑖
.
– A term describing the background within a pattern, usually a polynomial.
– The intensity of the incident X-rays.
𝛷(𝑄 𝑖
)
𝐴(𝑄 𝑖
)
𝑄 𝑖
– The X-ray absorption factor.
– The scattering vector magnitude at position 𝑖
, in all of these terms.
Methodology | 88
The Precipitation of Hydrides in Zirconium Alloys
The second line describes the contribution of each reflection of a phase to the overall profile, where 𝑘 describes the reflection number. Where a number of phases exist within a pattern, this summation is then repeated for each, such that each reflection within each phase has been considered. In this second set of set of terms:
𝑆 – The scale factor of a structure, incorporating phase fraction and cell volume. 𝑚 𝑘
𝐹 𝑘
– The multiplicity of a given reflection (number of contributing planes).
– The crystal-structure factor, which accounts for a number of material related properties including atomic scattering factor, atomic sites, atom temperature factor (vibration), occupancy, inter-planar spacing, etc.
𝐸 𝑘
𝑃 𝑘
𝐿(𝑄 𝑘
)
– The extinction correction factor (for time-of-flight neutron patterns).
– The factor describing preferred orientation.
– The Lorentz-Polarisation factor, which corrects for an expected decrease in energy with increasing 2
.
𝑄 𝑘
– The spatial position of each reflection centroid, described by the interplanar spacing.
𝜙(𝑄 𝑖
− 𝑄 𝑘
)
– A term describing the profile of each reflection.
As previously stated, the Rietveld method is a way in which a structural model for a crystal system can be refined from a diffraction pattern; the key here being that this approach is used to refine a model, rather than create one. As such, the process of refining a model must begin by creating a model, a process that is most often accomplished by accessing a crystallographic database, where the crystal structures published by others in the open literature are collated.
These structures are often attainable in the standardised Crystallographic Information File (“.cif”) format, containing some, or all, of the details required to construct a model.
Fundamental to the structural model itself is the space group, which establishes an initial set of parameters as to the shape and size of the unit cell, through the ‘a’, ‘b’ and ‘c’ length
in calculating the structure factor is also supplied, namely atoms within the unit cell, their coordinates in three-dimensional space, the probability of occupancy at each site, and the isotropic temperature factor (also known as the Debye-Waller factor [195,196]) for each atom
(describing their motion). These core parameters can then be supplemented with terms describing line broadening from crystallite size and strain, or preferred orientation convolutions, linking texture within materials to the diffraction pattern profile. Through refining these parameters in the way mentioned before, an accurate model can be attained for a given crystal structure, and where multiple structures are present within the pattern, accurate measurements
89 | Methodology
The Precipitation of Hydrides in Zirconium Alloys of phase fractions can also be performed. Finally, modern software packages are also able to calculate automatically parameters relating to other physical properties of a structure, such as cell volume, mass and density, from the supplied or refined variables.
The importance of being able to describe profiles in this way is twofold. Firstly, Rietveld refinement of structural models allows for highly accurate determination of certain crystallographic properties, where lattice parameters, for example, can be based upon the position of a number of reflections, rather than a single line. Additionally, in profiles containing a significant amount of reflection overlap, through numerous or low symmetry structures, the linking of reflections can allow for the deconvolution of complex regions of a diffractogram. An
illustration of this is given in Figure 35, where an observed profile is known to contain
contributions from two structures. Here, three examples of possible solutions to a single observed profile are demonstrated, using Bragg reflections from each structure.
Figure 34. Unit cell schematic showing length and angle parameters [197].
Methodology | 90
The Precipitation of Hydrides in Zirconium Alloys
Figure 35. Schematic showing multiple solutions to reflection overlap during analysis of a single
Bragg reflection.
In this case, the least-squares regression will find a solution such that the difference between the observed and simulated pattern is at a minimum, but this minima may not reflect the actual contributing profile from each structure. Instead, the refined parameters will represent those describing a good match between patterns, rather than being related to the actual diffracting structures being illuminated. To compensate for this, the diffraction/angular region of interest can be expanded to include multiple observed reflections; these can then be simulated using a pair of structural models, where the position of each reflection is defined by the initially supplied lattice parameter(s) for each crystal structure. When the regression is performed in this case, the two isolated reflections have only one solution, and as the angular relationship between the two reflections in each profile is linked to the lattice parameters of the each crystal, this means only one possible solution exists and the central observed reflection is described properly,
Figure 36. Increasing the number of Bragg reflections considered in conjunction with performing full pattern simulation potentially provides a single solution.
91 | Methodology
The Precipitation of Hydrides in Zirconium Alloys
The Rietveld methodology, however, is not without its own limitations, as the strong link between physical parameters and the simulated pattern makes it necessary to model accurately all aspects of a crystal, or set thereof. This is not always desirable, especially in cases where users are not interested in atomic positions or texture, and simply want an accurate reading of lattice parameters or pattern/reflection intensities, the latter of which is not always possible with such a structurally relevant approach.
3.6.3.
Preparation for Rietveld Refinement of Structural Models
Prior to the commencement of pattern simulation, models were acquired from the CDS for the potential phases of α-zirconium (ICSD entry 164572 [198]), δ-hydride (CrystMet entry
26514 [199]) and γ-hydride (ICSD entry 56197 [199]). A representation of the pattern recorded
from sample S2 at 40 °C is provided in Figure 37. Here, the pattern is first shown using a linear
intensity scale, (a), which illustrates the dominance of the matrix reflections (identified from (c)), but by plotting with a logarithmic axis, (b), it becomes possible to resolve the small hydride reflections and a number of other unindexed features.
A comparison of the positions of the simulated positions of γ-hydride reflections with the observed pattern shows minimal agreement, and so it is thought that this phase does not exist in any significant volume within the material. That said, a crystal that is sufficiently small will not produce any significant diffraction signal, and so there may be some population of ultra-fine
γ-hydrides within the material that cannot be detected. Additionally, there remain a small number of unindexed reflections within the observed pattern, predominantly between ≈1.9 Å and ≈2.3 Å, as well as at ≈1.5 Å. All of these were observed to be present at both the 40 °C floor temperature, and also the 500 °C and 570 °C soak temperatures.
A preliminary investigation into these unidentified features was performed, where poor correlation with Bragg peak positions from a number of different Zr x
N x
and Zr x
C x
crystal structures was observed. An uncommonly reported, low symmetry triclinic ZrC
0.7
structure [200] did show some correlation, but this may have been due to the large number of densely spread reflections generated by this crystal system.
Similarly, a comparison of the patterns produced by the monoclinic and tetragonal oxides with the unindexed reflections was also undertaken. The tetragonal oxide demonstrated little correlation, while the monoclinic oxide did produce some strong correlation with a number of the unidentified features, although the lack of other monoclinic reflections outside of this limited area of the diffractogram (being a low symmetry phase that produces many Bragg reflections) suggests this could possibly a false positive. From [90] it is also known that diffraction from the
Zr(Fe,Cr)
2
phase was observed in patterns from this material, and simulating this phase demonstrated a very strong correlation with a number of these reflections. The majority of these
Methodology | 92
The Precipitation of Hydrides in Zirconium Alloys unidentified features are thus suggested to be either monoclinic oxide or Zr(Fe,Cr)
2
phase, but a deeper analysis was not performed. At this time it remains unclear what phase the feature at ≈2 Å might belong to, save to say the breadth of the reflection is indicative of a significant strain gradient or very fine domain size within the phase. Given the small size of these features, their separation from the matrix and hydride reflections of interest, and the divergent focus of this thesis, all of these minor reflections are ignored in further analyses.
(a)
(b)
(c)
Figure 37. Observed diffraction pattern from sample S2 at 40 °C using (a) linear and
(b) logarithmic scales, and (c) spatial positions of Bragg reflections.
3.6.4.
Application of the Rietveld Method for Refinement
The first attempt made within this work to refine structural models from the observed patterns was through the use of the Rietveld method. It was intended that information pertaining to the crystal structure of each phase and the proportionality of phase fractions could be extracted from properly refined models, to be used in the analysis of the material.
To accomplish this, a ‘seed’ INP file was created that could be used as a basis to simulate all diffraction patterns during the automatic process of structural model refinement. To this, the standardised headers for TOPAS was added, describing the quality of the fit (further details on the various R parameters are found in [179], and a discussion of the merits of these terms is presented in [189]), the convergence criterion and the number of iterations to be performed during the regression.
93 | Methodology
The Precipitation of Hydrides in Zirconium Alloys
A single diffractogram was chosen containing examples of reflections from all phases to be analysed, which was a pattern acquired at 40 °C, a temperature at which all hydrogen was expected to be precipitated as hydrides. The file containing the full 360° integration of this acquisition was specified within the INP, and the known Fundamental Parameters describing the instrument and emission profile were added, as derived from the LaB
6
SRM. The corrections calculated from the LaB
6
SRM for axial divergence and zero point error were included, along with the Lorentz-Polarisation correction of 0°. A Chebyshev polynomial [201] was used to describe the background, where the order of polynomial applied is dependent on the background of the material, and was chosen to be the 5 th
order based on the diffractogram in Figure 37. Spatial limits
were chosen to be 1.3 Å and 3 Å, with the region between 1.95 Å and 2.33 Å masked, allowing unnecessary data points to be ignored outside of the useful range, and thus preventing them from biasing the R factors indicating the quality of the simulated pattern.
Each of the CIF files was then inserted into the INP, using the macro built into jEdit for this purpose, which added the three structures to the file with a, b and c lattice parameters; α, β and γ unit cell angles; and details on atomic sites, their occupancy and temperature factors. Space groups, if not already imported from the CIF, were also added, as was a scale parameter for each structure. The scale and lattice parameters were allowed to refine, but the limits were set on the lattice dimensions to prevent erroneous values being generated. Additionally, the temperature factors were allowed to refine freely (although sensible limits were imposed), while the atomic occupancies were fixed to appropriate values. For δ-hydride, the occupancy of the hydrogen is ⅚, accounting for the sub-stoichiometry of the phase (ZrH
1.66
); similarly for the γ-hydride (ZrH
1
) the occupancy was set such that the number of hydrogen atoms was equal to zirconium atoms
(although the number of such atoms was seen to vary between Crystallographic Information Files from different authors).
To simulate any texture seen within the material, preferred orientation terms could also be enabled, using either the March-Dollase approach [202], or a spherical harmonic. In the case of the present experiment, the March-Dollase method was implemented for α, with directions chosen as
{011̅3} 𝛼
and
{022̅0} 𝛼
, based on a preliminary evaluation of a difference between the observed and simulated pattern produced where no preferred orientation correction was included. The terms describing the extent and fractional direction of the preferred orientation was allowed to refine freely. For the small δ -hydride reflections, no term accounting for preferred orientation was needed, thought to be the result of the high symmetry in the unit cell of that structure and the use of a full 360° integration when trialling the Rietveld method.
For each phase, a Lorentzian term describing profile broadening from crystallite size was enabled and allowed to refine, although limits were also enabled to prevent the line profiles of phases with small reflections being broadened to infinity. This was necessary as allowing such
Methodology | 94
The Precipitation of Hydrides in Zirconium Alloys over-broadening could produce flat profiles for structures, subsequently leading to an artificial minima in the regression where a flat profile ceases to contribute to the pattern, and so it cannot then be sharpened again without first degrading the quality of the fit. This was particularly important when hydrides were dissolved, as the software often attempted to broaden the hydride reflections to infinity to cope with reflection extinction, rather than solely reducing the intensity.
Once all of these parameters were established, the process of regression could then be run, with options for “Continue after Convergence” and “Randomise as a Function of Errors” enabled, thus making the software perform multiple attempts to optimise the parameters, and report those providing the best fit between simulated and observed patterns. What followed was an iterative process of running the regression, manually tweaking the model, and rerunning the regression, until an ideal set of parameters was found. A specific description of this process is difficult, as it required numerous attempts, repeated backtracking and some level of trial and error. Similarly, it is difficult to state an explicit method, as some degree of intuition is needed in terms of knowing when to fix and refine parameters, what sensible values are, and what options need to be enabled and disabled at each step to improve the model. Instead, the structural models resulting from the process of Rietveld refinement are listed in the appendices, illustrating the parameters and options that provided the optimum simulated pattern.
Once a seed fit was created that accurately described the pattern, limits were examined and redesigned in such a way that adjustments to the simulated pattern could be made automatically as a function of changes to the conditions of the sample, but were still restrictive enough to maintain the structural relevance of the model. For example, the present experiment used thermal operations to affect the microstructure of the material, which changed the presence of phases (seen as variations in intensities) and the dimensions of unit cells for the various crystal structures (observed as differences in reflection positions). As such, a seed model needed to be designed in such a way that the lattice parameters could vary between diffractograms, describing the thermal expansion, with no user intervention, but without ‘running away’ to unlikely positions.
In addition to this, it was also necessary that the seed was limited in a way such that if the reflections from a phase disappeared (from dissolution, for instance) then the lattice parameters weren’t distorted until the simulated reflections from that phase became overlapped
with the observed reflections of another. An example of this is illustrated in Figure 38, where the
extinction of an observed reflection in one phase leads to the simulated reflection being drawn towards its nearest neighbour, where it should not be. To give an example of how parameters can be sensibly limited, a known lattice parameter can be measured at 40 °C, and the known thermal expansion in this dimension can be used to predict a likely range of values that might be
95 | Methodology
The Precipitation of Hydrides in Zirconium Alloys seen. Limits can then be established to keep the lattice parameter within this range, although it may be beneficial to expand this range by the magnitude of the error in the parameter. It is usually clear where a limit is poorly set, as the regression will produce a parameter either close to, or at, the limit, which TOPAS will indicate in the INP.
Figure 38. Excessive reflection drift from a lack of limits, after reflection extinction.
With a properly constructed seed, it was possible to automate the process of refining models for each diffractogram from the fully and partially integrated patterns, using the batch processing interface for TOPAS (“tc.exe” as opposed to the GUI executable, “ta.exe”). This is documented in the user manual [179] as being possible through batch files (“.bat”), but the method of doing this was cumbersome when the number of files was in the thousands and the batch file needed to be written out line by line. Instead, a software package was developed as part of this project titled RunTOPAS, intended to take a seed INP file, scan it to identify variables that were to be refined, ready the INP for use with TOPAS and then batch process the data in a way that allowed the user to keep track of the quality of sequential model refinements through a GUI. Once complete, a table of the parameters resulting from the refinement was created, ready to be imported into external software. This application was developed within Matlab and was packaged as a stand-alone executable to allow deployment where Matlab is not available.
When attempting to process the Rietveld refinements of the current data, however, it was found that the seed and software could not cope with the extinction of the reflections associated with the hydride phase. This method was thus deemed unsuitable for batch processing this set of data. It was, however, used to provide strong structural models of the crystals within the sample at chosen points during the experiment, providing “snapshots” in time to support the alternative method used. Additionally, the Rietveld seed that was developed could be easily converted into that for the Le Bail methodology for Whole Powder Pattern Decomposition
(WPPD), the method chosen for batch simulating all data within this thesis.
Methodology | 96
The Precipitation of Hydrides in Zirconium Alloys
3.6.5.
The Le Bail Method for Structural Model Refinement
The Le Bail method [203] is based upon the system of equations that make up the
Rietveld method, albeit with a different approach to the process of refinement itself. As with the previous method, unit cell, reflection profile and measurement error parameters are refined, but the intensities of individual reflections are considered independent of the structural model(s) being considered, and the scale parameter is not refined through least squares [204]. In the original paper by Rietveld [193], it is stated that the integrated intensity of an observed reflection
can be approximated by the Rietveld decomposition formula, Equation 7, which is used in the
calculation of R values (describing the quality of the model) [204].
𝐼
𝐾
(𝑜𝑏𝑠) = ∑ [𝑤 𝑗.𝐾 𝑗
∙ 𝑆 2
𝐾
(𝑐𝑎𝑙𝑐) ∙ 𝑦 𝑗
(𝑜𝑏𝑠)/𝑦 𝑗
(𝑐𝑎𝑙𝑐)]
Equation 7
In this, the terms are as follows:
𝐼
𝐾 𝑤 𝑗.𝐾
– The integrated intensity of a reflection at position 𝐾 .
– A weighting term describing the contribution of a reflection at position 𝐾 in the reflection, to the profile at position 𝑗 .
𝑆 2
𝐾
– The sum of magnetic and nuclear structure factors, describing their 𝑦 𝑦 𝑗 𝑗
(𝑜𝑏𝑠)
(𝑐𝑎𝑙𝑐) contributions to diffracted intensity.
– The observed intensity at point 𝑗 .
– The simulated intensity at point 𝑗
.
The Le Bail method makes use of this equation, but instead of using the nuclear and magnetic structure factors that would be calculated in the Rietveld method, the 𝑆 2
𝐾
terms within the refinement are all set to a single nominal value (over a given range, 𝑗 , a term will exist for each reflection,
𝐾
, within each structure considered) [204]. Once the parameters describing the positions of the reflections are initialised, an iterative process takes place, where 𝐼
𝐾
(𝑜𝑏𝑠)
is calculated for each reflection using the set 𝑆 2
𝐾
, this integrated intensity is used to set 𝑆 2
𝐾
in the next iteration of the process, while a regression on profile and cell parameters takes place [204].
By starting with identical 𝑆 values for all reflections, those that overlap perfectly are treated equally, apportioning 50 % of the observed intensity to each reflection [204]. In this way, the successive iterations result in well-refined structural parameters through accurate positioning of reflections, coupled with integrated intensities that correspond strongly to the observed pattern, irrespective of preferred orientation.
Modern computational power is such that the efficiency of the Le Bail method over that published by Rietveld is effectively unnoticed in all but the most complex of systems, however,
97 | Methodology
The Precipitation of Hydrides in Zirconium Alloys other advantages still remain. Namely, complex patterns can be simulated using a minimal number of parameters, without developing a full structural model of the material. Moreover, a well-parameterised and properly limited model can be used to simulate a successive series of changing diffraction patterns, where significant changes to intensity occur as a function of time, which the Rietveld method often cannot accomplish. This characteristic of the Le Bail method is the underpinning reason that it was chosen for the analysis presented herein, as the hydride phase dissolves entirely. As a result, the process of pattern modelling needed to cope with reflection extinction with no user input, which a properly constrained Le Bail model was able to do successfully.
3.6.6.
Application of the Le Bail Method for Refinement
As with the Rietveld method, the Le Bail approach requires a similar INP for use within
TOPAS, and so details of the emission profile, corrections, file name, start/finish points, masking and background were copied to the new INP file. This was essentially all contents of the old INP, with the exception of the str type structures themselves. For each of the phases being considered, an hkl type structure was added instead, with the Le Bail option enabled for each (as the default for hkl type structures is a Pawley refinement [179]). Under all of these structures, the corresponding space groups, lattice parameter and scale terms were added (using values from the Rietveld INP), but unlike the str type structures, terms describing atomic positions, occupancy,
temperature factor and preferred orientation are not required. As explained in section 3.6.5, the
intensities of reflections are calculated using nominal values for the structure factor, and so the observed pattern intensities can be simulated with relative ease, allowing lattice spacing parameters to also be refined accurately. This has the added advantage that where hydride reflections deplete to extinction, the Le Bail method can easily follow this progression and report a null intensity for the hydride phase.
Without details on the atomic sites, however, it is not possible to calculate automatically unit cell masses, from which TOPAS would normally derive phase weight percentages. Instead, the mass-volume-weight (MVW) line from each str structure within the Rietveld INP, containing a cell mass derived from the atomic structure information given there, can be transferred to the
Le Bail INP. This provided the software with what it required to calculate nominal weight percentages during Le Bail refinements. It should be noted that the Le Bail method makes no direct account for the way in which the isotropic temperature factor (or Debye-Waller factor
[195,196]) might change the intensities of Bragg reflections when performing thermal transients.
By using the outlined approach to calculating phase weight percentage from the Le Bail method, where the intensity of the δ phase as a proportion of the α + δ intensity determines the phase fraction of hydride, a correction for the Debye-Waller effect is approximated. This occurs under
Methodology | 98
The Precipitation of Hydrides in Zirconium Alloys the assumption that the change in intensity with temperature in both phases in a similar (but proportional) amount, such that any variation in the intensity of the hydride relative to the matrix is considered as only arising from a change in phase fraction. A study of the influence of the
Debye-Waller factor on the δ-hydride phase, published in [90], saw no trend in the relative intensity of several Bragg reflections with temperature, and in that work the influence of the isotropic temperature factor was considered negligible.
Once the INP was established, limits were created in a similar way to those outlined previously, after which, it was then tested with a number of diffractograms taken from different temperatures (with differences in reflection intensities and positions). As the
{111} 𝛿
reflections were observed to overlap with the
{011̅0} 𝛼
, and the
{002} 𝛿
with the
{011̅1} 𝛼
, it was seen that this led to distortion in the hydride lattice parameter, and the more isolated
{022} 𝛿
and
{311} 𝛿 reflections were not being properly simulated. Given that these latter reflections were of a significantly higher multiplicity than those with overlap, it was judged that the
{022} 𝛿
and
{311} 𝛿 were a more important reference for the hydride phase, and so the spatial range of the refinement was reduced to span from 1.3 Å to 1.85 Å. This encompassed the
{022} 𝛿
and
{311} 𝛿 hydride reflections, with multiplicities of 12 and 24, respectively, along with the
{112̅0} 𝛼
,
{011̅3} 𝛼
,
{022̅0} 𝛼
,
{112̅2} 𝛼
and
{022̅1} 𝛼
matrix reflections, with multiplicities of 6, 12, 6, 12 and 12, respectively. As the Le Bail method still defines the position of reflections based on the lattice parameters and space group of a structure, this number of high multiplicity reflections in each phase was seen as suitable for extracting accurate measurements from the observed patterns.
Once the INP had been tested and was seen to provide high quality simulations of the observed patterns at a range of temperatures, the process of batch refinement was performed using RunTOPAS. Parameters for the lattice dimensions of the metal and hydride structures were monitored, along with the weight percent and the numerical area of the simulated pattern for each phase. This batch processing was undertaken in sequence for all three integration types
(15°, 45° and 360°), where the two partial integration data sets required a pass through of the data for each of the four ‘compass points’. The resulting spreadsheets were then collated in such a way that the data from each was held centrally, while remaining uniquely identifiable.
3.7.
Data Analysis
Compared with the process of developing a functional seed for pattern simulation, the steps necessary to analyse the results of the refinements were relatively trivial. The analysis can essentially be divided into two sections; that which made use of the integrated intensities to
99 | Methodology
The Precipitation of Hydrides in Zirconium Alloys calculate phase weight percentages, and that using the lattice parameters derived from the position of Bragg reflections to examine strain evolution.
3.7.1.
Phase Weight Percentages
Initially, the integrated intensity of the δ-hydride phase (sampling all reflections produced by that structure within the specified inter-planar spacing range) was to be used to calculate the amount of hydrogen in solution, which is reported by TOPAS as the “numerical_area” parameter.
parameter was not considered to be suitable, and instead an alternative method was implemented.
From a Rietveld analysis, TOPAS is able to calculate the weight percentage, 𝑊 , of a phase, 𝑝
, present within the simulated pattern containing 𝑖
phases, based on the unit cell volume,
𝑉
, the formula unit mass,
𝑀
, the number of formula units per unit cell,
𝑍
, and the Rietveld scale factor,
𝑆
, using the expression in Equation 8 [205].
𝑊 𝑝
=
𝑆 𝑝
∑ [𝑆 𝑖
∙ (𝑍 ∙ 𝑀 ∙ 𝑉) 𝑝
∙ (𝑍 ∙ 𝑀 ∙ 𝑉) 𝑖
]
Equation 8
The Le Bail method is able to perform a similar calculation, instead making use of the user supplied value for cell mass for each phase. With an essentially nominal value for the scale parameter being calculated from the Le Bail method for each structure, however, those values for weight percent produced from this approach were significantly divergent from what was expected. In fact, δ -hydride was calculated to be the majority phase from this approach, by some considerable margin. It was observed, however, that while the magnitudes of the weight percent were incorrect, the parameters changed relative to their starting values as a function of time (and temperature).
With proper quantification of the material, the hydrogen content of the sample was known, and so when all hydride reflections were entirely extinct (marking complete dissolution of the phase), then the known quantity of hydrogen was all assumed to be in solution. This provided the first boundary condition used to recalibrate those values for
𝑊 𝑝
calculated from the
Le Bail method. The second boundary condition came from the literature, where equations from
McMinn et al. [77] determined the hydrogen solubility to be in the parts per billion at 40 °C. By assuming a linear relationship between the change in 𝑊 𝑝
and a change in the amount of hydrogen in solution, it became possible to derive a value for dissolved hydrogen from any given
diffractogram in the series, using Equation 9.
Methodology | 100
The Precipitation of Hydrides in Zirconium Alloys
𝐶
𝐻
=
𝑊 𝛿
𝑊 𝑚𝑖𝑛
− 𝑊 𝑚𝑎𝑥
− 𝑊 𝑚𝑎𝑥
∙ 𝐶 𝑡𝑜𝑡𝑎𝑙
Equation 9
Here, the amount of solute hydrogen,
𝐶
𝐻
, is a function of:
𝑊 𝛿
– The weight percentage of δ -hydride calculated from a diffractogram.
𝑊 𝑚𝑎𝑥
𝑊 𝑚𝑖𝑛
– The weight percentage reported by TOPAS at 40 °C.
– The weight percentage reported when all hydride reflections are extinct.
𝐶 𝑡𝑜𝑡𝑎𝑙
– The known quantity of hydrogen within the material.
Given that the thermal gradient produced by Joule heating was expected to cause hydrogen migration away from the hot axial centre of the sample, the 𝑊 𝑚𝑎𝑥
value was recorded from the sample in its initial condition, before any thermal transients that would have caused hydrogen diffusion. Furthermore, as a single weight percentage value is taken to represent the initial hydrogen content at the axial centre of the material and then used throughout the experiment, any depletion that occurs at the axial centre of the sample will be accounted for without human intervention, through the 𝑊 𝑝
being less than the 𝑊 𝑚𝑎𝑥
value.
3.7.2.
Strain Evolution
The evolution of strain within each crystal structure is calculated from the lattice parameters of the hydride and matrix phases, by simulating diffractograms generated from partial integrations in the rolling and transverse directions of the material. Integrating in this way gave directionality to the strains, such that any difference in their evolution between the RD and
TD could be examined. As the lattice parameters are, in fact, principle dimensions relating to the unit cell, observing the strain that developed in them during the experiment allowed an investigation into the way in which the unit cell itself evolves as a function of the in-situ environment and processes taking place within the metal. The strain, ε , relative to 40 °C in a given lattice parameter (‘a’ or ‘c’), 𝐿𝑃 , at a given temperature, 𝑇
, is described using Equation 10.
𝜀 =
𝐿𝑃
𝑇
− 𝐿𝑃
40°𝐶
𝐿𝑃
40°𝐶
Equation 10
Similarly, where strain evolution is used to calculate the difference in temperature
between two points on the thermal gradient, Equation 11 is used; where the temperature,
𝑇 , at a position, 𝑖 , is calculated by dividing the difference in strain between the thermocouple position, 𝜀
0
, and that position, 𝜀 𝑖
, by the thermal expansion, 𝛼 , and subtracting the resulting temperature from that read by the thermocouple, 𝑇
0
.
101 | Methodology
The Precipitation of Hydrides in Zirconium Alloys
𝑇 𝑖
= 𝑇
0
− 𝜀
0
− 𝜀 𝑖 𝛼
Equation 11
One important point to note is that when studying zirconium and its alloys, the anisotropic thermal expansion of the matrix unit cell results in inter-granular stresses that preclude an effective a
0
and c
0
(unstressed lattice parameters) from being measured experimentally. There are methods from which an unstressed lattice parameters can be calculated, including the use of stress-free samples, enforcing equilibrium conditions of a mechanical nature, or deriving them from other measurements [206]. Finding an accurate measure of the stress-free lattice parameters was, however, deemed as being beyond the scope of the present campaign, and instead only relative strain evolution is considered.
3.8.
Experimental Discrepancies
During the process of experimentation and data analysis, a number of anomalies were observed, each of which requiring deeper investigation to understand properly both their mechanisms and ramifications. The three most significant of these issues are outlined in the following subsections.
3.8.1.
Temperature Measurement
The first issue to be observed was that the ETMT thermocouple and pyrometer both displayed significantly divergent temperatures. As the pyrometer was incapable of providing readings of temperature below a threshold of ≈350 °C, an assessment of the deviation between the two methods could only be made above this level. To examine the difference between the two measures, the values from each for the entire experimental campaign were extracted from the beamline log file, and then filtered such that a like for like comparison could be performed. A filter for temperature was first needed, to factor out acquisitions where the reading from the pyrometer was below the minimum threshold. This was followed by a filter for axial position, such that the thermocouple (which remained fixed to the hottest region of the sample) and pyrometer spot (which scanned the sample when the ETMT was moved) were in a similar place. The remaining points were then separated according to sample (being that each had a different thermocouple, making temperature readings from each susceptible to variations in the quality of the spot weld) and the pyrometer temperature was plotted as a function of the thermocouple temperature. A linear model ( 𝑦 = 𝑚 ∙ 𝑥 + 𝑐
) was subsequently applied to each using a robust
regression with bisquare weighting, Figure 39.
Methodology | 102
The Precipitation of Hydrides in Zirconium Alloys
Figure 39. Pyrometer temperature as a function of thermocouple temperature.
Here, S1, S3 and S4 all showed relatively close agreement in both gradient and intercept; only S3 demonstrated any significant divergence from the other samples; the values for the linear
models are given in Table 8. S1, S2 and S4 were all similar enough that the deviation between
them could well fall within experimental error. What could be drawn from the model parameters, however, was that the relationship between the two was essentially linear for the majority of samples, and that there exists only some offset between the thermocouple and pyrometer readings, ranging from ≈51 °C to ≈73 °C. This was especially interesting, given that the manufacturer of the pyrometer quotes the device as being sensitive from 300 °C – 2000 °C [207], and the pyrometer begins providing readings when the thermocouple temperature was above
300 °C and the pyrometer reads temperatures to be above ≈350 °C.
Table 8. Thermocouple and pyrometer linear model parameters.
Sample Gradient Intercept (°C)
S1
S2
S3
S4
1.08
1.06
1.17
1.07
51.0
55.9
-26.0
73.1
As a secondary check of the validity of the temperature measurements, an evaluation of lattice parameters as a function of temperature was performed on S2. Integral to this, however,
103 | Methodology
The Precipitation of Hydrides in Zirconium Alloys was the identification of acquisitions prior to any heating current being applied to the sample, of which a total of eight were found from the beginning of the experiment, during a period in which the detector gain was being configured for the sample. Of these, only the first four were of similar parameters to the rest of the experiment, and so these were chosen for this analysis. While the thermocouple was able to give a reading of the temperature at these points, these values were ignored, in case of poor calibration of that sensor. Instead, the ambient air conditioning temperature of 20 °C was chosen for these points, which assumes the water cooling in the ETMT grips was not active at this point. Should the water-cooling have been active, this would have shifted these points to lower (leftward in the following figure), rather than higher temperatures, which would not change the outcome of the following argument.
Figure 40. Lattice parameter evolution during C1, comparing the thermocouple and pyrometer as measures of temperature.
Figure 40 illustrates the change in the ‘c’ lattice parameter from the matrix unit cell as a
function of the two measures of temperature, from a full 360° ring integration. The choice of this integration allowed an average parameter from the TD and RD to be calculated, thus mitigating against the effect that texture might have on lattice parameter evolution. Within this figure are four data series, the first being points with no current being applied to the sample, plotted against the ambient air conditioner temperature, rather than either of the sensors (thus being independent of aberrations in either measure). The thermocouple and pyrometer data series
Methodology | 104
The Precipitation of Hydrides in Zirconium Alloys were both taken directly from the beamline log file, although the pyrometer series was filtered to remove the null points below the threshold of 350 °C. The final series is that simulated from
the linear model parameters for S2 taken from Table 8 to form Equation 12. The lattice parameter
values used in the latter three series are taken from models refined using the Rietveld method, with error in the parameter averaging 0.0001739 Å.
𝑇 𝑝𝑦𝑟𝑜
= 1.06 × 𝑇
𝐸𝑇𝑀𝑇
+ 55.9
Equation 12
Considering the scatter in data points in Figure 39, the simulated series pyrometer points
demonstrated reasonable agreement with the recorded pyrometer points, but allowed the series to be extended to temperatures lower than the device was able to measure. When examining this lower temperature region, it could be seen that the thermocouple was the temperature measurement method where the linear thermal expansion line (extended to lower temperatures) correlated most closely to the pre-experiment points, an assessment that also proved true for the ‘a’ parameter. Given these findings, it was decided that the thermocouple was the correct and reliable measure of temperature during the experiment.
3.8.2.
Non-Systematic Noise
During the process of post-experiment data analysis, the integrated intensity of the profile for each structure was initially to be used for calculations of the diffracting volume of hydride (or concentration of hydrogen), an extension of the method employed by Zanellato et al.
[90] who used the intensity of individual reflections. An example of the trend in this data, taken
from C3 (150 °C) for the δ phase, can be seen in Figure 41 as the orange line, where values were
calculated automatically by TOPAS. Also represented as the purple trace is a series containing the weight percentage of the same phase, calculated from the Le Bail method in the way described previously. For the graphical comparison in this figure, each of these two data series were
normalised using a function similar to Equation 9, parameterised in such a way that the values
from the dwell approximated unity, while the values from the soak approximated zero. In this way, the trends seen in each of these two measures of hydride precipitation can be compared, despite their dissimilar pre-normalisation magnitudes. To illustrate the relation of the intensity/weight percentage evolution to the temperature of the sample, a subplot containing the thermal profile for this cycle is also included.
105 | Methodology
The Precipitation of Hydrides in Zirconium Alloys
Figure 41. Non-systematic noise in phase profile intensity, with comparatively noise free weight fraction data.
The profile intensity for the hydride phase can be seen to fluctuate significantly during periods where the weight percentage remains essentially constant, and the scale of this noise is significant enough that the small curvature just after the quench (arising from continued precipitation after temperature stabilisation) is lost to the scatter. Furthermore, the difference in intensity between the 150 °C and 40 °C portions of this cycle is lost in the scatter within these two regions. As the weight percentage is calculated as a function of the relative intensity of the α and δ phases, this measure of phase distribution is insensitive to anomalous fluctuations in the illuminating beam or total (α + δ) diffracted intensity, making it a more reliable measure of the balance of phases. Furthermore, calculating phase fraction from the relative intensity of these two phases also serves as an approximate correction for the Debye-Waller effect, in the way
described in Section 3.6.6. To quantify the degree of noise in each, the standard deviation of
points in the dwell region of each was calculated, and this was converted to a percentage of the mean of values in the same region. From the weight percentage series, the standard deviation in values was found to be 0.26 %, while that from the profile intensity was more than an order of magnitude larger, at 3.16 %.
Given that the current used to heat the sample was controlled automatically, and was known to fluctuate in order to maintain a stable temperature, it was postulated that it (or some
Methodology | 106
The Precipitation of Hydrides in Zirconium Alloys other part of the diffraction setup) might be causing the noise. To investigate this, the area from the dwell region of each cycle was evaluated as a function of a number of different experimental parameters recorded in the beamline log file. An example of this, using the ETMT heating current,
is given in Figure 42 – (a), illustrating the complete lack of correlation between these parameters.
In fact, of all the parameters recorded in the log file, none demonstrated any form of link to the noise present in the integrated intensities, including the thermocouple temperature and beam
intensity. Furthermore, the histogram in Figure 42 – (b) illustrates the essentially random
distribution of values found in this data, indicating the non-systematic nature of the noise. Given this assessment it was decided that the scatter aberration in the intensity was caused by some mechanism beyond the ability of measurement and quantification, precluding it from being filtered out. Instead, the weight fraction, being far more stable, was chosen, and the previously discussed method of calibrating these values was established.
Figure 42. Phase profile intensity noise (a) as a function of current, and (b) represented as a histogram of intensity values.
3.8.3.
Hydrogen Concentration
A concentration of 550 ppm wt.
was originally charged into the sample, approximating the hydrogen content of cladding material after a burn-up of 55 GWd/t
U
; the goal of some reactor operators for current and future fuel assembly life [70,208]. During both experimentation and the analysis of the present data, however, a discrepancy was observed between the expected solubility temperatures, from McMinn et al. [77], and those recorded during thermal operations.
As the solubility of hydrogen was thought to be independent of the alloy chemical composition and microstructure [77], and heating/cooling rate was thought to have only a limited effect on the observed solubility [77] (although evidence in the literature suggests it may be as high as a
20 °C shift [90]), this was potentially indicative of the hydrogen content of the sample not being what was expected. Potential causes for a loss of hydrogen may include sample confusion during measurements, either during or prior to the synchrotron experiment, any undocumented work
107 | Methodology
The Precipitation of Hydrides in Zirconium Alloys carried out on sample S2 prior to the synchrotron beam time, the effect of spot-welding the thermocouple, or perhaps persistent hydrogen trapping (effectively increasing the solubility).
To verify the amount of hydrogen within the sample, two approaches were implemented, intended to provide redundancy to the measurement. The first made use of the offset method from Barrow et al. [107] to measure accurate dissolution and precipitation solubilities, which could be compared with the equations provided by McMinn et al. [77] to approximate hydrogen concentration. The second employed the lattice distortion model from Zanellato et al. [90] to derive the concentration required to distort the matrix unit cell by the amount recorded when all hydrogen was dissolved into solution.
The Barrow offset method involves first identifying the linear thermal expansion coefficient in each lattice parameter (again using a full 360° integration), then drawing a line with
this gradient through the high temperature region of a strain trace for the matrix, as in Figure 43.
This line was then offset by an amount equal to the uncertainty in the measurement, quoted as
±5 x 10 -6 in [107], but calculated by TOPAS for this work to be ±25.5 x 10 -6 and ±173.9 x 10 -6 in the
‘a’ and ‘c’ parameters, respectively. The point at which the strain trace crosses this extrapolated line on heating and on cooling gives the temperatures at which dissolution is complete during heating or precipitation begins during cooling.
Figure 43. Terminal solid solubility determination using the offset method.
Methodology | 108
The Precipitation of Hydrides in Zirconium Alloys
𝐶 𝑑𝑖𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
= 106,446.7 ∙ 𝑒
𝐶 𝑝𝑟𝑒𝑐𝑖𝑝𝑖𝑡𝑎𝑡𝑖𝑜𝑛
−4,328.67
𝑇
𝐾
= 138,746.0 ∙ 𝑒
−4,145.72
𝑇
𝐾
Equation 13
Equation 14
From McMinn et al. [77], two expressions describing the hydrogen solubility during
dissolution (TSSD) and precipitation (TSSP) were taken, Equation 13 and Equation 14, from which
the hydrogen concentration corresponding to the temperatures calculated from the offset method could be derived. Here, the temperature,
𝑇
𝐾
, is in degrees Kelvin. The results of these
calculations are presented in Table 9. The spread of hydrogen concentrations was not ideal from
this method, and the magnitude of these values was less than half the expected hydrogen content of sample S2. This method of verification alone, however, was not seen as sufficient, and so the
aforementioned lattice distortion model, Equation 15, was employed as well.
Table 9. Solubility temperatures and hydrogen concentration calculated from the offset method.
‘a’
‘a’
‘c’
‘c’
Lattice Parameter Solubility
TSSD
TSSP
TSSD
TSSD
449
368
438
361
Temperature (°C) Hydrogen (ppm wt.
)
265
242
216
201 𝜀̅ 𝑑 𝑎
=
(1 − 𝐶 𝑛
𝑍𝑟 𝑎𝑡
𝐻
∙ 𝐶 𝑎𝑡
𝐻
) ∙ (2 + 𝐾)𝑣̅
0
∙ ∆𝑣
Where: 𝑛
𝑍𝑟
– The number of zirconium atoms per unit cell.
𝐶 𝑎𝑡
𝐻
– The dissolved molar hydrogen concentration.
𝐾
– The coefficient of anisotropy [90].
Equation 15 𝑣̅
0
– The initial cell volume, 𝑣̅
0
=
√3
2
∙ 𝑎 2 ∙ 𝑐 .
∆𝑣 – The unit cell volume increase from interstitial deuterium 20 .
Using this expression, a linear model describing evolved matrix lattice strain as a function
of the quantity of hydrogen in solution is developed, illustrated in Figure 44. The parameters
chosen for use in this evaluation are similar to those used in the original work by Zanellato et al.
[90] when studying the same Zircaloy-4 material, sharing the same processing history. Because
20 Substituted as an analogy of hydrogen.
109 | Methodology
The Precipitation of Hydrides in Zirconium Alloys of the similarity between that work and the present study, it was thought that the model from
[90] was well suited for describing the material employed in this thesis. The value used for interstitial induced volume expansion was 2.78 Å, the value for deuterium from [209], since no value for hydrogen was available. The expansion in the ‘c’ parameter is calculated as a function of that in the ‘a’ parameter, using the difference in dilatation between the two directions of 1.65 from [209].
Figure 44. Modelled matrix lattice distortion from dissolved hydrogen.
Once a linear model relating evolved strain to hydrogen concentration in solution was established, strain evolution in the ‘a’ and ‘c’ lattice parameters was calculated from the 30° integration in the TD direction, in keeping with the data presented in [90]. Instead of visualising these strains as a function of temperature, as in previous figures, this time the strains were traced temporally, allowing changes in matrix strain occurring during the soak period of each thermal operation to be examined. As the evolution of strain is a convolution of thermal expansion, chemical dilatation and mechanical interactions, it was first necessary to separate these three effects. Given that during the soak it is assumed all hydrogen is in solution, it was also assumed that no mechanical interactions relating to the hydride would distort the matrix lattice parameters at soak temperatures. This is supported both by hydride reflection intensity extinction and from the return to strain evolution linearity at high temperature. The thermal expansion coefficients of the metal are known from a similar sample that underwent no hydrogen charging, S1, that was heated and measured, C0, and so these terms can be used to deconvolute the effect of thermal expansion, leaving only chemically induced lattice strains. An example of
Methodology | 110
The Precipitation of Hydrides in Zirconium Alloys
those calculated from sample S2 during C1 to C8 is given in Figure 45 for the ‘a’ lattice parameter.
This parameter is pictured here as it is that with the lower error (±25.5 x 10 -6 versus ±173.9 x 10 -6 ), thus making it the more reliable indicator; furthermore, points not calculated from the axial centre of the sample are removed (thus shortening the C1 soak series) and points where hydrogen is not fully dissolved have also been filtered out.
Figure 45. Chemically induced lattice dilatation in the ‘a’ lattice parameter.
In Figure 45 it can be seen that the strain evolved during the soaks pictured above is fairly
consistent from cycle to cycle, indicating a minimal amount of hydrogen depletion from the axial centre of the sample during these cycles; more on the topic of hydrogen redistribution will be explored in the first proposed manuscript. It is also evident that the evolved strain trace is fairly stable in the latter portion of each soak, allowing accurate averages of strains in each of these periods to be calculated, providing robustness to the measurement. A gradual climb at the beginning of each soak is noted, which is thought to be rate limited dissolution owing to rapid heating of the sample. The final block of data in this figure is also longer than those others, as both the soak and dwell from C8 are illustrated, supporting an observation of nil precipitation during the final thermal cycle.
As the material was thought to be close to its initial state during C1, the evolved strain during the soak in this cycle was assumed to be a descriptor of the bulk quantity of hydrogen in the material prior to the commencement of C1. For reasons that are discussed later, this was seen as a fair approximation, as hydrogen depletion at the axial centre of the sample takes some amount of time to develop. An average evolved strain of 1343.5
x 10 -6 was recorded from the
111 | Methodology
The Precipitation of Hydrides in Zirconium Alloys stable period of the C1 soak, with maximum and minimum values of 1351.9 x 10 -6 and
1334.5 x 10 -6 , producing a mean approximate hydrogen concentration of 431.3 ppm wt.
, with an upper and lower values of 434 ppm wt.
and 428.4 ppm wt., calculated for sample S2. Given the accuracy in the measurement, approximately ±7.5 ppm wt.
calculated from an uncertainty of
±25.5 x 10 -6 , this value was rounded to 430 ppm wt.
throughout this thesis. When using the ‘c’ lattice parameter, a mean concentration of 433.2 ppm wt.
is calculated, with an upper and lower value of 442.1 ppm wt.
and 423.2 ppm wt.
, with an associated uncertainty of approximately
±34 ppm wt.
.
With regard to the discrepancy between these two approaches to measuring hydrogen concentration, there is evidence in the work by McMinn et al. for the influence of other experimental parameters on the observed solubility temperatures for hydrogen in zirconium [77].
In that work, a reduction in the hydride precipitation memory effect is cited as a reason for a shift to lower solubility temperatures, as a function of the peak temperature and time-at-temperature during thermal operations [77]. It seems possible, then, that variations in matrix defects will have a marked effect upon the solubility temperatures of material, as dislocations and substitutional species are known to trap hydrogen [42,77,118], potentially influencing its apparent solubility.
Given this knowledge, it was decided that the hydrogen concentration calculated from the lattice distortion model would be that used throughout the present thesis. This choice was made owing to the fact that those equations from Zanellato et al. were derived for the same material as in this work, making them the ideal choice for calibrating the hydrogen content of S2.
Additionally, while the temperature at which hydrogen enters solution may be the product of microstructure, the author knows of no evidence for significant changes in the way in which solute hydrogen dilates the parent matrix as a function of processing or history. The exception to this may be dislocation structures, which complicate the issue, as trapped hydrogen and would thus not contribute to bulk lattice dilatation to the same extent as interstitial hydrogen. It seems possible, however, that at the elevated temperature at which dilatation measurements were taken, the depth of traps may have been sufficiently diminished that only a small proportion of
hydrogen was bound by them. Table 10 is thus updated to accurately describe the samples used
within the diffusion, kinetics and strain evolution portions of the campaign, based on strain-based measurements of hydrogen concentration.
Table 10. Sample descriptions and calculated hydrogen content.
Sample
S1
S2
0
430
H (ppm wt.
) Details
Standard sample.
Identical to S1, but charged with hydrogen.
Methodology | 112
The Precipitation of Hydrides in Zirconium Alloys
4.
First Proposed Manuscript – Diffusion
4.1.
Foreword
This first proposed text focuses on the effect of thermal cycles on the redistribution of hydrogen within Zircaloy-4, as a product of the thermal gradient that arises from Joule heating.
This manuscript bares the names of a number of listed authors, and so the contribution of each are briefly described:
The experiment was designed by O. Zanellato, with input from M. Preuss, F. Ribeiro and
J. Andrieux; it was performed at the ESRF by M. S. Blackmur and O. Zanellato, with J. Andrieux as the resident scientist supporting the experiment. Data processing and analysis was undertaken by M. S. Blackmur, after being trained to use TOPAS by R. Cernik, whom also provided assistance with X-ray crystallography topics, and O. Zanellato. The manuscript was written by M. S. Blackmur, with technical and editorial supervision and proofing provided by M. Preuss and J. Robson.
Note that the references contained in this manuscript, and those that follow, refer to the bibliographies at the end of each of these sections, and not the overall thesis bibliography.
Furthermore, those references in the annex of the first and second papers refer to the overall bibliography at the end of the thesis.
113 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
4.2.
Manuscript
Thermal Diffusion and Redistribution of Hydrogen in Zircaloy-4 Observed with
Synchrotron X-Ray Diffraction
M.S. Blackmur a , M. Preuss a , J.D. Robson a , O. Zanellato b , R.J. Cernik a , F. Ribeiro c , J. Andrieux d, e a Materials Performance Centre, School of Materials, The University of Manchester, Manchester, M1 7HS,
United Kingdom b PIMM, Ensam - Cnam - CNRS, 151 Boulevard de l'Hôpital, 75013 Paris, France c Institut de Radioprotection et de Sûreté Nucléaire, CEN Cadarache, 13115 St. Paul Les Durance, France d Beamline ID15, European Synchrotron Radiation Facility, Grenoble, France e Laboratoire des Multimatériaux et Interfaces, Université de Lyon, 43 Bd du 11 Novembre 1918, Villeurbanne, 69100,
France.
Keywords
Synchrotron X-Ray Diffraction, Hydrogen Diffusion, Zirconium, Zirconium Alloys, Joule
Heating, Resistive Heating, Thermal Gradient, Thermal Diffusion, Thermo-Diffusion, Soret Effect,
Fickian Diffusion.
Abstract
An evaluation of the redistribution of hydrogen under a thermal gradient was performed, as part of a broader experimental programme to investigate kinetics and strain evolution during hydride precipitation in Zircaloy-4. Thermal expansion coefficients were measured from a sample that was considered to be essentially hydrogen free, 𝛼 𝑎
= 6.04 × 10 −6 𝐾 −1
and 𝛼 𝑐
= 8.97 ×
10 −6 𝐾 −1
. These values were used in conjunction with axial strain profiles to assess the magnitude of a thermal gradient arising from Joule heating to a series of reactor-relevant temperatures. From the axial gradients, an evaluation of the potential for thermo-diffusion (from the Soret Effect) was performed, and an axial diffusion flux profile was predicted. The effect of the thermal gradient on the axial solubility profile was also assessed, and it was seen that under all experimental conditions, hydrides would remain undissolved at the cold end of the axial gradient, increasing the propensity for thermo-diffusion. Diffusion distance calculations indicated the high mobility of hydrogen during experimentally implemented temperatures, and so it was expected that significant depletion at the hottest region would occur. X-ray diffraction measurements of hydrides (from hydride reflection intensity) and dissolved hydrogen (from matrix dilatation observations) demonstrated that depletion was not as significant as may have been expected. Possible reasons were thought to be trapping and the countering effect from
Fickian flow of hydrogen from enriched regions to depleted regions. Additionally, while the magnitude of the thermal gradient was often significant, the steepest regions were located close
First Proposed Manuscript | 114
The Precipitation of Hydrides in Zirconium Alloys to the coldest point, while a large axial range of material close to the warm axial centre was found to be far closer to thermal isotropy. In all, a maximum of 30 ppm wt.
depletion (out of a total of
430 ppm wt.
) was recorded at the axial centre of the sample by the end of the experiment. Finally, to examine the combined influence of both thermal and concentration gradients, the axial flux profile at 40 °C and 500 °C is presented and discussed.
1.
Introduction
Zirconium alloys have been adopted as structural materials in water-cooled reactors for decades, owing to their high neutron transparency, thermal stability and corrosion resistance [1,2]. The largest use by volume of these materials within a reactor core is as fuel cladding, where it acts as a protective barrier between the fuel and aggressive coolant, as well as encapsulating fission products to prevent their release into the primary coolant loop [3–5]. Whilst considered corrosion resistant in aqueous environments, zirconium alloys do experience an oxidation process under reactor conditions, which produces hydrogen as a product [6]. A fraction of this is then taken up into the cladding [6,7], where it can precipitate into a number of possible hydride phases [8,9] that deleteriously affect the materials properties of cladding [10–15] and introduce new modes of failure [16–22].
Given the design and geometries of Light Water Reactor (LWR) cores and fuel assemblages, thermal gradients are seen both axially and radially within the cladding tubes [23,24]. The radial (inner to outer surface) gradient develops as the cladding material is sandwiched between the fuel, where thermal energy is released by the process of fission, and the turbulently flowing coolant passing over the cladding, which removes thermal energy.
Modelling of this process, undertaken by Davis, yielded a radial gradient that ranges from 10 °C, at the base of cladding tubes, to 35 °C, close to the axial centre [25,26].
An axial (tube end-to-end) thermal gradient is produced by a number of factors, including variations in power distribution (and thus fuel temperature), coolant temperature and coolant density [26]. This gradient evolves dynamically with time, as the axial distribution of power within the rod changes, owing to variations in the burnup profile of the fuel [26,27]. Similar modelling of the axial temperature distribution produces a gradient magnitude of between 50 °C and 70 °C at the outer surface of the cladding, with the peak temperature initially located just above the axial centre and then migrating with burn-up towards the top of the tube [25,26]. Small, localised thermal gradients can also exist at surface flaws, like sites of spallation in the protective oxide, where coolant can reach the underlying metal [28], as well as in cladding close to the pellet-pellet interface between stacked fuel within the rods [25,28].
The gradients in temperature have a pronounced effect on the distribution of dissolved hydrogen and hydrides, both during and after fuel assembly burnup, owing to the known
115 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys prevalence of the Soret Effect on dissolved hydrogen [29]. This is a process of thermally induced diffusion, whereby solute hydrogen will diffuse from a region of higher thermal energy to lower thermal energy, or from warmer to cooler [30]. This flow can then either bolster, or compete against, the flow induced by concentration gradients, described by Fick’s Law [31], or that aided by stress gradients (although thermo-diffusion usually dominates stress induced diffusion) [32].
The effect of the Soret Effect on hydrogen redistribution has been modelled on the macro- [33] and micro-scale [34], showing a significant impact on the localisation of hydrides.
It should be noted that Cox, in his review of hydriding mechanisms, states that significant thermo-diffusion will only occur where the solubility of hydrogen has been exceeded at the cold end of a gradient and hydrides exist there, although some amount of thermo-diffusion will occur before equilibrium is achieved [35]. This is because some form of sink for hydrogen is required at the cold end of the thermal gradient, such that equilibrium is not reached between flow from the
Soret Effect and the competing diffusion from Fick’s Law. The requirement of existing hydrides is notable, because in addition to diffusion, temperature gradients also influence the local solubility of hydrogen in zirconium, whereby the matrix in warmer regions is able to host more dissolved hydrogen, and vice versa [9,36]. Additionally, a suitably large thermal gradient may affect the way in which hydrogen exists in solution from region-to-region, where Wipf et al. propose that an increase in thermal energy allows hydrogen to occupy interstitial sites other than the tetrahedral positions seen at lower temperature [37]. Here, the occupation of other interstices, like octahedral sites, could increase diffusivity, through the availability of new sub-lattice positions through which to migrate, intensifying the process of thermo-diffusion [37].
In contrast, cooler regions will demonstrate a lower hydrogen solubility, and so hydrides are more likely to form there, enhanced by a supply of hydrogen from Soret Effect flow. The presence of hydrides is also significant, as the existence of these particles leads to the creation of a localised depleted zone surrounding them. The resulting concentration gradients surrounding these depleted areas could then act as a sink into which hydrogen can flow.
The presence of these regional differences in solubility and diffusion become important when one considers the way in which the hydride phase is known to degrade cladding material.
The radial gradient, for instance, is known to enable the formation of a highly enriched hydride rim close to the colder outer surface of the cladding, containing a mean hydrogen content of
1300 ppm wt.
compared to the average of ≈430 ppm wt.
found globally in the cladding [30,38]. This high rim concentration is well above the values cited in the work by Lin et al. and Yeniscavich et al. thought to cause significant degradation of the ductility and strength of cladding material
[10,16,39].
Where very localised ‘cold spots’ occur, as the result of oxide spallation or damage, thermo-diffusion can lead to the development of hydride blisters [40], a large continuous region
First Proposed Manuscript | 116
The Precipitation of Hydrides in Zirconium Alloys of brittle hydride known to be capable of catastrophic failure [20,21]. Additionally, the presence of notches or defects in cladding material is known to introduce a hydrostatic tensile stress raiser, which can lead to long range diffusion towards the tip of a flaw, either through Fickian or stress-driven diffusion [41–43]. Hydrides precipitated at crack tips then coarsen until a critical condition for their failure is met, and the cyclic growth and fracture allows a crack to propagate through cladding over an extended time period [17–19]. This process occurs under a load that is below the yield stress of the material, and is known as Delayed Hydride Cracking (DHC) [17–19].
The redistribution of hydrogen towards the outer surface of cladding material, where DHC is thought to initiate, would significantly increase the local supply of hydrogen, diminishing the degree of diffusion required for the DHC process.
This article seeks to investigate the impact of thermal gradients on hydrogen distributions in Zircaloy-4, resulting from the Soret Effect and Fickian diffusion. The observations made herein are intended to support publications on the kinetics of hydride precipitation [44] and the evolution of strain during precipitation [45], as part of a broader experimental programme. In addition to this, they will provide some insight into the redistribution of hydrogen under temperatures and thermal gradients relevant to reactor operating conditions.
2.
Experimental
2.1.
Sample Specification
Two Zircaloy-4 coupons were provided by the Institut de Radioprotection et de Sûreté
Nucléaire (France) for use within this experimental programme, with the same processing conditions as in [46]. To summarise, the samples were rolled to 400 μ m, cut to 50 mm and 5 mm in the rolling and transverse directions, respectively, after which they were recrystallised [46].
From Electron Backscatter Diffraction, an average grain size of 8-10 μ m was recorded, along with a texture showing the expected split basal poles associated with rolled and recrystallised hexagonal materials. The geometry of the samples, and the way in which they were installed into the experimental assemblage, is shown schematically in Figure 1.
The first sample contained a concentration of 430 ppm wt.
(±3 ppm wt.
mm -1 axially) at the time of experimentation, charged using the methodology from [46], while the second sample remained non-charged, to act as a baseline for measurements. When evaluated against the hydrogen content in service fuel cladding, the chosen value is comparable to fuel assembly hydrogen content after an average burnup of approximately 49 GWd/t
U
[47]
.
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The Precipitation of Hydrides in Zirconium Alloys
Figure 1. Sample geometry and mounting assemblage.
2.2.
Synchrotron X-Ray Diffraction Parameters
This experimental programme was conducted at the European Synchrotron Radiation
Facility (France), on high-energy diffraction beamline ID15B; technical details can be found in
[48,49]. Transmission (Debye-Scherrer) geometry was used to illuminate each sample, with the beam orthogonally incident to the sheet and parallel to the normal direction. This allows for bulk measurements of hydrides through the thickness of the sheets. Debye-Scherrer cones were bisected and imaged using a Trixell Pixium 4700 detector in 5 second acquisitions, each with 4-5 seconds of disk-write time. An energy of E = 87.17 ± 0.01 keV was used to illuminate the sample, with an associated wavelength of λ = 0.14223 Å and spot size of 300 μm x 300 μm.
2.3.
Thermal Transients
The temperature of each sample was manipulated using resistive (Joule) heating, where the sample was mounted in an Instron ETMT8800 (Electrothermal Mechanical Tester). The driving current for heating was controlled automatically by the software and was adjusted against readings taken by an S-Type thermocouple mounted at the axial centre of both samples, Figure
1. This current was adjusted dynamically to mitigate against heat loss into the water-cooled grips through conduction and into the surrounding atmosphere by radiation. The atmosphere was chosen to be argon, supplied as a continuous flow throughout the experiment to mitigate against further oxidation of the sample during elevated temperature transients.
2.3.1
Non-Hydrogen-Charged Sample
Prior to performing thermal operations on the hydrided sample, it was seen as important to understand the thermal gradients experienced by the material during Joule heating. For this, the non-charged (0 ppm wt.
) sample was heated to a series of shelf temperatures, during which measurements of matrix lattice strains were made along the axial length of the sample. This set of thermal operations is labelled Cycle 0 (C0), as it was both performed before those undertaken
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The Precipitation of Hydrides in Zirconium Alloys on the hydrided sample, and was undertaken on a sample containing 0 ppm wt.
of charged hydrogen. The term ‘shelf’ will be used in this work to describe the holds at various temperatures in C0 for the non-charged sample only. For axial measurements of strain, the gauge volume was displaced laterally (in the RD) with respect to the centroid of the sample, in 0.5 mm increments between -10 mm and 10 mm, with respect to the axial centre of the sample.
Figure 3. Thermal operations and gauge volume displacement relative to material axial centre as a function of time for the non-charged sample.
2.3.2
Hydrogen-Charged Sample
The thermal profile for the main experimental programme, undertaken on the hydrided sample, combined a single ramped thermal operation (C1) with seven sequential quench and dwell transients (C2 to C8). C1 was designed to allow the measuring of dissolution and precipitation solubilities during continuous heating and cooling at 1 °C s -1 between 40 °C and
570 °C, above the expected eutectoid temperature [36,50,51]. From this cycle, the apparent dissolution solubility was found to be 429 °C, and so all subsequent cycles used a soak temperature of 500 °C. The term ‘soak’ will be used throughout this article to describe these maximum temperature regions, where hydrides are fully dissolved.
As a memory effect for hydride precipitation has been reported in the literature [52,53], it was expected that repeated cycles of dissolution and precipitation would encourage heterogeneous nucleation at damage sites left behind by previous hydrides. By soaking at
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The Precipitation of Hydrides in Zirconium Alloys elevated temperatures these damage structures may be allowed, at last partially, to recover, thus mitigating heterogeneous precipitation from cycle to cycle.
Cycles 2 to 8 involved heating to the soak temperature and dwelling for 15 minutes to ensure all hydrides were fully dissolved, after which a quench operation was performed to each of a series of chosen temperatures. The term ‘dwell’ will be used throughout this work to describe the hold at specific temperatures, after quenching from the soak. This quench was controlled using a sharp reduction in heating current, but the loss of thermal energy through conduction and radiation precluded an instantaneous quench, yielding a maximum effective cooling rate of
30 °C s -1 . Once the target temperature was reached, it was then maintained for a long duration, during which kinetics and strain observations were made. These temperatures were chosen to start at 100 °C, rising by 50 °C in sequence up to a maximum dwell temperature of 400 °C. Due to time constraints, the final two cycles were shortened from 60 minutes, implemented in all other cycles, to 30 minutes. The precipitation solubility for the sample was measured to be 361 °C, and so the final cycle, C8, demonstrated no measurable diffraction.
Finally, a second 1 °C s -1 heating ramp was added at the beginning of the penultimate cycle, C7, to allow a comparison with the dissolution observed at the beginning of C1. No significant change was observed between these two cycles (within the bounds of experimental error), indicating that the memory effect was sufficiently mitigated against by the experimental design, maintaining cycle-to-cycle similarity. The average error present in measurements of hydrogen was found to be ±15.5 ppm wt.
throughout this programme, while that for strain evolution was ±25.5 x 10 -6 and ±173.9 x 10 -6 for the prismatic and basal parameters, respectively.
All thermal and displacive operations on the hydrided sample are schematised in Figure 2.
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The Precipitation of Hydrides in Zirconium Alloys
Figure 2. Thermal operations and gauge volume displacement as a function of time for the hydrided sample.
The process of Joule heating induces a thermal gradient across the distance between the grips, further exacerbated by heat loss into the water-cooled grips [54]. As hydrogen is known to diffuse down thermal gradients, the heating technique employed could combine with long dwell times to produce significant depletion at the axial centre of the sample [16,33,55]. The impact of this upon the overall experimental programme is potentially significant, and so full quantification of the hydrogen distribution within the sample is necessary to underpin observations made elsewhere on kinetics and strain evolution [44,45].
To perform this, two different forms of check were undertaken during the programme, those at high and low temperatures, as indicated by the points marked in Figure 2. At 40 °C, where all hydrogen is assumed precipitated, axial hydride distribution checks were performed by displacing the gauge volume with respect to the axial centre of the sample along the RD, from
0 mm to 10 mm in increments of 0.5 mm. Each of these displacements and their positions in time are illustrated in Figure 2, and at each axial position a diffraction pattern was recorded, from which a hydrogen distribution was calculated using the intensity of hydride Bragg reflections. As a confirmation of the positioning of the axial scans, two were expanded to range from -10 mm to
10 mm (not pictured in Figure 2). The error in axial position, arising from thermal expansion, was thought to be no more than 25-50 μm.
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The Precipitation of Hydrides in Zirconium Alloys
At the soak temperature (500 °C/570 °C), all hydrogen is thought to dissolve into solution, meaning that no diffraction signal from the hydride phase was expected, and so measurements of hydrogen within the gauge volume were instead performed using observations of lattice dilatation in the matrix. At these points, also indicated in Figure 2, no axial scanning was performed and instead a series of acquisitions at the sample centroid were made, allowing a highly accurate measure of chemically induced evolved strain. As hydrides dissolve, the hydrogen released into the matrix requires time to diffuse and homogenise, in order to find an equilibrium distribution within the matrix. Given this, matrix strain measurements performed during the soak were only considered after matrix strain evolution had stabilised, which typically took ≈7 minutes out of the 15 minute duration of the soak.
Finally, to investigate the desorption of hydrogen, a mass spectrometer was used to monitor the atmospheric exhaust from the ETMT chamber, which yielded no signal from hydrogen throughout the programme. This is logical as hydrogen is more stable when dissolved within α-zirconium than when it exists as a diatomic gas [16].
2.4.
Synchrotron Data Analysis
In order to perform a quantitative analysis of the hydride phase, a complete integration of the Debye-Scherrer rings was performed over 360°, ensuring that diffraction from the maximum number of crystals was considered. Pattern geometries (ring centroid and detector non-orthogonality related distortion) were calibrated from a CeO
2
standard, imaged with parameters intended to be identical to those for the samples. Fit2D was used to perform the process of integrating Zircaloy-4 diffraction patterns, yielding a diffractogram for each temporally resolved pattern (a plot of intensity, nominal counts, against a spatial term – Q, inter-planar spacing or 2θ). Each of these was normalised against the incident beam intensity, measured by sensors in the path of the beam, to mitigate any decay in the storage ring current that occurs with time that might influence experimental results.
TOPAS-Academic V5 was then used to refine a structural model from each diffractogram using an in-house Matlab R2014b function for batch processing. Artificial/instrumental Bragg reflection broadening is accounted for through simulating patterns recorded from a Standard
Reference Material with Fundamental Parameters, and then implementing the same profile in all further analysis on the sample. Any further changes in reflection shape can then be attributed generally to material related observations [56,57].
A preliminary attempt to batch refine models from sequential patterns using the Rietveld methodology [58,59] proved unsuccessful, owing to the small hydride reflections and the significant variation between patterns, where hydride reflections both grew from, and diminished to, extinction. Instead, two boundary conditions were established where the extinction of hydride
First Proposed Manuscript | 122
The Precipitation of Hydrides in Zirconium Alloys reflections was taken to represent full dissolution of the phase, while the maximum intensity seen in the initial state was taken to indicate full precipitation. From the equations published by
McMinn [36], the solubility of hydrogen at 40 °C is in the parts per billion, and so it is assumed that this intensity represents complete precipitation of the 430 ppm wt.
hydrogen concentration.
A linear relationship linking diffracting volume of hydride to Bragg reflection intensity then allows the precipitated concentration of hydrogen to be calculated from each successive diffractogram.
The Le Bail methodology for refining structural models [60] can be employed to refine models of the hydride and matrix phases in a similar way to the Rietveld method, except that reflection intensities are able to vary freely. Taking values of cell mass from the initial Rietveld models and supplying them to the Le Bail models allows TOPAS to generate a nominal value for phase weight percentage. These values, however, were significantly divergent from the established boundary conditions, and so they are calibrated to meet the boundaries properly.
This provides values representing the true concentration of precipitated hydrogen at any time.
Like the Rietveld method, the Le Bail methodology links crystal structure and lattice parameters, to define the spatial position of Bragg reflections for any given phase. This allows for the accurate derivation of lattice parameters by refining a structural model to fit the recorded pattern, especially where multiple reflections are sampled for each phase. From tracking the change in these parameters it then becomes possible calculate strain evolution in the unit cell of each phase.
Figure 4 illustrates three diffractograms generated from a 360° azimuthal integration at key experimental temperatures, where the inter-planar spacing range displayed on the x-axis is that chosen to be used. The hydride reflections within this region are the high multiplicity
{311} 𝛿 and
{022} 𝛿
reflections, selected to maximise trend stability when measuring such a low intensity phase. The maximum intensities recorded for these reflections, measured from the material’s initial state at 40 °C, represent full precipitation of the 430 ppm wt.
hydrogen content of the sample. The 500 °C pattern shows no evidence of Bragg diffraction from the hydride phase, and so the phase is considered to be fully dissolved, where 430 ppm wt.
of hydrogen is assumed to be in solution. An intermediate pattern is also displayed, showing that at temperatures between the maximum and minimum, partial precipitation is represented by a reflection intensity that is between the two boundary conditions.
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The Precipitation of Hydrides in Zirconium Alloys
Figure 4. Representative diffractograms from 40 °C, 300 °C and 500 °C for the considered range of inter-planar spacing.
3.
Results & Discussion
3.1.
Thermal Gradient
Before an investigation into the redistribution of hydrogen can be performed, it is first necessary to understand the precise nature of the thermal gradients experienced within the sample at various points during the experimental campaign. As a first step in this process, it was necessary to derive the thermal expansion coefficients for the matrix. Given that interstitial deuterium (as an analogy for hydrogen) is known to distort the parent α-lattice [61], it was critical that the thermal expansion was measured from a sample that had not undergone hydrogen charging. This involved acquiring a number of diffraction patterns, at a series of experimentally relevant temperatures, at the axial centre of the specimen where the thermocouple was mounted. This was done at the shelf temperatures seen during Cycle 0 (C0), on the non-charged material. The results of linear models of thermal strain in the lattice parameters with change in temperature are present in Table 1 along with the parameters calculated by Zanellato et al. [86] for similar base material, and those calculated by Goldak et al. [62] for single crystal zirconium in the range of 300 K to 800 K. It can be seen that those values calculated in the present study compare favourably with those from Zanellato et al. [86], although a small and unexplained
First Proposed Manuscript | 124
The Precipitation of Hydrides in Zirconium Alloys positive bias does appear in both parameters, which falls outside the bounds of uncertainty
(α a
± 0.167 x 10 -6 , and α c
± 0.297 x 10 -6 ). When compared with single crystal values, the prismatic plane expansion is above the maximum of the range given in the literature, while the basal plane expansion is somewhat below the highest value. This likely arises from the polycrystalline nature of the sample, whereby the texture means that orientation mismatch causes neighbouring grains to constrain one another. As a result of this, basal planes serve to over-dilate prismatic planes, while prismatic planes act to restrict the dilation of basal planes, thus potentially resulting the values given in Table 1. As the calculated lattice parameters are derived from a Le Bail model encompassing the five higher multiplicity matrix reflections seen in Figure 4, it is thought that the thermally induced strain measured in them is highly accurate.
Table 1. Non-charged Zircalloy-4 thermal expansion coefficients.
Parameter Direction
Prismatic (a) ⟨112̅0⟩ 𝛼
Basal (c)
6.036
⟨0002⟩ 𝛼
8.966
Thermal Expansion Coefficient (x 10
Measured Zanellato [46]
5.77
7.62
-6 K -1 )
Single Crystal [62]
4.99 – 5.19
7.36 – 11.84
As the temperature in the material is measured by a thermocouple positioned at the axial centre of the sample, this temperature does not correspond to the temperature within the gauge volume when the beam position is not at 0 mm (the axial centre). Because of this, it is only possible to measure indirectly the temperature within the gauge volume using measured thermal lattice strain evolution and the known thermal expansion coefficients for the material, Table 1.
For each shelf temperature in C0, the evolved strain in either lattice parameter at 0 mm corresponds to the hottest region of the sample, equal in temperature to the value given by the thermocouple. For a given axial position, 𝑖 mm, the difference in temperature with respect to the central temperature ( 𝑇
0
) can be calculated by dividing the difference between the central strain
( 𝜀
0
), and that from the position ( 𝜀 𝑖
), by the corresponding thermal expansion coefficient. The local temperature ( 𝑇 𝑖
) can then be calculated by subtracting this difference from the central temperature, as in Equation 1. The results of this calculation are presented in Figure 5, where the average experimental error is approximately ±7 °C. As a method of notation, 𝑇 𝑖
will be used to indicate the temperature at position 𝑖 in further discussions in this work.
𝑇 𝑖
= 𝑇
0
− 𝜀
0
− 𝜀 𝑖 𝛼
Equation 1
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The Precipitation of Hydrides in Zirconium Alloys
Figure 5. Axial temperature profiles for shelf temperatures implemented during cycle C0.
In this figure, each colour series corresponds to the thermal profile present during each of the shelf temperatures in C0, where 0 mm corresponds to the location of the target temperature set by the ETMT (and the location of the thermocouple), those in Figure 3. For the lowest shelf, T
0
= 40 °C, there appears to be little evidence of a thermal gradient, which would be expected from the minimal current required to raise the temperature from ambient and maintain it. As T
0
is increased to successive shelves, a gradient begins to develop between 0 mm and
10 mm, the magnitude of which becomes larger with increasing T
0
temperature.
Interestingly, while an increasingly large thermal gradient does develop with higher heating current, the temperature profile in the central region of the sample (specifically 0 mm to
4 mm) remains relatively flat. Indeed, it is not until the highest T
0
that T
4
begins to diverge significantly from the central temperature. This temperature homogeneity between 0 mm and
3-4 mm is important, as regions with a shallow temperature gradient will be those over which thermo-diffusion is at its lowest, a fact that will likely impact on hydrogen redistribution at these temperatures. Considering the magnitude of the thermal gradient alone, those points close to a displacement of 10 mm would be those where the flux of hydrogen is highest. At the lower shelf temperatures, however, the gradient steepness is minimal anywhere within the measured region, and so it seems likely that the Soret Effect will have little impact during dwells at these temperatures. It should be noted that the grips (which begin at ≈11 mm) are water-cooled, so
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The Precipitation of Hydrides in Zirconium Alloys the material within them will experience the lowest temperature seen within the sample. This will likely encourage the diffusion of hydrogen from the measurable area of the sample (0 mm to
10 mm) into that within the grips (11 mm and above), where it cannot be accounted for.
Assuming that the magnitude of the thermal gradient alone accounts for hydrogen flux neglects the effect of the magnitude of the temperature on the rate of hydrogen diffusion. Given the trends in Figure 5, the lower temperatures close to the grip will mean that the flux will, in fact, reach a maximum somewhere before 10 mm, after which it should diminish leading up to the grip, owing to reduced diffusivity. Sawatzky et al. proposed a model for hydrogen redistribution in Zircaloy-2 under a thermal gradient [33], designed to determine the concentration of hydrogen resolved spatially and temporally under the influence of a thermal gradient. This model, however, is unable to effectively describe the redistribution under the experimental conditions within this programme. Instead, the equation for atomic diffusion flux can be extracted to calculate the one dimensional thermo-diffusion flux [33] resulting solely from the measured thermal gradients in C0, Figure 6.
Figure 6. Axial atomic hydrogen diffusion flux under experimental thermal gradients.
In this figure, a number of important points are apparent, beginning with the magnitude of each series. With increasing T
0
, the flux of hydrogen increases, where all measured thermal gradients show a positive flux (i.e. flowing from 0 mm to 10 mm, where a negative flux would
127 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys indicate a reverse of this). The lower shelf temperatures, those up to 200 °C, show relatively little thermo-diffusion flux, appear flat when compared with those from gradients with higher T
0 temperatures. In each of the elevated shelf data sets, a clear parabolic shape can be seen, where the maximum value in each corresponds to point of interchange between the dominance of increasing thermo-diffusion and increasing ‘thermal braking’. As has been outlined previously, the increasing gradient with axial displacement would suggest a maximum flux at 10 mm. The decrease in temperature towards this point, however, has the effect of lowering diffusivity closer to this end of the axis, counteracting any increase from a steeper gradient in this region. This assessment does not, however, consider the impact of hydrogen concentration on the diffusion flux, and as hydrogen enrichment will likely occur close to the grips, a component of Fickian diffusion will be introduced there, promoting the flow of hydrogen away from enrichment. The impact of this will be considered later.
It is also important to remember that these predicted thermo-diffusion fluxes are only apparent when hydrogen exceeds the solubility limit at the cold end of the thermal gradient [16].
Where this is not the case and all hydrogen is dissolved into solution, the difference in the enthalpy of solution at the cold end of the gradient will result in only a small amount of local enrichment at equilibrium [16]. Because of this, it is important to consider the solubility profile seen axially at each of the T
0
temperatures considered. From the work published by McMinn et al. [36], the solubility for precipitation and dissolution can be calculated as a function of the thermal gradients present axially at the various shelf temperatures seen in C0, Figure 7. The solubility equations put forward by these authors are thought to be mostly independent of chemical composition or microstructure, making them suitable as predictors for the solubilities seen in this work [36]. Taking the initial ‘ideal’ hydrogen distribution (a uniform 430 ppm wt.
) as a reference, it can be seen that even when heated to the highest experimental temperature (the soak at 570 °C in C1) McMinn’s equations predict a region of the sample where hydrides do not dissolve. Similarly, when cooling from soak temperatures, these equations also predict that given the ideal distribution of hydrogen, there will always be hydrides in existence.
This is, however, a simplistic assessment, as regions of enrichment and depletion will develop as a function of time. As the region where hydrides are predicted to persist, even at high temperatures, is also that where enrichment is most likely to develop, it seems probable that hydrides will always remain there, and so thermo-diffusion will occur during all thermal operations, C1 to C8.
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The Precipitation of Hydrides in Zirconium Alloys
Figure 7. Hydrogen solubility profiles under axial thermal gradients, where legend denotes the measured temperature at the axial centre (T
0
).
A final assessment on diffusion that can be made, before the experimentally observed hydrogen redistribution can be discussed, is the distance it is possible for hydrogen to diffuse during each thermal cycle. Taking the coefficients for diffusivity from Kammenzind et al. for
Zircaloy-4 [7], it becomes possible to calculate the total diffusion length for hydrogen during each cycle, C1 to C8, using a d = √D ∙ t approximation, Figure 8. It should be noted that as C1 both goes to higher temperature than C2 and also spends longer at elevated temperatures, a greater amount of hydrogen diffusion is possible during that thermal operation. Here it can be seen that the diffusion length of each cycle is close to 1 mm, and cumulatively the diffusion length reaches
≈6.38 mm, which is a significant proportion of the axial width of the sample. Given these data, it is evident that hydrogen is highly mobile during each cycle and will be sensitive to any concentration or thermal gradients seen in the sample. It should be noted, however, that these values are ‘random walk’ distances, rather than linear path lengths, and so will tend to over-estimate unidirectional diffusion along the length of the sample.
With high mobility, the long soak times and the large thermal gradients seen during certain operations, it would be expected that a large amount of hydrogen would be lost from the central region, to be displaced towards the grips. This, however, may not be entirely the case, as it is thought that dislocations (like legacy structures from dissolved hydrides) and interstitial
129 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys oxygen can trap solute hydrogen [63], potentially impeding Fickian or Soret diffusion.
Furthermore, ab-initio calculations have shown that individual lattice vacancies are capable of trapping up to 9 atoms of hydrogen, while substitutional chromium (2 atoms) and nickel are also capable of trapping hydrogen [64,65].
Figure 8. Hydrogen diffusion distances during each experimental cycle.
3.2.
Hydrogen Redistribution
Each time the sample was cooled to the floor temperature of 40 °C during cycles C1 to
C8, diffraction patterns were recorded in sequence axially to map the distribution of hydrides.
From the known boundary conditions, the concentration of hydrogen relating to these patterns can then be calculated, in the way described previously. Figure 9 contains the results of these measurements, coloured to indicate how many thermal cycles the sample has been exposed to prior to each map.
The first, and most notable, feature of these profiles is that the significant enrichment predicted previously by the flux equations has occurred, spanning approximately 3 mm of the measured range, from 7 mm to 10 mm. Interestingly, the balancing depletion that would be expected to occur throughout the remainder of the material to supply the enriched zone does not seem to occur as expected from the profiles published by Sawatzky [33]. Instead, a depleted
‘bowl’ appears to form close to the enrichment, with a sharp ‘ledge’ separating it from the central
First Proposed Manuscript | 130
The Precipitation of Hydrides in Zirconium Alloys region at 5 mm. Comparing this position to the thermal gradients in Figure 5, however, suggests that the lack of depletion in the central region may be because an insufficient thermal gradient exists there to drive thermo-diffusion. That said, while the order of lines close to 10 mm is logical, that close to 0 mm is poor, and some series (the Pre-C1 profile, for example) diverge significantly from their temporal neighbours.
Figure 9. Raw axial hydrogen distributions measured at 40 °C after sequential thermal cycles.
This discrepancy highlights the closeness of these values to the experimental uncertainty in these measurements, where fluctuations in intensity from electrical noise in the detector and changes in the flux of the beam result in uncertainty in the data. Given that there is no hydrogen in solution at the temperature at which these measurements were made, it is not possible to substantiate them with measurements of matrix lattice chemical dilatation. However, diffraction patterns are recorded at 0 mm when temperatures are elevated to the soak portion of each cycle, where all hydrogen is dissolved. Here, the matrix lattice will be free of any mechanically induced strains [45], and the remaining strains will be primarily the product of thermal expansion and solute hydrogen [61].
Using the lattice distortion model published by Zanellato et al. in [46], Equation 2, it then becomes possible to quantify the amount of hydrogen that occupies solution at 0 mm shortly after each axial measurement is made. The values for hydrogen concentration calculated from
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The Precipitation of Hydrides in Zirconium Alloys
Equation 2 can be used to calibrate the axial profiles recorded at 40 °C, using their central point at 0 mm. The raw 40 °C, raw 500 °C/570 °C, and calibrated 40 °C central (0 mm) concentrations are presented in Figure 9. 𝜀̅ =
(1 − 𝐶 𝑛 𝑎𝑡
𝐻
𝑍𝑟
𝐶 𝑎𝑡
𝐻
)(2 + 𝐾)𝑣̅
0
∆𝑣
Equation 2
Where: 𝑛
𝑍𝑟
– The number of zirconium atoms per unit cell.
𝐶 𝑎𝑡
𝐻
– The dissolved molar hydrogen concentration.
𝐾 – The coefficient of anisotropy. 𝑣̅
0
– The initial cell volume.
∆𝑣 – The unit cell volume increase from interstitial deuterium 21 .
Figure 10. Axial centre (0 mm) hydrogen concentration evolution.
In this Figure, the raw 40 °C concentration points are both scattered and fail to follow any form of logical progression; the raw 500 °C points, however, follow what could be considered a
21 Substituted as an analogy of hydrogen.
First Proposed Manuscript | 132
The Precipitation of Hydrides in Zirconium Alloys more expected progression. In this series, the central region starts by showing essentially no depletion during C1 and C2 soaks, followed by some small amount of depletion occurring as cycles become warmer and thermal gradients increase (C3 to C6 soaks), increasing to significant depletion as thermal gradients are at their largest (C7 and C8 measurements). Temporally, the
40 °C intensity-based measurements are separated from the soak strain-based measurements by a shorter, but higher temperature soak on one side (typically ≈7 minutes of the 15 minute soak elapsed before strain evolution stabilised and the resulting value was recorded for hydrogen induced lattice dilatation measurements), and a longer but lower temperature dwell on the other.
Given this, it seems reasonable to assume that the corrected 40 °C points should lie at some intermediate point between successive 570 °C/500 °C points, chosen to be half-way in this work for simplicity.
Considering both the raw soak measurements and the calibrated 40 °C measurements, the sequence of depletion occurs such that the initial cycles have minimal impact on hydride loss from the central region. This seems to be owing to little thermal gradient existing in this region during the long dwells, but also possibly from the propensity for hydrogen to be trapped, preventing significant diffusion during the high temperature soaks. As cycles become warmer, some depletion does occur, although undulations in the measured hydrogen concentration exist.
Between the C6 soak and C7 soak, a significant increase in depletion is recorded, which will predominantly be the result of the increased magnitude of the thermal gradient during the dwells associated with these cycles. Another consideration to be made is the availability of interstitial sites and the impact this might have on diffusion, where Wipf et al. suggested that increasing temperatures might enable hydrogen to occupy octahedral interstices, in addition to the tetrahedral sites it normally inhabits [37]. This could potentially increase the number of diffusion pathways through the matrix, increasing the diffusivity of hydrogen through the sample at elevated temperatures, which is significant given the 500/570 °C soak in each cycle. From ab-initio modelling, the energy barrier for hydrogen transfer from tetrahedral to octahedral sites is, however, almost a factor of four higher than from tetrahedral to tetrahedral [65].
Further to this, the higher temperatures in these later dwells may increase vacancy diffusion, which will transport any trapped hydrogen [65]. Alternatively, elevated temperatures could also encourage some recovery of matrix defects that have been preventing hydrogen from diffusing. This could be supported by the observations of others [66,67] indicating a reduction in dislocation loop densities during hour long heat treatments at temperatures relevant to those involved in this experiment. While the experimental results from the work of Adamson et al. indicates a progressive decrease in loop density with operations at increasing temperature, modelling by Ribis et al. shows a sharp step change in the effect of operations above 400 °C
133 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
[66,67]. Similarly, Pande et al. saw the recovery of dislocations arising from cold work between room temperature and 450 °C [68].
While matrix defects from cold work and irradiation damage are not present in this material (being non-irradiated and recrystallised), the formation of dislocation loops surrounding hydrides has been observed [69,70]. If matrix damage from those other sources has been known to recover under the aforementioned conditions, then it seems plausible that hydride-related dislocation structures may also recovering during the present experiment.
Figure 11. Axial hydrogen distributions measured at 40 °C after sequential thermal cycles, calibrated by central measurements at soak temperatures.
Using the method for calibration based on the concentration at 0 mm, it becomes possible to offset the axial profiles recorded at 40 °C, to give those presented in Figure 11. These calibrated profiles follow a much more logical sequence close to 0 mm, although the ordering at
10 mm has degraded from that present in the un-calibrated data, Figure 9. Given the error in measurement, however, it seems probable that the deviation from profile to profile in the region of enrichment may be minimal, and that its magnitude and gradient remains fairly-constant once it has been established.
As time through the experimental programme proceeds, a region of enrichment begins to develop at 10 mm during C1, initially spanning only 1 mm, and with minimal impact on the
First Proposed Manuscript | 134
The Precipitation of Hydrides in Zirconium Alloys concentration from 0 mm to 9 mm. C2 to C5 see the establishment of far greater enrichment, in terms of the magnitude and span of the region, as all material from approximately 7.4 mm to
10 mm is enriched. Preceding this region is approximately 2 mm of material that shows marked hydrogen depletion, taking the form of a parabola. Closer to the centre of the material, where thermal gradients are shallower, little depletion is seen, although that which does manifest appears to occur uniformly from 0 mm to 5 mm. Cycles C6 to C8 are host to significant hydrogen depletion throughout the recorded profiles, most notable between 0 mm and 5 mm. In C6, this occurs as a uniform reduction in concentration across this region, but by C7 and C8 a concentration gradient develops close to the axial centre, between 0 mm and 5 mm. By the end of C8, 0 mm to 4 mm has levelled out, with an upturn between 4 mm and 5 mm, where a local maximum in concentration occurs. Beyond this, the parabola of depletion that developed initially has expanded a small amount into region that was previously enriched, up to approximately
7.9 mm.
Given the amount of hydrogen that is lost between 0 mm and 8 mm during C6, C7 and
C8, it would be expected that a similar amount of enrichment would occur close to 10 mm.
Instead, the enriched region close to 10 mm actually shows marginal depletion when compared with the post C5 profile, likely signifying the continued flux of hydrogen into the grips at 11 mm and above, although this may be the product of uncertainty. Interestingly, the evolution of depletion and enrichment seen in this sample does not follow that presented by Sawatzky et al. for Zircaloy-2 [33], and instead an unexpected local maximum appears at 5 mm. Similarly, as the region of enrichment develops and the area in which hydrogen solubility is exceeded expands
(moving in the direction of 10 mm to 0 mm), Sawatzky predicts a sharp interface between enrichment and depletion. The profile seen experimentally in this work is tapered up to maximum enrichment, although it is expected that hydrogen concentration will tail off after a peak at some position greater than 11 mm. To understand the development of the profile seen here, including the unexpected deviation at 5 mm, the equation for diffusion flux factoring stress-induced diffusion, the Soret Effect and Fickian Diffusion, published by Kammenzind et al. [32] can be employed, Equation 3.
135 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
𝐽 = −𝐷 ∙ 𝛻𝐶 − 𝐷 ∙ (
𝑄 ∗ ∙ 𝐶
𝑅 ∙ 𝑇 2
) ∙ 𝛻𝑇 + 𝐷 ∙ (
𝐶 ∙ 𝑉
𝑅 ∙ 𝑇
) ∙ 𝛻𝜎
𝐻
Where:
Equation 3
R – The universal gas constant,
D
C
– The diffusivity of hydrogen,
– The concentration of hydrogen
∇C – The hydrogen concentration gradient,
Q ∗
– The heat of transport,
T
– The temperature,
∇T
– The temperature gradient,
V – The partial molar volume of solute hydrogen.
∇σ
H
– The hydrostatic stress gradient.
As the ETMT was programmed to maintain zero load within the sample, the linear separation of the grips was dynamically adjusted to ensure no stress developed within the sample from thermal expansion within a rigid mounting. That being said, given the texture of the sheet and the anisotropic thermal expansion of single crystal zirconium, inter-granular stresses will decrease during heating [71], which may possibly influence diffusion. With the associated thermal gradient, there will also be a gradient in the inter-granular stresses from region to region, which may enhance diffusion flux. It seems possible, however, that because stresses must be balanced, the development of inter-granular stresses will simply change local distributions, rather than causing long-range redistribution of hydrogen. Given the lack of availability of an equation describing the effect of temperature on inter-granular stresses, the final term in Equation 3 is treated as zero in this work. Furthermore, the term for thermo-diffusion in the equation from
Kammenzind et al. differs from that published by Sawatzky, as Kammenzind includes a term describing concentration, and Sawatzky does not. As a result, the thermo-diffusion flux from this equation will differ from that in Figure 6, which considers solely the thermal gradient. From this equation, the flux profile can then be predicted for each soak and at 40 °C. To illustrate this, two thermal gradients are chosen for representation, the 500 °C soak during C8 and the 40 °C point prior to this soak and post C7, Figure 12 and Figure 13, respectively.
In these figures, a positive flux indicates flow from 0 mm towards 10 mm, while a negative flux indicates the opposite; also note the change in magnitude between these two, where values in Figure 12 are x 10 -5 and those in Figure 13 are x 10 -8 . This discrepancy in the magnitude of diffusion is the product of the absolute temperature of the sample (as opposed to the magnitude of the gradient), where high temperatures lead to a higher diffusivity, and vice versa.
First Proposed Manuscript | 136
The Precipitation of Hydrides in Zirconium Alloys
Data in the lower subplot of each figure describe the temperature and concentration profiles supplied into Equation 3, which produce the flux in the upper subplot. In order to improve trends, the density of data points has been increased. Given the simple inverse parabolic temperature profile, a second order polynomial was modelled to each. The concentration profile, being considerably more complicated, could not be treated in the same way, and so a “shapepreserving piecewise cubic interpolant” was applied using Matlab 2014b, the result of which is present in both figures. Using this method of interpolation has the advantage of providing a smooth profile, which still passes through the known points from the actual measured profile, indicated with circles in each figure. This smooth cubic interpolation leads to curves in the flux subplot, where a linear interpolation would produce a series of flat regions.
Figure 12. Atomic diffusion flux profile during cycle C8 soak at 500 °C.
137 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
Figure 13. Atomic diffusion flux profile post cycle C7 at 40 °C.
Firstly, the high temperature gradient, Figure 12, shows significant flux of hydrogen from the centre of the sample (0 mm) towards the water-cooled grips, as expected. This is due to the large thermal gradients seen axially and the high diffusivity of hydrogen at the range of temperatures seen. From 0 mm to 3.5 mm, the flux begins close to zero, where the thermal gradient is least, and overall the flux gradient in this region is positive, although a dip into negative
(denoting right-to-left flow) occurs, owing to a small but sudden increase in concentration gradient between the 0.5 mm and 1 mm points. Here, the positive gradient in concentration creates a negative flux, but the negative gradient in temperature (generating a positive flux) around these points is insufficient to counteract this in any significant way. Between 3.5 mm and
6 mm a period of undulation occurs, where changes in the concentration gradient from positive to negative (owing to local maxima) cause fluctuations in local flux. Unlike previously, the thermal gradient is sufficiently large at these positions that even with the steeper concentration upturn between 4.5 mm and 5 mm, the flux remains positive (albeit arrested somewhat).
From 6 mm to 10 mm, the magnitude of flux remains relatively constant, when compared with the significant changes that occur in the concentration profile. Indeed, the only notable impacts on flux in this region from concentration are the two dips brought about by sudden, steep changes in gradient in the hydrogen profile. Despite the sharp increase in concentration gradient between 7.5 mm and 10 mm, where enrichment is most clear, the magnitude of flux is
First Proposed Manuscript | 138
The Precipitation of Hydrides in Zirconium Alloys approximately equal to the value found at 6 mm, where depletion is comparatively uniform and the concentration gradient is low. This arises from the balancing effect of the thermal gradient, where increasing steepness in concentration is matched by increasing steepness in the temperature profile, producing a relatively uniform flux profile. With regard to the local maximum seen at 5 mm, it seems possible that the development of a positive gradient in concentration acts as a breaking point; seen as a local minimum in flux just before 5 mm. This could allow hydrogen to build up here, before flowing into the larger depleted bowl that exists to the right of this point.
At lower temperatures, where thermo-diffusion is lower, this local minimum in flux approaches zero (and is negative in some cases), counteracting the redistribution from centre to edge.
Considering the overall flux pattern, it would seem that while the soaks will cause significant flow of hydrogen, the loss from the centre of the sample would not be as great as expected. This seems likely to be the result of the low thermal gradient centrally, and the balancing effect of local concentration gradients that develop with time.
When cooled to room temperature, however, a different story can be told, Figure 13.
Here, the same concentration profile as at high temperature is assumed, which could be analogous to the axial profile that would be found post C7, for example. As with the previous data, the same undulations in flux occur at the same positions, owing to changes in local concentration gradients, and it is only the overall trend that diverges from the previous figure.
Instead of an overall positive flux (from left-to-right), cooling the sample to 40 °C has the effect of inducing a negative flux of hydrogen, where flow from regions of significant enrichment towards those of depletion is seen. This is characteristic of the thermally-induced hydrogen profile attempting to ‘self-right’, and reach the uniform equilibrium distribution that would be present in the absence of any thermal or stress gradients. This negative flow, however, is significantly lower than that seen at elevated temperatures, and given the short times at 40 °C seen during the experimental programme, this contraflow will only serve to slow the process of central depletion with successive cycles, rather than reverse it. It should be noted, however, that when the temperature is reduced to 40 °C the solubility is reduced to parts per billion, and so the vast majority of hydrogen will be bound within these precipitates, irrespective of Soret or Fickian drivers for diffusion.
As a final point to make, this analysis again neglects the impact of traps on the flow of hydrogen, where, at the elevated temperatures seen in Figure 12, the dislocation structures left behind by dissolved hydrides act as energetically favourable sites for hydrogen to occupy, as will certain substitutional atomic species. This means that some fraction of the hydrogen that enters solution when hydrides dissolve will be unable to diffuse out of the local matrix without a significant driving force, and so some amount of the hydrogen population should be considered immobile throughout the experiment. Similarly, where temperatures are elevated (producing a
139 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys population of mobile solute hydrogen) but hydrides still exist in some diminished capacity, the hydrides themselves can act as sinks for hydrogen. In this case, regions of depletion form around these precipitates, which develop from localised stress-induced (from the misfit) and Fickian
(from the local concentration profile leading to the precipitate interface) diffusion. The concentration profile intrinsic to these regions could then cause hydrogen in the process of long-range Soret or Fickian diffusion to be drawn towards these precipitates, where it could be absorbed, shortening the distance these atoms are capable of travelling before being immobilised.
Given the high diffusivity of hydrogen at reactor relevant temperatures, the development of thermal gradients can cause significant redistribution of hydrogen, through the Soret Effect.
This mechanism for diffusion will often be counteracted by Fickian diffusion, where regions of enrichment and depletion develop, but at elevated temperatures the contribution of Fickian diffusion to flux is second order to the Soret Effect. Finally, throughout this programme, an observation of no more than 30 ppm wt.
of depletion was measured at 0 mm, underpinning observations made in other works that have been part of this experimental programme [44,45].
4.
Conclusion
Synchrotron X-ray diffraction was used successfully to evaluate the redistribution of hydrogen in Zircaloy-4 at a range of reactor relevant temperatures, where the Joule heating used to attain these temperatures induced an axial thermal gradient, known to induce thermodiffusion through the Soret Effect.
Prior to measuring redistribution, a non-hydrogen charged sample was used to measure the thermal expansion coefficient of the material, where values of 𝛼 𝑎
= 6.04 × 10 −6 𝐾 −1 and 𝛼 𝑐
= 8.97 × 10 −6 𝐾 −1
were calculated from thermal strain evolution. These coefficients were then used in conjunction with measurements of lattice parameters at a series of axial points along the length of the sample to calculate a temperature profile, relative to that at the centre of the material. The profiles of a number of gradients were recorded for temperatures relevant to the thermal transients seen by the hydrided sample.
Using these profiles, purely thermal diffusion flux was assessed, where the gradients with a peak temperature of 570 °C, 500 °C and 400 °C showed a markedly higher flux than for gradients with 300 °C, 200 °C, 100 °C and 40 °C maximums. The peak in diffusion flux was not found where the thermal gradient was steepest, as the lower temperature in this region reduced the diffusivity of hydrogen, shifting peak flux by an amount linked to the temperature at the cold end of the gradient. Diffusion distance calculations demonstrated that solute hydrogen is significantly mobile, thus making the distribution profile highly sensitive to thermal and concentration gradients.
First Proposed Manuscript | 140
The Precipitation of Hydrides in Zirconium Alloys
Synchrotron X-ray diffraction was able to record hydrogen distribution profiles axially at
40 °C. In addition, the quantity of hydrogen in solution at the axial centre of the sample was measured during the dissolution soak seen in each sample, through the evolution of solute hydrogen induced lattice dilatation. These latter measurements were used to calibrate the recorded 40 °C profiles, and the results were seen to follow an expected logical progression, whereby the majority of diffusion occurred during the highest temperature cycles, and a total depletion at the axial centre reached approximately 30 ppm wt.
. In addition, a region of heavy hydrogen enrichment was observed close to the cold end of the gradient, preceded by a region of heavy depletion. The lower than expected depletion at the axial centre of the sample was thought to be the result of Fickian counter-flow and hydrogen trapping by matrix defects and substitutional species.
From these concentration profiles, in conjunction with the known thermal gradients, an assessment of the flux profile seen in the sample was made. At elevated temperatures, the Soret
Effect dominated, and hydrogen diffused towards the cold end of the sample; although regions of higher and lower flux existed where concentration gradients emphasised/impeded hydrogen flow. These regions of impedance were thought to account for regions of localised enrichment seen to develop consistently with successive cycles. At 40 °C, where a minimal thermal gradient existed, a low flow of hydrogen was seen, driving hydrogen away from enriched regions and back towards the depleted axial centre of the sample.
Overall, it would appear that the observed change in concentration profile, as a function of the established thermal gradients and cyclic thermal operations, was not found to be as significant as might have been expected from the literature. It seems possible that the complex profile that develops may result in competing thermally- and chemically-driven hydrogen fluxes, which could also combine with trapping obstacles to hinder the migration of hydrogen along the established thermal gradients, producing the lower rate of redistribution seen experimentally.
5.
Acknowledgements
Thanks are given to the Institut de Radioprotection et de Sûreté Nucléaire for providing samples and experimental programme funding, as well as the Engineering and Physical Sciences
Research Council and Rolls-Royce for project funding and case awards. The University of
Manchester and the Materials Performance Centre are acknowledged for their infrastructural support. From the University of Malmö, J. Blomqvist and T. Maimitiyili are thanked for two-way exchanges of synchrotron analytical technique best practices. Final thanks are also given to
S.R. Ortner of the National Nuclear Laboratory and S.C. Connolly of The University of Oxford for technical and editorial support.
141 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
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4.3.
Annex – Phase Field Modelling
4.3.1.
Background
The presented manuscript discusses at length the effect that temperature and concentration have on the diffusion of hydrogen on a macroscopic scale. Further to this work, it is also possible to evaluate the effect of Fickian diffusion and stress induced diffusion on the redistribution of hydrogen on a mesoscopic scale using Phase Field Modelling (PFM).
The phase field methodology for representing microstructure evolution is a powerful tool, as the partial differential equations on which it is based are derived from general kinetic and thermodynamic principles [210,211]. Through the introduction of experimental or theoretical properties for the material being simulated, complex microstructural morphologies can develop, thanks in part to the diffuse nature of interfaces present in the system [211].
In a phase field model, the input parameters that describe physical properties of a phase assemblage are conserved throughout the system, whereas field variables used to describe the state of regions within the model are not [210]. In practice, this allows variables representing phase, concentration, or stress state to vary freely throughout the model as a continuous function of time and space [210,211]. When compared with models that feature a sharp interface, the field variables representing state in a PFM will be of a similar value, but the region of interface between two discrete sectors will be smooth and continuous as opposed to changing instantaneously [211]. The equations used to describe the system, however, are not designed to represent the behaviour seen at an atomic scale, limiting the phase field methodology to meso- and macro-scale simulations [211].
The phase field model utilised in this work was originally published in [210,212], considering a γ-hydride in zirconium system; it was then updated in [213] with a description of the chemical free energy Landau polynomial for that hydride phase, allowing fully quantitative simulations to be performed. More recently, the system was extended to both describe δ-hydride and also allow dynamic temperatures to be implemented in space and time [214]. For the purpose of this work, the model is used to simulate δ-hydrides in a single crystal of α-zirconium, using variables relating to each of these two phases. For simplicity, all simulations consider a binary alloy of pure zirconium and 430 ppm wt.
of hydrogen. While the developed model could be extended to function in three-dimensional space, for computational efficiency all results presented herein will be calculated on a two-dimensional plane, vertically bisecting the precipitate and observing the matrix unit cell in the
[11̅00] 𝛼
direction, with the
[0002] 𝛼
direction as vertical [210]. This observation direction is reflected in rotations of the tensors used to describe
the directionality of the system. Table 11 provides a list of variables employed in the simulations
presented herein, where temperature dependent variables were calculated for a system
First Proposed Manuscript | 146
The Precipitation of Hydrides in Zirconium Alloys temperature of 313 K. This value was chosen as it is the baseline temperature seen during the synchrotron X-ray diffraction experiment, where the driving force for precipitation is large, and is also similar to the temperature used in [213].
The mechanical interaction between the matrix and hydrides within the model are all based on literature sourced mechanical properties, and so values generated are thought to be representative of the real system. That being said, plastic evolution is disabled in the following simulations to allow a greater understanding to be developed of the elastic stresses that are generated during the early stages of precipitation, before any plastic relaxation occurs.
147 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
Table 11. Phase field modelling parameters.
(
Variable
Temperature ( 𝑇 )
Matrix hydrogen content (
𝐶
0
)
Matrix equilibrium hydrogen concentration (
𝐶 𝛼
)
Hydride equilibrium hydrogen concentration ( 𝐶 𝛽
)
Interfacial energy 22
Interfacial width ( 𝑙 )
( 𝛾 𝑠
)
40 °C (≈313 K)
0.0377597
9.67 x 10
0.6226
2 J m -2
10 nm at.
-6
ƒ at.
at.
ƒ
Value
ƒ (≈430 ppm
Interfacial energy per unit width
( 𝛾 𝑠
⁄ 𝑙 )
Molar volume of the disordered phase ( 𝑉 𝑎
)
Diffusion coefficient of hydrogen in zirconium (
𝐷
𝐻
Yield strength (
) 𝜎 𝑦
)
Poisson’s Ratio ( 𝜈 )
2 x 10
535 MPa
0.365
8
1.67 m
J m -3
3 mol
8.45 x 10 -14
-1
m 2 s -1
Modification factor on strain energy 1 (No modification) wt.
)
Interstitial deuterium induced
( matrix microstrain 23 𝜀
[11̅00]
= 𝜀
[112̅0]
)
Interstitial deuterium induced
𝜀
[0002]
)
Matrix-hydride interfacial strains
( 𝜀
[112̅0]
)
Matrix-hydride interfacial strains
( 𝜀
[11̅00]
)
Matrix-hydride interfacial strains
( 𝜀
[0002]
)
3.29 %
5.42 %
3.1 %
0.5 %
5.5 %
Matrix zirconium elastic constants
𝐶 𝑖𝑗𝑘𝑙
)
[
142.63
65.3
73.19
65.3
164.3
65.3
73.19
65.3
142.63
0
0
0
0
0
0
0
0
0
All in GPa.
0
0
0
31.75
0
0
0
0
0
0
34.705
0
0
0
0
0
0
31.75]
–
–
Source
JMatPro
JMatPro
[213]
[213]
[213]
[213]
[213]
[215]
[216]
–
[209]
[209]
[86]
[86]
[86]
[217 ]
22 This value is high, as the interface width must be close to the size of a pixel, and the ratio of 𝛾 𝑠
⁄ 𝑙 is conserved to a value of 2 x 10 8 J m -3 , which is consistent with [210,212–214].
23 Value for hydrogen substituted with that of deuterium, owing to the unavailability of a value for hydrogen. This is consistent with previous work using the same model [210,212–214].
First Proposed Manuscript | 148
The Precipitation of Hydrides in Zirconium Alloys
4.3.2.
Results
From phase field simulations run within Matlab, a number of two dimensional arrays are produced, describing the physical state of the system after a given period of time. In the presented simulations, a mesh was implemented that measured 128 pixels x 128 pixels, with isotropic pixel dimensions of 10 nm, producing a simulated space of 1.28
m in the X and Y
the mesh, representing a 10 nm diameter nucleus. This hydride was then allowed to precipitate up until its length was close to 200 nm, after which, the simulation was automatically terminated;
in the case of the hydride in Figure 46, this took approximately 0.01 seconds (or 1,000 time steps
where Δt = 1 x 10 -5 s).
(a) (b)
(c) (d)
Figure 46. Single hydride phase field model simulation showing (a) XX planar stress, (b) YY planar stress, (c) XY shear stress, and (d) the Von Mises stress, for a single hydride measuring 190 nm after 0.01 seconds of precipitation.
The phase field variable, η, describes the phase state of material at any point in the system, where η = 0 represents α, while η = 1 represents δ. To isolate the matrix from the hydride,
149 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
become established in the matrix that surrounds the precipitating hydride, when no plastic deformation is allowed to take place in either phase. The fourth subplot contains the von Mises stress calculated from these three planar figures. The maximum compressive and tensile stresses
present within each of these subplots are given in Table 12, corresponding to the regions of
deepest blue (compressive) or red (tensile).
Table 12. Maximum compressive and tensile stresses in the matrix.
Stress Component
XX Planar
YY Planar
XY Shear
Von Mises
1,134
2,801
2,229
Maximum Matrix Stress
Compressive (MPa)
5,907
Tensile (MPa)
841
4,576
2,229
From these values, which are far in excess of the yield stress of the matrix (535 MPa for non-irradiated Zircaloy-4 [215]), it is clearly evident that some degree of plastic deformation must occur within the matrix, prior to the hydride reaching any significant size. From the von Mises stress map, the high combined stress acts at the tips of the precipitating hydride, where the majority of growth occurs laterally, thus being the position where the majority of deformation must occur. These values in themselves are not directly useful, as without plastic deformation they are not descriptive of the true system. Instead, an examination of hydrogen distribution in the matrix may provide some potentially interesting insight into why hydrides are observed to form in strings [99].
First Proposed Manuscript | 150
The Precipitation of Hydrides in Zirconium Alloys
Figure 47. Hydrogen concentration relative to the initial uniform hydrogen content.
Figure 47 contains a map of hydrogen concentration in the system, relative to the initial
uniform matrix hydrogen concentration of 430 ppm wt.
, where the concentration from within the hydride has been set to zero for clarity. As would be expected, a large ‘halo’ of depletion is established around the hydride, where hydrogen has been drawn out of the surrounding matrix to feed the precipitating hydride. In those regions just outside the hydride and immediately adjoining the flat surface of the top and bottom of the precipitate, the concentration is close to zero, where hydrogen has jumped across the precipitate boundary, into the hydride. The relative concentration gradient is such that it changes smoothly from approximately -430 ppm wt.
at the interface to the value of -50 ppm wt.
found at the edge of the dark blue halo around the hydride in
Figure 47. From the edge of the halo, the depletion extends out in the four compass-point
directions, tailing away until the values come close to convergence with the bulk hydrogen content of the material, a relative concentration value of 0 in the above figure (describing an actual content of 430 ppm wt.
).
Immediately adjoining the tips of this precipitate, regions of considerable enrichment exist within the matrix, where hydrogen is accumulating in regions that are about to become hydride. There, the phase field variable for these points is in the process of changing towards unity, where the diffuse boundary is progressing outwards. More significantly, further regions of enrichment extend out diagonally from the edge of the depletion halo, where the point of greatest enrichment in these zones is closest to the enrichment/depletion border. A maximum concentration of ≈13.2 ppm wt.
is simulated in each of these points, where values tail off with increasing distance from the precipitate, towards the bulk matrix value.
To understand better the reason for the existence of these enriched areas, the planar
stress plots presented in Figure 46 must be considered. In work by Kammenzind et al. [115], it is
stated that under applied and thermal cycling, hydrogen will diffuse away from regions of
151 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys hydrostatic compression and towards regions of hydrostatic tension. In the absence of thermal cycling, no observable migration was seen in that work, and so it was suggested that in the absence of cycling temperatures, any effect of stress on the chemical potential of solute hydrogen
or the postulated change in solvus is small. From those planar stress subplots in Figure 46, it
would indeed appear that those regions outside the central halo experiencing a degree of depletion are also those in which some amount of compression is experienced in one of the two planes considered. It is important to note, however, that although observations in the literature state that a hydrostatic stress is required for hydrogen redistribution, the presented simulation appears to show redistribution away from regions of uniaxial stress. 𝜎
𝐻𝑦𝑑𝑟𝑜𝑠𝑡𝑎𝑡𝑖𝑐
= 𝜎
𝑋𝑋
+ 𝜎
𝑌𝑌
3
+ 𝜎
𝑍𝑍 Equation 16
Figure 48. Calculated hydrostatic stress map.
From a hydrostatic stress map, Figure 48, calculated using Equation 16 and remembering
that no ZZ component is considered, it would appear that the overriding stress vertically above and below the precipitate is compressive, explaining the depletion seen there. Horizontally left and right of the precipitate, however, the overriding stress is tensile, suggesting that the region should experience enrichment, which is not the case. The cause of depletion in this area remains unclear, but it is possible the region of very high hydrostatic stress at the tip of the hydride may induce a gradient that is sufficiently large as to deplete the matrix horizontally to either side. .
With regard to the diagonal regions of enrichment, these occur at the areas within both planar stress maps where interchange between tension and compression occurs, thus also being where
First Proposed Manuscript | 152
The Precipitation of Hydrides in Zirconium Alloys stress magnitudes are lower, compared to the compass point directions. When considering the shear stress plots, the correlation between the maximums in enrichment and areas of heightened shear, suggests that this stress component may interact with the regions of diminished planar stresses in some way that makes the accommodation of solute hydrogen favourable in those areas. As for why the previously mentioned hydrostatic tensile stress concentration may not deplete these diagonals, the slope of the stress gradient in these directions appears shallower than in the compass-point directions, which may allow enrichment to develop diagonally from the precipitate.
This simulated redistribution is thus thought to be primarily the result of stress-induced movement of hydrogen (although a contribution of Fickian diffusion will likely also be involved).
Despite the unrealistically large stresses required to induce the small amount of enrichment that is observed, it seems possible that with the introduction of thermal cycling, the degree of redistribution seen may well increase [115]. In the real system, where the stresses generated by a precipitate will be partially relieved by plastic deformation in the matrix, producing a lower driving force for stress-induced diffusion, it may well be the case that the remaining stresses are not sufficient to cause significant enrichment on their own. Instead, the addition of thermal transients and cycles to the system may make up for this reduction in stress, creating favourable locations for sympathetic nuclei to form where enrichment occurs, which is thought to lead to
the formation of strings of hydrides, as in Figure 49 – (a). Furthermore, an elastic
deformation-only simulation has the additional benefit of indicating the locations where yield initiates and greatest plastic deformation will occur, thus being where the greatest density of dislocations will likely be. These damage structures, being known to trap hydrogen [97], could then become an additional cause for hydrogen accumulation in matrix material close to preexisting hydrides, thus exacerbating the mechanism of sympathetic nucleation.
153 | First Proposed Manuscript
(a) (b)
The Precipitation of Hydrides in Zirconium Alloys
≈2.5
m
Figure 49. (a) Experimentally observed hydride strings/stacks in Zircaloy-4 [218], and (b) hydride precipitation simulations after 0.01 seconds, demonstrating the result of potential sympathetic nucleation.
The result of a simulation with noise-generated nuclei is given in Figure 49 – (b), where
the phase field variable, η, is used to represent areas of hydride. In this simulation, random fluctuations in concentration with each time step over the first 0.003 seconds led to the formation of nuclei as a function of stress and concentration induced hydrogen migration. It can be seen that there are a number of examples of hydrides that stack or adjoin in a way similar to those
observed optically in Figure 49 – (a). One additional consideration to be made in the case of this
simulation is that a population of undeveloped nuclei exist, having seeded during the early noise generation stage, and then failing to coarsen unlike other larger precipitates. It seems probable that this will be linked to the way in which the stress fields of neighbouring nuclei interact. Again,
from the hydrostatic stresses in Figure 48, it can be seen that the stresses above/below the
precipitate are predominantly compressive, while the stresses extending laterally from the hydride are more tensile. This may lead to nuclei that are positioned in such a way that they are close to being aligned vertically may retard the growth of one another, through increasing the compressive stresses they are exposed to. Similarly, side-by-side nuclei may induce tensile stresses in one another and their surrounding matrix regions that allow the precipitates to coarsen more easily. This does not, however, explain why some examples of horizontally neighbouring nuclei have failed to grow, demonstrating the potential complexity of the
interactions occurring in Figure 49 – (b).
As an final point, some authors suggest a stress effect on the position of the solvus
[136,219], which is not considered here, and so there may be some additional implications
First Proposed Manuscript | 154
The Precipitation of Hydrides in Zirconium Alloys relating to the stress fields surrounding hydrides that influence sympathetic nucleation sites.
Finally, this simulation only considers a two-dimensional plane, and so it is thought that further developing the model to simulate three-dimensional structures may give further insight into the redistribution of hydrogen and the implications it might have on sympathetic nucleation of hydrides.
155 | First Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
5.
Second Proposed Manuscript – Kinetics
5.1.
Foreword
This second text studies the kinetics of hydride precipitation during the outlined synchrotron X-ray diffraction campaign, and seeks to support some of the experimental observations with a model of the nucleation process. This manuscript has been published in the
Journal of Nuclear Materials, with the DOI 10.1016/j.jnucmat.2015.04.025. Some minor modifications/additions are included in the version presented in this thesis. A description of the contribution of the listed authors follows.
As with the previous text, the experiment was designed by O. Zanellato, as the principal investigator, with input from M. Preuss, F. Ribeiro and J. Andrieux. The experiment was performed at the ESRF by M. S. Blackmur, O. Zanellato and J. Andrieux, and the post-experiment analysis of data was performed by M. S. Blackmur, using training given by R. Cernik and O. Zanellato.
The fundamental equation describing the nucleation model, Equation 1, was provided by
J. Robson, and the development of the model software itself, as well as parameterisation of the modelled system, was performed by M. S. Blackmur. Additionally, S.-Q. Shi provided support with the process of parameterising the system. Again, J. Robson and M. Preuss provided primary technical and editorial support for this article, and all other named authors also reviewed the article prior to its submission to the literature.
The TEM micrographs provided in the annex of this document (section 5.3) were imaged
with the assistance of D. Tsivoulas, after sample preparation supported by A. J. Harte.
Second Proposed Manuscript | 156
The Precipitation of Hydrides in Zirconium Alloys
5.2.
Manuscript
Zirconium Hydride Precipitation Kinetics in Zircaloy-4 Observed with
Synchrotron X-Ray Diffraction
M.S. Blackmur a , J.D. Robson a , M. Preuss a , O. Zanellato b , R.J. Cernik a , S.-Q. Shi c , F. Ribeiro d ,
J. Andrieux e a Materials Performance Centre, School of Materials, The University of Manchester, Manchester,
M1 7HS, United Kingdom b PIMM, Ensam - Cnam - CNRS, 151 Boulevard de l'Hôpital, 75013 Paris, France c Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom,
Kowloon, Hong Kong, China d Institut de Radioprotection et de Sûreté Nucléaire, CEN Cadarache, 13115 St. Paul Les Durance,
France e Beamline ID15, European Synchrotron Radiation Facility, Grenoble, France
Keywords
Synchrotron X-ray Diffraction, Hydrides, Zirconium alloys, Kinetics, Precipitation,
Nucleation, Diffusion Length
Abstract
High-energy synchrotron X-ray diffraction was used to investigate the isothermal precipitation of δ-hydride platelets in Zircaloy-4 at a range of temperatures relevant to reactor conditions, during both normal operation and thermal transients. From an examination of the rate kinetics of the precipitation process, precipitation slows with increasing temperature above
200 °C, due to a reduction in the thermodynamic driving force. A model for nucleation rate as a function of temperature was developed, to interpret the precipitation rates seen experimentally.
While the strain energy associated with the misfit between hydrides and the matrix makes a significant contribution to the energy barrier for nucleation, a larger contribution arises from the interfacial energy. Diffusion distance calculations show that hydrogen is highly mobile in the considered thermal range and on the scale of inter-hydride spacing and it is not expected to be significantly rate limiting on the precipitation process that takes place under reactor operating conditions.
157 | Second Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
1.
Introduction
1.1.
Zirconium & Zirconium Alloys
Zirconium alloys have been widely adopted as cladding material for fuel rods in Western light water reactors (LWRs) ever since nuclear reactor technology was first conceived at the end of the 1940s [1]. The function of this cladding is to act as a structural component, containing fuel pellets, holding them in place within a fuel assembly and allowing the desired turbulent flow of coolant between rods, while conducting heat energy from the fuel into the fluid [2]. Additionally, it also acts as a buffer between the fuel pellets and the encompassing reactor environment by containing fission products that escape the fuel, whilst preventing degradation of the fuel from exposure to the coolant medium [2–4]. This means that the structural stability of these components is of paramount importance, as it is linked intrinsically to the safety, efficiency and operability of the fuel assembly [2]. The choice of available materials is limited, as fuel assembly components are expected to last years under typical operating conditions – where temperatures range from 280 °C to 400 °C and coolant pressures are in excess of 15 MPa – as well as performing adequately during potential accident scenarios, where conditions are significantly more harsh
[2,5,6].
The selection of zirconium alloys as cladding stems from the advantageous mechanical properties, good corrosion behaviour and, critically, the low neutron absorption cross-section that they demonstrate [1,4,7]. However, the common commercially deployed alloys of zirconium display a high affinity for both oxygen and hydrogen [8,9]. When exposed to the light water coolant, some of the hydrogen by-product of the oxidation reaction is absorbed into the cladding, though the mechanism for this ingress through the oxide is still debated [10]. While the solubility limit of oxygen in
-zirconium is as high as 28.5 at.
% under typical light water reactor operating conditions [11], the hydrogen solubility in the same environment is at most 3 at.
% [12]. Once the local hydrogen concentration exceeds the terminal solid solubility of the alloy for the local temperature, any excess will then precipitate into hydride phase. Given the general tendency for hydrogen to diffuse down thermal and concentration gradients, and up hydrostatic stress gradients, macroscopic hydrogen distribution can often be non-uniform within components [13].
This is further compounded in fuel cladding, where the coolant removes heat from the outer surface of the material, while the fuel itself heats the inner surface. Together, these mechanisms lead to dramatic differences in concentration and solubility between different regions, leading to phenomena like the formation of hydride rims [14].
1.2.
Zirconium Hydrides
Since the early days of nuclear technology, researchers have investigated the impact of hydrogen on zirconium alloys, as well as various aspects of the formation and properties of
Second Proposed Manuscript | 158
The Precipitation of Hydrides in Zirconium Alloys hydrides [15–21]. When precipitating, hydrides take the morphology of either needles or platelets, based on the cooling rate and the availability of hydrogen [21]. These variables influence which of the hydride phases precipitate, where the most commonly observed form is the nonstoichiometric face-centred cubic delta (δ) phase [22]. Less commonly, the stable/metastable
(based on temperature and interpretation [23]) gamma (γ) or stable epsilon (ε) hydrides, both taking a face centred tetragonal crystal structure, may also precipitate [23].
The physical shape that each of these different phases take, on a fine scale and in isolation, is primarily ascribed to the anisotropic directionality of the stress-free transformation strains of each, generated during phase change [15]. This misfit is the product of an increase in volume that occurs in newly developed hydrides due to their lower density, when compared to that of the parent matrix [24]. In the case of δ-hydride, where the face-centered cubic unit cell is isotropic in the three principle axes, the anisotropy of the hexagonal close packed cell of the parent α-zirconium matrix leads to similar anisotropy in the transformation strain [15]. When δ precipitates, the misfit normal to the basal plane is calculated by Carpenter to be 7.2 %, while that normal to the prismatic plane is only 4.58 % [15]. This encourages isotropic growth in the basal plane while retarding that in the prismatic plane, potentially yielding a ‘micro’-hydride with a platelet type morphology. These precipitates will be oriented with platelet normals parallel to the matrix hexagonal unit cell basal normal. More recently, Barrow measured interfacial strains of 5.5 %, 3.1 % and 0.5 % in the
[0001] 𝛼
,
[112̅0] 𝛼
and
[1̅100] 𝛼
directions, respectively, which are those remaining after plastic deformation has relaxed the misfit of a coarsened precipitate
[25]. Interestingly, these values imply that δ-hydrides would not precipitate with the commonly described platelet morphology, and are instead described as needle-like structures by the author
[25].
During their evolution, micro-hydride precipitates have a tendency to group or stack with discrete separating distances to form the comparatively large hydride features often observed through optical microscopy [21,26–28]. This chaining effect is attributed to the development of a hydrogen atmosphere at the core of dislocations generated locally by hydride precipitation, as encouraged by the resulting lattice dilation in these defects [29]. The morphology, distribution and orientation of these ‘macro’-hydrides are produced as a function of the thermal history, residual and applied stresses, texture, and microstructure of a component [24].
For example, where there are high cooling rates or large matrix grains, a predominance of intra-granular hydrides are observed, while lower cooling rates or small grain sizes produce more inter-granular or grain boundary hydrides [21,28,30]. Similarly, macro-hydride orientation is heavily influenced by applied stresses, where compressive forces reorient hydrides with their normal perpendicular to the loading direction [21]. An applied tensile load, however, will align macro-hydrides with their normal parallel to the loading direction [15,21].
159 | Second Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
This macroscopic reorientation of hydrides is actually a process wherein the existing micro-hydrides within a macro-precipitate will dissolve and re-precipitate with a new macrodistribution, possessing an apparent normal parallel with the tensile component of an applied three-dimensional stress. In practice, the thermomechanical history of the alloy will control the natural orientations of macro-hydrides precipitated in a component with no load [31]. However, should a fuel rod be exposed to an applied stress above a certain threshold, the reorientation phenomena occurs, where the threshold value is determined by processing and microstructure
[31]. Despite differences in macro-morphology and orientation, all micro-hydrides are found to possess the same orientation relationship relative to the matrix of
(0001) 𝛼
∥ (111) 𝛿
[24,28,30], irrespective of reorientation; although there are some examples of
{101̅7} 𝛼
∥ {111} 𝛿
found in radially oriented inter-granular hydrides [32]. Phase field and finite element models have gone on to simulate and explain this orientation relationship in works like [33,34].
Hydrides, once precipitated in zirconium, degrade the mechanical properties of a component, leading to reductions in tensile strength, ductility and fracture toughness [35–40].
These changes can ultimately compromise the integrity of cladding during normal operating life, accident conditions and fuel storage [13]. As well as the degradation of mechanical properties, the presence of hydrides can also affect phenomena like pellet cladding mechanical interaction
(PCMI); or introduce mechanisms for failure, such as delayed hydride cracking (DHC). The former mechanism is the product of thermal expansion in fuel pellets introducing stresses into the cladding, which may then lead to the formation of cracks in areas made brittle by large hydride concentrations [13]. The latter mechanism, DHC, is a sub-critical, time dependent cracking phenomenon that requires long range hydrogen diffusion for repeated local hydride growth and fracture at a hydrostatic tensile stress raiser [5,41,42]. The process occurs over an extended period of time under a continuously applied load that is below the yield stress of the material
[5,41,42].
Experimental techniques employed to investigate the general morphology and distribution of hydrides during precipitation/dissolution, as well as during the related mechanisms of failure, are limited because microscopy can only provide information for a single point in time.
Moreover, investigating components that have been irradiated during service life is both costly and difficult, making evaluations of real end of life microstructures problematic [43]. Synchrotron
X-ray diffraction, on the other hand, provides an excellent tool for studying bulk processes taking place within materials, giving the ability to sample relatively large volumes of material while performing in-situ experiments [27]. The propensity of a synchrotron to produce a highly collimated, high-flux beam yields a significant degree of angular resolution, allows for rapid diffraction pattern acquisition, and generates very well defined peaks with minimal artificial broadening. This is especially valuable when studying the precipitation process that takes place
Second Proposed Manuscript | 160
The Precipitation of Hydrides in Zirconium Alloys when hydrogen saturates zirconium, as measurements of very weak reflections, that may otherwise be overlapped by dominant zirconium peaks, can be made during thermal [23,27,44] or mechanical [22,24,31] experiments.
In tandem with the experimental work undertaken to study the zirconium-hydrogen system, modelling has also been performed to understand better the precise mechanisms involved in the nucleation, growth, mechanical properties of these precipitates and their effect on zirconium cladding. Following on from the work undertaken by Carpenter to define the stressfree transformation strains in δ- and γ-hydrides, Singh et al. were able to extend the methodology to describe volumetric misfit as a function of temperature [15,45]. This work serves to illustrate the temperature dependence of the misfit in the hydride system, where an additional
≈11 % misfit arises from a 275 °C increase in temperature, demonstrating the significant impact of thermal changes on hydride properties [45].
Barrow et al., in their evaluation of the impact of chemical and strain energy on hydride nucleation, model both the chemical driving force and strain energy associated with hydride nucleation, as a function of terminal solid solubility on precipitation, or TSSP, temperature (and thus bulk hydrogen content) [46]. From a comparison of the magnitude of these values, this work demonstrates the dominance of the chemical free energy contribution to driving force as the primary factor influencing the nucleation of hydrides [46]. Further to this, it is stated that the energy barrier to nucleation is dominated by the surface (or interfacial) energy, as opposed to strain energy [46], but on coarsening the large elastic strains that develop, which tend to be plastically relaxed through the formation of dislocations, may result in strain energy becoming the dominant barrier to nucleation.
Interestingly, in other work, Barrow puts forward a precipitation process where γ-hydride nucleates and grows, before transforming into δ-hydride, yielding a precipitate with a core consisting of δ- and tips of γ-hydride [25]. Given that the γ-hydride has a lower accommodation energy than the δ-phase, it may be physically reasonable to suppose it acts as a precursor, before transforming during the process of coarsening [25]. If δ were considered the stable phase and γ metastable, this would imply there was some other factor preventing the stable phase from forming initially. Another interpretation states that the γ-phase is stable and δ metastable, which would account for the initial formation of γ, the transformation to δ would then be the product of a destabilisation of γ, in favour of δ.
More recently, advances in phase-field modelling have allowed for the simulation of hydride precipitation with defined time and length scales, both with and without applied load
[43,47,48]. The evolution of elastic stresses within the surrounding matrix can then be predicted for a range of hydride distributions, and the work presented in [48] shows a good agreement between simulated morphologies and those seen experimentally. While these simulations have
161 | Second Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys only been performed on γ-hydride thus far, the methodology employed can easily be extended to model δ-precipitates. The phase-field methodology has also been used to demonstrate the effect of uniaxially applied load on hydride precipitation, where precipitates whose normals are aligned close to the tensile force are those predicted to show the most growth [49].
This work, stemming from a set of kinetic synchrotron X-ray diffraction experiments, seeks to quantify the rapid isothermal precipitation that takes place where significant undercooling is in effect. To support these observations, a simple model describing nucleation rate as a function of the experimental temperatures is described. This model and associated calculations are designed to build upon the work of other authors whom have produced expressions that describe the chemical, strain and interfacial energies of either a misfitting precipitate or the hydride system itself [50–52].
2.
Experimental
2.1.
Sample Specification
A single specimen of Zircaloy-4 measuring 50 mm x 5 mm x 0.4 mm was used in this work, which was provided by the Institut de Radioprotection et de Sûreté Nucléaire, France. As with the work presented by Zanellato et al., the material was rolled to 400 μm and recrystallised, yielding an average grain diameter of 10 μm and the strong basal texture associated with recrystallisation within rolled plate with a hexagonal close packed crystal structure [27]. The Kearns factors (details in [53]) for this material, as calculated from EBSD analysis, were ƒ
RD
= 0.107, ƒ
TD
= 0.219 and
ƒ
ND
= 0.673. Following thermo-mechanical processing, the sample was charged with hydrogen to a specified average concentration using the methodology for charging and verification described by Zanellato et al. [27]. Hot extraction was used to verify the concentration, and the result of charging was found to be within ±15 ppm wt.
of the desired content, with gradients across the sample of 3 ppm wt.
mm -1 on average [27]. At the time of the experiment, the hydrogen concentration within the sample was measured to be approximately 430 ppm wt.
, corresponding to the approximate hydrogen content of cladding material that has had a burnup of 49 GWd/t
U
; close that listed for current fuel assemblies [54,55].
2.2.
Synchrotron X-Ray Diffraction Parameters
The experimental work presented herein was carried out at the European Synchrotron
Radiation Facility (France), on high-energy beamline ID15B; a full technical description of the beamline can be found in [56,57]. Diffraction was undertaken using transmission geometry with the beam normal to the surface of the specimen, allowing for a large volume of material to be sampled through the thickness of the sheet. Debye-Scherrer rings were recorded using a Trixell
Pixium 4700 detector. An acquisition time of 5 seconds and an average disk write time of 4-5
Second Proposed Manuscript | 162
The Precipitation of Hydrides in Zirconium Alloys seconds was achieved, yielding a temporal resolution of 9-10 seconds per recorded diffraction pattern. Throughout this experiment a monochromatic beam with a consistent energy of
E = 87.17± 0.01 keV, and corresponding wavelength of λ = 0.14223 Å, was used to illuminate the specimen, in conjunction with a beam geometry of 300 x 300 μm 2 .
2.3.
Thermal Transients
The material was mounted in the water-cooled and electrically conductive grips of an
Instron ElectroThermal Mechanical Tester (ETMT8800), which was used to drive the thermal cycles using resistive (or Joule) heating. As zirconium alloys display a strong tendency to oxidise at elevated temperatures, a slow flowing atmosphere of inert argon gas was supplied into the sealed and oxygen purged chamber in which the sample was mounted. The temperature of the sample was set and maintained by an automatic feedback loop, which measured the temperature of the sample using an S-Type thermocouple spot-welded to the axial centre of the sample, close to the location of the incident beam. The readings of the thermocouple were fed back to the control unit in order to adjust the heating current accordingly, to produce the desired temperature.
As a check of the thermocouple, Laboratory X-Ray Diffraction (LXRD) was undertaken on the same sample, and a comparison of thermal expansion coefficients measured through SXRD and LXRD was made. This secondary check of thermal expansion is employed as flaws in the spot welding of the thermocouple used in the ETMT can lead to erroneous temperature readings [58].
Both techniques showed good agreement in measured thermal expansion, and so the thermocouple was deemed a reliable measure of temperature.
The thermal profile for the experiment was comprised of one ramped transient, followed by seven quench and dwell cycles. The initial cycle (C1), designed to measure solubility curves, heated at a rate of 1 °C s -1 from a base temperature (T floor
) of 40 °C up to a peak (T max
) of 570 °C, above the expected eutectoid temperature [59,60]. Holds were implemented in this cycle at T max and at 300 °C as part of both heating and cooling ramps, during which lateral scans along the axial length of the sample were made to evaluate hydride distributions across the sample at elevated temperature. During cooling in this cycle, a rate of 1 °C s -1 was employed to mirror the heating operation.
The terminal dissolution solubility for the sample was measured from C1 to be 439 °C, which is lower than the 513 °C predicted by McMinn [60], the 519 °C by Khatamian and Ling [61],
499 °C by Une and Ishimoto [32], and the 491 °C by Kearns [20], each for 430 ppm wt.
of hydrogen.
Due to this lower observed dissolution temperature, a T max
of 500 °C was set for all following transients. The specific cause of this shift in temperature is presently unknown, but it seems possible that some feature of the microstructure or experiment may be responsible. Of the
163 | Second Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys experiment, evidence in the literature has suggested that faster heating/cooling rates may lead to changes in TSS temperature [27], although the shift seen in the present work is far beyond that in the literature. Alternatively, both the peak temperature and time-at-temperature in a thermal cycle have also been identified as sources for more significant changes in the observed TSS temperatures [60], thought to be related to changes in the postulated memory effect [19].
Additionally, it may be possible that a high number of hydrogen trapping features in the microstructure may increase the effective solubility of the material. This could lead to hydrogen released from dissolving hydrides on heating being caught in traps, thus allowing more hydrogen to leave the hydrides and be accommodated in solution than would otherwise occur at a given temperature. Experimental evidence of a minimal influence of cold work on TSS temperatures from the literature [60], however, suggests this may not be the case.
Each of the subsequent quench-based cycles (C2-C8) involved raising the temperature to
T max
and holding for 15 minutes in order to fully dissolve all hydrides. Given that a hydride precipitation memory effect has been discussed in the literature, [19,62], this process would impact on the precipitation solvus and kinetics recorded during all cycles. By dwelling at elevated temperatures for a period after all hydrides have been dissolved, some of the dislocations left behind by previous hydride structures or cold work were given the chance to recover. Along with this, residual stresses may also have been allowed to relax, the combination of which could reduce the possibility of heterogeneous nucleation at preferential sites, supporting an assumption of homogeneous nucleation throughout the experiment.
Following each dissolution hold, the sample was then ‘quenched’ by reducing the current used to heat the sample to achieve the desired dwell temperature for kinetics observations. In practice, heat loss through conduction into the grips and surrounding atmosphere, along with convection in the argon gas and radiation from the sample, did not allow instantaneous quenching, and a maximum cooling rate of approximately 30 °C s -1 was observed. In the case of the largest change in temperature seen in this experiment (ΔT = 400 °C), this would mean it took
13.3 seconds to reach the target temperature, however, observations were made from the onset of the cooling operation.
Following each quench, the temperature was held steady in the isothermal region that forms the basis of the analytical work presented, and from which all kinetics observations are made. Finally, the sample was cooled back to T floor
, where axial hydride distribution checks were made after each thermal cycle. The desired dwell temperatures started at 100 °C and rose by
50 °C in 7 cycles up to 400 °C. No measurable hydride peak was detected during the final 400 °C cycle, despite the hold temperature being below the TSSP predicted by McMinn (445 °C) [60].
From C1, the TSSP measured for the sample was found to be 361 °C, potentially explaining why no hydride signal was detected during C8 and indicating that only minimal precipitation would be
Second Proposed Manuscript | 164
The Precipitation of Hydrides in Zirconium Alloys expected during C7 at 350 °C. Additionally, a 1 °C s -1 heating ramp was added at the beginning of the 350 °C cycle to investigate long term changes to solubility towards the end of the experimental run. Only a minimal change in the TSSD curve was observed, which was well within the expected experimental error of ±15.5 ppm wt.
. A schematic diagram, presented as Figure 1, shows the thermal regime implemented throughout this experiment.
Figure 1. Schematic of thermal operations as a function of time, with measured terminal solid solubility temperatures and those predicted by McMinn et al. [60].
The hydrogen distribution checks made at T floor between each cycle and at elevated temperatures during C1 were performed as resistive heating produces a thermal gradient across the axial length of the material, emphasised by the loss of heat from the edges of the specimen due to water cooling in the grips [58]. This is particularly significant in this work as it is well documented that hydrogen has a strong tendency to diffuse towards cooler regions, potentially leading to hydrogen depletion in the significantly hotter axial centre of the sample, where measurements were taken [13,63,64]. The result of these checks confirmed that the thermal gradient did result in regions of marked depletion and enrichment, however, the most significant of these were primarily localised to material within 5 mm of the grips (the total length between grips being 20 mm). The central region, from where measurements were taken, showed only a gradual depletion of hydrogen available for precipitation, where the difference at the point of diffraction between the initial state and the final state was no more than 30 ppm wt.
. The depletion measured during each cycle was accounted for in all calculations involving hydrogen
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The Precipitation of Hydrides in Zirconium Alloys concentration, and is reflected in both solubility plots that follow. Additionally, a mass spectrometer was used to monitor the atmosphere exhaust from the test chamber, to detect any significant loss of hydrogen from the sample through desorption, although this was thought unlikely to occur.
2.4.
Data Reduction & Analysis
For hydride phase analysis, the recorded Debye-Scherrer ring patterns were integrated using Fit2D over the entire azimuthal range, rather than using partial integrations representing the transverse and rolling directions of the material. This method was chosen as it allows for the sampling of all diffracting hydride crystals, rather than those with planes aligned to diffract close to the two principle directions. This also allows for greater counting statistics to be incorporated, giving more accurate definition to low intensity peaks, along with significantly reduced background noise relative to the magnitude of the diffraction peaks of interest, thus improving the signal to noise ratio. To investigate the impact of this choice of integration, an analysis of fullwidth-half-maximum (FWHM) was performed on hydride peaks from a full integration (360°) and
15° azimuthally integrated data (ψ ± 7.5°), taken from the two principle directions. The results showed an average of 9 % peak broadening in hydride reflections from fully integrated data, which was considered acceptable.
The XY format diffractogram files generated by Fit2D were normalised against the incident beam intensity to remove synchrotron energy decay and then batch processed using the command line operator for TOPAS-Academic V5, in conjunction with an in-house developed
Matlab R2014a function. In order to account for instrument broadening, peak shape parameters were defined from modelling a standard reference material and fixed throughout the analysis. As peak shape is a function of beam, detector and sample, defining this with a calibrant allows the isolation of the effect of sample on peak profile [65,66]. This then allows for any peak broadening or asymmetry to be defined using parameters related to the material being studied.
Initially the diffraction patterns were simulated using a Rietveld structural model [67,68] for accurate measurements of phase weight percentage ( wt.
%). However, it was quickly noted that the software was not correctly emulating hydride reflections where intensities were near to extinction. Instead, an alternate method was employed, where the diffracting weight percentage of hydride from the sample in its initial condition was measured using the Rietveld method, to provide a boundary condition. This boundary condition was established as the diffracting weight fraction for the essentially-complete precipitation of 430 ppm wt.
at T floor
, where the solubility of hydrogen was predicted by JMatPro to be 0.19 ppm wt.
and was considered negligible [60]. A second boundary condition comes from the assumption that when all hydrogen was dissolved into solution, the diffracting volume was at zero and no peak existed. Using these two conditions,
Second Proposed Manuscript | 166
The Precipitation of Hydrides in Zirconium Alloys in conjunction with the assumption of a linear relationship linking volume fraction with integrated intensity, makes it possible to calculate the volume fraction of δ-hydride from the measured area of each phase within the modelled pattern [27].
Figure 2 illustrates the diffractograms generated from fully integrated data at a number of key temperatures from throughout the experiment, over the interplanar spacing range considered. The chosen reflections for volume fraction analysis are the
{311} 𝛿
and
{022} 𝛿
, with lattice spacings of ≈1.43 Å and ≈1.68 Å, respectively; decided for their high multiplicities (24 and
12) and good degree of separation from nearby matrix peaks. The 40 °C data set shows the hydride peaks at their maximum value, representing approximately 100 % precipitation.
Conversely, the 500 °C line shows total peak extinction where all hydrogen is in solution. The final pattern, from the end of the 300 °C isothermal hold, represents the diminished peak intensity representative of the lower volume of diffracting hydride associated with an increased solubility at this temperature.
Figure 2. Representative diffractograms from 40 °C, 300 °C and 500 °C acquisitions for the considered range of lattice spacing.
Diffractogram modelling during batch processing was performed using the Le Bail method of the hkl function within TOPAS, described in detail in [69]. As with the Rietveld method, peak positions were defined by the space group and lattice parameters of the phase, while the
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The Precipitation of Hydrides in Zirconium Alloys intensities of individual reflections were allowed to vary independently of texture parameters and one another [27]. By inputting values of cell mass into the hkl structure of 371.616 for the hydride and 182.448 for matrix, taken from the fully refined Rietveld model, TOPAS was then able to calculate a weight percentage for each phase. Similarly to the Rietveld method, this was calculated as a function of peak area for all peaks in both phases over the given 2θ or interplanar spacing range, illustrated as the x-axis in Figure 2. As the scale parameters used in each phase were allowed to refine freely to give the best possible fit to the data while accounting for the differences in peak profile between the two phases, the initial software calculated weight percentage values deviated significantly from the known boundary conditions. However, by using the aforementioned relationship it became possible to calibrate these values to show the true phase distribution for any given acquisition. In addition, JMatPro 7.0 and the ZRDATA database were used both for experimental planning and to calculate parts of the thermodynamic data underpinning the model presented.
3.
Results
3.1.
Isothermal Precipitation
From the calculated volume fraction of hydride, it becomes possible to derive the completion percentile for the precipitation process that takes place during the isothermal hold in each cycle, seen in Figure 3. The first point on this plot, at t = 0, is taken as the last acquisition before the quench is performed. Given that the quench is not truly instantaneous, the second point in each series tends to lie during a period of rapid thermal change. This may artificially increase the time taken to reach completion thresholds by a small amount.
For the 100 °C to 250 °C hold cycles (C2 – C5), more than 95 % of hydrogen has precipitated by t = 15 s; recorded from the second acquisition after the quench commences. This is likely to have occurred partially during the rapid quench and partially during the first seconds of the isothermal hold. The temporal resolution derived from the method employed for diffraction pattern acquisition is insufficient to deconvolute these two effects. For the final two cycles, at temperatures greater than 250 °C, the rate of precipitation is lower and reaching maximum completion takes significantly longer than at lower temperatures. For cycle C7, a cycle that was only half the duration of others, there appears still to be some upwards gradient towards the end of the data series, potentially indicating incomplete precipitation at the cessation of the cycle. Unfortunately, time constraints cut this and the precipitation-free cycle (C8) short, and so
100 % completion was taken as the weight percentage value reached at the end of this dwell.
This may artificially reduce the completion time for precipitation recorded at this temperature.
For this reason, the final hold two hold temperatures (cycles C7 and C8) are excluded from Figure
4.
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The Precipitation of Hydrides in Zirconium Alloys
Figure 3. Precipitation completion percentage as a function of time.
Taking all other percentage completion data sets, it becomes possible to plot a transformation map for the precipitation process, Figure 4. Unlike a conventional
Time-Temperature-Transformation (TTT) diagram, a linear scale is used as the temporal resolution of 9-10 seconds per acquisition would make a logarithmic scale unclear in the low time region. Additionally, due to the rapid rate of precipitation that is observed, the percentage completion thresholds chosen for this analysis are limited to being close to 100 %.
This map demonstrates the time taken to reach a threshold completion state in the precipitation process, as a function of the temperature at which each isothermal hold takes place.
The curvature towards longer times seen in the elevated temperature region reflects the significant reduction in precipitation rate seen in later cycles. It should be noted, however, that while the highest temperature dwells do show significantly slower precipitation than the those at lower temperatures, 90 % precipitation still occurs in just 58 seconds during the 300 °C hold. In all series, it is clear that completion times are at their lowest at some temperature below 200 °C.
For the 90-98 % curves, the temporal resolution of the diffraction imaging setup acts as a limiting factor, preventing an accurate determination of the peak precipitation temperature beyond this accuracy from these curves.
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The Precipitation of Hydrides in Zirconium Alloys
Figure 4. Transformation Map.
In the 99 % and 100 % completion plots, however, curvature continues to the lowest recorded hold temperature, possibly indicating a maximum rate to precipitate hydrides close to, or lower than, the minimum experimental dwell temperature of 100 °C. It should be noted, however, that for all hold temperatures scatter in the data of between ±1 % and ±3 % (depending on cycle) means accurate judgement of 100 % completion is difficult, and so the trend in this final series should be considered carefully.
3.2.
Solubility
Values for hydrogen solubility during dissolution are calculated from the recorded weight percentage of δ-hydride during the heating ramp in cycle C1, and from the identical ramp at the beginning of the final quench cycle (C7). The diffracting weight percentage can be converted into a ppm wt.
value, and this can subsequently be subtracted from the boundary condition of
430 ppm wt.
to give the amount of hydrogen in solution. The dissolution solvi taken from C1 and
C7 were compared as a cursory investigation into changes in solubility resulting from repeatedly cycling thermal transients. As previously mentioned, the curve measured from the final cycle showed good agreement with the initial cycle, within the bounds of expected experimental error and known depletion, indicating that the solubility is stable throughout the experimental programme.
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The Precipitation of Hydrides in Zirconium Alloys
The curve for dissolved hydrogen, determined from precipitation occurring during cycle
C1, is presented in Figure 5 alongside data for slow heating and cooling rates taken from the literature. Both the TSSP and TSSD from the literature are plotted, but the current experimental data does not show agreement with the expected TSSP from McMinn. It should be noted that the cluster of points seen at 300 °C is those recorded during a short dwell at this temperature.
Figure 5. Predicted and recorded hydrogen in solution curves [60].
The data produced by McMinn are representative of Zircaloy-2 and -4 with a number of processing states and were put forward as evidence that microstructure and chemical composition have little effect on solubility [60]. Additionally, the range of thermal transient rates used in his work, considered to be slow rates when compared with the present study, were also said to have little effect on hydrogen solubility [60]. Later work, undertaken by Zanellato, put forward evidence that significantly increasing the heating or cooling rate will lower the terminal solid solubility temperature observed during each thermal operation. The greatest magnitude of shift seen in that work is of the order of 20 °C, where the cooling rate was increased by an order of magnitude from 10 °C s -1 to 100 °C s -1 [27]. Similarly, the curve for solute hydrogen concentration recorded during rapid continuous cooling in the present study shows little agreement with the slower examples published by McMinn. However, such a deviation can arise from a kinetic effect due to insufficiently fast hydride precipitation rather than a true change in solubility. To investigate this in more detail, the evolution of solute hydrogen was investigated during the series of isothermal dwells that followed C1.
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The Precipitation of Hydrides in Zirconium Alloys
Figure 6. Supersaturation in isothermal holds after quenching from rate limited kinetics [60].
Figure 6 again shows the TSSP and TSSD curves calculated by McMinn from slow cooling studies. Also plotted are the measured quantities of hydrogen in solution at the beginning and end of each isothermal dwell region (C2 – C8), as illustrated by the subplot schematic. In this figure, the black dashed and solid lines represent data from literature continuous cooling transients, while the dotted lines with cross and circle markers are those from quench and hold transients during the present study. It should be noted for clarity that no TSSD data from the present experiment is included in this figure, and that the literature TSSP has been plotted for clarity. The final points in each quench series, at 400 °C, are both set at a concentration of
400 ppm wt.
, given that no precipitation was seen during that cycle and a depletion of 30 ppm wt.
was observed by this point in the experiment.
As with the solute hydrogen measurements from continuous thermal transients, C1 and
C7, the initial recorded solute hydrogen concentration during each isothermal hold has a significant positive systematic bias when compared with the literature TSSP. Instead, these points, indicated as blue crosses, show reasonable agreement with the dissolved hydrogen level recorded from continuous rapid cooling cycle, Figure 5. When quenching at high cooling rates to elevated hold temperatures (those above 250 °C), the process of hydride precipitation continues during the hold and hydrogen leaves solution until a final concentration is recorded. The final value is well below the initial quenched solubility and that of rapid continuous cooling cycles, instead being in very close agreement with the TSSP predicted by McMinn.
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The Precipitation of Hydrides in Zirconium Alloys
Given this information, it seems possible that the TSSP curves put forward from experiments where rapid continuous cooling operations are used, do not truly represent the equilibrium solubility. In the present work, this is reflected by the process of hydride precipitation clearly being unable to occur fast enough to keep pace with the rate of temperature change. This substantiates the findings of Root, whom suggested that significant incubation times are required for the quantity of hydrogen in solution to reach true equilibrium [70].
The ramifications of this mean that proposed shifts in precipitation solubility temperature, as a function of heating/cooling rate, seen in [27] are not likely to be changes to the equilibrium solubility of the material. Instead, they may be the mark of significant supersaturation developing, as the result of the precipitation kinetics being rate limited by a reduced driving force at these temperatures. This possibility is further evidenced by the fact that in that work the dissolution solubility shifts towards lower temperatures with increasing heating rate, rather than towards higher temperatures [27]. With a high heating rate, one would expect the resulting dissolution solubility curve to either show little/no change from equilibrium or be shifted to higher temperatures, where the kinetics of the process are not fast enough to keep pace with the change of temperature. While the true equilibrium solvus temperature is defined entirely by free energy curves (and is thus free of the influence of heating and cooling rates), a shift in the apparent TSS temperature may possibly occur with high heating or cooling rates. This would be the product of a non-equilibrium microstructure being obtained at the cessation of cooling or heating.
Lastly, those values for final hydrogen in solution recorded at lower temperatures show little difference from the initial solubility points, being only a small amount above the literature
TSSP line. This is because hydride precipitation is essentially complete by the first diffraction acquisition, and little or no supersaturation remains owing to the rapid kinetics at these temperatures, brought about by a high driving force for precipitation. While within expected experimental error, the positive bias at these lower temperatures (when comparing the final dissolved hydrogen concentration against the literature) may be the product of a transformation between γ- and δ-hydride, thought to occur below 260 °C [32]. While no diffraction from γ was recorded, its existence in low quantities or very fine precipitates would potentially not generate any recordable diffraction signature, and other authors have said that hydride peaks are undetectable below 20 ppm wt.
[46]. This could then tie up hydrogen and thus reflect in an artificially increased reading of hydrogen in solution when calculated solely from δ-hydride reflections. The observation of γ-hydride tips on δ-hydrides, made by Barrow, may go some way towards justifying this possibility, as they could be in small enough volumes and quantities to minimise diffraction [25].
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The Precipitation of Hydrides in Zirconium Alloys
4.
Discussion
The experimental results show that hydride precipitation kinetics become increasingly rapid with decreasing temperature over the range studied in this work. Hydrides in zirconium precipitate through a diffusion controlled process of nucleation and growth phase transformation
[71,72], and in such transformations, the TTT diagram typically follows a C-shaped curve. The present results from this set of experimental data, Figure 4, follow a profile that would correspond to the upper part of this C-shape only. In this regime, transformation kinetics are essentially limited by the thermodynamic driving force available, and as the temperature increases, the transformation is slower, as the product of a lower driving force. The lower part of a typical C-curve, which is not observed in this study, corresponds to a regime where diffusion becomes rate limiting. The present results therefore suggest that over the investigated temperature range it is the availability of sufficient driving force to overcome the significant energy barrier to hydride nucleation that dominates, and hydrogen diffusion never becomes rate limiting. This energy barrier arises from the elastic strain that is generated as a product of the misfit that forms from the large volume expansion that takes place during precipitation, as well as the energy required to form new interfaces. To explore whether this hypothesis is physically reasonable, simple classical models for nucleation and diffusion have been used to estimate the undercooling required to produce the peak nucleation rate and the diffusion distance of hydrogen. An equation that describes nucleation rate ( 𝐼 𝑣
) as a function of temperature is presented as Equation 1.
𝐼 𝑣
= 𝑁 𝑜 𝑘𝑇 ℎ 𝑒𝑥𝑝 (
−(𝐺 ∗ + 𝑄) 𝑘𝑇
)
Equation 1
Here,
𝑁 𝑜
represents the number of nucleation sites (zirconium atoms per unit volume for homogeneous nucleation),
𝑄
is the activation energy for diffusion, ℎ
and 𝑘
are the Planck and
Boltzmann constants, respectively,
𝑇
is the temperature in Kelvin and
𝐺 ∗
is the energy barrier for hydride nucleation, described by Equation 2 [52].
𝐺 ∗ =
9
2 𝜋𝛾 𝑓 𝛾 𝑔
Equation 2
This expression is comprised of three primary components, where two terms describe interfacial energy ( 𝛾 𝑓
and 𝛾 𝑒
), and the term 𝑔 𝑛
represents nucleation energy density. As
δ-hydrides are typically considered to take the form of a disc or oblate spheroid, two distinct surface types can be identified; the large, relatively flat surfaces possess a lower interfacial energy of 𝛾 𝑓
= 0.065 J m -2 , while the edge has an interfacial energy taken to be 𝛾 𝑒
= 0.28
J m -2 [52].
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The Precipitation of Hydrides in Zirconium Alloys
From the derivation in [73] for critical nucleus volume, it would appear that the interfacial energy of the edge, 𝛾 𝑒
, is squared in this equation to account for the geometry of the simulated precipitate. There [73], total interfacial energy is described as 𝛾 = (𝛾 𝑓
+ 𝑐 𝑎 𝛾 𝑒
) 2
, and when minimising the formational free energy change with respect to the dimensions of the precipitate
( a and c ) to find their critical values, the squared term is created. The final term in this expression can be calculated from Equation 3 [52]. 𝑔 𝑛
= 𝑘
𝐵
𝑇𝐶 𝑥 𝑙𝑛(𝐶 𝑠
/𝐶 𝑒𝑞
) − 𝑔 𝜖
+𝑔 𝑒𝑥
Equation 3
Here, 𝑘
𝐵
is Boltzmann’s Constant, 𝑇 is absolute temperature, 𝐶 𝑥
signifies hydrogen concentration in hydride precipitates per unit volume, calculated as a function of temperature using equilibrium values taken from JMatPro,
𝐶 𝑠
is the amount of hydrogen dissolved in the matrix and
𝐶 𝑒𝑞
denotes the equilibrium solubility of hydrogen in the matrix, also from JMatPro [52]. The final two terms, 𝑔 𝜖 and 𝑔 𝑒𝑥 represent contributions from the strain energy associated with the volumetric misfit and that from externally applied forces, respectively [52]. As the system being considered has no externally applied load, this final term will be excluded from the model.
From Equations 2 and 3, there are three energies influencing the nucleation of hydrides, one acting to promote nucleation and precipitation, and two acting to hinder it. The chemical free energy that drives precipitation is described by the term 𝑘
𝐵
𝑇𝐶 𝑥 𝑙𝑛(𝐶 𝑠
/𝐶 𝑒𝑞
) in Equation 3, and arises from an excess of hydrogen in solution over the equilibrium concentration. The two converse terms are those of the energy required to form new interfaces during nucleation and precipitation, described in Equation 2, and the energy required to form a precipitate that misfits with the encompassing matrix and must generate strain to exist.
Equation 4 calculates the strain energy of any shape of precipitate, given uniform dilatation, through the Eshelby approach, while assuming no plastic relaxation takes place [74].
This technique describes a precipitate with an associated isotropic misfit and isotropic elastic properties, within an infinite and elastically isotropic parent matrix, and simulates equal deformation in both the parent and precipitate [50]. 𝑔 𝜖
=
2
9
∙
(1 + 𝜈)
(1 − 𝜈) 𝜇(∆ 𝑇 ) 2 𝑣 𝛽 Equation 4
In this expression, 𝜈 is Poisson’s ratio, 𝜇 is the shear modulus for the parent matrix, ∆ 𝑇
is the cubic dilatation in an unconstrained transformation, and 𝑣 𝛽 is the specific atomic volume of the precipitate phase [74]. For the purpose of this work, the expression derived by Sing et al. for volumetric expansion as a function of absolute temperature will be used, where ∆ 𝑇 = 0.1506 +
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The Precipitation of Hydrides in Zirconium Alloys
7.38 × 10 −5 𝑇 [45]. When utilising the Eshelby method to calculate strain energy, it is then assumed that this overall volume expansion is split evenly between all directions, rather than occurring anisotropically. The value for 𝑣 𝛽
in this expression is taken as the volume of a stable nucleus, calculated for an oblate spheroid morphology with the two major axes being equal to the critical radius ( 𝑟 ∗
), derived for each temperature considered within the model. It should be noted that from the work of Barrow et al., elastic strains in the matrix are up to 4x greater than those seen in the hydride, and as the Eshelby model considers uniform deformation in both, values predicted through this method are an approximation rather than being absolute.
In previous attempts to model the hydride precipitation, a single temperature independent value of 1 x 10 8 J m -3 for strain energy has been used [52]. Accounting for the temperature dependence of the misfit, the values produced by the Eshelby model range from
1.21 x 10 7 J m -3 at 0 °C to 5.79 x 10 9 J m -3 at 500 °C. When compared with the isothermal value given by Massih et al., this would correspond to a temperature of approximately 265 °C in the present system. From the work of Puls, and later used by Barrow et al., a value of 1.66 x 10 7 J m -3 is calculated, which corresponds to the strain energy calculated through the Eshelby method at
50 °C [46,75]. The present results suggest that if the misfit varies as reported in [45], then the range of misfit strains with temperature is large and cannot be ignored in attempts to simulate hydride precipitation. In reality the situation is further complicated because plastic relaxation may take place, the degree of which will also be temperature dependent, where softening will occur at elevated temperatures. Nevertheless, in the nucleation stage, it is expected that the larger misfit at elevated temperature exacerbates the effect of decreased chemical driving force, further slowing the nucleation kinetics.
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The Precipitation of Hydrides in Zirconium Alloys
Figure 7. Calculated nucleation rate as a function of temperature, strain energy and geometry.
Figure 7 contains the result of the nucleation model for three considered scenarios; with no strain energy contribution, where the rate and peak temperature are highest, and including strain energy, derived from the Eshelby model, for both a disc and an oblate spheroid precipitate.
Also given is the TSSP recorded from the presented experiment, such that an indication of the undercooling associated with these nucleation rates is given. From this, it can be seen that the peak nucleation rate is predicted between 113 °C and 149 °C, depending on the chosen system, which is reasonably consistent with the transformation map, Figure 4. Strain energy is shown to have a significant effect on both the magnitude and position of the nucleation rate peak, reducing the optimum temperature for nucleation by 17 °C and 36 °C for an oblate spheroid and disc morphology, respectively. However, the main factor that is responsible for the high degree of undercooling required to reach the peak nucleation rate is the relatively high interfacial energy reported for the hydride phase, an observation also made in previous studies [46]. Below the peak nucleation temperature, the process of hydrogen diffusion becomes the controlling influence within the model, where the local jumping of hydrogen over the interface regulates the rate of the process. It is noted that at high temperatures (300 °C and greater), where experiments show continued precipitation, this figure suggests a nucleation rate close to zero. This is untrue, as substantial nucleation is still predicted by the model at these elevated temperatures in the strain-free system (of the order of 10 27 m -3 s -1 at 300 °C, for example), although the introduction of strain energy does reduce this considerably.
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The Precipitation of Hydrides in Zirconium Alloys
Clearly, the present model is very simple, and in practice, nucleation of hydrides is heterogeneous, rather than homogeneous. However, heterogeneous nucleation of hydrides at features such as dislocations or sympathetically in the strain field created by other hydrides would serve only to reduce the strain energy component of the nucleation energy barrier. As Figure 7 shows, even if there is no strain energy required (through complete, instantaneous relaxation), a large undercooling for nucleation is still required, owing to the interfacial energy terms.
To understand why the lower portion of the expected C-curve was not observed, even at precipitation temperatures as low as 100 °C, simple diffusion distance calculations have been performed for hydrogen dissolved in zirconium. Taking the diffusion coefficient determined by
Kammenzind et al. for hydrogen in Zircaloy-4 (288 °C to 482 °C), and extrapolating to cover a range relevant to the present work, it becomes possible to estimate the diffusion length for hydrogen [76]. This is done using a simple 𝑑 = √𝐷𝑡
approximation, where
𝐷
is the diffusion coefficient and 𝑡 is time.
Figure 8. Diffusion distance as a function of temperature, showing distances relevant to (a) axial sample length and (b) inter-hydride spacing.
Figure 8 shows the result of these diffusion distance calculations at two length scales, where (a) is scaled to half the axial length of the test piece, giving an indication of how far from the centre of the sample, where diffraction measurements are taken, hydrogen is able to diffuse.
Both subplots consider diffusion to be isotropic for simplicity, however, given the highly textured nature of zirconium cladding this may not be true of all directions within a component. The data
Second Proposed Manuscript | 178
The Precipitation of Hydrides in Zirconium Alloys contained in (a) serve to illustrate that with elevated temperatures and long hold times, hydrogen is able to diffuse moderate distances through the zirconium matrix. Given an hour at 500 °C, the diffusion distance is calculated as 1.2 mm, which is 12 % of the distance from the point of beam incidence to the ETMT grips, demonstrating why axial hydrogen distribution checks are important.
Figure 8 – (b) looks specifically at distances relevant to both the inter-hydride spacing and overall precipitate length related to the sample being studied. The average zirconium grain diameter for the sample measures 10 μm, micro-hydride lengths typically range from 10 nm to
200 nm (although examples of large 1 μm precipitates exist) and the inter-hydride spacing taken from transmission electron micrographs is no more than 2 μm. These values were recorded for the specific sample being examined in this work, and as hydride geometry and distribution will change with hydrogen concentration, thermal history and mechanical processing, this assessment is intended to be representative, rather than definitive. Taking the curve for 1 second, it is evident that hydrogen is capable of rapidly diffusing the average measured inter-hydride spacing at temperatures close to 150 °C. Similarly, it is also able to diffuse half of the width of a matrix grain in just ten seconds at this temperature.
The overall rate of transformation is limited either by the energy barrier or diffusion rate at upper and lower temperatures, respectively, giving the customary C-shaped curve to TTT diagrams. The values for local diffusion distances above would suggest that while the diffusion of hydrogen controls the process of precipitation at temperatures below 0 °C, the presence of rapid diffusion at temperatures relevant to fuel assemblies would mean that diffusion is never rate limiting. This explains the extremely fast precipitation observed below 150 °C, where 98 % of precipitation is complete almost immediately. As temperatures increase above 150 °C, the drop in precipitation rate observed in Figure 4 then occurs through the activation energy becoming the rate limiting process. It should be noted, however, that while hydrogen diffusion is considered not to be rate limiting above 0 °C the process of nucleation is still dependent on short range diffusion, where the local jumping of hydrogen across the interface regulates the speed of nucleation.
Where hydrogen concentrations are significantly lower, such as in the case of CANDU pressure tubes where the life design allowance is 100 ppm wt.
of hydrogen, the inter-hydride spacing would in-turn be larger [77]. Such increases in the required distance for hydrogen to travel could then lead to diffusion becoming a rate-limiting factor. From the diffusion data above this would seemingly not be until inter-hydride spacing was in the order of tens of microns, at least. For the purpose of this work, however, the above assessment of diffusion distance seems sufficient to explain the lack of the lower half of the C curve expected in a conventional TTT diagram.
179 | Second Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
5.
Conclusion
Synchrotron X-ray diffraction was able to investigate successfully the isothermal precipitation of hydrides within Zircaloy-4. From completion percentage data, a peak in precipitation rate was measured close to, or below, 100 °C. The measured concentration of hydrogen in solution while precipitating, recorded during a 1 °C s -1 cooling transient, was shown to be in poor agreement with the literature. During quench and hold cycles, the initial solubility showed a similar agreement with the continuous cooling values, but then continued to drift towards the position of the literature solubility. This was explained as being the product of significant residual supersaturation, where the process of precipitation was unable to keep pace with the rate of temperature change. This effect was primarily seen at temperatures above
200 °C, while those below this threshold showed little or no recordable residual supersaturation after the quench, within the bounds of experimental error.
A simple model was used to predict the peak temperature for hydride nucleation using the Eshelby method for estimating misfit strain energy in two geometries of precipitate, as well as performing a strain energy-free calculation. This represents a lower and upper bound to nucleation rate behaviour, respectively. The temperature dependence of the misfit was included in this model and shown to be significant in the calculation of strain energy. While only a simple approximation, this model is reasonably consistent with the experimental observations, predicting a peak in nucleation rate at between 113 °C and 149 °C. Strain energy has a modest effect, reducing the temperature of peak nucleation rate by up to 36 °C, depending on the precipitate geometry considered. The reason a large undercooling is required to reach the peak nucleation rate is mainly attributed to the relatively high interfacial energy reported in the literature for the hydrides. Diffusion distance calculations showed that hydrogen diffusion was not significantly rate limiting given the diffusion distances required at temperatures relevant to the life of zirconium clad fuel assemblies.
Ultimately, these simulations act to justify the experimental observations made through synchrotron X-ray diffraction. However, it should be noted that while precipitation at these higher temperatures is considered relatively slow when compared with the lower thermal region, the overall process of hydride precipitation in zirconium alloys is very rapid, owing to the high mobility of hydrogen and the large driving force that develops with increased undercooling.
6.
Acknowledgements
The author would like to thank the Institut de Radioprotection et de Sûreté Nucléaire for funding the synchrotron experiment and providing the samples utilised in this experiment.
Rolls-Royce and the Engineering and Physical Sciences Research Council are thanked for providing sponsorship funding, as well as the Hong Kong Polytechnic University for the help and support
Second Proposed Manuscript | 180
The Precipitation of Hydrides in Zirconium Alloys given with numerical modelling and providing funding during international secondment. Further acknowledgements should also be given to the infrastructural support of the Materials
Performance Centre at the University of Manchester, and the University as a whole. Thanks are also given to J. Blomqvist and T. Maimaitiyili of the University of Malmö for fruitful exchanges on synchrotron analysis technique and best practice. Finally, thanks should be given to A.T.W.
Barrow and S.C. Connolly for advice and technical guidance towards readying this work for publishing.
7.
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5.3.
Annex – Transmission Electron Microscopy
In the second proposed manuscript, statements are made as to the approximate size and spacing of hydride precipitates in the studied material, which were determined from a limited
Transmission Electron Microscopy (TEM) investigation. Namely, that hydride lengths ranged between 10 nm and 200 nm, with examples of large hydrides in excess of 1 μm, with inter-precipitate spacings of no more than 2 μm. Here, a series of micrographs are given as examples illustrating these distances and measurements, where imaging was performed ex-situ using an FEI Tecnai G2 20 with a LaB
6
filament, operating at 200 kV.
The sample was mechanically ground to a thickness of 200
m and 3 mm diameter disks were punched out of this material, which were subsequently ground to a final thickness of
160
m. Samples were electro-polished in a solution of 10 % perchloric acid (itself a 70 % HClO
4 solution), 20 % 2-Butoxyethanol and 70 % ethanol [220], a chemistry that is known to minimise the tendency for polishing-induced hydriding of zirconium samples. The temperature was maintained at 0 °C during polishing, and a current of 60 mA (with an associated current density of 2.39 mA mm -2 ) was applied to the sample with a voltage of 21 V.
Figure 50. Zircaloy-4 TEM micrograph at 17,000x magnification, observed in the
[0002] 𝛼 direction.
185 | Second Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
Figure 50 contains a representative micrograph imaged from the sample material,
projected in the
[0002] 𝛼
direction relative to the central grain, where a clear grain boundary can be seen at the top of this image. For clarity, the brightness and contrast levels have been adjusted, owing to a large region of dark strain contrast in the upper-right quadrant. From this micrograph
and others, a number of features can be quantified, as in Figure 51. From Figure 51 – (a), large
hydrides range in size from 0.34
m to 1.35
m, with the nearest-neighbour distance from centroid-to-centroid being between 0.89
m and 1.20
Figure 51. (a) Geometry boxes drawn on large hydrides, (b) nearest neighbour centroid-to-centroid distances, (c) projections of hydride major axes for relative angle measurements, and (d) identification of small hydrides from ‘coffee-bean’ contrast strain lobes, and potential SPPs.
Second Proposed Manuscript | 186
The Precipitation of Hydrides in Zirconium Alloys
From an assessment of the angle between the major axes of these features Figure 51 –
(c), the two in the lower right quadrant are essentially parallel, while the smaller centre-left and upper features are angled by 44° and 62° from away from the two largest objects, respectively.
Needle type hydrides (γ, for instance) are expected to be oriented with their major axis in line with the ⟨112̅0⟩ 𝛼
directions [99], meaning that the angle between hydrides would be expected to be 60° or 120°, which follows for three out of four of the features in this figure. Of the centre-left object, it seems possible that either the orientation of the major axis was misjudged owing to complex contrast in the region, or that this feature is composed of smaller hydrides with the correct axes, which have amalgamated to form a larger object with an irrational apparent orientation.
Something of particular interest in this micrograph is the needle-like nature of these features, as the known presence of δ hydride would suggest disc or platelet like morphologies, from the transformation strains of Carpenter [85]. Those interfacial strains reported by Barrow et al. [86], representing the remaining elastic misfit after plastic relaxation, suggest needle like objects, which are also apparent from these micrographs. This is a concept explored further in
the third proposed manuscript. The final subplot, Figure 51 – (d), highlights a number of other
features in the microstructure, where SPP-like objects are differentiated from small features highlighted by the ‘coffee-bean’-like strain contrast that envelops them. These latter features are thought to be small hydrides, which have not reached sufficient volume to create the plastic deformation and associated dislocation structures that are observed surrounding the much larger hydrides. A significant number of them are intra-granular in nature, but there is also a population of similar features adjoining the grain boundary at the top of this subplot.
Figure 52 illustrate these features at a range of magnification, where the dark ‘halo’ is
thought to be the strained matrix surrounding a hydride, which occupies the centre of each feature. In these micrographs, the axial length of the light core, taken from the point of convergence between the dark mirrored fields at either tip, ranges from 14.5 nm to 179.3 nm, with a mean size of 73.19 nm. The centroid-to-centroid separation between features of this type was between 44.9 nm and 631.7 nm, with a mean value of 265.1 nm.
Finally, Figure 53 highlights an altogether different morphology of feature observed
within the microstructure, being that they were entirely devoid of the strain fields or dislocations associated with hydrides, but still took on the needle-like morphology expected of the phase.
These objects were relatively uncommon, when compared with the ‘coffee-bean’ type features, and were typically between 160 nm and 190 nm in length. Unfortunately, no deeper analysis was performed on these features, and so their nature remains unclear at this time.
187 | Second Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
Figure 52. ‘Coffee-bean’ strain contrast features, thought to be hydrides, at (a) 350,000x,
(b) 125,000x, (c) 125,000x, and (d) 26,000x magnification.
Figure 53. Other potential hydride-like features at 86,000x magnification.
Second Proposed Manuscript | 188
The Precipitation of Hydrides in Zirconium Alloys
6.
Third Proposed Manuscript – Strain Evolution
6.1.
Foreword
This final manuscript documents the evolution of strains arising from the process of hydride precipitation, during the same thermal operations as those characterised in the second
(kinetics) manuscript. The contributions of the listed authors follow.
The experiment was designed by O. Zanellato, with input from M. Preuss, F. Ribeiro and
J. Andrieux. The experiment was performed at the ESRF by M. S. Blackmur, O. Zanellato and J.
Andrieux, and the post-experiment analysis of data was performed by M. S. Blackmur, using training given by R. Cernik and O. Zanellato. The manuscript was written by M. S. Blackmur, with technical and editorial supervision provided by M. Preuss and J. Robson.
189 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
6.2.
Manuscript
Strain Evolution during Hydride Precipitation in Zircaloy-4 Observed with
Synchrotron X-Ray Diffraction
M.S. Blackmur a , M. Preuss a , J.D. Robson a , O. Zanellato b , R.J. Cernik a , F. Ribeiro c , J. Andrieux d, e a Materials Performance Centre, School of Materials, The University of Manchester, Manchester, M1 7HS, United
Kingdom b PIMM, Ensam - Cnam - CNRS, 151 Boulevard de l'Hôpital, 75013 Paris, France c Institut de Radioprotection et de Sûreté Nucléaire, CEN Cadarache, 13115 St. Paul Les Durance, France d Beamline ID15, European Synchrotron Radiation Facility, 6 rue J Horowitz, 38043 Grenoble, France e Laboratoire des Multimatériaux et Interfaces, Université de Lyon, 43 Bd du 11 novembre 1918, Villeurbanne, 69100,
France.
Keywords
Synchrotron X-Ray Diffraction, Hydride Precipitation, Zirconium Alloys, Strain Evolution
Abstract
High-energy synchrotron X-ray diffraction was used to evaluate the strain evolution observed in a Zircaloy-4 sample undergoing hydride precipitation during a range of thermal operations at reactor-relevant temperatures. A continuous heating and cooling thermal cycle was employed to investigate the way in which the parent matrix constrained the hydride during constant rate heating and cooling transients. A change in the constraining effect of the matrix was also observed, at a temperature of 280 °C, thought to be the result of matrix dilatation from interstitial hydrogen. A series of quench and dwell cycles were utilised to investigate the isothermal evolution of strain both during and after the precipitation of hydrides. A deconvolution of the thermally, chemically and mechanically induced strain was performed, and a non-negligible mechanical effect was observed in the matrix from a low (≈2 %) volume fraction of hydrides
During these dwells, a slow strain rate relaxation of elastic strains was seen in the matrix and hydride, suggesting that time dependent relaxation of misfit stresses may be possible at reactor relevant temperatures. Notable anisotropy was observed in the strain evolution recorded between the rolling and transverse directions, identified as being the likely product of a similar anisotropy in the relaxation of the hydride misfit between the
⟨112̅0⟩ 𝛼
and
⟨11̅00⟩ 𝛼
matrix directions, owing to the differing coherency of these two interfaces.
1.
Introduction
Since the early days of defence and civil nuclear energy, zirconium alloys have been ubiquitous as a structural material in water-cooled reactor cores owing to their low cross section
Third Proposed Manuscript | 190
The Precipitation of Hydrides in Zirconium Alloys for neutron absorption, aqueous corrosion resistance and mechanical properties at elevated temperatures [1,2]. The corrosion that does take place, however, generates hydrogen as a product of the oxidation reaction, and zirconium has a strong propensity to absorb a fraction of this [3,4]. Once within the material, the precipitation of hydrogen into hydrides is governed by the local solubility, where thermal gradients across components can lead to solubility gradients, and thus non-uniform hydride distributions [5].
Taking coolant temperature to be representative of that of zirconium cladding (at the outer surface, at least), a representative Pressurised Water Reactor (PWR) might see inlet and outlet temperatures of approximately 290 °C and 323 °C, respectively [6]. Given this operating range, the maximum solubility for hydrogen would be around 143 ppm wt.
[7], compared to a bulk hydrogen content of approximately 290 ppm wt.
after a common service life burn up of 44 GWd/t
U for Zircaloy-4 [8]. In fact, hydrogen pick-up curves for this alloy suggest that the hydrogen content of fuel cladding exposed to coolant at 323 °C could potentially reach the precipitation solubility limit after just 23.3 GWd/t
U
, assuming a simplistic uniform hydrogen distribution [6–8]. Where temperature decreases occur, during thermal transients or refuelling shutdowns for example, the solubility falls rapidly. At ambient temperatures the solubility of hydrogen in zirconium is in the parts per billion, rather than parts per million, and almost all hydrogen will rapidly precipitate into hydrides.
Once formed, this brittle phase has been shown to degrade the bulk mechanical properties of zirconium cladding [9–16] and introduce mechanisms for failure through Delayed
Hydride Cracking (DHC), secondary hydriding and hydride blistering [17–23]. As such, a strong understanding of the impact of hydrides on zirconium alloys is critical to ensure the integrity of nuclear fuel assemblies is maintained during service life and storage. This will become even more critical in the future, where any extension of fuel assemblage burn-up may lead to a notable hydrogen content increase in end of life components [8].
Numerous studies have sought to quantify the zirconium-hydrogen system, although the complex nature of the processes involved means many areas are still unclear [24–26]. The most widely observed and discussed phase is the non-stoichiometric face-centered cubic δ-ZrH
≈1.66
hydride, considered the stable phase at room temperature by most researchers [27,28].
However, additional complexity arises since the face-centered tetragonal γ-phase is thought to be metastable alongside stable δ-hydride or even entirely stable itself, as a function of cooling rate, hydrogen concentration and alloy composition [29–33]. Given the metastable nature of γ, the balance between the two phases can be influenced by external factors and both phases can also coexist. For example, stress stabilisation of γ has been recorded [27] and γ-tipped, δ-cored precipitates have been observed [34]. Examples of ε- and ζ-hydride phases have also been
191 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys reported in the literature, however, the precise conditions of their formation are still somewhat unclear, aside from high concentrations of hydrogen [35–39].
Irrespective of which hydride phase forms, the zirconium to zirconium-hydride transformation is associated with a volume expansion, owing to the lower physical density of hydrides, and so newly formed precipitates have an associated misfit with their parent lattice
[34,40,41]. Discrepancies exist in the literature between theoretically predicted transformation strains [41] and experimentally measured (post-plastic relaxation) [34] interfacial strains for δ, and so its morphology is generally reported to be either needle-like or that of a platelet, based on the anisotropic misfit with the parent matrix. The needle morphology may develop as a function of the anisotropic relaxation of the misfit strains during the growth phase of precipitation
[34]. This would then have the potential to cause hydrogen to be preferentially drawn up the stress gradient [42] towards the edges in the
⟨112̅0⟩ 𝛼
directions, where stresses would be higher than those in
⟨11̅00⟩ 𝛼
, encouraging the formation of needles. When precipitating, the strain field and dislocation structures surrounding hydrides, generated by the particle-matrix misfit, are thought to encourage the sympathetic nucleation of ‘daughter’ hydrides [33,43–46]. This is owing to the trapping of hydrogen within lattice defects [44] or a lowering of the elastic accommodation energy by the tensile stresses that a misfitting hydride will generate in the surrounding matrix
[43,46]. These daughter hydrides often stack or chain to form the comparatively large hydride regions observed through optical microscopy, which can appear to be a single very large hydride
[47–51]. The orientation, distribution and morphology of these larger hydride regions is the product of numerous factors, including thermal history, component stress state, microstructure and texture [40]. That said, the micro-hydrides, which constitute them, predominantly display an orientation relationship of
(0001) 𝛼
∥ (111) 𝛿
with the parent lattice [40,48,52] and will always precipitate with the platelet normal parallel to the matrix basal normal.
The generated misfit is also thought to impact on the terminal solid solubility of hydrogen in zirconium, where the additional undercooling required to precipitate the phase is reflective of the energy required to produce first elastic and then plastic deformation in the matrix and hydride
[53–55]. Other work postulates that the hysteresis may even be an artefact seen where the concentration of hydrogen in solution has not reached equilibrium, owing to rate limited kinetics
[51,56]. Given that the strain contribution to the energy barrier is thought to be second order to interfacial energy by some [57], the solubility curves recorded experimentally will also be heavily influenced by the energy associated with a change in interfaces.
Synchrotron X-Ray Diffraction (SXRD) has grown as a major technique employed for investigating hydrides, owing to the large spatial, small temporal and sharp achievable angular resolutions. These studies cover a wide range of aspects and topics of the zirconium-hydrogen system, showcasing the diverse capabilities of modern synchrotron facilities. Some works have
Third Proposed Manuscript | 192
The Precipitation of Hydrides in Zirconium Alloys investigated thermal cycles and their effect on stresses and strains within the matrix and hydride, as well as hydrogen solubility and hydride nucleation [51,57,58]. Others have looked at hydride reorientation [40,59,60] or the impact of a notch and resulting stress-field on hydride precipitation and fracture [61,62]. Phase identification and quantification has been performed
[35], phase diagrams have been constructed [33] and phase transformations have been observed
[27]. The impact of the matrix on hydride formation has also been studied, where texture [55], mechanical properties and microstructure [63] have been shown as significant to the process.
The present work uses high-energy synchrotron X-ray diffraction to investigate the evolution of strain in both the matrix and hydride precipitates during a series of isothermal holds over a range of reactor-relevant temperatures. A model for matrix lattice distortion from dissolved hydrogen [51] is employed to deconvolute the components to strain evolution.
2.
Experimental
2.1.
Sample Specification
The Zircaloy-4 sample utilised here was supplied by the Institut de Radioprotection et de
Sûreté Nucléaire, France, and possessed the same processing history as the sheet material used in [51]. After rolling to 400 μ m, the sample was cut to 50 mm x 5 mm in the rolling and transverse directions, respectively, and recrystallised [51]. EBSD analysis showed the material to possess an average grain size of 8-10 μ m, with the expected split basal texture of rolled and recrystallised zirconium sheet material. In this, basal poles are normally tilted by ± 20-40° from normal, where the secondary direction is determined by the 𝑐/𝑎 ratio [64]. The texture of this material is shown in Figure 1 – (a), and the corresponding Kearns factors (details in [65]) are
𝑓
𝑅𝐷
= 0.120
, 𝑓
𝑇𝐷
= 0.248
and 𝑓
𝑁𝐷
= 0.631
. The sample geometry and the relationship between the beam, detector and Rolling/Transverse/Normal Directions (RD/TD/ND, respectively) are presented schematically in Figure 1 – (b).
193 | Third Proposed Manuscript
(a)
(0002)
TD
RD
(11̅00)
TD
The Precipitation of Hydrides in Zirconium Alloys
(112̅0)
TD
RD
(b)
Figure 1. (a) Recorded texture of rolled and recrystallised Zircaloy-4 sample, measured through
EBSD orientation mapping, and (b) the sample geometry and RD/TD/ND relationship
After thermomechanical processing, hydrogen was charged into the sample using the methodology described by Zanellato et al. [51], and the concentration at the time of experimentation was 430 ppm wt.
, with a gradient of no more than 3 ppm wt. mm -1 . This was selected as the relatively high content of hydrogen produces a sufficiently large diffracting volume of hydrides within the sample, yielding more detectable diffraction signals. When compared with expected hydrogen contents in Zircaloy-4 cladding at the end of fuel assembly life, this value is similar to that found in components with 49 GWd/t
U
burn-up; close to the end of life hydrogen content for some operators [8]. The size and quality of hydride reflections becomes important in the zirconium-hydride system; as while the angular resolution of synchrotron diffraction is good, there is still some overlap with the dominant matrix reflections or their tails.
2.2.
Synchrotron X-Ray Diffraction Parameters
The present experiment was undertaken at the European Synchrotron Radiation Facility
(France), on beamline ID15B. This instrument is a high-energy diffraction beamline for which the full technical details are available in [66,67]. X-ray diffraction was performed under transmission
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The Precipitation of Hydrides in Zirconium Alloys
(Debye-Scherrer) geometry, where the beam was incident orthogonally to the surface of the specimen. This allowed for the sampling of a large material volume, through the sheet thickness, yielding bulk measurements of hydrides within the sample. Diffraction patterns were imaged with a Trixell Pixium 4700 detector; where acquisitions were made over 5 seconds, followed by 4-
5 seconds of disk write time. This resulted in a temporal resolution of 9-10 seconds per imaged
Debye-Scherrer ring pattern. A monochromatic beam with a constant energy of
E = 87.17 ± 0.01 keV was used to illuminate the sample during this work, with a wavelength of
λ = 0.14223 Å and beam size of 300 μ m x 300 μ m.
2.3.
Thermal Transients
Thermal operations were performed using resistive (Joule) heating, driven by an
Electrothermal Mechanical Tester (ETMT8800), manufactured by Instron, in which the specimen was mounted. Heat loss through conduction into the water-cooled grips and radiation into the atmosphere was counteracted automatically by the equipment, where the temperature close to the beam (at the axial centre of the sample) was measured using an S-Type thermocouple and the driving current was adjusted to compensate. Due to the high affinity of zirconium for oxygen at elevated temperatures, the chamber of the ETMT was purged with inert argon gas, which continued to flow through the chamber throughout the experiment.
The experimental programme involved a single ramped thermal operation, followed by seven quench and hold operations. Cycle 1 (C1) allowed for the measurement of solubility curves during heating and cooling at a continuous 1 °C s -1 , from a minimum temperature of 40 °C (T floor
) to a maximum of 570 °C (T max
), above the expected eutectoid temperature [68]. Given the hydrogen content of the sample, the dissolution solubility was found to be 429 °C, and for all subsequent quench cycles a T max
temperature of 500 °C was implemented.
Given the postulated memory effect for hydrogen precipitation [32,69], the repeated cycling of dissolution and precipitation would likely impact upon the hydrogen solvi observed. It seems possible, however, that the presence of elevated temperature soaks would encourage the recovery of dislocations, thus reducing the propensity for heterogeneous nucleation at preferential sites, minimising the impact of repetitive cycles on solubility curves. The postulated damage recovery at temperatures present in this work is potentially supported by the reduction of irradiation induced dislocation loop density [70,71] and cold work dislocations [72] at similar temperatures.
The subsequent cycles, C2-C8, were based on raising the temperature above the TSSD of the sample and holding for 15 minutes to completely dissolve all hydrides. A quench was then performed using a sudden reduction in current to a level required to attain the isothermal dwell temperature present in each cycle. These actions were all performed automatically by the ETMT
195 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys software using a pre-programmed operational plan. In practice, the loss of heat through radiation and conduction was not sufficient to instantaneously quench the sample, and the maximum rate of cooling was observed to be ≈30 °C s -1 . For the most significant quench, Δ T = 400 °C, the time taken to reach the target temperature was around ≈13.3 seconds. For this reason, all isothermal kinetics and strain observations were made starting from the initiation of the quench operation.
After a prolonged hold, the sample was cooled to T floor
, and hydrogen distribution checks were made along the axial length of the sample, between the grips. The hold temperatures implemented in the experimental design began at 100 °C and rose to 400 °C in increments of
50 °C. Given that the TSSP was found to be 361 °C, the final cycle, C8, demonstrated no detectable precipitation, and so it is excluded from any further analysis.
Cycle C7, the penultimate quench and hold operation, was modified to include a 1 °C s -1 ramp, intended to investigate the effect of multiple thermal cycles on dissolution solubility. Very little change in the TSSD curve was seen between the dissolution stages of cycles C1 and C7, well within the average experimental error of ±15.5 ppm wt.
seen in concentration throughout this programme. The average error in strain evolution was found to be ±25.5 x 10 -6 determined from the prismatic lattice parameter and ±173.9 x 10 -6 from the basal lattice parameter. The error in the basal lattice parameter strain value is large compared to the measured strain value, and this introduces some uncertainty into the interpretation of the results for this plane. Figure 2 contains a schematic diagram of all thermal operations that took place during this experiment.
The axial checks for hydrogen distribution, made at the T floor
temperature between each cycle were performed owing to the fact that resistive heating leads to a thermal gradient across the sample between conductive contacts, which is exacerbated by the loss of heat energy into the water-cooled grips [73]. This has the potential to impact on the present experiment given the fact that hydrogen is known to have a strong propensity to diffuse to cooler regions, leading to depletion at the axial centre of the sample, where diffraction measurements are taken [5,74,75].
These checks indicated that while regions of enrichment and depletion did develop during the experimental framework, they were localised primarily to within 5 mm of the grips. The axial centre demonstrated only a small amount of depletion as a product of the dwell cycles, by no more than ≈30 ppm wt.
, a value only marginally more than the average experimental error. Finally, at all times during the experiment a mass spectrometer was used to monitor the exhaust atmosphere of the ETMT chamber, with the intention of detecting any hydrogen desorption from the sample. This confirmed that no measurable quantity of hydrogen desorption was detected during the experiment.
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The Precipitation of Hydrides in Zirconium Alloys
Figure 2. Thermal operations as a function of time.
2.4.
Synchrotron Data Analysis
For measurements of diffracting volume of hydride, integration over the full azimuthal range of the Debye-Scherrer rings was performed, to ensure that diffraction from the maximum number of crystals of the precipitate was recorded. For strain analysis, however, partial integrations were used for the matrix and hydride in the four principle directions (considered
‘compass points’) of the Debye-Scherrer ring patterns. With the geometry of the sample-detector relationship, 0° and 180° represent the TD, while 90° and 270° represent the RD; these directions are illustrated in Figure 1 – (b). The reason for using a narrow segment of the full pattern comes from the desire to give directionality to the recorded strain evolution. For the matrix, an integration with an azimuthal range of 15° (ψ ± 7.5) was performed, however, for the weak hydride phase this sampling range was insufficient to resolve Bragg reflections. Instead, a partial integration with an azimuthal range of 45° (ψ ± 22.5)
The diffractogram files produced by Fit2D were normalised as a function of beam intensity to remove the effect of synchrotron energy decay, after which they were simulated using TOPAS-Academic V5. Batch processing was handled using Matlab R2014b and a proprietary function. Instrumental broadening is accounted for by defining profile parameters from a
Standard Reference Material and using these in the analysis of patterns recorded from the sample. Changes in profile shape, being a function of beam, detector and sample, can then be accounted for predominantly as the product of sample, as beam and detector contributions are
197 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys fixed from the calibrant [76,77]. Consequently, any asymmetry or line broadening can be defined with parameters that consider the properties and structure of the sample.
A first attempt at batch diffraction pattern modelling utilised a Rietveld refined structural model [78,79] to give accurate weight percentage measurements. It was quickly observed that where hydride reflections were close to extinction, the software was not properly simulating these reflections. As an alternative method two boundary conditions were established, where complete signal extinction was taken to represent all hydrogen entering solution, while the intensity of the reflections at their maximum (and initial thermally un-cycled state) signified full precipitation. To support this, it can be seen from the work by McMinn that at the T floor temperature the solubility of hydrogen is less than 1 ppm wt.
[7], and so it is assumed throughout this work that all hydrogen has precipitated when close to room temperature. The combination of these two boundary conditions, along with an assumed linearity to the relationship linking integrated intensity of the hydride reflections and volume fraction, allows for the calculation of
δ -hydride volume fraction from the recorded diffraction patterns.
Figure 3. Representative diffractograms from 40 °C, 300 °C and 500 °C acquisitions for the considered range of lattice spacing.
In order to account for signal extinction, the Le Bail method [80] was employed to model both structures within TOPAS while batch processing. Unlike the Rietveld approach, reflection
Third Proposed Manuscript | 198
The Precipitation of Hydrides in Zirconium Alloys intensities are able to vary freely and independently of any texture parameters or one another
[51]. Taking the values of cell mass from the Rietveld model and importing them into the Le Bail structure, TOPAS is then able to generate a nominal weight percentage for each phase. For reasons thought to be related to the free refinement of the scale parameter, allowed in order to grant the best possible fit for each modelled phase, these values were significantly different from the assumed boundary conditions. Using the boundary values, however, allows for the calibration of the weight percentage to represent the supposed true diffracting volume of hydride at any given point in the experiment. Additionally, the Le Bail model, like the Rietveld model, describes the spatial relationship between Bragg reflections as a function of crystal structure and lattice parameters. By refining the model to match the recorded pattern, sampling multiple reflections within the region of interest, it becomes possible to accurately measure the lattice parameters of each phase present within imaged patterns.
Figure 3 demonstrates three patterns generated from a full (360°) azimuthal integration at key temperatures seen throughout the experimental programme; where the lattice spacing range represented on the x-axis is that which was modelled during data analysis. The hydride reflections shown were chosen due to their high multiplicities (24 for the
{311} 𝛿
and 12 for the
{022} 𝛿
), along with being reasonably isolated from the tails of the dominant matrix reflections.
The maximum intensities in these reflections, recorded in the material’s initial state at 40 °C, are taken to represent 430 ppm wt.
of hydrogen fully precipitated as hydride (or 100 % precipitation).
The high temperature data set shows no hydride reflections, and thus all hydrogen is treated as being in solution. The intermediate temperature plot, at 300 °C, shows partial precipitation, where the hydride intensity is half way between the high and low temperature boundary conditions.
Thermodynamic calculations to compute equilibrium solubilities were performed using
JMatPro 7.0 in conjunction with the ZRDATA database. The MTEX 4.0 toolbox for Matlab was used for pole figure calculation and visualisation.
3.
Results and Discussion
3.1.
Precipitation
A full investigation into the solubility and precipitation behaviour of hydrides during the isothermal holds is presented elsewhere [81]. The following, however, summarises the precipitation observations necessary to underpin the strain behaviour presented in this work.
Figure 4 illustrates the completion of the precipitation process as a function of time, during each of the dwells that took place during the experimental regime. Dashed vertical lines are included to show the time at which precipitation is considered to be complete for each series. From this figure, it is evident that for cycles C2 to C5 close to 98 % of precipitation has occurred rapidly,
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The Precipitation of Hydrides in Zirconium Alloys within approximately the first 20-30 seconds, followed by a more gradual increase in completion.
For the higher temperature cycles, C6 and C7, the driving force for precipitation is lower and so the process is slower, leading to increasing curvature in the data with elevating temperatures.
This additional time to completion is important, as dissolved deuterium occupying a tetrahedral site within the hexagonal close packed matrix unit cell leads to an ≈ 2.78 Å 3 volume expansion of the parent lattice [82]. A similar volume expansion can be expected for hydrogen, and thus when it leaves solution en-masse a net contraction (or negative lattice strain) will occur in the α zirconium phase, which will be reflected in the strain traces presented herein [51].
Another aspect to consider is the amount of hydrogen that forms hydrides at the end of each cycle, collated in Table 1 along with a calculated value for hydride volume percentage associated with each concentration. While these values are only a few percent, it is notable that the hydride volume of the alloy is more than 1.5 % even at the highest dwell that showed precipitation (C7). This is indicative of a steep increase in solubility between 350 °C and 400 °C
(400 °C showing no precipitation), and highlights the non-negligible volume fraction of hydrides in each of the isothermal dwells. The importance of these observations will become evident later.
Lastly, the penultimate cycle (C7) was shorter than all others, but the curvature of the precipitation curve is still significant up until the end of recording. Given the long time for the previous cycle (C6) to precipitate, it would appear likely that C7 was still some time away from completion, and was cut short by the experimental programme.
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The Precipitation of Hydrides in Zirconium Alloys
Figure 4. Precipitation process completion as a function of time.
Table 1. Approximate precipitated hydride volume fractions at experimental dwell temperatures.
40
100
150
200
250
Temperature
(°C)
300
350
400
430
426
403
398
362
333
267
0
Precipitated Hydrogen
Concentration (ppm wt.
)
2.9
2.8
2.6
2.6
2.3
2.1
1.7
0
Approximate Equivalent
Hydride Volume (%)
3.2.
Texture
Before an investigation into the experimentally observed strains is performed, it is important to qualify the influence texture might have on these results. Given the recorded texture in Figure 1 – (a), mechanical loading along RD would allow for easy activation of prismatic
⟨𝑎⟩
slip, the slip mode with the lowest Critical Resolved Shear Stress (CRSS) [83]. Mechanical loading along the TD would promote a dominance of basal
⟨𝑎⟩
, and to a certain degree prismatic
⟨𝑎⟩
, slip.
Finally, loading along ND requires activation of pyramidal
⟨𝑐 + 𝑎⟩
slip, which has a significantly higher CRSS [83]. These observations are reflected in the macroscopic stress-strain curves
201 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys presented in [84], where yield stresses are lowest when deformed in the RD; although the effect appears more significant in compression than in tension in that work. This assessment is echoed by models in [83], where yield is lowest in the RD, followed by the TD and ND in sequence, owing to the texture of zirconium. Lastly, given that ⟨0002⟩ 𝛼
is elastically stiffer than ⟨112̅0⟩ 𝛼
( 𝐶
⟨112̅0⟩
11=22 𝛼 = 142.63 𝐺𝑃𝑎 and 𝐶
⟨0002⟩
33 𝛼 = 164.3 𝐺𝑃𝑎 from the stiffness tensor in [85]), it may be possible that the greater degree of basal pole orientation in the TD could also mean that this direction might be marginally more elastically stiff, when compared with the RD.
3.3.
Zirconium Lattice Strains
Matrix lattice strain evolution derivations are performed using relative changes in the prismatic and basal lattice parameters, which are calculated from the Le Bail model for the matrix and hydride phases. This approach allows for accurate calculations of unit cell parameter from sampling all reflections within the considered inter-planar spacing range of the diffraction pattern, Figure 3, rather than using a single reflection analysis. It does, however, sample across the entirety of material of a phase within the gauge volume, so those reported matrix strains average across material close to hydrides (experiencing more misfit induced strain) and that further away (subject to less strain). All strains presented in this work are relative, due to the formation of inter-granular stresses in α-zirconium, resulting from the significant anisotropy in the thermal expansion coefficients of the matrix, which prevents the accurate measurement of a
0
and c
0
values [51,86].
Figure 5 contains separate subplots for the prismatic and basal lattice parameters, showing the strain evolution calculated for the end of each isothermal dwell in the rolling and transverse directions. Also included is the lattice dilatation resulting from thermal expansion in each lattice parameter calculated from a similar, but hydrogen-free, sample to illustrate the effect of hydrogenation on the zirconium lattice. Below each of the line plots is a series of bars that visualise the difference between the base thermal expansion and that recorded from a hydride sample. The evolution of matrix strain during a continuous heating ramp (C1 and C7) will be discussed in section 3.4, when it will compared with strain in the hydride during the same thermal operation.
With the exception of 100 °C in the basal plot, the three lower temperatures in each subplot show close agreement with the expected thermally induced strain in each direction of the hexagonal close-packed unit cell. Of the basal parameter 100 °C points, it seems probable that because the material is both polycrystalline and possesses a strongly anisotropic unit cell, the inter-granular stresses that develop on cooling (from <a> and <c> thermal expansion mismatch) could constrain the basal inter-planar spacing, producing the lower than expected strain evolution that is observed. Above 200 °C, the recorded strain in both directions of the
Third Proposed Manuscript | 202
The Precipitation of Hydrides in Zirconium Alloys material departs from that predicted by thermal expansion alone, to an ever increasing degree.
This deviation is the product of the increase in hydrogen solubility when moving towards higher temperatures, where the rise in dissolved hydrogen interstitially occupying the α-zirconium lattice leads to an expansion of the matrix unit cell [82].
A second feature of note within these subplots is that the TD consistently shows a higher degree of lattice dilatation than the RD. This might be the result of the texture, where a greater degree of basal poles oriented in the TD, as opposed to the RD (although the majority are actually in the ND), may cause a greater thermal strain in that direction for both the ‘a’ and ‘c’ parameters, from the interaction of neighbouring grains. Given this assessment, it might also be expected that the coefficients of thermal expansion should be different between the RD and TD, which is not apparent from Figure 5, and so a clear cause for this systematic bias remains unclear.
Figure 5. Additional strain evolution present in the prismatic and basal lattice parameters of the zirconium matrix at the end of each isothermal hold, compared to base thermal expansion.
In the following figures, plotted temporally, the initial data point at t = 0 seconds is taken as the final acquisition before the onset of the quench, and so a large initial thermally induced strain (up to ≈2000 x 10 -6 ) is recorded. Thermal contraction ceases to be a cause of strain evolution once the temperature, and thus lattice parameters, stabilise at the onset of the dwell.
As the present evaluation is not concerned with thermally induced strains, and given the inability
203 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys to calculate absolute matrix strains, all following strain traces are zeroed to the final value in each hold so that an assessment of strain evolution over the course of the isothermal dwell can be made, relative to their post-quench equilibrium state.
Figure 6 and Figure 7 show the recorded strain in the prismatic and basal lattice parameters for both the rolling and transverse directions of the α-zirconium lattice. The isothermal holds are divided into two groups, where Figure 6 contains the three lower temperature cycles (C2-C4) and Figure 7 contains the remaining upper temperature cycles
(C5-C7). This is done for ease of interpretation, as it separates cycles into those that show rapid precipitation (under 750 seconds for those including and below 200 °C) and those showing slower precipitation (over 1000 seconds for 250 °C and higher).
Firstly, considering the low temperature cycles in Figure 6, C2-C4, two distinct trends are apparent: the RD shows more elastic contraction than the TD, and the basal lattice parameter demonstrates more elastic strain evolution than the prismatic lattice parameter. In the following description, subplots are addressed in the order of least strain evolution to most.
Looking specifically at the prismatic TD subplot, the 150 °C and 200 °C traces (orange and yellow) indicate a very slight positive gradient, deviating from the trends observable in all other traces within this figure. The magnitude of this gradient is small, however, when compared to the measurement error, and so drawing conclusions from these two series should be done with caution. That being said, the formation of hydrides is thought to induce large compressive stresses within the precipitate, owing to the large misfit, and so an equal balancing in the matrix with tensile stresses is also necessary. As such, a positive or dilative change in the lattice parameter may be indicative of this stress balancing.
In the basal TD subplot, a modest amount of negative elastic strain evolution occurs during hydride formation, but appears to cease once the process of precipitation is considered complete (marked by vertical dashed lines for each series). From this point onwards, only noise fluctuations appears to occur up until the end of each cycle. For the prismatic RD data, continuous negative strain evolution is featured in all three series, and the cessation of precipitation appears to have little impact on the rate of strain evolution. Finally, the basal RD subplot shows a considerable amount of negative elastic strain evolution in all three cycles, where the majority occurs while hydrides are formed, and once precipitation is completed a marked change in the rate of strain evolution is recorded (although the lattice does continue to contract). Overall, increasing the precipitation temperature appears to generally decrease the amount of elastic strain evolution recorded during the dwell in all directions and both matrix parameters.
Figure 7 shows a similar set of plots arranged in the same way as Figure 6, but for the three higher temperature hold cycles. A gap exists in C6 where a storage ring top-up event occurred, which significantly destabilised recorded trends, and so a small portion of the data is
Third Proposed Manuscript | 204
The Precipitation of Hydrides in Zirconium Alloys excluded for clarity. Unlike the previous figure, precipitation continues well into each of these cycles, and so a like-for-like comparison with the previous set of three temperatures is difficult.
Considering only the points after precipitation is completed (and discounting C7 entirely owing to its artificial shortening), very little strain evolution is observed for either of the lattice parameters and in any direction.
Figure 6. Recorded relative strain evolution in the lattice parameters of the α-zirconium matrix during cycles C2-C4, where dashed vertical lines indicate the completion of precipitation at each temperature.
205 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
Figure 7. Recorded relative strain evolution in the lattice parameters of the α-zirconium matrix during cycles C5-C7 where dashed vertical lines indicate the completion of precipitation at each temperature.
Given that a number of complex mechanisms are likely inducing strain in the matrix, it would not be prudent to analyse the recorded elastic strain evolution any further without attempting a deconvolution of the contributing components. For this reason, the equation describing lattice distortion resulting from solute hydrogen (from Zanellato et al. [51]), Equation
1, is used in conjunction with the tracked precipitation of hydrides to calculate the chemically induced lattice dilatation. Here, 𝑛
𝑍𝑟
is the number of zirconium atoms per unit cell,
𝐶 𝑎𝑡
𝐻
is the dissolved molar hydrogen concentration,
𝐾
is the coefficient of anisotropy, 𝑣̅
0
is the initial cell volume, and ∆𝑣 is the cell volume increase from interstitial deuterium (substituted in place of hydrogen). The resulting lattice contraction from interstitial hydrogen leaving solution to precipitate into hydrides is represented in Figure 8. 𝜀̅ = 𝑛
𝑍𝑟
𝐶 𝑎𝑡
𝐻
(1 − 𝐶 𝑎𝑡
𝐻
)(2 + 𝐾)𝑣̅
0
∆𝑣 Equation 1
Third Proposed Manuscript | 206
The Precipitation of Hydrides in Zirconium Alloys
Figure 8. Lattice contraction induced in α-zirconium from hydrogen leaving solution.
From the calculated chemical strains, it is evident that for the three lower temperature cycles, the effect of dissolved hydrogen on strain evolution is limited to the first 200-500 seconds.
Past this time, both the prismatic and basal lattice parameters stabilise and only a degree of scatter appears within each trace. For the upper three cycles, where the kinetics of precipitation are rate limited by the chemical driving force for precipitation, the chemically induced negative strain evolution extends well into each dwell, as the result of the additional time it takes to complete the process of precipitation. The lowest temperature of these, C5, shows only a small magnitude of strain in the order of ≈30 x 10 -6 , whereas the uppermost two cycles demonstrate as much as ≈150 x 10 -6 strain, owing to the significant change in the quantity of dissolved hydrogen. It should be noted, however, that these relative strains are normalised to zero at the end of each cycle, and so Figure 8 only shows the change in chemically induced strain evolution that results from the precipitation occurring during each dwell period. The absolute value of the chemical dilatation at the end of each of these holds without this normalisation will be a positive value, because some amount of hydrogen will still remain in solution, dilating the α-lattice. Figure
5 gives an indication of the magnitude of this effect, where the increase in strain above baseline thermal expansion is indicative of the strain induced by solute hydrogen.
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The Precipitation of Hydrides in Zirconium Alloys
Using the interstitial hydrogen induced negative lattice strain evolution, it becomes possible to remove the chemical contribution to strain from the data present in Figure 6 and
Figure 7. Given that the temperature is stabilised by the third pattern acquisition at the latest, any remaining elastic strain evolution past this point will likely be the sole product of mechanical phenomena within the sample induced by the misfit between hydride and the matrix. With this being said, Figure 9 and Figure 10 contain the derived mechanically induced elastic strain evolution during each dwell, separated as in previous figures. Unfortunately, this process effectively combines the noise present in the original recorded strain traces with that produced by the calculation for chemical dilatation, and so the magnitude of scatter present in these is larger than in previous figures. Nonetheless, the amounts of strain recorded, and the scatter in these values, remain very small. It should be noted that for simplicity it has been assumed that no change in stoichiometry of the hydride occurs, which would likely lead to another source of apparent strain [87]. Similarly, where a transformation from delta to gamma or vice versa would occur, a change in the misfit of each precipitate would then follow, which would impact upon the mechanical interaction, and may influence the resulting strains [34,41].
Considering first the three lower temperature cycles, Figure 9, it is evident that there is still some degree of measurable strain evolution in the matrix for each of these temperatures, albeit predominantly in the RD of the material. The data for the TD show very little change overall in both the prismatic and basal lattice parameters. In all four subplots, mechanically induced strain evolution (that occurring after the precipitation complete dashed lines) ranges from essentially zero (prismatic and basal parameters in the TD) up to ≈150 x 10 -6 of negative elastic strain (basal parameter in the RD).
As hydrides form, the misfit of the particles produces predominantly tensile stresses in the matrix, that continue to build as the precipitates grow and coarsen. Eventually, these stresses will reach the local yield stress of the material, and plastic relaxation will take place through the creation of dislocation structures. Where elastic strain evolution is seen in the lower temperature dwells after precipitation is complete, the mechanically induced lattice parameter strain evolution is negative with time during the dwell, before reaching equilibrium (taken as the 0 point in these plots). This indicates that a continuous, time dependent process seemingly takes place after precipitation, suggesting that slow strain rate plastic relaxation is in effect.
As
⟨0002⟩ 𝛼
is stiffer than
⟨112̅0⟩ 𝛼
, a recorded quantity of strain evolution in the basal inter-planar spacing will correspond to a larger stress relaxation than for the same strain recorded in
⟨112̅0⟩ 𝛼
. Of the two lattice parameters, a greater degree of elastic strain relaxation is seen in
⟨0002⟩ 𝛼
, and so this corresponds to a significantly larger stress relaxation in this direction. The difference between
⟨112̅0⟩ 𝛼
and
⟨0002⟩ 𝛼
strain magnitudes can be explained using the stress
Third Proposed Manuscript | 208
The Precipitation of Hydrides in Zirconium Alloys free transformation strains derived by Carpenter [41], or the interfacial strains measured by
Barrow et al. [34].
In the case of Carpenter, the δ-hydride transformation strain is thought to be isotropic in
⟨112̅0⟩ 𝛼
and ⟨11̅00⟩ 𝛼
(4.58 %), while the expansion in ⟨0002⟩ 𝛼
is higher, at 7.2 %, with a coefficient of anisotropy between the former pair and latter direction of 1.57 [41]. From Barrow, the interfacial strains in
⟨112̅0⟩ 𝛼
and
⟨11̅00⟩ 𝛼
measured from a formed precipitate (thus being the residual misfit strains after plastic relaxation has likely occurred) are anisotropic. The values reported by both authors are listed in Table 2.
From Barrow et al., the residual interfacial strain in
⟨11̅00⟩ 𝛼
is minimal, whereas those in the other two directions are substantially more, and the coefficient of transformation strain anisotropy between
⟨112̅0⟩ 𝛼
and
⟨0002⟩ 𝛼
is 1.77. Given the high anisotropy between
⟨0002⟩ 𝛼 and
⟨112̅0⟩ 𝛼 directions from both authors, the misfit between precipitate and parent lattice would be far greater in
⟨0002⟩ 𝛼
, thus generating larger stresses in this direction.
Comparing the values from these two authors for the
⟨0002⟩ 𝛼
direction suggests that the reduced misfit measured by Barrow et al. may be indicative of the degree of plastic relaxation that has taken place in this direction. This may then support the observation of notable elastic strain relaxation seen in the RD basal subplot.
Table 2. δ-Hydride stress fee transformation strains (Carpenter)/interfacial strains (Barrow et al.) [34,41].
⟨0002⟩ 𝛼
⟨112̅0⟩ 𝛼
⟨11̅00⟩ 𝛼
Direction
7.2 %
4.6 %
4.6 %
Carpenter
5.5 %
3.1 %
0.5 %
Barrow
Interestingly, the strong anisotropy between the residual misfit strains in
⟨112̅0⟩ 𝛼
and
⟨11̅00⟩ 𝛼
from Barrow et al. may go some way towards explaining why so little elastic strain evolution is seen in the TD of the material, when compared with the RD. From the measured specimen texture, Figure 1 – (a), it can be seen that the
{11̅00} 𝛼
poles are oriented predominantly in the RD direction, while the
{112̅0} 𝛼
poles are oriented in the TD. The relatively low residual misfit reported in
⟨11̅00⟩ 𝛼
is thought to be the result of the incoherent nature of the interface in those directions [34], which likely acts as a source for dislocations that are needed to plastically relax the misfit strains in
⟨11̅00⟩ 𝛼
. For the semi-coherent
⟨112̅0⟩ 𝛼
(the growth direction of needles), the tight radius of the tip aids in the accommodation of the misfit strain
[34], and so less plastic relaxation would likely occur in those directions. This is manifest in a comparison of the predicted and observed strains reported in Table 1, where the difference
209 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys between Barrow et al. and Carpenter is greater in the incoherent
⟨11̅00⟩ 𝛼
direction, than the coherent
⟨112̅0⟩ 𝛼
[34,41]. This direction, being that with greatest plastic relaxation of the misfit, being oriented predominantly in the RD (as a function of the texture) is then likely why significant negative strains (thought to be indicative of relaxation) are also recorded in the RD in the present study.
From the data in Table 2, it is also evident that some relaxation of the misfit may also take place in
⟨112̅0⟩ 𝛼
(oriented in the TD), but no notable evidence of any time dependent relaxation is seen in Figure 9 for the TD. It is thus suggested that any relaxation that does occur in
⟨112̅0⟩ 𝛼
does so while the process of precipitation is ongoing, rather than after it is complete.
It should be noted that if this is the case, some fraction of the ⟨11̅00⟩ 𝛼
misfit likely also relaxes during precipitation, and so it is suggested that the post-precipitation relaxation accounts for the further diminishment of interfacial strains in
⟨11̅00⟩ 𝛼
.
In other published work [51], the mechanical interaction between hydride and matrix has been considered second order owing to the low hydride volume fraction. This may be a fair assessment when the greatest magnitude seen is no more than ≈150 x 10 -6 strain, although it cannot be considered as entirely negligible during, or shortly after, the process of precipitation.
Even though a maximum of only ≈2 % of the diffracting volume of material is composed of precipitate, a clear mechanical interaction is seen on average in the metal matrix during the three lower temperature experimental dwells.
Of the higher temperature cycles, Figure 10, the vast majority of experimentally recorded strain evolution is accounted for by hydrogen leaving solution, and so the matrix lattice strains presented show minimal change. The lowest temperature of these, the 250 °C dwell (purple), does show evidence of the same trends observed in the lower temperature cycles (Figure 9), particularly in the RD. The 300 °C and 350 °C cycles, however, show essentially no mechanically induced strain evolution, and any deviations (such as that in series C7 within the basal RD subplot) are likely a mismatch between the modelled and recorded chemically induced strain. This seems unusual, considering that the misfit predicted by Singh et al. [87] becomes larger with increasing temperature, so it would be expected that this would produce larger stresses, and thus greater strain relaxation within the parent lattice at these temperatures.
This extra relaxation, however, is not seen in the present work, as hydrides take longer to form with raised temperature [81], so the excess stresses produced by the increased misfit may be relieved as quickly as they are produced while precipitation progresses. This is potentially exacerbated by the yield strength of the matrix being lower during these upper cycles, meaning that less stress is needed for plastic relaxation to ensue, and so it may begin much earlier in the precipitation process.
Third Proposed Manuscript | 210
The Precipitation of Hydrides in Zirconium Alloys
Figure 9. Mechanically induced strain evolution in α-zirconium during lower temperature dwells, where dashed vertical lines indicate the completion of precipitation at each temperature.
Figure 10. Mechanically induced strain evolution in α-zirconium during higher temperature dwells, where dashed vertical lines indicate the completion of precipitation.
211 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
There are two final considerations to be made as to the validity of this assessment of matrix strain evolution, pertaining to the averaging of strains in the matrix and the source of the strain evolution. The presented strain evolution traces are based on the lattice parameters calculated from a Le Bail model of the α phase. These are, in turn, calculated from the centroid positions of the matrix reflections being sampled in the diffraction pattern, which are indicative of the average strain in the phase. Given that matrix strain arising from the misfit is non-uniform
(in that it tails off rapidly with increasing distance from the precipitate), the Bragg reflections are essentially a composite of many smaller reflections, each representing a point on the strain gradient, the majority falling at the low strain end.
To cause a change in overall reflection centroids, the maximum magnitude of the misfit strain would need to be sufficiently large, such that it counteracts the far larger volume of material that experiences minimal strain. To help mitigate this, increasing the quantity of local strain sources throughout the material could aid in maximising the volume of the matrix affected by it. This latter point may be helped by the thermal profile of the experiment, as it is known that rapid cooling to precipitate hydrides generally leads to a distribution of fine precipitates [88], which may help increase the volumetric coverage of the misfit strain fields. It should also be remembered that the maximum mechanical strain relaxation being reported here is only
≈150 x 10 -6 , or 0.015 %, compared with the interfacial misfit strains given in Table 2 (up to 5.5 % measured experimentally by Barrow et al. [34]), so it is not unrealistic that the relative strains reported in this work are in fact those averaged throughout the matrix.
With regard to the source of the observed strain evolution, it could be suggested that some mechanism related to the time-dependent releasing of hydrogen from trapping features may be responsible for the observed trends. Here, the dislocations, vacancies, or other features in the matrix that trap hydrogen can act to effectively increase the solubility of the material local to the traps, which, in turn, would increase the dilatation of the parent lattice in those regions.
Were these traps to slowly release hydrogen, then the lattice would see negative strain resulting from hydrogen forming further hydrides, either within the traps themselves or from the excess solute hydrogen in the matrix, in order to maintain the equilibrium solubility.
There are two reasons that suggest that this alternate hypothesis may not be true, starting with the way in which precipitation might occur in the presence of hydrogen traps. It is known the dislocations left behind by dissolving hydrides act as traps for the hydrogen they release back into solution, and that on further precipitation the hydrogen saturated traps act to promote heterogeneous nucleation at these features, in a way known as the memory effect [69].
Given that the isothermal hold temperatures that see the most strain evolution in the present work are also those with the greatest driving force for precipitation, it seems likely that hydrogen in the traps would have formed hydrides rapidly after the quench, leaving few traps that might
Third Proposed Manuscript | 212
The Precipitation of Hydrides in Zirconium Alloys be able to release hydrogen. Were precipitation of trap released hydrogen to happen slowly over time, then the diffraction signal would show this through an increase in the intensity for the hydride phase, and as the present study reports strain evolution that occurs after the intensity has stabilised, it does not appear likely that further hydride is formed during the dwell.
Additionally, the sensitivity for measuring precipitation completion is around 1 % (5-6 ppm wt.
) when hydride reflections are developing, so the maximum strain evolution that could be unaccounted for due to noise in the intensity signal would be only 15-20 x 10 -6 and 22-28 x 10 -6 in the ‘a’ and ‘c’ parameters, respectively.
A second and more significant reason why the release of trapped hydrogen may not be the source of the recorded strain, however, is a feature of the four subplots in Figure 9, namely the absence of any strain evolution in the TD. Were hydrogen to leave traps, the resulting lattice contraction would likely occur in both lattice parameters (to greater and lesser extents) and, significantly to this argument, in both processing directions, as there is a dilatational component in both ⟨112̅0⟩ 𝛼
and ⟨11̅00⟩ 𝛼
. As there is none recorded in the TD, it is concluded that the presented matrix strain evolution is, indeed, likely a feature of the mechanical interaction between the misfitting precipitates and the parent lattice and not the slow release of trapped hydrogen.
3.4.
Hydride Lattice Strain Evolution
In a similar way as to follow the strain evolution in the matrix, it is also possible to track the hydride reflections within the inter-planar spacing range of interest, Figure 3, from which a lattice parameter for the phase can be calculated. This makes it possible to calculate the strain evolution seen in the hydride. Before considering the isothermal dwell cycles, Figure 11 displays the matrix and hydride strain evolution measured along the RD and TD, as a function of temperature, during the initial (C1) and final (C7) 1 °C heating ramps. This allows for a deeper investigation into the interaction between matrix and hydride during continuous heating transients. For both phases and in both processing directions, the data can be separated into two distinct regions of lower and higher temperature separated at ≈280 °C, each with a different gradient. This kink is present in both the initial and final experimental cycles, and so it is believed to be inherent to the material, rather than introduced through experimental cycling (although a short thermal operation did occur pre-experiment). Additionally, the good degree of agreement between C1 (closed markers) and C7 (open markers) in all four subplots suggests a minimal impact of the aforementioned memory effect as the experiment progressed. This is likely attributed to the elevated temperature soaks allowing precipitation related matrix defects to recover somewhat, minimising the propensity for further heterogeneous nucleation at lattice defects produced by previously existing hydrides.
213 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
Figure 11. Relative strain evolution recorded in the hydride (upper) and matrix (lower) lattice parameters, from the rolling and transverse directions of the sample during continuous 1 °C s -1 heating cycles (C1 – closed markers and C7 – open markers).
From the literature, the reported thermal expansion coefficient for bulk δ-hydride varies by a large margin, from author to author. For example, Yamanaka et al. report a range of
25 x 10 -6 K -1 to 30 x 10 -6 K -1 (based on stoichiometry) [89], while Kolas et al. report a lower value of 14.2 x 10 -6 K -1 [40]. When compared with the matrix, both of these sources present values that are significantly more than the values calculated for either of the matrix parameters from the current work. Here the prismatic and basal coefficients for the α phase are measured to be
6.04 x 10 -6 K -1 and 8.97 x 10 -1 K -1 , respectively, from a base metal sample containing no charged hydrogen and derived from a full 360° Debye-Scherrer ring integration.
With these values in mind, the measured dilatation in the hydride phase in both upper subplots of Figure 11, and over the entire thermal range, is significantly lower than would be expected from the literature sourced bulk hydride thermal expansion coefficients [40,89], which can be understood by considering that the hydrides are constrained by the metal matrix.
Below 280 °C the measured hydride expansion gradient in both processing directions is lower even than the smallest expansion coefficient of the matrix, however, the geometrical relationship between matrix and hydride unit cells must be considered before further assessment can be made. Given the known habit plane of
(0001) 𝛼
∥ (111) 𝛿
[90], the
⟨100⟩ 𝛿
family of
Third Proposed Manuscript | 214
The Precipitation of Hydrides in Zirconium Alloys directions, in which ‘a’ lattice parameter dilatation will occur, will not be aligned with the
⟨112̅0⟩ 𝛼 and
⟨0002⟩ 𝛼
matrix directions, corresponding to the ‘a’ and ‘c’ lattice parameters, respectively.
Instead, a comparison must be drawn between the
⟨111⟩ 𝛿
family of hydride directions and these two matrix directions, as seen in Figure 12.
Figure 12. Planar relationship between matrix (left) and hydride (right) unit cells.
Table 3 – Hydride
⟨100⟩ 𝛿
to
⟨111⟩ 𝛿
strain direction relationship, matrix
⟨112̅0⟩ 𝛼
and
⟨0002⟩ 𝛼 directional thermal expansion, and associated uncertainties.
Material
Direction
RD
RD
TD
TD
Temperature
Region
40–280 °C
> 280 °C
40–280 °C
> 280 °C
Thermal Strain (ε x 10 -6 )
⟨100⟩ 𝛿
⟨111⟩ 𝛿
4.32
±0.46
7.49
±0.80
16.71
±2.87
28.93
±4.98
3.75
±0.40
6.49
±0.70
10.20
±2.08
17.67
±3.59
⟨112̅0⟩ 𝛼
⟨0002⟩ 𝛼
6.00
±0.07
7.74
±0.12
Non-Linear
6.63
±0.11
8.44
±0.08
Non-Linear
Taking the gradient of strain evolution for the hydride in the upper and lower temperature regions, it becomes possible to calculate the expansion in the
⟨111⟩ 𝛿
directions, presented in Table 2, where the linear regression to determine the gradient incorporates the uncertainties in lattice parameters calculated by TOPAS. From these values, the strain evolution in the
⟨111⟩ 𝛿
directions below 280 °C are similar to the matrix thermal expansion coefficients
(the
⟨0002⟩ 𝛼
in the RD, and
⟨112̅0⟩ 𝛼
in the TD).The similarity between these parameters indicates that the matrix imposes significant constraint on the thermal expansion of the hydride
215 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys in the lower thermal range. What is not clear, however, is why the
⟨111⟩ 𝛿
expansion shows close agreement with
⟨0002⟩ 𝛼
in the RD, but the
⟨112̅0⟩ 𝛼
in the TD, although the margin of uncertainty for the
⟨111⟩ 𝛿
precludes a deeper assessment of whether this is true, or simply an artefact.
Above 280 °C the gradient of hydride expansion with temperature increases to a value that is larger than either of the thermal expansion coefficients for the matrix. In the TD, the value is still below the bulk hydride thermal expansion coefficient, suggesting that while the matrix is still constraining the precipitate, the effect is significantly lower in this thermal region. In the RD, however, the measured thermal strain coefficient shows good agreement with literature thermal expansion coefficients for the hydride phase from Yamanaka et al. [89], suggesting that minimal constraint is imposed by the matrix in this direction. This deviation between these two directions may be explained by the study of Barrow et al. [34], whereby the incoherent boundary (in the
⟨11̅00⟩ 𝛼
directions) oriented in the RD may encourage more plastic relaxation through slip in that direction, when compared with the TD (in which a semi-coherent boundary is oriented). This may then act to relax the matrix constraint on the hydride in the RD, while only partially relaxing it in the TD.
At elevated temperature, the observed reduction in the constraining effect of the matrix will also be partly the product of thermal softening, which will increase the ease of deformation system activation. From examining the strain in the matrix, however, it may seem possible that another mechanism might also be involved in reducing the constraint on the hydride. As the change in the gradient of evolved hydride strain coincides with the onset of significant chemically induced matrix lattice dilatation, it seems possible that the expansion of the parent lattice, caused by interstitial hydrogen, also allows an increase in hydride lattice expansion.
It should be noted, however, that this evaluation again assumes that no change in stoichiometry occurs in the hydride with increasing temperature, as does no change in phase stability. The importance of phase stability to the strain in the hydride is high, as the large difference between the misfit in the δ and γ phases would result in significantly different magnitudes of elastic and plastic deformation. Other authors [32,63,91,92] have reported a range of transformation temperatures for δ ⇌ γ interchange between 180 °C and 255 °C, the upper limit of which coincides well with the experimentally observed change in regime. It seems possible, then, that an alternate interpretation of this sharp step change may be a change from
δ + γ below 260 °C to solely δ above it. The existence of a bimodal hydride phase distribution, where the misfit of γ needles is lower, might dilute the mechanical interaction with the parent matrix. This would lower the amount of plastic relaxation needed and increase the elastic constraining effect of the matrix.
Where only a single phase exists, the higher misfit of δ might increase plastic relaxation, thus reducing the constraining effect of the parent matrix, and creating the increased gradient at
Third Proposed Manuscript | 216
The Precipitation of Hydrides in Zirconium Alloys higher temperatures. Barrow et al. [34] have reported evidence of composite precipitates that consist of needles with δ cores and γ tips, illustrating the potential complexity of the mechanisms driving this change [34]. During experimentation, however, no evidence of reflections belonging to another phase were observed within the recorded diffractograms. For this hypothesis to hold, the γ phase would have to exist in such low quantities as to not show any measurable diffraction signal, the gamma precipitates could be too fine to produce Bragg diffraction, or the γ phase could overlap heavily with the δ phase, thus making it impossible to deconvolute the two. It is noted that there would be γ reflections suitably isolated from those of δ, which would indicate the presence of this phase, which were not observed in the present study.
From the isothermal holds, Figure 13 is produced, containing the evolution of the elastic strain for the hydride phase, separated into the two principle directions and the two temperature ranges being considered. In the lower temperature subplots, little elastic strain evolution is recorded, predominantly occurring before precipitation is complete. This would indicate that while the hydride lattice is able to dilate during the precipitation process, there is minimal elastic expansion after hydrides have fully formed. Of the higher temperature cycles, the hydride shows significant dilatation during the process of precipitation, possibly owing to the parent matrix being both elastically softer and yielding more easily, thus constraining the hydride to a lesser degree.
Beyond completion, both C5 and C6 continue to show some small elastic expansion up to their final recorded state, suggesting a slow-strain rate relaxation effect could be taking place.
Elsewhere [40,58], it has been reported that hydrides are under some amount of compressive stress, which is likely true of newly formed precipitates or those that are continuing to grow. In those works, the temperature continues to decrease during measurements, leading to further precipitation of hydrides, introducing further stresses concurrent with thermally induced matrix hardening. Of hydrides formed isothermally under reactor operating conditions, however, it seems entirely possible that the softness of the matrix and slower rate of precipitation may allow the progressive relaxation of some portion of these stresses over an extended time period, through plastic deformation in the parent lattice. This could have ramifications for
Delayed Hydride Cracking, where the failure of the hydride requires overcoming the ‘shielding’ compressive stress within the hydride, which result from the hydride misfit [93]. Should substantial stress relaxation take place in hydrides formed at under these conditions, it seems likely that the stress intensity required to cause hydride failure would also be reduced. As the strains recorded within the experiment are all relative, however, a comment as to the magnitude of stresses exerted on the hydride cannot be made.
Another interesting feature to note from the high temperature subplots in Figure 13, is that unlike the matrix, where almost all elastic strain is recorded in the RD with little at all in the
TD, the hydride shows considerable elastic expansion in both directions. This may be an artefact
217 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys of the expanded integration of the Debye Scherrer patterns used for the hydride, where increasing the azimuthal range of the integration from 15° (ψ ± 7.5°) to 45° (ψ ± 22.5°) would increase the dilution of the RD strain evolution with an amount of that recorded in the TD, and vice versa. If not an artefact, the presence of hydride strain where there is none recorded in the matrix might indicate a change of stoichiometry or that coarsening of the hydrides is taking place.
Here, growing precipitates would generate further plastic deformation in the surrounding metal, but the diffracting volume of hydride may not change in any recordable way, owing to smaller hydrides dissolving to feed larger ones. At this time, however, it remains unclear what the precise cause of this behaviour is.
Figure 13. Recorded relative strain evolution in the hydride lattice parameter during all isothermal holds (C2-C7), where dashed vertical lines indicate the completion of precipitation at each temperature.
4.
Conclusion
An in-situ experimental programme investigating the δ-hydride and α-matrix phases was successfully able to monitor and track the evolution of very small strains during a series of thermal operations. The impacts of precipitation, along with matrix texture and hydride/matrix mechanical interactions, were evaluated as mechanisms underpinning the observed trends.
Third Proposed Manuscript | 218
The Precipitation of Hydrides in Zirconium Alloys
The introduction of hydrogen to zirconium induces a large amount of additional strain evolution in the matrix, echoing the observation of other authors that interstitial hydrogen causes significant lattice dilatation. Deconvolution was performed to separate the mechanical contribution to strain evolution from thermal and chemical effects. Mechanical strain was seen to be non-negligible during holds at temperatures of 100 °C to 250 °C, where negative relative strains were observed during and after precipitation. These strains were thought to indicate slow strain rate relaxation of the misfit stresses.
The most significant matrix relaxation was observed in the RD, thought to be indicative of the incoherent ⟨11̅00⟩ 𝛼
hydride-matrix boundary being oriented in the RD, allowing for easier generation of dislocations and activation of slip. In the unit cell, the majority of strain evolution was observed in the basal lattice parameter, owing to the greatest misfit being oriented in that direction, and thus the highest stresses.
Of the 300 °C and 350 °C dwells, little mechanical relaxation was recorded, despite an expected misfit increase with temperature. This was explained through thermal softening preventing the build-up of significant misfit stresses, in conjunction with the longer times for hydrides to precipitate from a reduced chemical driving force.
During continuous heating transients, two distinct gradients were observed in the strain within the hydride, separated at around 280 °C. Below this, the thermal strain in the
⟨111⟩ 𝛿
was similar to the matrix thermal expansion coefficients. This was indicative of the matrix constraining the hydride, although no judgement could be made as to which planes in the matrix acted as the primary control.
An increase in hydride thermal strain was observed above 280 °C, where a gradient larger than either of the thermal expansion coefficients of the matrix was recorded. That in the RD matched a literature coefficient for hydride thermal expansion, but that from the TD did not. This was suggested to be linked to the proposed anisotropy in misfit relaxation between the
⟨11̅00⟩ 𝛼 and
⟨112̅0⟩ 𝛼
directions, related to the coherency of the interfaces in these directions and their ease of activation plastic deformation. The reduction in constraint at elevated temperature was suggested as being due to a combination of thermal softening and matrix lattice dilatation caused by an increase in interstitial hydrogen.
During isothermal holds, little elastic strain evolution is observed in the hydride during the lower experimental temperatures, occurring mainly during precipitation. At higher temperatures, significant elastic dilatation is seen during precipitation, likely indicative of an elastically softer and weaker matrix constraining the hydride less. After precipitation is complete, a slow strain rate relaxation effect was seen, suggesting that at reactor operating conditions hydrides may be capable of relaxing some degree of internal compressive stresses over time.
219 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
5.
Acknowledgements
The author would like to thank the Institut de Radioprotection et de Sûreté Nucléaire for funding the beam time and providing the samples utilised in this experiment as well as Rolls-
Royce and the Engineering and Physical Sciences Research Council for providing sponsorship funding (EP/I003290/1, EP/I005420/1). Further acknowledgements should be given to the infrastructural support of the Materials Performance Centre at the University of Manchester, and the University as a whole. The author is also grateful to J. Blomqvist and T. Maimaitiyili of the
University of Malmö for helpful two-way exchanges of technique and best practice for synchrotron analysis. Finally, thanks should be given to A.T.W. Barrow, of Rolls-Royce,
S.C. Connolly, of Oxford University, and S.R. Ortner, of the National Nuclear Laboratory, for technical guidance and discussions assisting the preparation of this work for publication.
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223 | Third Proposed Manuscript
The Precipitation of Hydrides in Zirconium Alloys
7.
Additional Manuscripts
Aside from the three manuscripts presented here, the author was also involved in a number of other works submitted for publication during the production of this thesis. For the following two publications written by T. Maimaitiyili, M. S. Blackmur was part of the team that performed an in-situ hydrogen charging experiment at the ESRF. M. S. Blackmur also visited
Maimaitiyili at Malmö University to collaborate on the first steps of the process of data analysis for these works, during which a mutual exchange of analysis technique and best practice guidelines took place, which benefitted the present thesis and proposed publications greatly.
Title: The phase transformation between the δ and ε Zr-hydrides
Author: Tuerdi Maimaitiyili
Co-Authors: Axel Steuwer, Jakob Blomqvist, Matthew S. Blackmur, Olivier Zanellato, Christina
Bjerkén, Jérôme Andrieux, and Fabienne Ribeiro
Abstract: We investigate the formation and dissolution of hydrides in commercially pure zirconium powder in-situ using high-energy synchrotron X-ray radiation. Experimental results showed a continuous and reversible phase transition between the δ and ε zirconium hydride phases with clear signs of second order phase transformation.
Submitted to: The Journal of Nuclear Materials on the 16 th of August 2014
Title: In-situ hydrogen loading on zirconium powder
Author: Tuerdi Maimaitiyili
Co-Authors: Jakob Blomqvist, Axel Steuwer, Christina Bjerken, Olivier Zanellato, Matthew S.
Blackmur, Jérôme Andrieux and Fabienne Ribeiro
Abstract: For the first time, various hydride phases in the zirconium-hydrogen system were prepared at a high-energy synchrotron X-ray radiation beamline and their transformation behaviour has been studied in-situ. First, the formation and dissolution of hydrides in commercially pure zirconium powder were monitored in real time during hydrogenation and dehydrogenation process, then, the whole pattern crystal structure analysis such as Rietveld and
Pawley refinements were performed.
Published in: J. Synchrotron Rad. (2015). 22, pp. 995-1000, DOI: 10.1107/S1600577515009054.
Additional Manuscripts | 224
The Precipitation of Hydrides in Zirconium Alloys
8.
Final Conclusions
This thesis describes a series of experiments undertaken during an extended synchrotron campaign, which was designed to study various aspects of the zirconium-hydrogen system; namely diffusion, precipitation kinetics and strain evolution during a series of thermal operations.
Given the complexity of both the experimental set up and the mechanisms taking place within hydrogen charged Zircaloy-4, the analyses outlined in this text were intended to be mutually supportive, where observations made in each allowed deeper understanding of the phenomena occurring within the specimen. Furthermore, given the added complexity of the loading portion of the present campaign, the three topics discussed in this thesis were designed in such a way that observations made here could be used to support those made during the loading experiments. Given that individual conclusions were provided in each of the proposed manuscripts, this section will instead draw these concepts together into a single, cohesive narrative on the experiment.
The topic covered in the first proposed manuscript was that of hydrogen diffusion and redistribution, which was further revisited in the second text, owing to its impact on the process of precipitation. The significance of the movement of hydrogen on both embrittlement mechanisms (hydride rims, DHC, etc.) and also on the fundamental process of precipitation cannot be understated, and so the observations made herein were thought to add to those already made within the literature. With the knowledge of a thermal gradient that was induced across each sample by the process of Joule heating, the propensity for hydrogen to diffuse down this gradient was observed to cause substantial redistribution across the specimen being investigated. The point of lowest temperature and highest gradient, was not, however, that with the highest diffusion flux, as the lower temperature acted as a braking mechanism for diffusion in that region. There was also an additional flow of hydrogen resulting from local concentration gradients established within the sample as a function of the redistribution, which either hindered or enhanced thermo-diffusion, but these were second order to flow from the Soret Effect seen at high experimental temperatures. When cooled close to room temperature, where the thermal gradient was minimal, this Fickian flow was thought to encourage a homogenisation of hydrogen across the sample, such that the regions of depletion and enrichment would progressively have levelled out, if given enough time.
Although the large amount of enrichment close to the cold grips was established rapidly, the axial centre did not demonstrate any significant depletion until much later in the campaign.
When depletion did occur, it was found that a significant amount developed rapidly, and it was postulated that the higher temperature seen in the latter cycles may have allowed diffusion through sites other than the normal tetrahedral interstices. Another cause may have been an
225 | Final Conclusions
The Precipitation of Hydrides in Zirconium Alloys increase in the diffusion of vacancies, as it is predicted that a single vacancy in the lattice can trap up to nine hydrogen atoms, meaning that the diffusion of these traps could have a marked influence on the effective redistribution of hydrogen in the material. Similarly, elevated temperatures may well have increased the recovery of matrix damage, releasing hydrogen trapped within these microstructural features and allowing for their diffusion.
Observations relating to hydrogen traps were thought to be significant, as it is possible that there may have been a population of hydrogen immobilised within the material, owing to substitutional species, vacancies and dislocations. This was especially notable, given that large hydrides are often encompassed by complex dislocation structures, and on dissolution of these precipitates, the fossil structures left behind could well retain some significant portion of the newly dissolved hydrogen, if not already saturated. Those legacy features could thus have encouraged heterogeneous nucleation at preferential sites because of local enrichment of hydrogen that remains trapped in the skeleton structures. In the first manuscript, evidence is given that potentially supports the recovery of matrix damage, albeit damage from sources other than hydride precipitation, at temperatures relevant to those experienced during the experimental programme. As successively precipitating hydrides will likely produce new damage structures with each sequential generation of precipitates, the recovery of damage thought to occur at high temperature during the thermal profile in the present work may actually stabilise the population density of heterogeneous nucleation sites from cycle to cycle, rather than reducing it.
Following on from this, diffusion distance calculations performed to underpin observations of precipitation kinetics in the second manuscript indicated that hydrogen was easily capable of travelling the inter-hydride distance in a matter of seconds, or even the half width of a matrix grain. This demonstrated that hydrogen diffusion does not limit the kinetics of precipitation temperatures pertinent to the present work. That being said, with the density of matrix defects seen in the TEM work presented here, it also seems probable that for some population of hydrogen within the material, nothing like half a grain would be traversed before it was trapped by some defect, creating a new enrichment site and promoting heterogeneous nucleation in the region.
Irrespective of the memory effect, hydride precipitation was observed to be rapid throughout the campaign, although at the highest precipitation temperatures (> 200 °C) the kinetics were rate limited enough that 99 % completion of precipitation took up to 40 seconds.
At lower temperatures (< 200 °C), however, this threshold was reached so rapidly that the temporal resolution of the technique was insufficient to resolve the process below 99 % completion. It seems likely that tracking precipitation at these temperatures would need something approaching the femtosecond temporal resolution offered by an X-ray Free Electron
Final Conclusions | 226
The Precipitation of Hydrides in Zirconium Alloys
Laser. From the transformation map presented in the first manuscript, the point at which the kinetics became rate limiting was above 200 °C.
A study of the precipitation kinetics during a ramped continuous cooling thermal transient did, however, demonstrate that this limited precipitation rate at elevated temperatures meant that the amount of solute hydrogen measured during cooling and heating was not reflective of the actual solubility of the material on precipitation. It was only by quenching to temperature and holding that gradual continued precipitation was observed, where the level of dissolved hydrogen declined slowly from the value reached instantaneously after the quench to the final value that was thought to be reflective of the TSSP.
A notable crossover between these kinetics observations and those of the strain evolution manuscript was that although precipitation occurred rapidly at the lower experimental temperatures, a time-dependent stress relaxation mechanism was seemingly still active within the parent matrix, long after hydrides had seemingly finished forming. At the elevated temperatures, where precipitation took longer to complete, however, this was not the case, and it was apparent that precipitation stresses may well have been relaxed as quickly as they were formed, thanks to the slower rate of coarsening and softer parent matrix. To support precipitation rate observations, a nucleation model was established, describing the rate of nucleation as a function of temperature and geometry. These calculations rendered strain energy second order to interfacial energy when nucleating hydrides, the former reducing the peak temperature by up to 36 °C, based on whether an oblate spheroid or disc morphology was simulated. This latter morphology was that modelled to have the most significant effect on both nucleation rate and peak rate temperature, but from experimental assessment of strain evolution, it was found that a disc or spheroid that is isotropic on the basal plane may not have been a representative description of the hydrides forming within the sample.
Through a process of deconvolution, the third manuscript was able to separate mechanical, thermal and chemical strains induced in the parent α-zirconium matrix, such that the mechanical interaction between it and the hydride phase could be evaluated. With the known texture quantified from the material, it was possible to identify a difference in strain relaxation between the
⟨11̅00⟩ 𝛼
and
⟨112̅0⟩ 𝛼
directions, which implied an anisotropic relaxation of the misfit between the precipitate and matrix in these directions. This supported observations of others in the literature, whom suggested that the residual δ-hydride interfacial strains were anisotropic on the basal plane, and that the phase formed in needle-like structures. This may have been further substantiated by observations of needle-like objects in TEM studies on the material used in this work, which was known from X-ray diffraction to not contain any significant population of γ-hydride; the phase normally considered to form in needles.
227 | Final Conclusions
The Precipitation of Hydrides in Zirconium Alloys
From further evaluations of strain evolution during ramped thermal transients, it was noticed that the thermal expansion of the hydride was well below that quoted in the literature for the bulk phase, identified as being the product of the parent matrix constraining the expansion of the precipitates. Above a threshold temperature of 280 °C, however, this constraint was relaxed and the hydride was able to expand at a rate close to the literature thermal expansion coefficient for the precipitate. This was thought to be from thermal softening of the parent matrix at elevated temperatures, and also a possible result of matrix lattice dilatation resulting from interstitial solute hydrogen. Finally, a study of the strain evolution within hydrides during isothermal holds found that at elevated temperatures, those above 250 °C, the phase clearly underwent some level of progressive time dependent dilatation, thought to be indicative of a slow strain rate relaxation of stresses within the phase. This was tentatively suggested as a way in which the ‘shielding’ compressive stresses inside a hydride may be overcome somewhat at these elevated temperatures, allowing fracture of hydrides with a lesser stress intensity during the process of DHC.
These three manuscripts provide some novel observations on hydrogen and hydrides in their own right, but with the information gleaned from these studies, the loading experiments discussed in Further Work (to be published in an article at a later date) will be far better supported. For example, from studies of Soret and Fickian diffusion it is now known how hydrogen might migrate within the sample in the absence of a stress gradient, such that when one is applied, any stress-induced redistribution can be deconvoluted from that from the other two effects. Studies on the kinetics of hydride precipitation mean that the nucleation and growth rate of notch-tip hydrides, which may form during the loading experiment, can be identified and compared against the nucleation and growth rates in the non-loading experiments. Similarly, the way in which load influences any strain evolution in the matrix or hydride could also now be deconvoluted, such that a change in the magnitude of hydride misfit could be understood as a function of the applied force. It is with a strong foundation of understanding of the broader concepts of precipitation, strain evolution and hydrogen redistribution that further publications based on the loading portion of the campaign can thus be made.
Final Conclusions | 228
The Precipitation of Hydrides in Zirconium Alloys
9.
Further Work
This thesis describes three out of four segments of an extended synchrotron campaign.
The fourth and final experiment was performed prior to this document being written, but insufficient time available to the author meant that no analysis could be performed for inclusion in this work. This section serves to describe the final study of the campaign, which is intended to be published in the open literature at a later date.
Samples S3 and S4 were distinct from S1 and S2 in that they were fabricated to have twin
notches of 1 mm diameters at the top and bottom surface, as in Figure 54 – (a). The purpose of
these notches was such that upon the application of a uniaxial load, a tri-axial stress state was established in the material close to the notch. This stress field was hoped to be similar to that which is thought to exist at a flaw in cladding tube material, thought to lead to the formation of notch-tip hydrides. The sample was modelled using Autodesk Inventor Fusion, and the stress fields resulting from the applied load were simulated using Autodesk Simulation Mechanical, the
results of which are shown in Figure 54 – (b). From the result of this finite element simulation of
a 250 N applied load, it can be seen that nodes at the tip of the notch experience a tensile planar stress in all three axes, albeit of a small magnitude in the ZZ plane.
(a)
X
Y
(b)
XX
YY Tension
ZZ
σ xx
= 19.9 MPa σ yy
= 393.3 MPa σ zz
= 6.7 MPa
Figure 54. (a) Sample S3 and S4 geometry (b) finite element simulation of the stress fields established under a 250 N applied load.
229 | Further Work
The Precipitation of Hydrides in Zirconium Alloys
As with the previous sections of this campaign, a study of a non-hydrogen-charged sample preceded that of the hydrogen charged material, so that the effect of the experimental parameters upon the base Zircaloy-4 metal could be quantified, thus allowing deconvolution of the effect of hydrogen and hydrides. The details of the samples used throughout the campaign
are revisited in Table 13, where S3 and S4 are those used during the loading investigations. A
sample with a lower hydrogen content was chosen for this part of the programme by IRSN, due to a lack of availability of material, sharing a similar processing history with S1 and S2, discussed previously. These samples were then notched using a drill with a 1 mm diameter. As before, this section will be further subdivided according to the sample used in each subsection.
Table 13. Sample specifications revisited.
S1
S2
S3
S4
Sample H Content (ppm wt.
)
0
430
0
200
Details
Standard sample.
Identical to S1, but charged with hydrogen.
Similar to S1, but with Ø1 mm notches.
Identical to S3, charged with hydrogen.
9.1.
Non-Hydrogen-Charged Sample (S3)
Sample S3 had not undergone any process of hydrogen charging, and so it was used as a reference for the way in which stresses developed around the tip of a notch when temperature was varied. This was considered important as it seemed possible that the anisotropic thermal expansion of the unit cell in conjunction with the texture of the material might lead to the development of some form of stress distribution surrounding the notch tip. This may then have led to stress fields that were dissimilar to those predicted from finite element simulations.
Similarly, with a lower cross-sectional area close to the notch it seemed probable that the thermal gradient in this sample would be considerably different to that found from S1, owing to a change in the cross sectional area of the sample in the volume between the notches.
To undertake an assessment of these, the sample was heated to a series of shelf temperatures, like those used during C0, and at each of these the sample was mapped in X and
Y, covering the material immediately below the notch, but also extending axially to one side. A grid of 10 x 17 points was imaged, using a step size of 0.2 mm and a beam size of 0.2 mm by
0.2 mm, to give a total illuminated area of 2 mm by 1.4 mm. During this process, no loading was applied to the sample, such that it did not influence the thermal stresses that were expected to
develop around the notch. These details are shown schematically in Figure 55.
Further Work | 230
The Precipitation of Hydrides in Zirconium Alloys
Figure 55. Non-charged sample tri-axial strain field mapping of sample S2.
9.2.
Hydrogen Charged Sample (S4)
The original experimental plan was to undertake similar mapping to that undertaken on
S3 while performing thermal operations, in order to study the way in which temperature and load influenced the distribution of hydrides, hydrogen solubility and strain in the area surrounding the notch. Time constraints during experimentation on this final sample meant that it was not
possible to perform full mapping of the area using the parameters in Figure 55, as was intended,
and so instead it was decided to map the area immediately under the notch, with a series of overlapping gauge volumes. This choice was made as the predicted region of three-dimensional tensile stress, close to the notch tip, would thus be the area in which any postulated changes in solubility might have occurred as a function of the applied stress. Furthermore, notch-tip hydrides were thought likely to form within this region, and so an investigation into the way in which applied load and temperature changed the behaviour of the matrix and hydrides in this region was thought to be of interest.
To accomplish this assessment, a gauge volume equal to that used in S3 was scanned through S4 in 0.1 mm increments over a total vertical distance of 0.6 mm, as schematised in
Figure 56. Three thermal cycles were implemented, with a fourth (not pictured) begun and ended
in its early stages owing to the expiration of the experimental beam time. For the first two cycles, performed with loads of 0 N and 125 N, respectively, the rate of temperature change was set to a continuous 4 °C per minute (or 0.0667 °C s -1 ), and featured both positive and negative thermal ramps between 40 °C and a soak temperature of 450 °C. For the third cycle, at 250 N (100 MPa), the ramped heating portion of the cycle was removed, and instead it was rapidly heated to the peak temperature, and cooled at 10 °C per minute (0.1667 °C s -1 ) back to 40 °C. These details are
The recording time implemented throughout these cycles was 10 seconds per pattern, with an associated average disk-write time of ≈8 seconds, making the total acquisition time
231 | Further Work
The Precipitation of Hydrides in Zirconium Alloys approximately 18 seconds. This is important, as the temperature was continuously ramped, rather than stepped, and so each sequential pattern was recorded at a slightly different temperature from the last; an effect that would require deconvolution later. Given the rate of temperature change and the time taken to capture the seven acquisitions in each series
(approximately 2 minutes and 6 seconds), that would mean a total difference of ≈8.4 °C in temperature between the first point recorded in each consecutive line scan. In the final cycle, this increases to ≈21 °C per positional scan series, and so both of these effects must be quantified using information on the material determined from each of the previous samples that were studied during this campaign. Ultimately, it is expected that these loading experiments may elucidate whether an applied tri-axial stress has any influence upon hydrogen solubility; the way in which precipitated hydrides might influence the stresses that develop in the matrix around a notch, or the converse of how the stresses in the matrix might influence a hydride precipitated at a notch; and the way in which dissolved hydrogen migrates in the presence of the complex conditions present at the defect.
Figure 56. Charged sample notch tip hydride mapping of sample S3 under applied load.
Further Work | 232
The Precipitation of Hydrides in Zirconium Alloys
10.
Appendices
The following sections contain structural models created and refined within this thesis, in a format ready to be loaded into TOPAS using ‘.INP’ file extensions.
10.1.
Appendix I – Rietveld Refined Structural Model (TOPAS INP Format)
r_exp 9.11148232 r_exp_dash 10.6943145 r_wp 7.17695517 r_wp_dash 8.42372441 r_p 4.81060802 r_p_dash 5.9996273 weighted_Durbin_Watson 0.509063138 gof 0.7876825 iters 10000 do_errors line_min continue_after_convergence randomize_on_errors chi2_convergence_criteria 1e-008 xdd "Zirc Diffractogram.xy" r_exp 9.11148232 r_exp_dash 10.6943145 r_wp 7.17695517 r_wp_dash 8.42372441 r_p 4.81060802 r_p_dash 5.9996273 weighted_Durbin_Watson 0.509063138 gof 0.7876825 x_calculation_step = Yobs_dx_at(Xo); bkg @ 22.4148664`_0.442191193
2.41860306`_0.590677698 -0.506783482`_0.438023442
Zero_Error(, 0.00424_0.00010)
LP_Factor(0) convolution_step 4 start_X 4.6 finish_X 6.2 extra_X_right 0.05
Absorption(, 57.17434_3.19574)
Simple_Axial_Model(, 1.02313_0.00895)
Rp 217.5
Rs 217.5 lam
la 1.0
lo 0.142231
lh 0.14655_0.08740
lg 0.39950_0.05802 ymin_on_ymax 0.00001
233 | Appendices
The Precipitation of Hydrides in Zirconium Alloys str r_bragg 193.909525 phase_MAC 1.36177506 phase_name "Alpha Zirconium"
MVW(@ 182.448,@ 46.801`_0.003,@ 97.824`_6.490) scale @ 3.75700878e-006`_1.839e-007 space_group P63/mmc
CS_L(@, 433.21314`_31.41316 min=5;)
Phase_LAC_1_on_cm( 8.81526`_0.00052)
Phase_Density_g_on_cm3( 6.47336`_0.00038)
Hexagonal(OutPrm_Alpha_a 3.235987`_0.000041 min=3.2; max=3.3;,
OutPrm_Alpha_c 5.160770`_0.000276 min=5.1; max=5.2;) site Zr num_posns 2 occ Zr 1 beq @ 3.83424`_0.17383 x =1/3; : 0.33333 y
=2/3; : 0.66667 z =1/4; : 0.25000
PO_Two_Directions(@, 2.98334`_0.11733,, 0 1 3,@, 0.47295`_0.00744,, 0 2
0,@, 0.54765`_0.03007) numerical_area OutPrm_Alpha_Area 141.529326 str r_bragg 1.05603729 phase_MAC 1.34264096 phase_name "Delta Hydride"
MVW(@ 371.616,@ 108.106`_0.160,OutPrm_Delta_W 2.176`_6.490) scale @ 1.77633078e-008`_5.416e-008
CS_L(@, 15.49941`_2.53160 min=5;)
*/
/* space_group Fm-3m
Phase_LAC_1_on_cm( 7.66395`_0.01131)
Phase_Density_g_on_cm3( 5.70812`_0.00842)
Cubic(OutPrm_Delta_a 4.763763`_0.002343 min=4.7; max=4.8;) site Zr num_posns 4 occ Zr 1 beq @ 2.74697 x 0 y 0 z 0 site H num_posns 8 occ H =5/6; : 0.83333 beq @ 0.50000 min =0.5; x =1/4; :
0.25000 y =1/4; : 0.25000 z =1/4; : 0.25000 numerical_area OutPrm_Delta_Area 3.99515134 str r_bragg 0.853356738 phase_MAC 1.35021096 phase_name "Gamma Hydride"
MVW(@ 184.464,@ 104.063,@ 1.711_194.492) scale @ 6.12223258e-008_7.081e-006_LIMIT_MIN_1e-015
CS_L(@, 94396.05267_3508434205.25362_LIMIT_MIN_12 min=12;) space_group P42/n
Phase_LAC_1_on_cm( 3.97434)
Phase_Density_g_on_cm3( 2.94349)
Tetragonal( 4.586, 4.948) site Zr num_posns 2 occ Zr 1 beq @ 19.00558 x 0 y 0 z 0 site H num_posns 4 occ H 0.5 beq @ 20.00000 min =0.5; x 0 y 0.5 z 0.25 numerical_area @ 0.0659101472
Appendices | 234
The Precipitation of Hydrides in Zirconium Alloys
10.2.
Appendix II – Le Bail Refined Structural Models (TOPAS INP Format)
r_exp 9.63040624 r_exp_dash 11.2087135 r_wp 6.66666731 r_wp_dash 7.75925358 r_p 4.62975204 r_p_dash 5.62197784 weighted_Durbin_Watson 0.666179431 gof 0.69225193 iters 10000 do_errors line_min chi2_convergence_criteria 1e-004 xdd "Zirc Diffractogram.xy" r_exp 9.63040624 r_exp_dash 11.2087135 r_wp 6.66666731 r_wp_dash 7.75925358 r_p 4.62975204 r_p_dash 5.62197784 weighted_Durbin_Watson 0.666179431 gof 0.69225193 x_calculation_step = Yobs_dx_at(Xo); bkg @ 16.8985756`_0.394142417 3.99779126`_0.412868425 -
4.73606878`_0.368275885
Zero_Error(, 0.00424_0.00010)
LP_Factor(0) convolution_step 4 start_X 4.6 finish_X 6.4 extra_X_right 0.05
Absorption(, 57.17434_3.19574)
Simple_Axial_Model(, 1.02313_0.00895)
Rp 217.
Rs 217.5 lam
la 1.0
lo 0.142231
lh 0.14655_0.08740
lg 0.39950_0.05802 ymin_on_ymax 0.00001 hkl_Is lebail 1 hkl_m_d_th2 0 1 0 6 2.802321 2.90834 I 0.00000 hkl_m_d_th2 0 0 2 2 2.580256 3.15871 I 0.00000 hkl_m_d_th2 0 1 1 12 2.462649 3.30959 I 0.00000 hkl_m_d_th2 0 1 2 12 1.898175 4.29420 I 0.71482 hkl_m_d_th2 1 1 0 6 1.617921 5.03848 I 0.05073 hkl_m_d_th2 0 1 3 12 1.466009 5.56097 I 0.00917 hkl_m_d_th2 0 2 0 6 1.401161 5.81856 I 0.01072
235 | Appendices
The Precipitation of Hydrides in Zirconium Alloys hkl_m_d_th2 1 1 2 12 1.370737 5.94782 I 0.04706 hkl_m_d_th2 0 2 1 12 1.352204 6.02941 I 0.05480 hkl_m_d_th2 0 0 4 2 1.290128 6.31981 I 0.00103 hkl_m_d_th2 0 2 2 12 1.231325 6.62195 I 0.00000 r_bragg 0.348570656 phase_MAC 0 phase_name "Alpha Zirconium" space_group "P63/mmc"
CS_L(@, 433.21314`_31.41316 min=5;)
MVW( 182.448,@ 46.795`_0.081,@ 17.524`_0.046)
Hexagonal(OutPrm_Alpha_a 3.235842`_0.002496 min=3.2; max=3.3;,
OutPrm_Alpha_c 5.160512`_0.003965 min=5.1; max=5.2;) numerical_area OutPrm_Alpha_Area 145.662716 hkl_Is lebail 1 hkl_m_d_th2 1 1 1 8 2.750557 2.96309 I 0.09028 hkl_m_d_th2 0 0 2 6 2.382053 3.42161 I 0.06540 hkl_m_d_th2 0 2 2 12 1.684366 4.83960 I 0.00194 hkl_m_d_th2 3 1 1 24 1.436432 5.67557 I 0.00235 hkl_m_d_th2 2 2 2 8 1.375279 5.92816 I 0.00000 hkl_m_d_th2 0 0 4 6 1.191026 6.84627 I 0.34141
CS_L(@, 14.08669`_1.17222 min=6;) r_bragg 0.448756841 phase_MAC 0 phase_name "Delta Hydride" space_group "Fm-3m"
MVW( 371.616,@ 108.129`_0.286,Outprm_Delta_W 82.476`_0.046)
Cubic( OutPrm_Delta_a 4.764105`_0.004200 min=4.7; max=4.8;) numerical_area OutPrm_Delta_Area 9.09899058
Appendices | 236
The Precipitation of Hydrides in Zirconium Alloys
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