Mechanisms Governing the Growth, Reactivity and
Stability of Iron Sulfides
by
Francis William Herbert
M.Eng, Materials Science, University of Oxford, UK
Submitted to the Department of Materials Science and Engineering
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Materials Science and Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2015
c Massachusetts Institute of Technology 2015. All rights reserved.
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Materials Science and Engineering
November 20, 2014
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bilge Yildiz
Associate Professor of Nuclear Science and Engineering
Thesis Supervisor
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Krystyn J. Van Vliet
Associate Professor of Materials Science and Engineering
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Donald Sadoway
John F. Elliott Professor of Materials Chemistry
Chair, Departmental Committee on Graduate Students
2
Mechanisms Governing the Growth, Reactivity and Stability of Iron
Sulfides
by
Francis William Herbert
Submitted to the Department of Materials Science and Engineering
on November 20, 2014, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy in Materials Science and Engineering
Abstract
The kinetics of electrochemical processes in ionic materials are fundamentally governed
by dynamic events at the atomic scale, including point defect formation and migration,
and molecular interactions at the surface. A corrosion system comprising an iron sulfide
film (passive layer) formed on iron or steel in contact with an hydrogen sulfide (H2 S)rich fluid can thus, in principle, be modeled by a series of unit reaction steps that control
the rate of degradation under given thermodynamic conditions. This overarching thesis
goal necessitates a concerted experimental and computational approach to determine
the relevant kinetic parameters such as activation barriers Ea and rate constants νo
for the homogeneous and heterogeneous reactions of interest. These fundamental values can be obtained experimentally via temperature-dependent measurements on pure,
model iron sulfide samples. This thesis therefore consists of three case studies on the
stable Fe-S phases pyrrhotite (Fe1-x S) and pyrite (FeS2 ) to identify the elementary corrosion mechanisms and their kinetic parameters. Pyrrhotite is of interest because the
off-stoichiometry of this phase leads to relatively rapid bulk processes such as diffusion;
pyrite has a comparitively inert bulk but this work showed that it has a chemically labile
surface.
The first study focuses on two basic, rate-controlling steps in the growth of pyrrhotite:
cation diffusion and sulfur exchange at the surface. First, iron self-diffusivity * DFe is determined across the temperature range 170-400 o C through magnetokinetic studies of
the diffusion-driven "λ" magnetic transformation, as well as direct tracer diffusion measurements in Fe1-x S crystals using secondary ion mass spectrometry (SIMS). This range
encompasses the sponteneous magnetic and structural order-disorder temperature T N
= 315 o C in pyrrhotite. The effect of spontaneous magnetization below T N is to increase
the Fe vacancy migration energy by a combined 40% increasing Ea for diffusion from
0.83 eV in paramagnetic Fe1-x S to ∼1.20 eV in the fully magnetized state. An extrapolation of the Arrhenius law from the paramagnetic regime would therefore overestimate
actual diffusivities by up to 102 times at 150 o C. Second, the surface exchange of sulfur
from H2 S into the solid state in Fe1-x S is measured using electrical conductivity relaxation, yielding Ea = 1.1 eV for sulfur incorporation into pyrrhotite. With their similar
thermal dependence, there is no clear temperature crossover from cation diffusion- to
surface exchange-limiting regimes, or vice versa. Instead, surface exchange is expected
to constrain pyrrhotite growth for films under ∼ 100 µm thickness, beyond which diffusion becomes the rate limiting mechanism, independent of external driving factors
such as temperature.
The second study explores the role of surface electronic states on the electrochemical reactivity of pyrite. Charge transfer between a solid surface and an adsorbate such
as H2 S requires the mutual availability of filled/empty electronic states at the same energy level. The semiconducting FeS2 (100) surface is predicted to have intrinsic surface
states (SS’s) from Fe and S dangling bonds, as well as extrinsic SS’s related to delocalized defects at the surface, both of which would affect charge transfer characteristics. A novel, broadly-applicable methodology is developed in this thesis to quantify
3
the energy and density of these SS’s, based on experimental scanning tunneling microscopy/spectroscopy (STM/STS) in conjunction with first principles tunneling current modeling. As a result, a decreased surface band gap Eg of 0.4 eV, compared to 0.95
eV in bulk pyrite, is measured. The findings highlight the need to differentiate between
bulk and surface electronic structure when assessing heterogeneous reactivity, and have
implications for the use of FeS2 in potential technological applications, for example as
a photovoltaic adsorber.
Finally, the dynamics of point defect formation and clustering on FeS2 (100) under
high-temperature, reducing conditions are investigated to understand the stability of
the surface under extreme conditions. Synchrotron x-ray photoelectron spectroscopy
(XPS) is used to measure a formation energy ∆H f for sulfur vacancies in the topmost
atomic layer of 0.1 eV up to approximately 240 o C. Above this temperature, however,
point defects are shown to condense into surface pits as measured by scnaning tunneling
microscopy (STM). The combined, experimental XPS and STM results are replicated
with high precision by a kinetic Monte Carlo (kMC) simulation, developed by Aravind
Krishnamoorthy towards his doctoral thesis, of surface degradation on realistic lengthand timescales of 10−10 − 10−7 m and up to several hours, respectively. The findings
have implications for the initiation of surface breakdown via pitting in ionic passive
films, as well as providing a broader understanding of the non-stoichiometry of the
pyrite surface.
The common thread is a focus on events at the atomic and electronic scale, with an
emphasis on point defects. The results thereby facilitate a bottom-up approach to modeling electrochemical processes such as corrosion in Fe-S phases, in which the unit steps
are cast into probabilistic simulation tools. While the three studies here comprise only
a partial examination of the atomic-scale events regulating the behavior of Fe-S passive
layers, this approach makes inroads towards more accurate component lifetime prediction and the design of robust materials for aggressive environments. Moreover, the
fundamental surface and bulk physical chemistry of iron sulfides explored in this work
has implications beyond corrosion to other uses of these materials, including potential
magnetic devices (Fe1-x S) and earth-abundant photovoltaic and photoelectrochemical
adsorbers (FeS2 ).
Thesis Supervisor: Bilge Yildiz
Title: Associate Professor of Nuclear Science and Engineering
Thesis Supervisor: Krystyn J. Van Vliet
Title: Associate Professor of Materials Science and Engineering
4
Acknowledgments
I am deeply grateful to my co-advisors, Professor Bilge Yildiz and Professor Krystyn van
Vliet, for their encouragement, guidance and support. It has been an immense pleasure
to witness both Bilge and Krystyn establish themselves with tenure at MIT during my
time here and be part of two flourishing laboratories. Meanwhile, Bilge’s passion for
solid state chemistry and keen eye for important details, and Krystyn’s diligent and
organized approach to high-quality scientific inquiry have greatly inspired me. I also
thank Krystyn for teaching me how to spell "properly": the word sulphide seems as alien
to me now as sulfide did five years ago.
This work would not have been possible without my ever-dependable collaborator and
friend Aravind Krishnamoorthy. He is gifted not only with a brilliant scientific intellect,
but an immensely humble and generous personality that has made working together on
this project a richer experience. His efforts truly allowed our combined computational
and experimental approach to become more than the sum of its parts.
I am also thankful to my collaborators on this project and others, including: Wen Ma,
Yan Chen and Qiyang Lu from the Laboratory for Electrochemical Interfaces at MIT; Peter Albrecht at Brookhaven National Laboratory; Predrag Lasic and Rickard Armiento
(Ceder group, MIT); Rupak Chakraborty and Katy Hartman (Buonassissi group, MIT).
Thank you to Prof. Randall Feenstra at Carnegie Mellon University for his help deciphering the SEMITIP code for tunneling spectroscopy simulations.
I would like to thank all members, past and present, from my two fantastic reasearch
groups: the Laboratory for Electrochemical Interfaces (LEI) and the Laboratory for Material Chemomechanics who have taught me so much, from defect chemistry in ionic
solids to the mechanics of living cells. In particular, I am very grateful to Roza Mahmoodian for her support and for putting up with my incessant complaining over failed
experiments. Also to Bal Mukund Dhar for his infectious enthusiasm and help with CVD,
and to Lucy Rands for her help and eagerness as a summer intern.
I am indebted to my thesis committee - Prof. Carl Thompson and Prof. Harry Tuller - for
their useful comments and constructive criticism. In addition, I greatly thank Prof. Chris
Schuh for providing invaluable feedback, despite not sitting on my final committee.
BP Plc. had already supported my education for over 20 years when they arrived at MIT
to propose this project, so I am delighted they extended their commitment to my graduate studies. In particular, I would like to thank Sai Venkatesweran, Richard Woolam,
Steve Shademan and their colleagues for their help and advice.
My parents, Richard and Kate, have inspired and guided me my whole life; I would not
be here without the opportunities and unwavering support they have provided. And I
cannot omit the other four fifths of my band of brothers who are my frame of reference
for everything and never stop injecting humour and happiness into my life.
Finally, thank you to all those who have made my time at MIT so special outside of the
lab. My family away from home; the eclectic and dynamic community at "Martha" (216
Norfolk St): Sam, Katy, Georgie, Jake, Benji, Ines, Chris, Nina, Alex, Federico, Elison,
Andre, James, Andre, Stephanie, Rob, Balthazar, Simon, Sebastian, Nico, Melissa, Serjumbi, Aron, all of our other guests, and last but not least Teresa for not losing faith in
me after all these years.
5
6
Contents
1 Introduction
13
1.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
1.2 Passivity: a brief introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
1.3 Iron sulfide phases and corrosion products . . . . . . . . . . . . . . . . . .
14
1.3.1 Sour corrosion mechanism: lab and field experience . . . . . . . .
17
1.3.2 Model phases: Pyrrhotite (Fe1-x S) and Pyrite (FeS2 ) . . . . . . . .
19
1.4 Towards a predictive, multiscale corrosion model . . . . . . . . . . . . . .
20
1.4.1 Existing passive film models . . . . . . . . . . . . . . . . . . . . . . .
20
1.4.2 Unit processes controlling Fe-S passive layer behavior . . . . . . .
23
1.4.3 The need for experimentally-derived parameters . . . . . . . . . .
24
1.5 Thesis goals and organization . . . . . . . . . . . . . . . . . . . . . . . . . .
26
2 Growth: cation diffusion and surface exchange as rate-limiting mechanisms
in pyrrhotite, Fe1-x S
27
2.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
2.2 Pyrrhotite: polytypes and transitions . . . . . . . . . . . . . . . . . . . . . .
29
2.2.1 Structural and magnetic properties . . . . . . . . . . . . . . . . . . .
30
2.2.2 The λ-transition in NC pyrrhotites . . . . . . . . . . . . . . . . . . .
34
2.3 Diffusion-limited λ transition . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
2.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
2.3.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
37
2.3.3 Continuous re-ordering of ferrimagnetic superlattice
. . . . . . .
40
2.3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
2.4 Isotope tracer diffusion measurements . . . . . . . . . . . . . . . . . . . . .
45
2.4.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
2.4.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
48
2.4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
2.5 Sulfur exchange kinetics at the Fe1-x S surface . . . . . . . . . . . . . . . . .
54
2.5.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
2.5.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
57
2.5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
2.6 Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
2.6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
2.6.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
7
3 Reactivity: quantification of electronic band gap and surface states on FeS2 (100) 69
3.1 Background and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.1.1 Electrochemical charge transfer in semiconductor-absorbate systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.1.2 Surface states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.1.3 Scanning tunneling spectroscopy and TIBB . . . . . . . . . . . . . . 74
3.1.4 The FeS2 (100) surface . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.2.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.2.2 Computational . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.3.1 Current-separation and current-voltage tunneling spectroscopy . 80
3.3.2 Simulated tunneling spectra based on DFT-calculated DOS . . . . 82
3.4 Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.4.2 Implications for other applications of FeS2 , e.g. PV . . . . . . . . . 89
3.4.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4 Stability: dynamics of point defect formation, clustering and pit initiation
on the pyrite surface
91
4.1 Background and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.1.1 Chapter goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.1.2 Passivity breakdown by pitting . . . . . . . . . . . . . . . . . . . . . 92
4.1.3 FeS2 surface chemistry and non-stoichiometry . . . . . . . . . . . . 94
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2.2 Computational . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.3.1 Evolution of pyrite surface structure and chemistry . . . . . . . . . 97
4.3.2 Mechanism of vacancy formation and coalescence . . . . . . . . . 103
4.4 Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.4.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5 Conclusions
109
5.1 Summary of activation barriers . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.3 Outlook and perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
A Pourbaix diagrams for the Fe-H2 S-H2 O system
113
B Chemical Vapor Deposition of Fe-S
119
B.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
B.2 Methods: CVD setup and apparatus . . . . . . . . . . . . . . . . . . . . . . . 119
B.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
C Diffusivity measurements using thin film samples
8
129
List of Figures
1-1
1-2
1-3
1-4
1-5
1-6
1-7
1-8
Potential E vs. current i (polarization) curve for a generic metal. . . . . .
Global sour oil and gas statistics. . . . . . . . . . . . . . . . . . . . . . . . . .
Thermodynamic predictions of corrosion products. . . . . . . . . . . . . .
Mechanism of iron sulfide formation on steels in H2 S-bearing electrolytes.
Iron sulfide stability phase diagram. . . . . . . . . . . . . . . . . . . . . . . .
Sulfide corrosion of 4130 carbon steel at 220 o C. . . . . . . . . . . . . . . .
Schematic of unit processes in Fe-S passive layers. . . . . . . . . . . . . . .
Overview of strategy to construct a non-empirical passive film model. . .
14
15
17
18
20
22
24
25
2-1
2-2
2-3
2-4
2-5
2-6
2-7
2-8
2-9
2-10
2-11
2-12
2-13
2-14
2-15
2-16
2-17
2-18
2-19
2-20
2-21
2-22
2-23
2-24
2-25
2-26
2-27
2-28
2-29
2-30
Collected literature values of Fe self-diffusivity. . . . . . . . . . . . . . . .
Structural unit cells of pyrrhotite. . . . . . . . . . . . . . . . . . . . . . . .
Pyrrhotite structural and magnetic phase diagrams. . . . . . . . . . . . .
Idealized Fe1-x S superstructures. . . . . . . . . . . . . . . . . . . . . . . . .
Distributions of vacancies in 4C and NC pyrrhotites. . . . . . . . . . . . .
The peak-like λ-transition in NC Fe1-x S. . . . . . . . . . . . . . . . . . . .
X-ray diffraction of synthetic pyrrhotites. . . . . . . . . . . . . . . . . . . .
Setup of cubic kinetic Monte Carlo (kMC) grid. . . . . . . . . . . . . . . .
Temperature-dependent magnetization σ(T ). . . . . . . . . . . . . . . . .
Magnetization vs. applied field (σ-H). . . . . . . . . . . . . . . . . . . . .
Reversible magnetic transformation at short timescales. . . . . . . . . .
Best fits to exponential equation. . . . . . . . . . . . . . . . . . . . . . . .
Long-timescale isothermal magnetization. . . . . . . . . . . . . . . . . . .
Differential scanning calorimetry (DSC) results. . . . . . . . . . . . . . .
Continuous re-ordering towards ferrimagnetic state. . . . . . . . . . . .
Cross section of sulfide scale. . . . . . . . . . . . . . . . . . . . . . . . . . .
Cu-kα powder XRD pattern. . . . . . . . . . . . . . . . . . . . . . . . . . .
Energy-dispersive X-ray spectroscopy (EDS) . . . . . . . . . . . . . . . . .
Sources of error considered in statistical analysis of diffusion data. . .
Secondary ion mass spectrometry (SIMS) profiles. . . . . . . . . . . . . .
Error function solution to diffusion profiles. . . . . . . . . . . . . . . . . .
Values for iron self-diffusion coefficient * DFe . . . . . . . . . . . . . . . . .
Sputter deposited thin films for ECR experiments. . . . . . . . . . . . . .
Electrical conductivity relaxation apparatus setup. . . . . . . . . . . . . .
Temperature-pressure equilibrium phase diagram for Fe-S. . . . . . . . .
X-ray photoelectron spectroscopy (XPS) from a Fe1-x S thin film sample.
Electrical resistance relaxation at 565 o C. . . . . . . . . . . . . . . . . . .
Electrical conductivity relaxation results. . . . . . . . . . . . . . . . . . . .
Drift, stability and repeatability of ECR experiments. . . . . . . . . . . .
Temperature- and film thickness dependence of rate limiting steps. . .
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32
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50
52
55
56
57
59
62
63
65
66
3-1 Charge transfer in electrochemical (corrosion) systems. . . . . . . . . . .
3-2 Band bending effects in STS measurement. . . . . . . . . . . . . . . . . . .
3-3 FeS2 single crystal samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
75
78
9
3-4 Distributions of surface states as defined in the SEMITIP program. . . . .
3-5 Scanning tunneling spectroscopy (STM) images of the as-grown FeS2 (100)
surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-6 Current-separation spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . .
3-7 Current-voltage spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-8 Pyrite valence band. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-9 Modeling tunneling spectroscopy with surface states . . . . . . . . . . . .
3-10 Density functional theory (DFT)-computed band structures. . . . . . . . .
3-11 Fitting to experimental surface Eg . . . . . . . . . . . . . . . . . . . . . . . . .
3-12 Visualization of FeS2 (100) surface charge q . . . . . . . . . . . . . . . . . .
3-13 Low surface bandgap implications for PV. . . . . . . . . . . . . . . . . . . .
3-14 Preliminary investigations on bulk and 2-dimensional MoS2 . . . . . . . .
4-1
4-2
4-3
4-4
4-5
4-6
4-7
4-8
80
81
82
83
83
85
86
87
88
89
90
Proposed mechanisms of passivity breakdown and pitting. . . . . . . . . .
Nanopits formed by vacancy agglomeration. . . . . . . . . . . . . . . . . .
XPS sample clamp for FeS2 crystals. . . . . . . . . . . . . . . . . . . . . . . .
S 2p photoelectron spectra of FeS2 (100). . . . . . . . . . . . . . . . . . . .
Atomic model of the FeS2 (100) surface as viewed side-on. . . . . . . . . .
Sulfur monomer vacancy concentration. . . . . . . . . . . . . . . . . . . . .
Proportion of the M and S components of the S 2p photoelectron spectra.
Scanning tunneling microscopy (STM) images of single crystal FeS2 (100)
surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-9 Pits are one half- or one lattice parameter deep. . . . . . . . . . . . . . . .
4-10 Illustration of atomic processes involved in the proposed mechanism of
pit formation and growth on pyrite (100). . . . . . . . . . . . . . . . . . . .
4-11 kinetic Monte Carlo simulation results. . . . . . . . . . . . . . . . . . . . . .
93
94
96
98
99
101
101
B-1
B-2
B-3
B-4
B-5
B-6
B-7
Home-made Chemical Vapor Deposition (CVD) system. . . .
Description and safety information for Fe and S precursors.
Iron sulfide films deposited from Fe(acac)3 and TBDS. . . .
Carbon contamination in Fe-S films from Fe(acac)3 . . . . . .
Iron sulfide films deposited from Fe(CO)5 and TBMS. . . . .
Iron sulfide films deposited from Fe(CO)5 and H2 S. . . . . .
Template stripping for ultrasmooth sulfide surfaces. . . . . .
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121
122
124
125
125
126
127
C-1
C-2
C-3
C-4
Iron self-diffusivity * DFe measurements. . . . . . . .
X-ray diffraction of thiin films for ECR experiments.
Representative diffusion profiles. . . . . . . . . . . .
Oxidation of samples annealed in quartz vials. . . .
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130
131
132
133
10
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102
104
105
105
List of Tables
1.1 Stable and metastable iron sulfide phases. . . . . . . . . . . . . . . . . . . .
1.2 Reactions describing the basic unit processes. . . . . . . . . . . . . . . . . .
16
23
2.1
2.2
2.3
2.4
2.5
2.6
2.7
31
37
41
47
51
57
Fe1-x S polytypes: composition and structure. . . . . . . . . . . . . . . . . .
Thermodynamic values for pyrrhotite compounds. . . . . . . . . . . . . . .
Best fit parameters n and τ. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Isotopic composition of naturally-occurring iron. . . . . . . . . . . . . . . .
Iron self-diffusion * DFe measurement results for Fe1-x S crystals. . . . . . .
K p (T) values used to calculate sulfur partial pressure. . . . . . . . . . . .
Deconvolution of Fe 2p and S 2p x-ray photoelectron spectroscopy (XPS)
peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Electrical conductivity relaxation results for oxidation experiments. . . .
2.9 Electrical conductivity relaxation results for reduction experiments. . . .
2.10 Key activation energies for pyrrhotite growth. . . . . . . . . . . . . . . . . .
59
61
61
68
3.1 Calculated bulk band gap Eg , and surface Eg . . . . . . . . . . . . . . . . . . 77
3.2 Experimental surface Eg measurements by scanning tunneling spectroscopy
(STS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3 Input parameters for tunneling spectroscopy simulations using the SEMITIP program. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.1 XPS core level shift (CLS) for S 2p peak. . . . . . . . . . . . . . . . . . . . .
97
5.1 Summary of experimentally determined activation barriers Ea . . . . . . . 109
A.1
A.2
A.3
A.4
A.5
A.6
Thermodynamic data for species in H2 S-H2 O-Fe system.
Input parameters. . . . . . . . . . . . . . . . . . . . . . . . .
Fe-H2 O Reactions and reversible potentials. . . . . . . . .
Mackinawite-Fe-H2 O system equilibrium reactions. . . .
Pyrrhotite-Fe-H2 O system equilibrium reactions. . . . . .
Pyrite-Fe-H2 O system equilibrium reactions. . . . . . . . .
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114
114
115
116
116
117
B.1 CVD of Fe-S phases by other authors. . . . . . . . . . . . . . . . . . . . . . . 122
B.2 Chemical Vapor Deposition conditions for Fe-S phases: literature. . . . . 123
11
12
Chapter 1
Introduction
1.1
Context
Vast amounts of energy are consumed in distilling ferrous and non-ferrous metals from
their ground states, married to reactive atoms such as oxygen and sulfur in ores. Once
fashioned into the components that undergird our energy, transportation and construction infrastructures, the thermodynamic tendency of these metals to regress to their
primitive compounds locks us in a Sysyphean struggle against materials degradation
and corrosion. But while thermodynamics dictates this ultimatly pessimistic outcome,
the slow kinetics of the required reactions ensures that metals and alloys can remain
uncompromised for many years, even under the most aggressive chemical, thermal and
mechanical conditions. Passivity - the ability of metals to self-protect by forming a thin,
inert skin of an ionic compound through a partial reaction at the environment interface
- thus constitutes one of our most useful tools in combating degradation. The growth,
reactivity and stability of these passive layers all contribute to their overall protectiveness. In this thesis we ask: is it possible to understand and subsequently simulate these
characteristics a priori, starting from the atomic scale? We can begin by defining a series of kinetically rate-limiting processes, including mass transport (i.e., diffusion) and
surface reactions such as oxidation, reduction and dissolution. By investigating the fundamental unit steps involved, and modeling these steps across multiple length- and
timescales, we can aspire not only to predict accurately how metals will behave when
placed in harsh environments, but also to design more robust materials that will better
self-protect and last longer.
1.2
Passivity: a brief introduction
The study of passivity as a scientific discipline perhaps originated with James Keir in
1790, who documented that although iron readily dissolves in dilute nitric acid, it counterintuitively remains inert in concentrated HNO3 . Michael Faraday, as early as 1830,
before the invention of the necessary characterization tools, correctly predicted the existence of an ultrathin, electronically conducting surface film that protects the underlying
metal. [1] We now have a better understanding of the passive state, as defined by Uhlig [2]:
A metal is passive if it substantially resists corrosion in a given environment
despite a marked thermodynamic tendency to react.
This definition gives us an insight into the essence of passivity; it is a metastable state,
one in constant flux. The formation of a passive film does not provide an infinite barrier to metal dissolution in a given aggressive environment, but it does reduce corro13
Schematic polarization curve for passive system
Active
Passive
1
Transpassive
Log i (A cm-2)
Pitting
(a) Cr, Ni
(b) Fe
(c) Valve metals
Al, Ti, Ta, Zr, Hf
(a)
(b)
10-6
Eo
Ep
Epit
(c)
E1
E (V)
Figure 1-1: Potential E vs. current i (polarization) curve for a generic metal, showing the active, passive
and transpassive regions, as discussed in the text. The valve metals form extremely stable oxide passive films
and display a very large transpassive region. After Marcus et al. [3]
sion currents by several orders of magnitude (as much as 106 times for certain alloys
such as stainless steels, and metals such as Al, Si, Ti, Ta and Nb, that form very stable passive films). Figure 1-1 shows a schematic of a typical polarization curve for a
generic, passive-film forming metal. [3] At a critical passivation potential Ep the corrosion current drops dramatically, coincident with the formation of a passive layer. The
thermodynamic conditions for this can be predicted from fundamental electrochemical principles, the basis of the Pourbaix diagram. [4] However, at higher potentials Epit
the passive layer can be prone to localized breakdown or pitting. Eventually, localized
failure avalanches into a full breakdown of the passive film and the corrosion current
shoots up in the transpassive region. The structure of passive films is typically bi- or
multi-layered. In the case of an oxide this typically means a thin (<100 nm), adherent,
dense inner barrier layer that forms rapidly under the correct anodizing conditions.
An outer layer can form by precipitation or solid-state reaction of cations transmitted
through the barrier layer with anionic species in the aqueous media, e.g. H2 S, CO3 2- ,
HS- . Depending on the exact conditions of temperature, pH, concentration of reactive
species, pressure etc., the outer layer - which can grow up to 100-1000x the thickness
of the inner barrier layer - may contain multiple compounds and different phases. In
oilfield brines with dissolved CO2 and H2 S, both FeCO3 and a variety of FeS phases may
be present in the outer layer, possibly along with oxides.
1.3
Iron sulfide phases and corrosion products
Early oil prospectors had a rudimentary test for the quality of their discoveries: a smudged
fingertip to the tongue, hence the terminology still used today: "sweet" or "sour" crude,
depending on whether the sulfur content is above or below 0.5 vol
The solution- and solid-state chemistry of iron sulfides has been studied by geochemists, microbiologists and thermodynamicists for many decades. A comprehensive
review by Rickard and Luther covers much of the accumulated knowledge in this field.
[9] The iron sulfide family of phases and their interrelations are complex: up to nine
discrete phases have been characterized, as listed in Table 1.1. Several of these are
metastable and will convert over time to either stable iron monosulfide (pyrrhotite,
Fe1-x S, 0 ≤ x ≤ 0.125 ) or iron disulfide (pyrite, FeS2 ). We limit the discussion here
to the three phases which came up most often while reviewing the literature on sour
14
(a)
World petroleum reserves with selected crude sulfur content (2013)
Urals 1.3-2.5%
North Sea
Brent 0.4%
Thunderhorse
0.9%
West Texas
1.9%
Saudi
2-3%
Nigeria
0.2%
Venezuela
1.5-2.3%
110
270
30
Proven oil reserves, bbl
(c)
Average % S
1.5
OPEC
1.3
1.2
1.1
World
Non-OPEC
1
0.9
2015
2025
Year
2035
Crude Oil
Sulfur Content
High pressure/high temperature
Reservoir Temperature oF
(b) Souring of world oil production
1.4
Indonesia
(Arjuna)
0.1%
600
HPHT-hc
260 oC
o
Ultra HPHT
400 205 C
o
150 C HPHT
200
0
69 MPa
0
Siberian Basin
0.8-1.8%
Iran
1-2%
241 MPa
US Midcontinent 0.4%
138 MPa
Canada- oil
sands 3.4%
10
20
40
60
0
Static Reservoir Pressure (kpsi)
Figure 1-2: Global sour oil and gas statistics. (a) Proven world crude oil reserves [5], with the average
sulfur content highlighted for several representative countries. [6, 7]. (b) The average sulfur content of oil
for Organization of the Petroleum Exporting Countries (OPEC) and worldwide. [5] (c) Definitions of high
pressure-high temperature well conditions by Schlumberger, Ltd. [8]
corrosion: mackinawite, pyrrhotite and pyrite. Mackinwawite, FeS1-x is a 2-dimensional
(2D) layered chalcogenide, generally considered to be the initial corrosion product to
form under most conditions in H2 S-bearing solutions. [10]
Figures 1-3a and b show potential vs. pH (Pourbaix) diagrams for the Fe-H2 S-H2 O
system under standard conditions of 1 atm pressure and 25 o C. Full details of the thermodynamic diagrams are provided in Appendix A and Refs. [11–14]. The stable phases
pyrrhotite and pyrite are excluded in Figure 1-3a, given that mackinawite manifests itself as the predominant metastable corrosion product for neutral to alkaline solutions.
This would correspond to "slightly" sour conditions of T < o C and hydrogen sulfide
partial pressures PH2 S < 0.01 MPa [15], or for relatively short exposures up to hundreds of hours. Naturally, the thermodynamic data would predict the stable phases to
predominate eventually (Fig. 1-3b), which in reality means after long steady-state exposure or higher temperatures. Evidently the kinetics of iron sulfide formation, dissolution
and transformation preclude the prediction of corrosion product phases from thermodynamic principles alone. In particular, the effect of H2 S partial pressure is omitted. Figure
1-3c is a summary of available phase identification from laboratory tests across a range
of sour conditions. Mackinawite prevails under slightly sour conditions, but pyrrhotite
or a mixture of pyrrhotite and pyrite is more often observed at moderately-highly sour
conditions as indicated on the diagram.
15
16
Hexagonal P6̄2c
Monoclinic A2/a or Hexagonal
P6/mmc
Trigonal-hexagonal R3m
FeSm , FeS1-x
FeSc
FeS
Fe1-x S (0 ≤ x ≤ 0.17)
Fe3+x S4 (0 ≤ x ≤ 0.3)
Fe3 S4
FeS2
FeS2
Mackinawite
Cubic FeS
Troilite
Pyrrhotite
Smythite
Greigite
Pyrite
Marcasite
Orthorhombic Pnnm
Cubic Pa3
Cubic Fd3m
Cubic F 4̄3m
Tetragonal, 2D layer P4/nmm
Amorphous/ nanocrystalline
FeSm , FeS1-x
Amorphous Iron
Sulfide
Structure
Composition
Phase
M
S
M
M
S
S
M
M
M
Meta- (M)/
Stable (S)
Commonly observed in hydrothermal systems; transforms to pyrite.
”Fools gold”: stoichiometric iron disulfide.
Contains mixture of Fe2+ and Fe3+ ions.more
Sub-phase from pyrrhotite group.
Iron-deficient monosulfide. Off-stoichiometry accomodated by iron vacancy superstructures below 315 o C.
Fully stoichiometric end member of the Fe1-x S family.
Transforms to mackinawite, pyrrhotite or pyrite. Not observed in nature.
Commonly observed first corrosion product in sour solutions.
Believed by some authors to be simply nanocrystalline form of mackinawite.
Comments
Table 1.1: Stable and metastable iron sulfide phases. Adapted from Refs. [9, 10].
(a)
Pourbaix diagram: metastable Fe-S
(b)
1.5
1.5
1 Fe3+
O2 +4
H ++4
0.5
e -=2
H2 O
Erev (V)
Erev (V)
1
Fe2O3
0.5
0
Fe2+
2H ++
0
Fe
2
4
6
pH
8
10
(c)
0
-0.5
2e -=
-1
Pyrite
Fe2+
Mackinawite
-0.5
-1.5
Pourbaix diagram: stable Fe-S
H2
12
Pyrrhotite
-1
14
-1.5
0
Fe
2
4
6
pH
8
10
12
14
Fe-S scales observed in lab/field tests
H2S Partial Pressure (MPa)
“Moderately Sour” “Highly Sour”
0
10
-2
10
Mackinawite
Pyrrhotite
Pyrrh. & Pyrite
-4
10
“Slightly Sour”
0
50
100
150
200
Temperature (oC)
250
Figure 1-3: Thermodynamic predictions of corrosion products are only of limited usefulness. (a) pHelectrode potential (Pourbaix) diagram constructed for the Fe-H2 S-H2 O system, excluding the stable phases
from reactions. (b) Once the stable products pyrrhotite Fe1-x S and pyrite FeS2 are added, the mackinawite
field disappears entirely. These diagrams cannot predict the existence of a given corrosion product a priori.
In (c), we show a temperature-H2 S partial pressure PH2 S diagram, overlaid with experimentally-observed
phase identifications from several sources. [15–18] Mackinawite is widely observed at lower temperatures
and PH2 S ("slightly sour" conditions; at elevated temperatures and partial pressures the product mix shifts to
the more stable pyrrhotite and pyrite phases. Exposure time is another factor not considered in these purely
thermodynamic diagrams; mackinwaite commonly forms first, but is more likely to transform over longer
times up to 100s of hours due to its metastability.
1.3.1
Sour corrosion mechanism: lab and field experience
Despite more than seventy years’ worth of investigations into iron sulfide corrosion
products, there is still no solid consensus surrounding the mechanism of sour corrosion
and the extent of protectiveness conferred by the passive state. The presence of an iron
sulfide scale is generally thought to reduce corrosion rates by up to several orders of
magnitude, at least upon initial formation on bare steel. However, there is uncertainty
regarding the long term stability of otherwise protective films comprising Fe-S. [19]
Here we briefly review the observations from laboratory and field experience that allow us to form an empirical picture of the sour corrosion process from a mechanistic
perspective. We refererence to Figure 1-4, we broadly describe a multi-stage growth
mechanism whereby mackinawite nucleates first, grows to a critical thickness and then
17
(a) Initial formation of bi-layered mackinawite film
Porous
outer layer
10’s of μm
Fe(s)+H2S(aq) = FeSm (s)+2H+(aq)+2e-
Inner layer
~ 100 nm
Fe2+(aq) +H2S(aq) = FeSm (s)+2H+(aq)
Dissolution:
0
+
FeS , FeHS
Fe-C
30µm
(b)
Pitting at delamination sites
Cl
-
20 μm
Fe-C
(c)
Nucleation & growth of stable iron sulfides
Figure 1-4: Mechanism of iron sulfide formation on steels in H2 S-bearing electrolytes. (a) A thin, adherent mackinawite film (∼ 100 nm thick) forms via solid state reaction or local precipitation at the bare steel
surface. The mackinawite continually dissolves and re-precipitates out of the supersaturated solution in the
adjacent boundary layer, building up a much thicker, outer porous layer of mackinawite. [16] (b) because of
volumetric stresees, the film may delaminate locally, leading to the formation of pits with bubble-like sulfide
deposits. [18] (c) At the repassivated pit sites, a high local concentration of cations in solution may lead to
the nucleation of more stable phases: needle-like crystals of hexagonal Fe1-x S or cubic grains of FeS2 . [17]
ruptures. Following film rupture, a second stage of FeS film growth occurs during which
it is possible that other, more stable Fe-S phases may form.
Mackinawite formation: Bare carbon steel - even with a pre-existing oxide pasive film is thought to undergo a solid state reaction (SSR) with H2 S in solution, in other words
a direct heterogeneous chemical reaction, to form nanocrystalline mackinawite FeSm
(occasionally referred to as "amorphous" mackinawite). The evidence for a SSR revolves
around the extremely rapid formation of iron sulfide on the surface over a timescale of
several seconds. By contrast, carbonate scale precipitation in CO2 solutions requires
minutes to hours for a semi-protective barrier film to form. [16, 19, 20] The formation
of a compact mackinawite layer with thickness << 1 mm confers a degree of passivity
to the steel, with a corresponding drop in measured corrosion rate on the order of 510 times. The film serves primarily as a diffusion barrier to ionic transport. Above the
18
compact, solid-state reacted mackinawite layer, a thicker - up to hundreds of mm - outer
mackinawite layer is typically observed (Figure 1-4b). This outer film is more porous
and less protective than the inner one. According to Nesic et al., mechanical instability
of the inner film caused by epitaxial stresses as it grows lead to a cyclic process of
microcracking, delamination and re-passivation that over time build up a thicker, porous
outer layer. [21] Either way, outer film growth rate and eventual thickness depend on
the temperature, pH and flow conditions of the solution. Its development leads to a
steady further reduction in corrosion rate over periods up to hundreds of hours. [18]
The corrosion rate is controlled by rate of mackinawite dissolution, the transfer of ions
through the compact inner film and porous outer film as well as mass transport through
the liquid boundary layer at the electrolyte-film interface.
Re-passivation: At a certain thickness, the mackinawite film can delaminate entirely from
the steel surface (Figure 1-4a). The solution in contact with the microcracks, or newly
exposed steel surface, becomes supersaturated with Fe(HS)+ or Fe2+ . At this point, there
are several developments that can occur, depending on the exact conditions at the damaged film locations. The first possibility is that the steel re-passivates with mackinawite
through either SSR, or by precipitation. This is most likely when the solution is less
acidic - above pH 6, atypical for oilfield brines - and at low temperatures since ferrous
ion and H2 S levels are close to saturation limits for other phases such as troilite and
pyrrhotite. Under these conditions the continuous spallation and repassivation of the
mackinawite film confers a semi-passive state with general corrosion rates on the order
of 1 mm/year.
Pitting: Another possibility is that the freshly exposed area of bare alloy becomes susceptible to increased local attack by species in the environment. Particularly where chloride ions are involved in the disruption of the passive state, such a situation has been
observed to lead to surface pitting of carbon steels and other alloys. [18, 22] Ex situ examinations of pitted regions have revealed large deposits of iron sulfide directly above
the pit (Figure 1-4b); this provides further evidence of increased, localized attack and
also suggests that pits may become re-passivated by precipitation from the electrolyte.
Pyrrhotite and pyrite nucleation: Finally, certain environments are conducive to the
formation of other iron sulfide phases. Mackinawite may undergo direct, solid state
transformation to pyrrhotite under reducing conditions, or supersaturated conditions in
breaks at the mackinawite layer may lead to the direct nucleation of elcongated troilite
needles or hexagonal pyrrhotite plates. [17, 23] Eventually, such a process would lead
to the build up of a thick scale (10s-100s of µm’s) of the more stable sour corrosion
products pyrrhotite and pyrite. These phases are more than an order of magnitude less
soluble than mackinawite. Once they have formed a continuous film, the further formation of mackinawite or other metastable phases is essentially inhibited by the greatly
reduced local ferrous ion activity in solution. [15]
1.3.2
Model phases: Pyrrhotite (Fe1-x S) and Pyrite (FeS2 )
Despite the fact that mackinawite is an important phase in the early stages of aqueous iron sulfide formation on steels, this thesis concentrates on pyrrhotite and pyrite.
This was motivated in large part by the relative ease with which high-quality and welldefined samples of the stable iron sulfides could be made. Mackinawite is a flaky brown
precipitate that can only be formed from solution and oxidises rapidly upon exposure
to air, therefore requiring careful handling under inert atmospheres and presenting additional technical challenges. Instead, pyrrhotite and pyrite served as model systems
to investigate the physical chemistry of processes involving point defects in iron sulfides. The equilibrium phase diagram and crystal structures of the stable Fe-S phases
19
(a)
Fe-S Equilibrium Phase Diagram
(c) NiAs-type Fe1-xS
(b) Troilite FeS
a
c
b
Fe
S
a
c
b
(d) Pyrite FeS2
a
c
b
Figure 1-5: Iron sulfide stability phase diagram. (a) Equilibrium Fe-S phase diagram. Pyrrhotite refers to
a set of iron monosulfide polytypes, described in more detail in Chapter 2. Pyrite is a line compound at the
fixed composition Fe:S = 1:2. (b) The crystal structure of the hexagonal pyrrhotite end-member, known as
Troilite; (c) other pyrrhotites can be described by a hexagonal, NiAs-like subcell. (d) Cubic pyrite unit cell,
described in Chapter 3.
is shown in Figure 1-5a. Pyrrhotite Fe1-x S forms a complicated series of polytypes at
low temperatures, from stoichiometric troilite (hexagonal FeS, Fig. 1-5b) to a range
of vacancy-ordered superstructures based on the NiAs structure (Fig. 1-5c). Pyrite, by
contrast, is a line compound that is nominally stoichiometric in the bulk. [24]
1.4
1.4.1
Towards a predictive, multiscale corrosion model
Existing passive film models
The broader aim of this thesis is to investigate a set of elementary processes at the atomic
scale which govern the protectiveness of passive sulfide layers. As we have seen above,
real passive layers are complex materials systems: often multi-phase, highly defective
and sensitive to changes in electrolyte chemistry as well as global variables such as
temperature and stress state. For the purposes of building a passive film model, we must
necessarily reduce the system to a series of elementary unit processes that occur on the
atmoic scale. Hence, in addition to thermodynamics we need to consider the kinetics
20
of the corrosion process also. The interest in analytical and computational modeling of
passive layers dates back at least 70 years. We do not attempt an exhaustive review of
all the available models here; instead, let us briefly examine some of the more relevant
examples to understand their advantages and shortcomings:
High Field Models account for the incipient oxidation of metals. [25–27] In the limit
of small passive layer thickness L (on the order of nanometers) the field strength that
drops across the film is extremely high, and the oxidation rate is inversely proportional
to time t, yielding a logarithmic law:
L(t) = ke log(αt + 1)
(1.1)
where ke and α are temperature- and field- dependent constants and L is film thickness.
However, this only holds for very thin passive layers, applicable to the very early stages
of oxidation or at low temperatures.
Wagner theory describes the growth of passive films in anhydrous environments, i.e. in
the absence of scale dissolution. [28] Assuming migration of ions through the film is
rate-controlling, a parabolic law is obtained of the form:
q
(1.2)
L(t) = k p t
where kp is the parabolic rate constant, a function of the ionic diffusivity D of the mobile
species. Dry sulfidation of iron at elevated temperatures > 500 o C is well described by
Wagner theory [29–31]; however, it cannot account for scale dissolution in aqueous
environments or the case when surface reactions, such as molecular dissociation, are
kinetically limiting.
The Point Defect Model (PDM) of Macdonald et al. is perhaps the most complete, deterministic analytical framework for describing the growth and protectiveness of generic
passive layers. [32,33] Originally inspired by Wagner’s theory of diffusion-limited growth,
it further incorporates interfacial reactions and scale dissolution. Interfacial reactions
such as cation injection from the metal and redox exchange at the surface typically
follow linear kinetics:
L(t) = ki t
(1.3)
where ki is a surface exchange coefficient. The passive layer is treated as a bi-layer of inner, compact and highly defective oxide plus outer scale up to 100x thicker. Besides L(t)
and corrosion currents i(t), the PDM can make quantitative predictions about passivity
breakdown.
Mackinawite formation models that describe iron sulfide scale formation have been proposed by Sun, Nesic et al.. [10, 16] The model assumes a bi-layered mackinawite film
comprised of a thin (10 nm), compact inner layer and porous outer scale, 100s of µm
thick. The corrosion rate is limited by mass transport (diffusion) through the mass transfer boundary layer at the scale-electrolyte interface, through the liquid in the porous
outer scale and finally thorugh the compact inner sulfide. In addition, scale damage
by hydrodynamic stresses is considered. However, the model is inherently empirical,
requiring several unknown parameters to be fitted using experimental data. Moreover,
the evolution of the scale to form stable sulfides at longer times is not considered.
Stochastic pitting models have been developed to simulate pit growth kinetics in stainless steels. [34, 35] Based on Monte Carlo simulations of stochastic pitting, they can
replicate pitting potentials observed using potentiodynamic experiements. However, the
21
(a) Gaseous Ar-10% H2S (220 oC)
(b) Aqueous 10% H2S, 1% NaCl (220 oC)
Figure 1-6: Sulfide corrosion of 4130 carbon steel at 220 o C. (a) Amount of sulfur reacted (mass gain of
sample) with time in a dry, gaseous environment of 10% H2 S. An initial logarithmic transient due to sufide
film formation gives way to a linear regime where the rate of sulfidation is limited by surface exchange of
2−
sulfur, described by the overall reaction: H2 S(g) + 2e− ⇔ S FeS
+ H2(g) . At approx. 225 hours, the linear
regime transitions to a "mixed" region in which diffusion of cations begins to limit the overall reaction rate.
(b) Corrosion rate as a function of time in aqueous solution containing H2 S. The scale grows under mixed
diffusion and interfacial (surface reaction) control. After 60 hours, the rate of scale growth is balanced by
scale dissolution to produce a steady state in the corrosion rate. [17]
models do not predict pitting initiation through passivity breakdown at the nanoscale,
instead the starting point is a just-nucleated pit.
To illustrate some of the rate limiting steps identified by the growth models above,
Figures 1-6a and b show experimental results for steel sulfidation by H2 S at elevated
temperatures of 220 o C, under dry gaseous and aqueous conditions, respectively. In
the dry case (Fig. 1-6a), from the amount of reacted sulfur we see a transition from
logarithmic sulfide scale growth (High Field Model) at short times, to linear growth
(surface reaction, as described by PDM) and finally after a certain thickness to a "mixed"
interfacial and diffusion-limiited regime (Wagner theory). By contrast, under aqueous
conditions (Fig. 1-6a; the y-axis is now corrosion rate CR), the CR initially falls rapidly
as the scale forms. After approximately 60 hours, a steady state CR is reached where
the scale growth rate matches that of scale dissolution.
22
Table 1.2: Reactions describing the basic unit processes used to model the kinetics of iron sulfide layer
formation, growth and breakdown. After the Point Defect Model. [32]
Partial process
Metal injection
Reaction
Parameters
00
−
Fe + VFe ⇔ Fe Fe + 2e
ν, φ
Fe ⇔ Fe Fe + VS•• + 2e−
ν, φ
(1)
(2)
Cation diffusion
Fe Fe ⇔ Fe Fe
∗
DFe (T, φ)
Anion diffusion
(1)
SS
∗
DS (T, φ)
Dissolution
2+
Fe Fe + SS + 2H + ⇔ H2 S + Fe(aq)
Surface vacancy formation
2+
Fe Fe ⇔ VFe + Fe(aq)
⇔
(2)
SS
S2 + 2H + ⇔ VS•• + H2
1.4.2
Kp
00
∆H Sf
Unit processes controlling Fe-S passive layer behavior
None of the models described above can successfully predict the transient and steady
state passive layer behavior in Figure 1-6 a priori. Moreover, localized breakdown phenomena such as pitting remain largely unaccounted for. The overarching motivation
for this project is to work towards a deterministic model. A robust model for such a
complicated electrochemical system must be able to predict a priori degradation rates
and trends under realistic pipeline corrosion conditions, using parameters that can be
measured and compared through experiment. Moreover, the model’s predictive capabilities should serve as a platform for designing more protective materials and chemical
inhibitors. Its characteristics should be:
1. Non-empirical: able to calculate passive layer growth rates L(t), transient and
steady state corrosion currents i(t) and passivity breakdown (e.g. pitting probability P(t) and stable pit growth rate dx/dt) using a "bottom-up" approach, i.e. by
simulating unit steps such as atomic diffusion and charge transfer reactions. The
model should have as few empirical (fitted) parameters as possible.
2. Predictive: able to make accurate predictions that can be related to corrosion tests
and cover a range of environmental conditions such as temperature, pressure,
sulfur concentration and applied potential.
3. Modular: complexity can be added or removed by considering unit processes as
separate elements of the model.
4. Bridges length- and timescales: can make predictions from the atomic- and
nanometer scale in fractions of a second, to the macroscopic level over timescales
of hours and years that can be compared to laboratory experiments and industry
tests.
As of writing in November 2014, a global Fe-S passive film model is under continued
development by Aravind Krishnamoorthy and others in the Yildiz and Van Vliet groups
at MIT, and will be presented in more detail in Aravind Krishnamoorthy’s PhD thesis, expected 2015. In Figure 1-7, the processes considered in the model are outlined
schematically. In Figure 1-7a, some of the key atomic steps investigated in these two theses thesis are shown; these include ionic diffusion, surface exchange (interfacial charge
transfer reactions) and vacancy formation at surfaces under reducing conditions. Figure
1-7b, on the other hand, depicts other important phenomena affecting the stability of
passive films. Although beyond the the scope of this thesis and a rudimentary version
of the proposed model, they are included for completeness. Finally, the basic chemical
reactions that define sulfide passive layer behavior are listed in Table 1.2.
23
(a) Elementary rate-limiting processes in iron sulfide films
HSELECTROLYTE
Fe-S
LAYER
H2
x
L
Dissolution
Hads
Fe2+ S2-
φ = - dV/dx
2e(cathodic)
S2-
H
+
VFe
(anodic)
0
STEEL
2e-
φ
Potential drop
across film
Ionic
diffusion
Interfacial charge
transfer
Vacancy formation
& pitting
(a) Other considerations for generalized passive layer model
Solution chemistry
& thermodynamics
ELECTROLYTE
+
Chemical
inhibitors
-
Flow/erosion
Pit chemistry
X- + Fe2+
+
↔ FeX
H2S ↔ H + HS
Fe-S
LAYER
g.b
STEEL
pearlite
Phase stability,
transformations
Voids/pores
Interfacial stresses,
film delamination
Alloy microstructure
& chemistry
Figure 1-7: Schematic of unit processes in Fe-S passive layers: (a) basic kinetic rate-limiting corrosion processes for a homogeneous iron sulfide passive film on steel. (b) additional considerations for multiphase films,
substrates, and different electrolyte chemistries. In addition, mechanical effects such as flow can influence
corrosion rate.
1.4.3
The need for experimentally-derived parameters
The high-level, proposed approach to formulate a non-empirical iron sulfide passive
layer model from fundamental atomic processes is outlined in Figure 1-8. Activation
barriers Ea and rate constants νo can be obtained by performing both ex situ and in
situ experiments, combined with predictions from first principles by Density Functional
Theory (DFT). In situ refers to corrosion tests using sulfidic electrolyte solutions; none
were completed in the course of this thesis, but we will come back to potential experiments in Chapter 5. In their simplest incarnation, experiments are designed to measure
a given kinetic process as a function of temperature, yielding the desired parameters
through fitting to a universal Arrhenius law of the form:
P = νo exp[−
Ea
]
kB T
(1.4)
where P is the probability (yielding average macroscopic rate) of the given process, and
kB is Boltzmann’s constant. A kinetic Monte Carlo simulation calculates the dynamics
of local unit steps at the metal-passive layer and passive layer-electrolyte interfaces.
24
Passive layer model: global strategy and thesis contributions
Experiments
“ex situ”
Growth
Chapter 2
Reactivity
Chapter 3
Density Functional
Theory
“in situ”
Stability
Chapter 4
Activation barriers Ea
Rate constants νo
P = νo exp[- Ea / kBT]
Thermodynamics
(literature)
kinetic Monte Carlo
Phase Field model
Laboratory tests
Field experience
Figure 1-8: Overview of strategy to construct a non-empirical passive film model. Contributions of this
thesis are shown in red font. Experiments and first-principles Density Functional Theory (DFT) are employed
to calculate activation barriers Ea and rate constants νo for the unit processes outlined in Figure 1-7. These are
fed into a probabilistic model on the atomic scale, which updates a kinetic Monte Carlo (kMC) simulation.
The microscopic fluctuations tend towards certain macroscopic states under an input thermodynamic bias
calculated from temperature, chemical potentials, etc. This macroscopic behavior is calculated through a
Phase Field model at greater lengthscales than kMC. Finally, the model should allow comparison to lab- and
field tests for re-optimization and iteration.
The kMC is coupled to a macroscopic Phase Field model which is able to update the
structure on greater length- and timescales. Finally, the proposed model will be merely
an academic exercise unless it can be usefully compared and contrasted to real results
on sour corrosion from laboratory tests and the field. In future studies, these should
be fed back into experimental design to improve the collection of useful, non-empirical
model inputs.
25
1.5
Thesis goals and organization
Having introduced the background and general strategy, the following three chapters
dig deeper into some of the phenomena depicted in Figure 1-7a, using the model iron
sulfide phases Fe1-x S and FeS2 . No in situ corrosion tests are conducted, nor do we consider the formation of sulfides on steel or iron substrates. Instead, this thesis comprises
three individual case studies that test the hypothesis that we can construct a global
model by considering local, atomic processes in isolation. The physical chemistry of
pure iron sulfide surfaces and bulk processes are investigated and, where appropriate,
the implications of the findings beyond passive film behavior are discussed.
• Chapter 2 ("Growth") addresses the unit processes of cation diffusion and surface exchange as rate limiting mechanisms in Fe1-x S (pyrrhotite). This phase
is interesting due to a magneto-structural transition at 315 o C, below which Fe
diffusion had previously not been studied. Is there an effect from magnetic and
structural ordering on Fe diffusion in Fe1-x S? Under what conditions does diffusion in pyrrhotite limit the rate of scaling or corrosion with respect to surface
reactions, and vice versa? Both phenomena are studied as a function of temperature to extract average activation energies which are cast into a rudimentary
pyrrhotite scale growth model.
• Chapter 3 ("Reactivity") explores the effect of surface electronic structure on redox charge transfer, by quantifiying the electronic band gap and surface states
on FeS2 (100) as a model sulfide phase. For semiconducting passive layers, electron exchange with redox species in the environment occurs by horizontal transfer
from (to) occupied (unoccupied) states. How does the surface electronic structure
differ from that of the bulk? To probe locally at the surface, the scanning tunneling microscope (STM) is used in spectroscopy mode (STS). However, there is no
well-defined protocol for interpreting STS results. A systematic methodology is
developed to identify tunneling current contributions from surface states which
mediate charge transfer during reactions, extendible to other similar materials.
Finally, the implications of these findings beyond passive layer electrochemistry
are discussed; for example, regarding earth-abundant, FeS2 photovoltaics for energy production.
• Chapter 4 ("Stability") describes the dynamics of point defect formation, clustering and pit initiation on the FeS2 surface. The inherent protectiveness of a
passive layer relies on the physicochemical barrier remaining intact against chemical, electrochemical or mechanical stimuli. A key postulate of the PDM is that passivity breakdown originates from vacancy condensation on the cation sublattice of
the barrier layer. Can we form a mechanistic picture of this process, informed by
experiment? The formation of sulfur defects at elevated temperatures and in UHV
on FeS2 is obsered and quantified using x-ray photoelectron spectroscopy (XPS)
and in situ STM. The experimental results are used to inform a kinetic Monte
Carlo (kMC) simulation for vacancy condensation that predicts the formation of
nanocavities at passive film interfaces that can serve as pitting initiation sites.
• Chapter 5 "Conclusions" summarises the findings and key contributions from
these three case studies above. The insights are contextualized under the scope
of the ambitious, global passive film model proposed in Chapter 1. The contribution of such precise physico-chemical studies on atomic processes in model
passive layers is revisited and appraised. Finally, the steps required for the future
development of a more practical, deterministic passive layer model are discussed,
including suggestions for in situ experiments under realistic aqueous conditions.
26
Chapter 2
Growth: cation diffusion and
surface exchange as
rate-limiting mechanisms in
pyrrhotite, Fe1-xS
Synopsis Cation diffusion and the surface exchange of sulfur, constituting the predominant kinetically-limiting processes in the growth of pyrrhotite (Fe1-x S) in sour environments, are investigated on model thin film and bulk samples. Diffusion is studied
via two methods to understand the influence of the spontaneous magnetic and structural order-disorder transition at the Néel temperature T N of 315 o C in Fe1-x S. The
self-diffusivity of iron * DFe in pyrrhotite above T N follows an Arrhenius law with an activation energy Ea = 0.83 eV. First, magnetokinetic measurements of the antiferromagnetic to ferrimagnetic "λ-transition" between 180-210 o C yield Ea = 1.1 eV for cation
diffusion. Second, we confirm this higher Ea in magnetic pyrrhotite using 57 Fe tracer diffusion measurements below T N , obtained via secondary ion mass spectrometry (SIMS).
These demonstate a downwards deviation from the extrapolated, paramagnetic Arrhenius trend by up to two orders of magnitude at 150 o C. The results are described by a
magnetic diffusion anomaly, whereby vacancy formation and migration energies for the
cation sublattice are increased by approximately 40% over the paramagnetic state, due
to spontaneous magnetization. Finally, we study sulfur exchange kinetics using the electrical conductivity relaxation (ECR) technique on Fe1-x S thin films, in which diffusion is
very rapid. The chemical exchange coefficient for sulfur incorporation, kox is found to
have an activation energy 1.0 eV. Our experimental activation barrier values for these
unit processes can be fed into a multiscale corrosion model to predict growth rates for
pyrrhotite scales. The similarity in surface exchange and diffusive barriers suggests that
the crossover from the former to latter rate-limiting steps should occur at approximately
the same film thickness of 100-1000 µm, independent of temperature. The computational work in this chapter, including the development of kinetic Monte Carlo codes,
was discussed and carried out in collaboration with Aravind Krishnamoorthy.
2.1
Background and Motivation
Pyrrhotite is a stable iron sulfide phase that forms under higher temperature, more
sour conditions (Chapter 1). It was selected for this study because iron diffusion is
known to be a relatively rapid process in Fe1-x S, due to its high degree of cation offstoichiometry. In fact, the surface exchange of sulfur can constitute a relatively slower
27
(b)
o
Temperature ( C)
-6
900 700
500 400
200 150
300
-10
X
-6
-16
-18
x in Fe1-xS
0.14
0.07
0.03
0.013
0.007
0.004
-8
-9
0.8
-12
-14
Non-stoichiometry X
-7
Y
?
Fryt†
Worrell†
Sterten†
Hobbins‡
Condit‡
Marusak§
1.0
1.0
1.2
1000/T (K-1)
(c)
?
-8
Z
1.5
2.5
2.0
-1
log[*DFe] (cm2s-1)
log[*DFe] (cm2s-1)
-8
log[*DFe] (cm2s-1)
(a)
1000/T (K )
Anisotropy Y
-9
II c-axis (x ≈ 0)
-10
c-axis
-11
-12
1.0
2.0
1.5
-1
1000/T (K )
Figure 2-1: Collected literature values of Fe self-diffusivity. (a) experimental ∗ DFe values obtained using
different techniques as listed. The aim of the work in this thesis was to measure a reliable set of data below 300
o
C. (b) magnified Fryt data from region “X” on the main graph. Variations in stoichiometry x account for up to
one order of magnitude variation in ∗ DFe . (c) magnification of Hobbins data (region “Y”): crystal anisotropy
can account for half an order of magnitude variation. Data from: Fryt [31] † , Worrell [37] † , Sterten [38]
†
, Hobbins [39] ‡ , Condit [40] ‡ , Marusak [41] § . († = sulfurization; ‡ = radiotracer; § = magnetokinetic
measurements).
kinetic process for pyrrhotite growth under certain conditions. [17,36] Solid-state mass
transport (diffusion) produces a parabolic time-dependence of film growth of the form:
p
X ∼ 4Dt
(2.1)
where X is film thickness and D is a diffusion coefficient. Surface exchange (the reaction
between Fe1-x S and H2 S) on the other hand should produce linear kinetics of the form:
X ∼ t/kchem
(2.2)
where kchem is a surface exchage coefficient. The primary aim of this work was to evaluate and compare the fundamental energy activation barriers for these two processes
by considering their Arrhenius-like temperature dependence:
•
˜
Em
D ∼ Do exp −
kB T
Eex
kchem ∼ ko exp −
kB T
•
(2.3)
˜
(2.4)
where Do and ko are rate constants, Em is the activation energy barrier for migration,
Eex is the barrier to surface exchange reactions and kB is Boltzmann’s constant. The
development of a multiscale, non-empirical passive layer model as the ultimate motivation for this project requires experimentally-determined values for these unit process
parameters.
28
Diffusivity: effect of order-disorder transition?
Fe1-x S undergoes spontaneous magnetic and structural disordering above the critical
Néel temperature T N of 315 o C. [42] Previous measurements of Fe self-diffusion *DFe in
paramagnetic Fe1-x S above T N have been carried out by several authors using thermogravimetric [31, 37, 38] and radiotracer [39, 40] methods, as compiled in Figure 2-1a.
An isothermal spread in *DFe of less than one order of magnitude is observed, stemming from variations in stoichiometry (Fig. 2-1a) or crystalline anisotropy (Fig. 2-1b).
Despite this, the results above ∼ 300 o C follow a standard Arrhenius law as a function
of temperature, given by D = Do exp[−Q P /kB T ], where Do is a prefactor, QP is the activation energy for diffusion in the paramagnetic lattice, and kB is Boltzmann’s constant.
However, already in 1974 Condit et al. predicted that vacancy ordering below T N would
lead to an increase in activation barrier for Fe self-diffusion. [40] Indeed, the only available *DFe measurements at temperatures lower than ∼ 300 o C, obtained via a unique
magnetokinetic method (Figure 2-1a, data labelled "Z"), may substantiate this claim if
it weren’t for a lack of auxiliary data. A secondary goal of this chapter is to clarify the
role of ordering at T N on Fe self-diffusion in Fe1-x S.
Chapter goals and layout
The primary aim of this chapter is to to compare the rates of the kinetically-limiting
processes of diffusion (bulk) and sulfur exchange (surface) by studying these processes
on controlled samples as a function of temperature. A secondary goal is to resolve the
uncertainty over the effect of magneto-structural ordering below 315 o C on cation diffusivity. This chapter is split into five main sections, which are summarized below:
• Section 2.2 "Introduction to pyrrhotite polytypes and transitions" describes
the closely-coupled structural and magnetic properties of Fe1-x S.
• Section 2.3 "Diffusion-limited λ transition" explores cation diffusion via magnetokinetic measurements of a single-phase reordering transformation in nonstoichiometric Fe1-x S, reviewing the experiments that gave rise to the data in region "Z" of Figure 2-1.
• Section 2.4 "Isotope tracer diffusion measurements" fills in the missing Fe selfdiffusivity data in the temperature range 170-400 o C through direct diffusivity
measurements using secondary ion mass spectrometry (SIMS) on Fe1-x S crystals.
• Section 2.5 "Sulfur exchange kinetics at the Fe1-x S surface" describes kinetic
measurements of the transfer of sulfur from gaseous H2 S to Fe1-x S thin films,
under conditions where diffusion is not rate-limiting.
• Finally, in Section 2.6 "Outcomes", the experimentally-determined rates of diffusion and surface reaction are compared to predict from first principles the controlling processes in the sulfidation of iron under a range of scenarios.
2.2
Pyrrhotite: polytypes and transitions
In this section, the crystallography and basic physical properties of Fe1-x S are reviewed.
This phase characterized by a complicated series of vacancy-ordered structures which
form below a common ordering temperature of 315 o C.
29
(a) NiAs unit cell
(b) Superstructure AB-plane
Fe
S
C
c
a
B = 2√3a
A
a
=2
Figure 2-2: Structural unit cells of pyrrhotite.(a) NiAs-like unit cell, common for all pyrrhotites. (b) ABplane of superstructure, showing only Fe atoms. Dashed rectangle indicates the unit area A = 2a, B = 23a.
2.2.1
Structural and magnetic properties
The term ‘pyrrhotite’ encompasses a set of cation-deficient iron sulfides across the narrow composition range 0 ≤ x ≤ 0.125 in Fe1-x S, where the stoichiometric end-member
(0 ≤ x < 0.05) is more specifically referred to as ‘troilite’. A comprehensive review
of the known structural and physical properties of pyrrhotites was previously written
by Wang and Salveson. [43] All pyrrhotites undergo a spontaneous magnetic ordering
transition at a Néel temperature T N = 315 o C which is known to be strongly coupled
to the ’β-transition’ or order-disorder transition for Fe vacancies, V Fe . [42] For the remainder of this chapter, we therefore use T N to describe the critical, magneto-structural
order-disorder transition temperature in pyrrhotite.
Below T N the accommodation of relatively large concentrations of V Fe up to 12.5%
produces a series of complex, structurally ordered Fe1-x S superstructures, a principal
feature of which is the formation of Kagome nets: tetrahedra sharing apexes in all
three dimensions which arise to minimize total vacancy-vacancy interaction energy
in magnetically-frustrated systems. [44] Such V Fe ordering in turn bestows a remarkably diverse range of low-temperature physical properties, such as magnetism and electronic conduction, which remain ambiguous despite many years of investigation. The
basic unit cell for all Fe1-x S compositions is NiAs-type hexagonal with lattice parameters a and c, and space group P62̄c (Fig. 2-2). However, x-ray diffraction refinement
[45–48] and high-resolution electron microscopy [49] studies have identified several
low-temperature superstructures based on a supercell of dimensions A = 2a, B = 23a
and C = c which can take either hexagonal or monoclinic symmetry. The supercell can
be described as a layering of iron AB-planes where vacancy segregation to certain planes
creates structures requiring different C-axis repeats to complete unit cell symmetry. The
generic superstructure is thus described as NC, where N is an integral or non-integral
repeat distance in the C-axis. The polytypes of Fe1-x S described below can be understood
with the help of Table 2.1 and the phase diagrams in Fig. 2-3.
The fundamental magnetic properties of non-stoichiometric pyrrhotites are known
to arise from ferromagnetic (↑↑↑↑) alignment of cations within metal AB-layers and
antiferromagnetic (↑↓↑↓) coupling between adjacent layers. [52] The inoccupation of
an AB-plane by iron vacancies reduces its overall ferromagnetic moment; net magnetism
is hence determined by the periodicity of full and partially-unoccupied layers. These
phenomena are discussed together in more detail for each phase below.
2C (Troilite. Fe1-x S: 0 ≤ x ≤ 0.05):
Troilite adopts a 2C structure with dimensions A = B = 3a and C = 2c. Magnetic moments on Fe atoms lying in AB-planes are anti-ferromagnetically ordered at room temperature but undergo a spin-flip transition (α-transition, see Fig. 2-3) at the 2C/1C
solvus - starting at 140 o C for FeS - to an in-plane ferromagnetic order with antiferromagnetic coupling between adjacent AB-planes, imparting net zero magnetization.
30
Table 2.1: Fe1-x S polytypes: composition and structure. [50, 51].
Type
Formula Composition
range
Symm.
Supercell unit
cell
Comments
1C
Fe1-x S
Full range
Hex.
A, 2C
Elevated temperature disordered form
2C
FeS
0 ≤ x ≤ 0.05
Hex.
3A, 2C
Troilite
NC
Fe1-x S
0.8 ≤ x ≤ 0.11
Hex.
2A, NC
5 ≤ N ≤ 11
4C
Fe7 S8
x = 0.125 ±
0.05
Mono.
23A, 2A, 4C
“Magnetic” pyrrhotite
NA
Fe1-x S
Unknown
Hex.
NA, 3C
High temp. metastable; 40
≤ N ≤ 90
MC
Fe1-x S
Unknown
Hex.
2A, MC
High temp. metastable; 3
≤M≤4
Beyond this, magnetic spins fully disorder to paramagnetic at T N = 320 ± 5 o C.
1C (high temperature, disordered form):
1C describes the disordered form of pyrrhotite where vacancies are randomly dispersed
and hence no long-range order exists. 1C is the established structure for all compositions
at temperatures higher than T N at which magnetic order is lost. 1C is antiferromagnetic
below T N , and paramagnetic above T N .
4C (Fe1-x S: x = 0.125 ± 0.05):
At the iron-deficient extreme of x = 0.125 ± 0.005, pyrrhotite adopts a monoclinic
structure in which the stacking sequence of cation layers alternates between fully occupied and -defective in the sequence (. . . FAFBFCFD. . . ), where F denotes a full layer and
A-D are defective layers with different in-plane vacancy arrangements. [43] The quadrupling of the c-axis stacking periodicity leads to the designation of this phase as 4C
(Fig. 2-4a). In the 4C superstructure, an uncompensated moment between alternating
full and vacant sublattices results in net ferrimagnetism which persists up to T N . The
temperature-dependent magnetization up to this point is described by standard Weisstype behavior. Powell et al. demonstrated using neutron diffraction that at T N , coincident with magnetic disordering, a structural disordering towards randomly-distributed
vacancies with hexagonal, 1C periodicity also occurs. [42]
NA and MC (210 o C < T < 320 o C, unknown composition range):
There has been some evidence to suggest that intermediate, metastable pyrrhotites exist
above ∼210 o C that can be refined with superstructure cell dimensions Ā = NA with 40
≤ N ≤ 90 and C̄ = 3C. [45, 48] and subsequently at around 260-300 o C as ‘MC’ (A
= 2A and C = MC with 3 ≤ M ≤ 4). [45, 53] Due to the large A-axis repeat units and
non-integral C-axis repeat units proposed for NA and MC pyrrhotites, respectively, these
phases are at best ill-defined and likely comprise a mixture of metastable, ordered solid
solutions that on average resemble the supercell structures described above.
NC (Fe1-x S: 0.08 ≤ x ≤ 0.11):
In the composition range 0.08 ≤ x ≤ 0.11, Fe1-x S forms a more complex set of hexagonal
pyrrhotite superstructures known collectively as ‘NC’, where the repeat distance N of
31
(a)
FeS-Fe7S8 phase diagram
Liquid
1C +
985
Liquid
1C + S(l)
o
Temperature ( C)
949
1C + FeS2
TN
325
MC
275
225
TC
1C
MC +
4C
NA
NA + 4C
175
Tα
125
75
6C 11C 5C
2C + NC
50
(b)
NC
+
4C
NC
2C + 1C
49
48
4C + FeS2
4C
33.3
47
at% Fe
FeS-Fe7S8 magnetism
o
225
175
125
Antiferro-
Ferri-
↑↓↑↓↑↓
↑↓↑↓↑↓↑
c-axis
50
c-axis
Tα
Antiferro-
75
↑
TN
325
275
↑
↑
↑
Para-
↑
Temperature ( C)
985
949
→←→←
Antiferro-
c-axis
49
Ferri-
↑↓↑↓↑↓ ↑↓↑↓↑↓↑
c-axis
48
47
at% Fe
c-axis
33.3
Figure 2-3: Pyrrhotite structural and magnetic phase diagrams.(a) showing existence ranges of 1C, NC,
4C, NA and MC pyrrhotite superstructures, as described in the main text. Experimentally determined temperatures for the α-, β− and λ−transition onsets Tα , T N and T C , respectively) are also shown. (b) Approximate
magnetic structures superimposed on phase fields; arrows refer to plane-by-plane magnetic moment along
the c-axis. After: [45, 53, 54]
the NiAs subcell may be either integral or non-integral between 5 and 11. [43] Figure 24b shows an idealized 5C structure with a series of full and vacancy-bearing AB-layers,
similar to 4C. However, the periodicity for 5C (...-AFFBFCFFDFA-...) has an antiferromagnetic symmetry due to compensation between sublattices. Although several ideal
crystal structure solutions such as this have been proposed for integral N values such as
Fe9 S10 (5C), Fe10 S11 (11C) and Fe11 S12 (6C), no exact vacancy distributions have been
conclusively determined. [46–48] NC pyrrhotites are better characterized by a distribution of probability of vacancy occupancy (Fig. 2-5). The observation of incommensurate c-axis stacking [56] in some pyrrhotite samples makes it likely that intermediates
32
..
.
A
(a) Ferrimagnetic 4C
0
(b)
Antiferromagnetic 5C
0
F
F
C
4
F
Layer #
Layer #
2
B
2
4
6
D
6
8
F
8
A
..
.
1
0.75
Occupancy
Fe2+
VFe
10
1
0.75
Occupancy
..
.
A
F
F
B
F
C
F
F
D
F
A.
..
Magnetic moment (size represents magnitude)
Figure 2-4: Idealized Fe1-x S superstructures: (a) 4C with alternating full and partially vacant occupancy
of AB-layers. An uncompensated magnetic moment results in net ferrimagnetism. (b) 5C with net magnetic
compenstation between full and vacancy-bearing layers; this idealized structure is antiferromagnetic. The
labels “F” refer to full Fe layers; A-D are vacancy-bearing layers with different in-plane vacancy arrangements.
After Vaughan et al. [55]
Fe1-xS vacancy-bearing superstructures
4C
5C
Fe2+
Probability of VFe occupancy
11C
6C
Figure 2-5: Distributions of vacancies in 4C and NC pyrrhotites.Vacancy distributions are represented by
the probability of site occupation for 4C, 5C, 11C and 6C pyrrhotites. [57]
(non-integral values of N) are simply mixtures of the well-structured 5C, 11C and 6C
polytypes. Irrespective, fully-ordered NC pyrrhotites are consistently antiferromagnetic
at room temperature due to a net compensation of magnetic moments between vacant
and full cation layers.
33
(b) FeS nanowires
6
c-axis
4
2
300
(c) Natural FeS
II c-axis
Cooling
3
500
0
300
400
500
T (K)
3
2
1
Heating
400
T (K)
σ (memu/g)
6
χ (memu/g)
σ (memu/g)
(a) Single crystal Fe9S10
8
600
0 100
300 500
o
T ( C)
Figure 2-6: The peak-like λ-transition in NC Fe1-x S (a) single crystals [64], (b) nanowires [61] and (c)
natural, geological samples [51].
2.2.2
The λ-transition in NC pyrrhotites
The unusual magnetic properties of pyrrhotite have long been studied for their fundamental interest. [58] The temperature-dependent magnetization of ordered NC pyrrhotites
is characterized by the appearance of a peak during heating, centered around 210 ± 10
o
C (Fig. 2-6) that is thought to arise from a structural rearrangement towards a ferrimagnetic superlattice. [59] More recently, Fe1-x S nanowires [60,61] and nanodisks [62]
that display the so-called λ magnetic transition have been fabricated by different means
and the phenomenon has even been proposed for technological purposes such as phasechange magnetic memory. [63] The kinetics of the λ-transition has been studied before
using magnetic techniques, notably by Townsend et al. [64] and Marusak et al. [41].
However, despite confirming the λ-transition to be a diffusion-controlled process, a
coherent mechanistic description is still lacking. For example, both authors assumed
simplified exponential time-dependence for isothermal magnetization kinetics.
2.3
Diffusion-limited λ transition
The λ-transition in NC (specifically, 11C and 6C) pyrrhotites was investigated using
temperature-dependent and time-dependent magnetization experiments (σ(T ) and σ(t),
respectively). During the first heating ramp from 30-350 o C, σ(T ) for the 11C and 6C
polytypes undergoes a peak, similar to that observed for 5C by other authors (Fig. 26), attributed to a rearrangement of the vacancy-bearing sublattice via diffusion. Our
work described here constitutes the first systematic investigation into the AF-FI transition in Fe1-x S since 1980. An initial attempt to replicate the earlier experiments of
Marusak et al. [41] revealed a more complex time-evolution of the ferrimagnetic superlattice. Instead of a simple exponential fit, we demonstrate the magnetokinetics are
better modeled by a phenomenological, stretched exponential function of the form:
α(t) = 1 − ex p [−(t/τ)n ]
(2.5)
where τ descrbes a temperature-dependent relaxation time, and n = 0.45 ± 0.05. Moreover, we describe a kinetic Monte Carlo (kMC) simulation of the λ-transition that reproduces the structural evolution on the experimental timescale from an AF to FI lattice
under cation vacancy diffusion alone. The kMC results similarly give a stretched exponential time dependence and help understand the transition as a continuous-ordering
transformation. A physical basis for the stretched exponential form of the kinetics is
discussed. Finally, we show the temperature dependence of τ in Eq.(2.5) yields an activation energy of 1.1 ± 0.1 eV for the λ-transition, which can be taken as the migration
energy for cation diffusion in ordered pyrrhotite.
34
(004)
(103)
(110)
(102)
(101)
(100)
4C
Intensity (arb. units)
4C
5C
5C
11C
11C
6C
6C
2C
30
(c) Composition
Measured at%Fe
(b) (102) peak
(a) X-ray diffraction
52
2C
50
48
46
6C
11C
5C
4C
48
50
at%Fe, Arnold et al.
(d)
2C
40
50
2Θ
60
70 42 43 44 45
2Θ
Figure 2-7: X-ray diffraction of synthetic pyrrhotites. (a) Comparison of as-synthesized 2C (FeS), 6C
(Fe11 S12 ), 11C (Fe10 S11 ), 5C (Fe9 S10 ) and 4C (Fe7 S8 ) samples with labelled pyrrhotite peaks . (b) (102̄)
peak, (c) the (102̄) peak position is used to estimate composition with reference to the calibration of Arnold
et al. [66]. (d) black pyrrhotites were stored in glass vials and were stable without a change in properties
over several months.
2.3.1
Methods
Preparation of well-ordered 2C, NC and 4C type pyrrhotites Synthetic pyrrhotite
samples of different stoichiometry were prepared by reacting the requisite amounts of
iron powder (99.999% purity, 200 mesh, Alfa Aesar, Haverhill, MA) and sulfur granules
(99.998% purity, also Alfa Aesar) in quartz tubes, sealed under vacuum to 10-3 mTorr.
The target stoichiometries were: Fe7 S8 (4C), Fe9 S10 (5C), Fe10 S11 (11C) and Fe11 S12
(6C). The sealed powders were subjected to an initial heat treatment to allow the elements to fully react [42]: 500 o C for 24 hours, then 800 o C for 48 hours, followed
by cooling at 0.5 o C/minute to 250 o C and held for 24 hours before removal from the
furnace. The products were removed from the quartz tubes, re-ground with a porcelain pestle and mortar, and re-sealed in fresh quartz tubes under vacuum. A second
heat treatment was subsequently applied to ensure each sample relaxed into its lowtemperature, equilibrium ordered structure: 800 o C for 72 hours, followed by cooling
at 0.1 o C/min to 250 o C, holding at 250 o C for 24 hours and finally cooled to 125 o C at
a rate of 0.1 o C/min, at which point the samples were removed from the furnace and
allowed to cool to room temperature.
Characterization of synthetic pyrrhotites: X-ray diffraction The structure and phase
purity of the as-synthesized powders was determined by x-ray diffraction (XRD) using a
PANalytical X’Pert PRO XRPD instrument with Cu-kα radiation (Fig. 2-7). All peaks can
be attributed to the hexagonal and monoclinic pyrrhotite structures (ICSD references
53528 and 151766, respectively). The position of the (102) peak was used to confirm
the iron content of the samples, using the peak position calibration described outlined
by Arnold et al. [65,66]. Only the as-synthesized 2C pyrrhotite did not follow the trend
in composition; however this phase was not of primary interest to this work and was
not used further.
Magnetic measurements Magnetic measurements were obtained using a variabletemperature Vibrating Sample Magnetometer (VSM), with an applied field of 10 kOe.
Powders of synthetic pyrrhotite weighing approximately 0.02 g were attached to quartz
rods using silver paste adhesive. The sample was purged with N2 during the measurement at a flow rate of 15 standard cubic feet per hour (scfh). For time-dependent mag35
Jump probabilities on kMC grid
P1
P2
P1
P1
P1
C
B
A
Figure 2-8: Setup of cubic kinetic Monte Carlo (kMC) grid. One superstructure unit cell is shown; hexagonal
symmetry was applied by biasing diffusion probabilities. There are four equivalent jumps, labelled P1 and one
non-equivalent jump, P2 > P1 .
netization measurements, the sample temperature was first raised to the setpoint, followed by turning on the applied field. The lag between reaching the set temperature
and recording the first data point was approximately one minute. The instrument was
calibrated using a nickel disk of known magnetization.
Differential scanning calorimetry Differential scanning calorimetry (DSC) was performed using a a Q2000 DSC (TA Instruments, New Castle, DE) under a dynamically
purged N2 environment.
Kinetic Monte Carlo simulations Kinetic Monte Carlo (kMC) simulations were performed on a model block of cation-deficient pyrrhotite to test the mechanistic hypothesis
that mass transport of vacancies between AB-planes at elevated temperatures can gradually convert an antiferromagnetic lattice to a ferrimagnetic one. The model aimed to
simulate the time-dependent magnetization of a superstructure containing randomlydispersed vacancies as it evolves towards a more 4C-like, layer-by-layer alternating occupancy structure. We defined an order parameter based on the ideal 4C pyrrhotite
vacancy distribution shown in Figure 2-4a. to continually assess the magnetism of the
structure as it evolved in time through diffusive jumps of V Fe alone. The setup of the
kMC model and the execution of unit processes are described step-by-step below.
1. A three-dimensional, cubic Ising model block consisting of 20 x 20 x 20 unit cells
was set up. Only iron sites were considered, under the assumption that the sulfur
sub-lattice is saturated and therefore does not contribute to mass transport. Individual lattice points can be full (1) or vacant (0) only. The hexagonal symmetry
of the NC-type pyrrhotite lattice was imposed by biasing the diffusion paths such
that a hop in one of the diagonals was 3 times as unlikely (Fig. 2-8).
2. One in every eleven sites was selected to be “0” at random to simulate an antiferromagnetic, 11C lattice. The start point for the lattice is not ordered; however,
there is no unique 11C structure established in the literature. Moreover, we found
that imposing a rigid initial structure only added to computation time without affecting the time-evolution results.
3. A vacant site in the structure was selected at random and its nearest neighbor
(NN) sites are evaluated as potential jump destinations. The only atomic process
modeled by the kMC code was the diffusion of V Fe in the a-, b- and c- directions. Occupied NN’s populated a list of diffusive jump locations; specifically, five
non-equivalent diffusion paths with different jump probabilities were considered
(Fig. 2-8). The probability P for a jump to any of these sites is calculated in a
36
Table 2.2: Thermodynamic values for pyrrhotite compounds. Enthalpy of formation ∆Hf, 298 K relative to
the elements in their standard states at 298 K, absolute third-law entropies S298 K at 298 K, and heat capacity
functions Cp . Data from: [67]
Compound
∆Hf, 298 K
(kJ/mol)
S298 K
(J/mol.K)
Cp (J/(mol.K))
FeS (2C)
-100.1
60.3
2437.1 − 9.9T + 0.01T 2 − (41.1 × 106 )T 2
Fe11 S12 (6C)
-1148.1
755.2
-
Fe10 S11 (11C)
-1048.5
693.0
-
Fe9 S10 (5C)
-950.8
623.5
170.6 − 0.5T + 0.0005T 2 − (3.0 × 106 )T 2
Fe7 S8 (4C)
-755.4
486.3
140.5 − 0.7T + (3.1 × 10−7 )T 2 − (3.9 × 106 )T 2
sub-routine, based on: (a) the self-diffusivity or intrinsic activation barrier to migration Em , in the absence of an imposed driving force; (b) an energy bias due
to a thermodynamic driving force towards ordering, Etherm , as described below
in step (4); (c) a bias due to the magnetic energy in the applied field of 10 kOe,
Emag :
˜
•
˜
•
˜
•
Emag
E ther m
Em
exp −
exp −
P = ν. exp −
kB T
kB T
kB T
(2.6)
4. Subsequent to each diffusive jump, the occupancy of the seven adjacent supercell
AB-planes above and seven below the elected vacant site was assessed (Fig. 28). The closeness of the layer-by-layer occupancy of this volume was compared
to the idealized ferrimagnetic 4C-type lattice occupancy (. . . full, vacant, full,
vacant. . . ) and was quantified by taking the root mean square (RMS) difference
from the ideal 4C structure occupancy.
5. The energy landscape of the simulation was biased such that the structure is thermodynamically driven to evolve towards a more 4C-like structure. A linear bias
of the form E ther m = AΘ + B was used, where the parameters A and B provide the
difference in Gibbs free energy ∆G between a disordered vacancy structure and
the 4C structure at a given temperature of interest, and Θ is the order parameter
we assign to the system, with 0 assigned to a randomly-ordered antiferromagnetic
lattice and 1 representing the full 4C structure. The free energy G of each phase
at a given temperature was approximated via the relation:
G = ∆H f ,298K +

ZT
ZT
C p d T − T S298K −
298K

Cp
T
dT
(2.7)
298K
where ∆H f , 298 K is the formation enthalpy at 298 K, S298 K is the entropy at
298 K and Cp the heat capacity. Values for these thermodynamic parameters, as
listed in 2.2, were obtained from Walder and Pelton. [67]
2.3.2
Results and discussion
Temperature-dependent magnetization
Temperature-dependent magnetization σ(T ) results for the 4C, 11C and 6C Fe1-x S samples are shown in Figure 2-9. The 4C sample followed typical FI, Weiss-type behavior
37
1
(c) 6C (Fe11S12)
2
2
2
M (emu.g-1)
20
(b) 11C (Fe10S11)
M (emu.g-1)
-1
Magnetization (emu.g )
(a) 4C (Fe7S8)
1.5
3
15
4
3
2
10
1.5
1
0.5
150 200 250 300 350
T (oC)
5
4
3
2
5
0
0
1
100
200
300
o
Temperature ( C)
0
1
0.5
150 200 250 300 350
T (oC)
1
100
200
300
o
Temperature ( C)
0
100
200
300
Temperature (oC)
Figure 2-9: Temperature-dependent magnetization σ(T ). (a) 4C, (b) 11C and (c) 6C pyrrhotite samples.
Multiple consecutive forward and reverse sweeps between 30-330 o C, as labelled 1-5 on each of the graphs,
were performed until no change from the previous sweep was observed. On (b) and (c) the inset graphs show
a magnified region around the peak observed on the first sweep. The heating and cooling rates were both 0.2
o
C/min; the applied field was 10 kOe.
11C (Fe10S11) Hysteresis Curves
3
σ (memu/g)
2
150 oC
220 oC
280 oC
325 oC
1
0
-1
-2
-3
-10 -5
0 5 10 -10 -5 0 5 10 -10 -5 0 5 10 -10 -5 0 5 10
H (kOe)
H (kOe)
H (kOe)
H (kOe)
Figure 2-10: Magnetization vs. applied field (σ-H). Obtained from 11C pyrrhotite samples held at different
temperatures, as indicated. Magnetization reaches a maximum at 220 o C in this series. Inset on each curve
is the region around zero applied field; the absence of hysteresis at 325 o C demonstrates paramagnetism.
as expected up to T N = 315 o C. This behavior is reversed upon cooling and can be repeated without hysteresis (three heating-cooling cycles are shown in Fig. 2-9a). The
as-synthesized 5C sample produced similar results to 4C, indicating that the desired,
equilibrium antiferromagnetic (AF) superstructure had not been formed. The 5C powders were not used further of this work.
However, the other NC samples, 11C and 6C, displayed markedly different σ(T)
behavior (Figs. 2-9(b) and (c)). On the first heating cycle, labelled (1) in the figures,
σ started close to 0 emu/g, consistent with AF ordering. The λ-transition peak first
appeared at ∼ 180 o C, with a maximum at 210 o C. This is also observed in Figure 210 which shows a series of magnetization vs. applied field (σ-H) curves at different
temperatures along the peak. The magnitude of σ for a given H first rose then fell between 150 and 280 o C. At 325 o C the magnetic behavior is paramagnetic, evidenced
by a lack of hysteresis. However, during cooling back from 350 o C, the λ peak was
not reproduced and σ increased with Weiss behavior back to room temperature. Multiple, repeated heating/cooling cycles (2-5) as indicated on the curves only served to
increase overall magnitization further. The maximum room temperature magnetization
σRT reached by 11C after several experimental cycles (∼ 13 emu/g) was greater than
that of the 6C sample (∼ 10 emu/g); neither reached the maximum of the 4C sample
(σRT ∼ 22 emu/g). Thus the final σ for a given structure is limited by the availability
of iron vacancy V Fe to maximize the magnetic asymmetry between vacancy-bearing and
full layers.
38
Time-dependent magnetization
The fact that several heating cycles were required to fully convert the 11C and 6C Fe1-x S
to a metastable, FI superstructure (Figs. 2-9b and c) suggests that the kinetics of the
λ-transformation are not instantaneous. To understand the transformation kinetics in
more detail, we performed isothermal, time-dependent magnetization σ(t) measurements on samples of 11C at various temperatures between 140-220 o C. Short-timescale
kinetics (< 10 minutes) and longer-timescale behavior (up to several hours) are discussed separately. Figure 2-11a shows the results of heating one sample consecutively
in steps of 10 o C, holding at each temperature for 10 minutes (solid line series). It can
be seen that σ in this series was history-dependent: each time the sample was heated,
the transformation proceeded from the end-point reached at the previous temperature.
Conversely, the dashed curves in Fig. 2-11a were obtained on fresh samples heated directly from 30 o C to the set temperature of 180-220 o C as indicated. The peak shape
was also reproduced, but a lack of transformation history means that σ did not reach
the same level as the sample subjected to consecutive heating steps.
We also observe from Fig. 2-11a that a large proportion of the rise in σ at a given
temperature occured very rapidly, within the first 5 minutes and is evidently at least partially reversible, since the curves overlap. The initial reversibility is more clearly seen in
Figure 2-11b where the σ(t) of an 11C sample held at 210 o C for 4000 s continuously is
compared against that of another sample which was cooled to room temperature three
times sequentially at 20 minute intervals between heating to 210 o C. We can infer from
this that much of the rapid, initial increase in σ t at a given temperature arose from a
small motion of V Fe between adjacent planes, easily reversed upon cooling. However
after a few minutes the gradient (dσ/d t) became less steep, i.e. the maximization of σ
requires a more coordinated re-shuffling of the vacancy sublattice that remains macroscopically irreversible, or metastable, once cooled back to room temperature.
To understand the transformation kinetics in more detail, we performed isothermal, σ(t) measurements on samples of 11C at various temperatures between 140-220
o
C for longer times up to 10,000 s. The kinetics of the λ-transition in 5C Fe1-x S, studied
via thermomagnetic techniques, has previously been shown to be limited by V Fe diffusion. [64] Assuming exponential growth in σ during the λ-transition, iron self-diffusion
coefficients on the order of 10-17 cm2 s-1 have been found by magnetokinetic methods
within this transition temperature range [41] that are inconsistently low compared to
extrapolated diffusivities obtained from high-temperature sulfidation [30, 31] and radiotracer diffusion studies [O(10-14 cm2 s-1 )]. [40] However, during an initial attempt to
replicate these experiments we found that our magnetokinetic data were not described
or fit by simple exponential functions. Instead, the stretched exponential in Eq. (2.5)
provided a more accurate description (Figure 2-12).
Isothermal σ t data were also collected at several temperatures along the λ-transition
for longer times up to 10,000 s. Magnetization was converted to ‘phase fraction’ of FI
ordering, α F I , according to:
αF I =
σ t − σi
σ f − σi
(2.8)
where σ t is the measured magnetization at time t, σi is initial magnetization at t = 0
and σ f is final magnetization assuming the transition were allowed to proceed to completion. σ f values for the different temperatures were therefore obtained from curve
number (4) in Figure 2-9b, i.e. the maximum FI magnetization at a given temperature
T.
39
(a)
Short time-dependent magnetization
3.5
210 oC
Magnetization (emu/g)
Same sample
Fresh samples
each run
3
o
200 C
220 oC
2.5
190 oC
2
o
180 C
o
1.5
170 C
o
160 C
150 C
140 oC
o
1
(b)
0 10 20 30 40 50 60 70 80 90
Time from start of experiment (min)
Reversible initial magnetization
5
o
Magnetization (emu/g)
210 C
4
3
2
3
2
Continuous
Sequential
1
1
0
1000
2000
Time (s)
3000
4000
Figure 2-11: Reversible magnetic transformation at short timescales. (a) Isothermal, time-dependent magnetization σ(t) of 11C pyrrhotite at different temperatures around the λ transition. The grey, solid curves
were obtained on the same sample, consecutively heated to the indicated set temperature, held for 10 minutes
and cooled to room temperature (“add-on” magnetization). The dashed lines correspond to a series where
each temperature measurement was performed with a fresh sample. (b) σ(t) of two 11C samples: one held
continuously at 210 o C for 4000 s (dashed line). The other is sequentially heated to 210 o C three times, with
cooling to room temperature between each step.
2.3.3
Continuous re-ordering of ferrimagnetic superlattice
Figures 2-13a and 2-13b display the results for the experimental and simulated λtransition magnetokinetics, respectively. For the experimental data, a common value
of n = 0.45 ± 0.05 was found to fit all curves reliably. For the kMC results, n = 0.67 ±
0.05; a sensitivity analysis and details of fitting procedures are provided in Table 2-21.
Nevertheless, the kMC model, based solely on cation diffusion, accurately replicated
the stretched exponential form of the experimental result. The parameters τ and n in
Eq. (2.5) are not indicative of any specific atomic mechanism. Generally, τ represents
a temperature-dependent relaxation time and n determines the lengthening of τ as the
transition progresses (i.e. a deceleration in transition kinetics). Stretched exponential
magnetokinetics of this form have been observed for Li2 (Li1-x Fex )N (n = 0.4-0.8) at low
temperatures < 20 K, related to finite magnetic moment relaxation. [68] However, this
is an unlikely explanation for the kinetics observed in this work at elevated temperatures, where magnetic relaxation should be instantaneous. Alternatively, we can think
40
(b) kinetic Monte Carlo (210 oC)
1
1
0.8
0.8
0.6
0.6
α
α
(a) Experiment (210 oC)
0.4
0.2
0
0.4
Data
Exponential fit
Stretched exp. fit
0
5000
10000
15000
0.2
20000
0
0
5000
Time (s)
10000
15000
20000
Time (s)
Figure 2-12: Best fits to exponential equation α(t) = 1 − exp [− (t/τ)] and stretched exponential equation
α(t) = 1 − exp [− (t/τ)n ] for (a) experimental magnetization data obtained at 210 o C and (b) kinetic Monte
Carlo simulated data at the same temperature.
Table 2.3: Best fit parameters n and τ in the fitting expression α(t) = αo [1 − exp [− (t/τ)n ]] + (1 − αo ) for
the experimental and kinetic Monte Carlo results.
Temp. (o C)
n
t
αo
Experimental: free parameters
180
0.48
548 ± 9
1.00
190
0.42
134 ± 2
0.99
200
0.40
78 ± 2
0.89
210
0.44
66 ± 3
0.90
Experimental: fixed n
180
0.45 ± 0.05
410 ± 211
1.00
190
0.45 ± 0.05
186 ± 95
0.98
200
0.45 ± 0.05
127 ± 65
0.86
210
0.45 ± 0.05
76 ± 39
0.89
kinetic Monte Carlo: free parameters
180
0.70
737 ± 38
N/A
190
0.73
651 ± 40
N/A
200
0.66
275 ± 19
N/A
210
0.62
150 ± 8
N/A
of the λ-transition as a classical nucleation and growth process, described by the semiempirical Johnson-Mehl-Avrami-Kolmogorov (JMAK) relation that takes the same form
as Eq. (2.5). For example, the first-order antiferromagnetic-ferromagnetic transition in
FeRh has been described by a JMAK equation with n = 0.86. [69] The Avrami exponent n is typically temperature independent and may provide information about the
nucleation and growth mechanisms. [70] A value of n = 0.5 to describe the formation
of FI phase out of a homogeneous AF lattice would suggest one-dimensional growth
with zero nucleation rate, implying small nuclei of FI phase were pre-dispersed in the
41
(a)
Experimental ferrimagnetic fraction
1
-3
210 200 190 180
1.1 ± 0.1 eV
Data
Fit
T oC
-1
ln( τ )
0.8
-4
-5
210 oC
-6
0.6
1/T x 10-3 (K-1)
200 oC
α
-7
0.4
190 oC
0.2
180 oC
0
0
(b)
5000
Time (s)
10000
kinetic Monte Carlo results
1
α
0.8
210 oC
200 oC
Data
Fit
190 oC
0.6
T oC
0.4
180 oC
210 200 190 180
-1
ln( τ )
-5
0.2
-6
-7
0
0
1.1 eV
5000
Time (s)
1/T x 10-3 (K-1)
10000
Figure 2-13: Long-timescale isothermal magnetization. (a) Transformed ferrimagnetic volume fraction α
measured over 10,000 s at four temperatures as indicated. We show every 20th point of the raw data as
well as a best fit line to the phenomenological, stretched exponential relation α(t) = 1 − exp [− (t/τ)n ],
with standard deviation error. Inset: Arrhenius fit of the temperature-dependent fitting parameter τ−1 , with
a slope corresponding to a transformation activation energy of 1.1 ± 0.1 eV. (b) kinetic Monte Carlo (kMC)
reullts for magnetization transformation at the same temperatures, and fit to a similar stretched exponential
fit. Inset: corresponding activation energy of 1.1 eV calculated from computational τ−1 .
equilibrium 11C lattice prior to transformation, and that the observed "growth" in α
arises from the change in the magnetization order parameter along one axis alone (for
example, the c-axis). However, we believe the microscopic transition mechanism can be
better described as a diffusion-limited, continuous re-ordering process akin to spinodal
decomposition. As such, the FI phase grows out of the AF lattice via an augmentation
in small, layer-by-layer vacancy occupancy fluctuations. A second-order transition of
this type is consistent with a continuity in enthalpy H but discontinuous heat capacity ∂ H/∂ T during the λ-transition, as measured by differential scanning calorimetry
(Figure 2-14). The absence of a pronounced discontinuity in heat Q confirms that the
diffusive rearrangement of the λ-transition is second order; that is, the new state of
increased symmetry develops continuously from the highly-ordered, lower symmetry
11C or 6C phases. The subsequent, spontaneous disordering at T N is then 1st -order,
similarly to the 4C case, but since an already higher degree of disorder exists in the
6C and 11C lattices which have not had time to form into a perfect alternating-layer
FI structure, much less diffusion (and therefore latent heat) is required to undergo the
42
Differential Scanning Calorimetry
Heat Flow (mW/g)
(a)
Heat Flow (mW/g)
(b)
500
4C
Exo.
0
-500
Endo.
200 11C
Heat Flow (mW/g)
30.1 J/g
316 oC
Heating
Cooling
100
2.2 J/g
4.9 J/g
1.4 J/g
4.7 J/g
0
-100
o
210 C
Heating
-200
(c)
30.5 J/g
314 oC
Cooling
200 6C
316 oC
Cooling
100
2.2 J/g
5.0 J/g
2.5 J/g
5.0 J/g
0
-100
210 oC
Heating
-200
50
100
150
200
250
o
Temperature ( C)
o
316 C
300
350
Figure 2-14: Differential scanning calorimetry (DSC) results from (a) 4C, (b) 11C, (c) 6C synthetic
pyrrhotite samples. The heating rate was 10 o C/min; endothermic heat flow is negative on the y-axes. The
integrated peak areas for heat uptake or evolution events, in units of J/g and demarcated with dashed lines,
are shown on each figure next to the event.
full disordering transition.
Figures 2-15a-e shows a series of magneto-structural order parameter Θ distributions on kMC lattice points, obtained at various times along the λ-transition at 200 o C.
Rather than observing the formation of discrete FI nuclei (red dots in the figure) which
grow along one axis and would thus be consistent with the JMAK interpretation, we instead visualize the emergence of regions of intermediate Θ that gradually spread across
other lattice points diffusely. This simulated phenomenon is also clearly seen in Figure
2-15f, where we see small fluctuations in layer-by-layer vacancy occupancy augment
with time into an alternating-plane, FI structure. The stretched exponential fits in Eq.
(2.5) to our σ(t) data take the same form as the Kohlrausch function [71], commonly
used to describe non-equilibrium dynamics in disordered condensed matter such as dielectric relaxation [72], relaxation in soft matter [73] and diffusion in complex systems,
incluiding glassy materials and H migration in amorphous Si. [74] Although generically
semi-empirical, a number of mathematical derivations for the Kohlrausch function have
been put forward which provide a more physical basis for the ubiquitously observed
stretched exponential behavior. [75] Kohlrausch behavior can arise in the presence a
small energy distribution of traps in systems with long-range correlations; this would
lead to deviations from "random walk" Brownian motion diffusion in amorphous structures. Alternatively, there may be a time-dependence in populating different energy
traps, such that relaxation occurs in stages. [76] Although we do not wish to compare
directly the stretched exponential magnetization observed in the λ-transition here to
Kohlrausch descriptions of decay in disordered materials, perhaps some parallels may
43
(a) 0 s
(b) 7,000 s
(c) 12,000 s
(d) 45,000 s
(e) 100,000 s
Order parameter Θ
1 FI
c
a
0 AF
(f)
Occupancy
0.95
average occupancy = 0.909
0.9
0.85
0
0s
2
12,000 s
4
6
100,000 s
8
10
12
Layer # along c-axis
z-axis
14
16
18
20
Figure 2-15: Continuous re-ordering towards ferrimagnetic state. Local order parameter Θ calculated
for individual lattice points in the kinetic Monte Carlo (kMC) simulation at 200 o C, where 0 refers to fully
antiferromagnetic (AF) and 1 is ferrimagnetic (FI), corresponding to: (a) 0 s, (b) 7000 s, (c) 12000 s, (d)
45000 s and (e) 100000 s along the λ-transition. (f) layer-by-layer occupancy for 20 planes along the c-axis
from the kMC results obtained at different times. As the transition progresses, the difference in occupation
between adjacent layers becomes more pronounced.
be drawn which give an intuitive physical insight into the phenomenon observed both
experimentally and in the kMC results of this work. We can dismiss the possibility of a
distribution in traps since Brownian motion was inherently assumed in our kMC model.
On the other hand, a time-decay in the rate of magnetization evolution may be more
coherently explained by a combination of rapid and subordiante, slower processes. In
other words, given sufficient thermal energy, cation vacancies may migrate rapidly to
adjacent planes under a large thermodynamic driving force and break the compensating
AF lattice symmetry. This leads to small regions with localized FI ordering that nonetheless contribute a large increase in σ on the scale of 10-100s of seconds. At longer times,
however, the formation of the optimal FI lattice structure for the available vacancy concentration requires a more labored rearrangement of vacancies into long-range order,
decelerating the growth in σ. Only inter-layer V Fe hops contribute to a rise in magnetization. We compared the ratio of inter- to intra-layer hops during the λ-transition in
the kMC model and found that it decreased over time. This is consistent with a relaxation in the exponential kinetics for σ; the further the transition progresses, the lower
the driving force for vacancy segragation and the smaller the probability of inter-layer
jumps.
Finally, we turn to the significance of the activation energy of 1.1 ± 0.1 eV measured
by fitting the experimental σ(t). A migration barrier for diffusion of 1.2 eV was originally cast into the kMC model. An analysis of the resulting kMC data using the same
fitting procedure as for the experiment returned an apparent barrier value of 1.1 eV,
confirming that the major rate-limiting step is cation diffusion. We therefore take 1.1
eV to represent a slight underestimate to the activation barrier Em to Fe self-diffusion
in magnetically-ordered Fe1-x S superstructures. The overall measured activation energy
includes a thermodynamic bias for the transformation on the order of 0.1 eV at 200
o
C (calculated from the data in Table 2.2), which serves to lower the diffusion barrier
44
Sulfidation of iron
Fe1-xS
Marker
Iron
Figure 2-16: Cross section of sulfide scale formed during the sulfidation of Fe for 20 mins at 800 o C. An
inert (Pt) marker indicates the position of the original iron-vapour interface. (100x) [30]
slightly.
2.3.4
Conclusions
In conclusion, we have investigated the antiferromagnetic to ferrimagnetic λ-transition
in NC-type pyrrhotites via magnetokinetic experiments and kinetic Monte Carlo simulations. In contrast to previous reports, the transformation is found to follow a stretched
exponential time-dependence. These experimental and computational results together
support a description of the λ-transition as a nucleation-free, continuous reordering
via diffusion on the cation sublattice. Magnetization initially rises rapidly due to small,
localized displacements, but a full optimization of the ferrimagnetic superstructure is
a more complex process that emerges only at longer timescales. The migration energy
barrier for Fe in magnetic pyrrhotite is shown to be approximately 1.1 eV. The results
are helpful in predicting the barrier properties of pyrrhotite scales on ferrous alloys
that are exposed to sulfur environments, for example in oil and gas systems. Further,
the eludication of the kinetics of the λ-transition encourages continued studies to identify practical applications for this interesting magnetic phenomenon in synthetic Fe1-x S,
for example magnetic switching or data recording devices based on earth abundant
chemical elements.
2.4
Isotope tracer diffusion measurements
Consistent with the metal-deficient nature of Fe1-x S, the diffusion of cations is known
to be the primary solid state mass transport mechanism in pyrrhotite scales in both
aqueous [36] and dry [29–31] sulfide corrosion conditions. The self-diffusion coefficient
for sulfur in Fe1-x S is known to be several orders of magnitude lower than for Fe2+ :
*DS = O(10-11 ) cm2 s-1 at 1000 o C compared to O(10-11 ) cm2 s-1 for *DFe . [40]. Hence
an inert marker placed at a steel-pyrrhotite interface will remain at the interface as
the Fe1-x S scale grows by the outward migration of cations (Fig. 2-16). In the previous
study, an activation energy of 1.1 ± 0.1 eV was measured for a diffusion-limited vacancy
superstructure rearrangement process in ordered pyrrhotites. This should represent the
barrier for Fe migration through a Fe1-x S lattice in which a thermodynamic driving force
exists for ordering. In this section, iron self-diffusion *DFe is measured directly in bulk
crystals of Fe1-x S by means of iron-57 isotope tracer measurements using secondary ion
mass spectrometry (SIMS).
45
(b) (102) peak
30
(110)
(103)
(101)
40
50
2Θ
60
o
(004)
43.65
(101)
(100)
(100)
Intensity (arb. units)
(102)
(a) Natural Fe1-xS XRD
70 42 43 44 45
2Θ
Figure 2-17: Cu-kα powder XRD pattern from a representative sample of research grade natural pyrrhotite.
(a) Hexagonal Fe1-x S peaks are labelled on the diagram. Inset: picture of crystals; approximately 5 x 5 x 1
mm3 polished to < 50 nm roughness. (b) the hexagonal Fe1-x S (102) peak’s position of 43.65o indicates an
average composition of 48.0 at% Fe.
2.4.1
Methods
Sample preparation
Natural pyrrhotite crystals were used for diffusion studies.1 Research-grade natural
crystals of pyrrhotite were obtained from Ward’s Science (Rochester, NY). Individual
specimens were approximately 5x5x5 mm3 and were sourced from North Bend, WA. A
representative sample of several individual crystals from the package was ground together into a powder in a porcelain mortar for XRD phase identification (Fig. 2-17a).
Hexagonal pyrrhotite was found to be the only phase present. The position of the (102)
peak (Fig. 2-17b) was used to estimate an average composition of 48.0 at% Fe, corresponding approximately to Fe11 S12 (6C). [66]
The chemical composition of the natural crystals was investigated using energydispersive x-ray spectroscopy (EDS) in a JEOL 6610LV scanning electron microscope
(SEM), to check for any large inclusions that may have affected the reliability of the
diffusion studies. Figure 2-18 shows a series of chemical maps of a randomly-selected
but representative surface, indicating that the majority elements were sulfur and iron.
Some minor inclusions of oxide were present in thin seams. An search for potential
metallic impurities such as Si and Al came up negative within the detection limit of the
instrument (approx. 0.1 wt% [77], implying that the inclusions are likely iron oxides.
These were deemed sparse enough to not greatly affect the accuracy of the subsequent
diffusion studies. The self-diffusion coefficient of iron in Fe2 O3 is very small below 500
o
C (< 10-28 cm2 s-1 . [78]
As-received crystals were polished using 1200, 2000 and 4000 grit sandpaper to
achieve a flat surfaces followed by an extended polish of 5-10 minutes using 50 nm
Al2 O3 suspension. The resulting average surface root mean square (RMS) roughness,
as measured by Atomic Force Microscopy (AFM) was < 50 nm; in some 50x50 µm areas
RMS roughness was as low as 17 nm.
Temperature-dependent magnetization studies as described in Section 2.3.1 confirmed the natural pyrrhotite samples to be antiferromagnetic at room temperature and
1
In fact, diffusion studies were attempted using three different types of pyrrhotite samples: Chemical vapor
deposited (CVD) thin films (∼ 200-500 nm thickness, Appendix B), Sputter deposited thin films (∼ 1000 nm
thickness, Section 2.5.1) and polished natural single crystals (100’s of µm thick). In this chapter, only the
data collected from the natural single crystals is included, since they are considered the most reliable from
this study.
46
Chemical composition of natural pyrrhotite samples
(a)
(c)
SEM
(e)
(g)
S
Fe
(f)
(h)
250 µm
(b)
(d)
Al
Si
O
25 µm
Figure 2-18: Energy-dispersive X-ray spectroscopy (EDS) maps of an unpolished surface from a natural
crystal used in this study. The scanning electron microscope (SEM) picture is reproduced and overlaid with
chemical analysis maps of sulfur, iron, oxygen, silicon and aluminium.
Table 2.4: Isotopic composition of naturally-occurring iron. [79]
Isotope
54
Nat. abundance (at%)
5.85
Half-life
> 3.1 × 10
56
Fe
22
years
Fe
57
Fe
59
Fe
91.75
2.12
0.28
Stable
Stable
Stable
to undergo a peak-like λ-transition starting at 160 o C as described for synthetic 11C
and 6C pyrrhotite in Section 2, followed by a full magnetic disordering at T N = 316 o C.
57
Fe deposition and diffusion annealing
To study iron self-diffusion, the stable isotope 57 Fe was used as a tracer. 57 Fe is a stable
isotope with abundance in natural iron of around 2% (Table 2.4). Solid chips of 57 Fe
(96.06% enriched, Nakima Ltd., Israel) comprising a total mass of 200 mg were evaporated onto the surface of ∼ 40 polished Fe1-x S crystals simultaneously using a Sharon
TE-1 thermal evaporator. The resulting deposit thickness, measured in situ with a quartz
crystal microbalance and confirmed ex situ by measuring a deposit shadow profile on a
glass substrate, was 130 nm.
Once coated in 130 nm of 57 Fe, pyrrhotite crystals were subjected to diffusion annealings at a range of temperatures between 170-400 o C for different lengths of time.
Annealing was performed in a horizontal quartz tube furnace under a dynamic H2 S:H2
atmosphere in a molar ratio of 1:3500 (i.e. 0.03% H2 S) which was within the sulfur
partial pressure stability window for Fe1-x S for the relevant range of temperatures (see
Fig. 2-25 in Section 2.5.1). Maintaining this dynamic, reducing atmosphere prohibited
the formation of oxide on the deposit or oxidatoin of the crystals themselves. Crystals
were mounted on a custom stage and inserted into the hot part of the furnace for a
predetermined period of time before being removed outside the tube furnace for cooling under the H2 S/H2 atmosphere. A thermocouple allowed in situ temperature profile
recording for each annealing run (e.g. Fig. 2-19a). Specimens that were left for periods
longer than 15 days to anneal were sealed under vacuum in quartz tubes and placed in
heated silicone oil baths, rather than in the dynamic atmosphere quartz tube furnace. 2
2
Only the 170 o C sample was annealed in a quartz tube. Thin film samples made by CVD and sputter
deposition were also annealed in quartz tubes. The surfaces of these specimens turned bright blue indicating
the formation of a surface oxide on the 57 Fe deposit of 10 nm thickness; for the thin film samples this affected
the diffusion results, lowering them by approximately three orders of magnitude. For more details, please
47
Secondary Ion Mass Spectrometry (SIMS)
Depth profiling of as-annealed specimens was performed in a CAMECA IMS-5f dynamic SIMS at the Materials Research Laboratory of the University of Illinois, UrbanaChampaign. Up to 12 specimens could be mounted in a spring-loaded holder simultaneously to expose a flat face to the primary ion beam. 57 Fe and 56 Fe depth profiles were
established by using a 10keV O- primary beam. In addition to these two species, the
instrument was calibrated to detect any metallic impurity elements (mainly Si, Al, Ca,
Mg) during each measurement. Only areas of the samples where the signal from these
impurities was below the detection limit of 10 ppm were used for diffusion analysis.
Anions such as sulfur and oxygen could not be simultaneously measured along with
cations using the O- primary beam and we do not include an analysis of these species
in this work. The 57 Fe concentration [57 Fe ] as a function of sputtering time was determined from the intensities I of the secondary positive ions 56 Fe + and 57 Fe + using
2.4.1
[57 Fe] =
I(57 Fe)
I(57 Fe) + I(56 Fe)
(2.9)
Conversion of sputtering time to profile depth was achieved by measuring the depth
of the SIMS craters using a Dektak profilometer and assuming a constant sputtering rate
(Figs. 2-19b and c). The main factors contributing to error in depth profiling are surface
roughness and sample tilt. Tilt can be seen clearly in Figure 2-19b with a distortion of
the square SIMS profile. However, the sputter rate was found to be correlated with
primary beam current, which could only be controlled accurately to within ± 25 nA
but was displayed on the instrument for every run (Fig. 2-19d). An ordinary linear
regression of the measured sputter rate on primary beam current was used to estimate
a standard deviation for diffusion profiles that are subjected to such systematic errors.
Diffusion profiles were fit to the error function solution in Eq. (2.12) using the Curve
Fitting application in MATLAB R2012b.
2.4.2
Results and Discussion
Fitting of diffusion profiles
Figure 2-20 compares the [57 Fe ] diffusion profile of an un-annealed sample with the
original 57 Fe deposit versus a typical profile of an annealed sample (275 o C, 5 minutes).
The original SIMS spectra as a function of time for the annealed sample are inset in the
figure. The un-annealed profile contains a sharp interface between the original 57 Fe
deposit and the Fe1-x S crystal, located at 130 nm depth. After annealing, a [57 Fe] tail
from diffusion extends approximately 800 nm into the crystal. Nevertheless, even after
diffusion annealing at 275 o C, a substantial proportion of the initial, pure 57 Fe remained
on the Fe1-x S surface. This essentially acted as a semi-infinite source of isotopic iron
in the limit of the relatively short annealing times used in this work. We can therefore
assume the concentration at the diffusion couple interface (i.e. at 130 nm depth) is fixed
at c = co for the duration of the annealing run. The initial and boundary conditions are
hence:
c(x, t = 0) = 0
(2.10)
c(x = 0, t) = co
(2.11)
and:
refer to Appendix C. For the bulk, natural sample the thickness of the surface 57 Fe deposit was too thick for
the formation of a surface tarnish oxide to affect the diffusion result.
48
(a)
Typical annealing cycle
400
(b)
SIMS crater for diffusion profile
Time at 95% of Tset
Temperatureo(C)
350
300
250
Heating
transient
200
Cooling
transient
150
100
(c)
100 µm
0
100
200 300 400
Time (s)
500
(d)
Depth profile of crater in (b)
2.5
1
-1
Sputter rate (nm.s )
0
-1
z (µm)
Sputter rate linear regression
-2
-3
-4
-5
2
1.5
-6
-7
0
100
200 300
x (µm)
400
1
150
500
200
250
Sputter current (nA)
300
Figure 2-19: Sources of error considered in statistical analysis of diffusion data. (a) representative annealing profile. The time used for each measurement was total time within 5% of the setpoint. (b) optical
micrograph of a tilted SIMS crater, indicating the position of the depth profile line scan in (c). (d) One way
to quantify the effects of sputtering error is to take the entire sample set and measure sputtering rate (=
crater depth/sputter time). This should be linearly correlated with primary ion sputter power; the standard
deviation is used to estimate error in the depth of the diffusion profiles.
SIMS depth profiles
Intensity (arb. units)
1
0.6
57
[ Fe]
0.8
0.4
56
8
10
57
Fe
Fe
6
10
4
10
0
500
1000
Time (s)
Original deposit 130 nm
0.2
Annealed 275 oC 5 min.
0
0
500
1000
Depth (nm)
1500
Figure 2-20: Secondary ion mass spectrometry (SIMS) profiles. The interdiffusion of a 130 nm-thick 57 Fe
deposit on Fe1-x S crystals was measured by SIMS. The black curve shows the SIMS profile from an un-annealed
sample, indicating the depth of the original deposit. Inset: raw SIMS data for a sample annealed for 5 minutes
at 275 o C; converted in the main plot to 57 Fe concentration vs. depth into the crystal (grey curve).
49
Error function fits
1
o
225 C
Measurement
n
Error f fit
0.6
57
[ Fe]
0.8
13000 s
0.4
1800 s
Residuals
0.2
0
0.02
0
-0.02
0.02
0
-0.02
0
1000
2000
Depth (nm)
3000
Figure 2-21: Error function solution to diffusion profiles. The tail of each profile was fit to Eq. (2.12).
Example fits for two samples annealed at 225 o C for approx. 1800 and 13000 s are shown.
Then it can be shown there exists an error function solution to Fick’s second law in the
form [70]:
•
c(x, t) = co 1 − er f

x
4Dt)
‹˜
(2.12)
The diffusion tails beyond the 130 nm original deposit were normalized to an initial,
interfacial concentration co = 1 and fit using Eq. (2.12). Figure 2-21 shows an example
of fitting two profiles from samples annealed at the same temperature of 225 o C but
for different times of 1.8 x 103 and 1.3 x 104 s. The sample annealed longer has a 57 Fe
profile that extends further into the sample, as expected. However, the measured * DFe
values from fitting were close: 4.6 and 3.4×10−13 , respectively. Wherever possible, more
than one measurement at a single temperature was obtained to check for consistency.
The best-fit error function solutions are overlaid on top of experimental data with a
range of uncertainty in Figure 2-21.
Increased diffusion activation energy from spontaneous magnetization
Values of * DFe obtained from error function fitting are listed in Table 2.5 and plotted in
Arrhenius form on Figure 2-22, alongside representatitive literature data from Fryt et
al. [31] and Condit et al. [40] (also shown in Figure 2-1). We include for comparison
only those data corresponding to the stoichiometry range of 0.03 ≤ x ≤ 0.1 in Fe1-x S,
which is close to the composition of our samples analyzed via SIMS. Above ∼ 300 o C, our
measurements are consistent with the previous results, corresponding to an activation
energy QP = 0.83 ± 0.03 eV, which represents the mean and standard deviation slopes
obtained by regression fitting. From Figure 2-22, we also observe that below T N our
*
DFe values are considerably lower than the extrapolated Arrhenius trend with a slope
of −Q P /kB . A deviation of this type beginning around 300 o C was previously observed
by Condit et al., who postulated that vacancy ordering reduced the number of mobile
vacancies by fixing Fe vacancies in equlibrium superlattice positions where they have
long residence times. Despite this observation, their experiments were not pursued to
low enough temperatures to confirm this hypothesis or to quantify the activation energy
in the new regime. In this study, we also considered the possilibity that vacancy ordering
may produce the observed, anomalous behavior at T ≤ T N . By comparison, however,
50
Table 2.5: Iron self-diffusion * DFe measurement results for Fe1-x S crystals.
Temperature
(o C)
Annealing
time (s)
*
DFe (cm2 s-1 )
170
1976400
5.14 x 10-16
6.12 x 10-17
186
54000
9.24 x 10-15
3.25 x 10-15
202
72000
3.02 x 10-14
7.75 x 10-15
202
72000
4.99 x 10-14
7.43 x 10-15
205
5762
1.27 x 10-13
1.78 x 10-14
209
145800
3.33 x 10-14
3.96 x 10-15
225
1794
4.63 x 10-13
7.47 x 10-14
225
12900
3.40 x 10-13
4.37 x 10-14
249
3348
1.08 x 10-12
1.36 x 10-13
249
19830
2.22 x 10-12
2.71 x 10-13
251
573
8.39 x 10-13
4.00 x 10-16
288
116
7.56 x 10-12
6.06 x 10-13
298
449
8.77 x 10-12
1.52 x 10-12
326
596
1.89 x 10-11
2.98 x 10-12
350
86
1.53 x 10-10
6.56 x 10-11
352
410
1.76 x 10-10
3.29 x 10-11
376
94
2.87 x 10-10
4.57 x 10-11
377
276
1.54 x 10-10
3.16 x 10-11
403
98
5.19 x 10-10
8.60 x 10-11
Error
in
(cm2 s-1 )
*
DFe
oxides that undergo structural order-disorder transitions display large, discontinuous
drops in diffusivity, by up to several orders of magnitude, at the critical ordering temperature. [80] Conversely, the change in Arrhenius behavior of * DFe in Figure 2-22 is
continuous and does not seem to be consistent with the expected effect of a first-order
structural reorganization, and is more reminiscent of the so-called "magnetic diffusion
anomaly" observed at the paramagnetic-ferromagnetic critical point or Curie temperature T C in ferromagnetic materials. Self-diffusion [81–83] and solute diffusion [84, 85]
in Fe, interdiffusion in Fe-Ni alloys [86] and, to a lesser extent, diffusion in Co [83] all
display a deviation from the Arrhenius law extrapolated from the paramagnetic region
at T C , characterized by a sharp spike or disontinuity in the effective activation energy
Qeff given by:
Q e f f = −kB
d(ln D(T ))
d(1/T )
(2.13)
In other words, the magnetic transition has a second-order effect on D, manifested in
an abrupt change in Arrhenius slope. Ruch et al. derived a theoretical model for the
magnetic diffusion anomaly, based on a constant diffusivity prefactor Do and a magnetic contribution to the activation energy for diffusion that varies with temperature as
S(T )2 , where S is the reduced magnetization relative to magnetization at zero Kelvin:
S(T ) = M (T )/M (T = 0K). [87] Beginning with a generic formula for the temperature
dependence of the diffusion coefficient:
51
Fe self-diffusion in Fe1-xS below ordering temperature
Temperature (oC)
-6
900 700
400
300
200
150
Paramagnetic
QP = 0.83 eV
-8
log[*DFe] (cm2s-1)
500
TN = 316 oC
-10
Literature
-12
Fryt *
Condit **
-14
This work
Data
Model fit
Magnetic
QM = QP + αS2
(outlier)
-16
1.0
1.5
2.0
2.5
1000/T (K-1)
Figure 2-22: Values for iron self-diffusion coefficient * DFe obtained in this work are compared to literature
data from Fryt et al. [31] and Condit et al. [40]. The known magneto-structural ordering (Néel) temperature
T N of 316 o C is indicated with a dashed line. Above T N the activation energy slope in the paramagnetic state
is Q P = 0.83 ± 0.03 eV. However, our results below T N deviate below the extrapolated Arrhenius relationship.
The data are fit using an activation energy QM for the spontaneously magnetized state that depends on
reduced magnetization S as: Q M = Q P + αS(T )2 . The outlying data point at 170 o C marked with an arrow is
excluded from the trendline fit. Literature data correspond to pyrrhotite stoichiometries close to the samples
used in tihs work (x in Fe1-x S ∼ 0.04) : * Fryt, x =0.04 [31]; ** Condit, average of data from 0.03 ≤ x ≤ 0.1.
[40]
D = f gd 2 Γ v C v
(2.14)
where f is a correlation function, g a geometrical factor depending on crystallography,
and d the characteristic jump distance, Γ v is defined as the frequency of diffusive hops
and Cv as the average vacancy concentration. Γ v depends on S according to:
Γ v = νe f f exp −
o
Em
+ C S2
(2.15)
kB T
o
where νe f f is an effective attempt frequency, Em
is the migration energy in the paramagnetic state, i.e. the difference in energy between an atom in an activated position
for a diffusive hop and that of a adjacent atom in an equilibrium position, and C is a
constant. Cv is likewise given by:
–
C v = exp −
E of + (zJ/2)S 2
kB T
™
(2.16)
where E of is the formation energy of a vacancy in a paramagnetic crystal, z is the coordination number and J the exchange coupling constant for magnetic spins. Defining:
α=
C + 21 zJ
Qp
(2.17)
then the generic diffusion coefficient in a magnetically ordered system can be written:
52
D(T ) = Do exp −
Q p (1 + αS(T )2 )
kB T
(2.18)
The * DFe data in Figure 2-22 are fit to Eq. (2.18) using the temperature variation of
the (001)NiAs magnetic reflection in synthetic Fe7 S8 obtained by Powell et al. [42] The
factor α thus quantifies the magnetic ordering effect on the vacancy formation and
migration energies, leading to an effective ferromagnetic activation energy for diffusion
Q M = Q P + αS(T )2 . From our results we obtained a best fit of α = 0.41 ± 0.06. In
other words, the activation energy for diffusion at maximum magnetization (0 K) is
approximately 1.18-1.30 eV, as opposed to 0.83 eV in the paramagnetic crystal at high
temperatures. We assume here that the vacancy concentration remained fixed at the
original bulk value of CV = 0.04 during the annealing experiments. In other words,
the effectively semi-infinite sample into which the Fe-57 exchanged remained at fixed
stoichiometry. In this case, the increase in overall diffusion activation energy can be
attributed solely to the magnetic influence on migration barrier, i.e. the constant C in
Eq. 2.17.
Nevertheless, it is worth adding a small comment regarding the reliability of our
results as pure self-diffusivity measurments. Since pure Fe-57 was used as the tracer
exchange material on top of the sulfide specimens, a small extent of chemical diffusion undoubtedly would have affected the measured diffusion profiles. The chemical
contribution to diffusion arises from a small concentration gradient developing during
annealing, altering the stoichiometry in the topmost, interdiffused volume towards a
Fe:S ratio of 1:1. Such a chemical diffusion component would thus be expected to increase the diffusion rate and hence lead to a slight overestimate in self-diffusion values
*
DFe . We did not quantify the extent of chemical diffusion contribution directly in our
analysis, but, judging by the overlap of our data with the literature values in Figure 2-22,
it is likely to be small. Moreover, an unintended overestimate in * DFe does not change
the key observation of a magnetic diffusion anomaly, which leads to values considerably
lower than the extrapolated, paramagnetic trend with temperature.
The implications of the magnetic diffusion anomaly in pyrrhotite are twofold. First,
the growth conditions for Fe1-x S in solution both as a by-product of H2 S corrosion on
iron and steels in energy infrastructure, as well as intentionally via solvothermal or electrodeposition methods, are typically below 300 o C. Therefore any a priori prediction of
growth rates from a consideration of cation diffusion must account for the effect of spontaneous magnetization, which reduces * DFe by up to 100x at 150 o C when compared
to a linear extrapolation of the Arrhenius slope from above the spontaneous ordering
temperature. The accuracy of predictive tools for H2 S corrosion as well as more careful
control of Fe1-x S nanocrystal synthesis both stand to benefit from these findings. Second, although Fe1-x S has long been studied for its interesting magnetic properties, to the
authors’ knowledge there is no example of a successful technological implementation of
this material. Since the magnetic switching phenomena of interest in Fe1-x S involve the
local, diffusive rearragement of vacancies, knowing the activation energy for Fe vacancy
migration and formation in the magnetized state permits the development of simulation
tools to design useful devices from this material, such as temperature- and/or electric
field-driven magnetic switching and memory applications.
2.4.3
Conclusions
In conclusion, 57 Fe tracer diffusion measurements were performed to determine iron
self-diffusivity * DFe in Fe1-x S as a function of temperature in the range 170-400 o C,
which extends across the known magnetostructural order-disorder transition temperature T N = 315 o C. Our results for * DFe above T N agree well with measurements from
previous studies in paramagnetic and structurally-disordered pyrrhotite, with an activa53
tion energy Q P = 0.83 eV. However, below T N , iron self-diffusivity deviates downwards
from the extrapolated paramagnetic Arrhenius trend by approximately a factor of 10
at 200 o C and 100 times at 150 o C. This can be rationalized by considering a magnetic
ordering effect on Fe vacancy migration energy, which increases the overall diffusion
activation energy by up to 41% or to approximately 1.18-1.30 eV in the fully magnetically ordered state. To our best knowledge, this work constitutes the first description of
a magnetic diffusion anomaly in an ionic compound or a ferrimagnetic material. More
practicallly, the knowledge of a magnetic contribution to diffusivity allows more accurate crystal growth rate predictions of ferrous sulfide barrier layers encountered in
energy systems containing H2 S and other aggressive sulfidizing agents, as well as in the
solution-based synthesis of Fe1-x S where temperatures are below 315 o C.
2.5
Sulfur exchange kinetics at the Fe1-x S surface
The final section of this chapter addresses the kinetics of sulfur transfer from the gas
phase into solid pyrrhotite. Aside from ionic diffusion through the sulfide corrosion
product barrier, this reaction is known to be the other major rate-limiting mechanism
for sulfide corrosion on steels. [17, 36] For example, with H2 S as the primary sulfurbearing molecule, the net rate of sulfur transfer reaction can be represented by:
H2 S(g) ⇐⇒ H2(g) + S(in Fe1−x S)
(2.19)
−
HS(ad)
at the sulfide surface is thought
where the dissociation of adsorbed H2 S(ad) or
to be the rate limiting step. [37] The kinetics of this process at 600 o C have been investigated using a resistance relaxation technique in sulfidized iron foils by Pareek et
al. [88], who similarly looked at sulfur transfer in the other non-stoichiometric sulfides
Cu2-x S [89] and Ag2+x S [90]. In this section, the results of an electrical conductivity relaxation (ECR) study on Fe1-x S thin films inspired by those studies are described. However, rather than focus on identifying rate-limiting steps and mechanisms, the primary
motivation here was to obtain a series of kinetic rates for sulfur transfer as a function of
temperature. Consistent with the theme of this chapter, the aim was to establish an experimental value for the activation barrier of this process such that it can be compared
to the kinetics of diffusion.
2.5.1
Methods
Preparation and characterization of Fe1-x S thin films
Pyrrhotite thin films were sputter deposited in an AJA International ATC-1800 sputter
deposition system in the Microsystems Technology Laboratory (MTL) at MIT. The target was 99.9% iron monosulfide (FeS) (Semiconductor Wafer, Inc., Taiwan). 1 x 1 cm2
soda lime glass pieces served as the substrates and 350 nm FeS was deposited at a rate
of approximately 1 Å/s using an Ar plasma at 250 W power. Figure 2-23a shows the
surface and through-thickness morphology of a typical, as-sputtered film. Grain sizes
were on the order of 50-100 nm in plan view; however, the tilted view reveals grains
are columnar with lengths on the order of several hundreds of nm. To test the thermal stability of the film morphology, the same sample was imaged after annealing for
4 hours under a dynamic, 0.001% H2 S-H2 environment at 450 o C. All samples used in
this work were subjected to a four-hour post-anneal treatment under these conditions
after sputtering to equilibrate the microstructure prior to ECR experiements. Although
grain boundaries became more clearly defined, there was no major coarsening or morphological change of the grain structure after four hours of post-anealing, and it can be
assumed that under subsequent ECR conditions no further structural change occurred
that could have affected the measurements. Figure 2-23c shows a Cu-kα radiation XRD
54
(a)
As sputtered film
(b)
H2S annealed 450 C
(d)
Pole figure scans
300 nm
(c)
Intensity (arb. units)
XRD: texture in annealed film
20
(100)
(100)
(102)
(102)
(110)
6x10
3
(110)
2x10
30
40
2Θ
50
3
60
Figure 2-23: Sputter deposited thin films for ECR experiments. (a) scanning electron microscope (SEM)
of as-sputtered film (inset: 60 o tilted view). (b) the microstructure coarsened slightly after annealing for 4
hours under a dynamic H2 S atmosphere; no additional changes were observed for further annealing up to
12 hours. (c) conventional Cu-kα x-ray diffraction (XRD) scan revealed only two hexagonal Fe1-x S reflexes,
as labelled. (d) pole figure XRD scans confirm the high (100) texture of the samples.
scan for such a post-annealed film. Only two peaks are visible that can be attributed
to (100)
and (110) in hexagonal pyrrhotite (ICSD reference 53528). Interestingly, the
102 peak, the predominant reflex from polycrystalline pyrrhotite was not observed
in 2Θ XRD scans. Pole figure scans at fixed 2Θ corresponding to the three peaks (100),
102 and (110) are shown in Figure 2-23d, suggesting a high (100) texture. Similar
oriented crystallite growth of pyrrhotite was observed by Birkholtz et al. during Fe-S
sputtering under reducing conditions. [91]
X-ray photoelectron spectroscopy (XPS) was performed on pre- and post-annealed
Fe1-x S films using Al-kα radiation at 1487 eV. Samples were cleaned by Ar+ sputtering
at 500 eV in the ultra-high vacuum (UHV) chamber. The base pressure during XPS
measurement was < 10-9 Torr. XPS spectra were obtained using a pass energy of 20
eV at steps of 0.1 eV. Fitting of the Fe 2p32 spectra was performed according to the
procedure outlined by Pratt et al. [92], for pyrrhotite and based on calculations by
Gupta and Sen of theoretical core p levels multiplet structures to distinguish between
Fe2+ and Fe3+ in Fe2 O3 . [93, 94] The S 2p spectra were fitted by assuming monosulfide
(S 2− ), disulfide (S22− ) and polysulfide (Sn2− ). [92]
Electrical Conductivity Relaxation (ECR)
A custom-built ECR setup was made using a Thermo Scientific TF55030A-1 tube furnace. A schematic of the experimental apparatus is shown in Figure 2-24. A buffered
H2 /H2 S gas mixture was flown through a 40 cm-long quartz furnace at predeterimined
flow rates up to 500 sccm, controlled by Omega FVL-Series mass flow controllers. The
pure gases used were of 5% H2 -balance N2 and either 100 ppm H2 S-balance He or 4%
55
Schematic of ECR apparatus
Pt contact wires
Al2O3 stage
Fe1-xS sample
Figure 2-24: Electrical conductivity relaxation apparatus setup. Schematic of experimental setup for electrical conductivity relaxation (ECR) experiements. The inset picture of the sample stage shows platinum wire
screw contacts on a 1 x 1 cm2 , sputtered Fe1-x S thin film sample.
H2 S-balance N2 , depending on the desired partial pressure. A four-way valve at the gas
inlet for the furnace tube allowed the atmosphere in the hot zone of the furnace to be
switched rapidly between two different gas mixtures and hence partial pressures of sulfur. The flush time of the reactor (i.e. time to fully replace the atmosphere with a new
mixture) was on the order of 30 s. In the following sections, conductivity relaxation results are presented where the experimental timescale is 102 -103 s. We therefore deem
the reactor flush time negligible in the analysis of our results. The Fe1-x S samples supported on glass were contacted directly with spring-like platinum wires in a four-probe
format (Fig. 2-24, inset). Each Pt contact was maintaned on the sample by compressing
it with stainless steel screws. 3
The contacts were connected via Pt wires to four stainless steel gas/electrical feedthroughs
which in turn were connected to a Keithley 2400 source meter for automated 4-probe
electrical conductivity measurement. The source meter was controlled by a customdesigned LabView program written by Qiyang Lu (MIT) and run from a standard laptop PC. The program initiated and recorded in situ conductivity measurements of the
Fe1-x S samples at intervals of 1-20 s. We do not provide conductivity measurements in
this work since we did not perform average four-probe (van der Pauw) electrical measurements between all the electrodes. Instead we kept the current-sourcing wires fixed;
even though the conductance was thus sensitive to the placing of electrodes, measuring
the relative change in conductance was adequate for these kinetic experiments.
Control of sulfur partial pressure
Atmospheres of fixed sulfur partial pressure were established in the apparatus by mixing
H2 /H2 S gases, as described above. The equilibrium relation H2 S(g) ⇐⇒ H2(g) + 12 S2(g)
was assumed, for which the equilibrium constant can be written:
K p (T ) =
pH2 pS212
pH2 S
(2.20)
The experimental values of K p (T) as determined by Yuan and Kröger [95], Pitzer
[96] and Fryt et al. [31] were compared and found to be consistent within a few percent
3
Additional, e-beam deposited contact pads of 200 nm Au or Pt with an adhesion layer of 10 nm Cr on the
samples were also tried; these facilitated the establishment of good electrical contact initially, but were found
to be unstable at elevated temperatures of > 350 o C and delaminated. The high conductivity of pyrrhotite
itself allowed the formation of decent electrical contacts simply by touching the compressed Pt springs to the
sample surface.
56
Table 2.6: K p (T) values used to calculate sulfur partial pressure.
Author
Expression
Ref.
− 4570
T
+ 2.35
− 10806
T
− 5.87
log K p (T ) =
Yuan and Kröger
ln K p (T ) =
Pitzer
ln K p (T ) = −
Fryt et al.
[95]
[96]
90249−50.08×T
RT
[31]
Thermodynamic stability range of pyrrhotite
Temperature (oC)
1000 800
600 500
400
300
4
2
log(fS /bar)
0
Liquid
Fe1-xS
-4
10
%
1%
-8
0.1
HS
2
2
%
HS
2
1%
H
0.0
2S
01
%
HS
2
0.0
-12
0.4
fcc
Fe
0.6
bcc
Fe
0.8
1.0
1.2
1.4
FeS2
HS
1.6
Fe7S8
1.8
2.0
1-
1000/T (K )
Figure 2-25: Temperature-pressure equilibrium phase diagram for Fe-S. Isomolar H2 S lines are superimposed to show the range of gas mixtures that could be used while maintaining Fe1-x S stability.
in the temperature range of interest 300-600 o C (Table 2.6). The mean value given by
these three literature sources was used to set the sulfur partial pressures used in ECR
experiments.
The stability range of pyrrhotite limited the range of sulfur partial pressures that
could be used in ECR experiments and had to be carefully controlled to not reduce the
samples to pure Fe, or conversely oxidize them to FeS2 . The T-pS2 phase diagram in Fig.
2-25 shows the stability range of Fe1-x S along with the predicted pS2 trends for different
H2 /H2 S gas mixtures containing between 0.001-10% H2 S.
2.5.2
Results and Discussion
In this section, we review the defect chemistry that allows electrical conductivity relaxation measurements to be made in Fe1-x S, by rapidly changing the partial pressure of
sulfur in the atmosphere and allowing the sample to equilibrate over time to a new sulfur activity. Experimental, kinetic measurements for oxidation and reduction of Fe1-x S
by sulfur as a function of temperature are presented. Although the influence of sulfur chemical potential difference ∆µS remained unclear, the temperature activation of
both oxidation and reduction was evident from the results. Finally, some of the incon57
sistencies and inaccuracies in the current ECR experiments on thin films are discussedincluding surface contamination, thermal history and lack of precise control over gas
composition.
Mechanism of electrical conductivity relaxation in Fe1-x S
Besides the work already mentioned on dignetite Cu2-x S [89] and silver sulfide Ag2+x S,
the vast majority of ECR studies investigated mixed ionic-electronic conduction in oxides. [97–103] Briefly, the technique can be described as follows: the electrical conductivity of the sample to be studied must have a dependence on the degree of offstoichiometry. Moreover, the intended sample must be appropriately thin such that
diffusional processes are very rapid in the temperature range of interest compared to
molecular dissociation and incorporation of the active species at the surface. When these
conditions are met, a sudden change in partial pressure of the reactive anion-bearing
molecule in the atmosphere (H2 S in this case) will cause the sample to equilibrate over
time with the gas, and the change in conductivity during this process can be measured
continuously in situ to determine the kinetics of the anion transfer process.
We can assume linear surface exchange kinetics to give the mass conversion law
[98, 99]:
∂ cS (t)
A
= − .k [cS (t) − cS (∞)]
∂t
V
(2.21)
where A and V are the surface area and volume of the film, respectively; k is the surface
exchange coefficient; cS (t) is the sulfur concentration at time t and cS (∞) the sulfur
concentration at the new equilibrium. Eq. (2.21) can be integrated to yield:
t
cS (t) − cS (0)
= 1 − exp −
cS (∞) − cS (0)
τ
(2.22)
with:
τ=
l
k
(2.23)
where l is the thickness of the sample.
For Fe1-x S we assume the only ionic defects to be iron vacancies V Fe . For different
sulfur valence states m = 2-8, the charge transfer process of interest can be written:
m−
H2 S(g) + me− ⇔ S(ad)
+ H2(g)
(2.24)
m−
S(ad)
⇔ S(ad) + me−
(2.25)
Adopting Kröger-Vink notation for defect equilibria, the adsorbed sulfur atom is
incorporated into a lattice site by the formation of a charged Fe vacancy.
S(ad) ⇔ SS + VFe
0
00
VFe + 2e ⇔ VFe
(2.26)
(2.27)
The conduction mechanism in iron sulfides has been proposed to involve hole hopping in a band of predominantly d character, requiring holes to be generated by the presence of Fe3+ ions. [52] Figure 2-26a shows the Fe 2p3/2 XPS spectrum of a pyrrhotite
sample in the H2 S post-annealed condition which reveals a substantial proportion (up
to 40%) of ferric ions in the near-surface. The S 2p peak for the same sample is illustrated in Table 2-26b, revealing a majority of monosulfide S 2− . Figure 2-26c and d
58
Intensity (arb. units)
(a) Fe 2p photoemission
(b) S 2p
(c) C 1s
Data
Fit
725 715 705
B.E. (eV)
As sputtered
Annealed
295
275
(d) O 1s
2-
2+
S
S22-, Sn2-
Fe
3+
Fe
285
As sputtered
Annealed
716
708
704
712
Binding Energy (eV)
170
166 162 158
Binding Energy (eV)
538
526
534
530
Binding Energy (eV)
Figure 2-26: X-ray photoelectron spectroscopy (XPS) from a Fe1-x S thin film sample. (a) Fe 2p spectrum,
deconvoluted into Fe2+ and Fe3+ according to [92]. (b) S 2p spectrum indicating an almost entirely S 2−
binding environment. (c) and (d) show the reduction in carbon and oxygen contamination, respectively,
after annealing the films under an H2 S atmosphere prior to ECR experimentation.
Table 2.7: Deconvolution of Fe 2p and S 2p x-ray photoelectron spectroscopy (XPS) peaks.
Peak
Chemical State
Binding
(eV)
Fe 2p3/2
Fe(II)-S
S 2p
Energy
FWHM
(eV)
Area (%)
706.5
1.4
10.9
Fe(II)-S*
707.4
1.8
31.6
Fe(II)-S
708.3
1.4
12.7
Fe(II)-S sattelite
713.3
2.7
4.9
Fe(III)-S
709.2
1.5
18.8
Fe(III)-S*
710.3
1.5
11.4
Fe(III)-S
711.3
1.5
5.6
Fe(III)-S
712.3
1.5
4.2
Monosulfide 2p3/2
161.2
1.2
85.2
Monosulfide 2p1/2
162.3
1.2
-
Disulfide 2p3/2
162.4
1.6
6.0
Disulfide 2p1/2
163.6
1.6
-
Polysulfide 2p3/2
162.9
2.0
8.8
Polysulfide 2p1/2
164.1
2.0
-
confirm that the carbon and oxygen content of the films, respectively, is reduced substantially by annealing in an H2 S atmosphere and that these likely do not contribute to
the existence of ferric ions in the lattice (e.g. as Fe2 O3 ). The fitting parameters for the
Fe 2p3/2 and S 2p1/2 peak deconvolution are shown in Figure 2.7. The photoemission
spectra taken together therefore indicate the presence of Fe3+ and substantiate a conduction mechanism that would involve hole hopping on ferric ion sites. A conduction
mechanism of this kind is also observed at high temperatures in metallic conducting
oxides such as Nd2 NiO4 , with itinerant electrons in the conduction band. [104]
Assuming a conduction mechanism of this type, where semi-mobile holes hop from
Fe3+ to Fe3+ ion sites, a net charge neutrality condition can be written:
59
00 2 VFe ≈ p ∝ n−1 ∝ ae−1
(2.28)
where p and n are the positive and negative charge carrier concentrations, respectively,
and ae is the chemical potential of electrons. The concentration of Fe ions cFe in a molar
volume V m of Fe1-x S is:
c Fe (t) = 1 − cS (t) =
1 − x(t)
Vm
(2.29)
Therefore:
p=
1
− c Fe (t)
Vm
(2.30)
Electrical conductivity se in a p-type dominated conductor is given by:
se = pµh F
(2.31)
where µh is hole mobility, which we assume to be constant during isothermal ECR experiments. From Eqs. (2.29), (2.30) and (2.31) therefore, we can write the normalized
conductivity g(t) during the measurements in terms of he concentration of sulfur in the
film:
g(t) =
cS (t) − cS (0)
se (t) − se (0)
=
se (∞) − se (0)
cS (∞) − cS (0)
(2.32)
With reference to Eq. (2.22), the normalized conductivity of a sample undergoing a
change in sulfur activity to a new equilibrium is expected to follow a single exponential
decay of the form:
t
g(t) = 1 − exp −
(2.33)
τ
Figure 2-27 illustrates the change of resistance of a Fe1-x S sample subjected to three
consecutive changes in gas concentration from 5-10% H2 S (balance H2 ), followed by
10-15% H2 S and finally 15-20% H2 S at 565 o C. The resistance fell in an exponentiallike manner each time the atmosphere is enriched in sulfur
and the sample incorporates
00 more S atoms, accommodated by an increased VFe and hence mobile hole concentration. In the following section, as-recorded resistance was converted to normalized
conductivity g(t) and fitted to an exponential function following Eq. (2.33).
Temperature-dependence of sulfur exchange kinetics
The full results of the ECR experiments are listed in Tables 2.8 (oxidation) and 2.9 (reduction). For each experiment, the sulfur partial pressure was changed from an initial
value pS2 ,i to a final value pS2 , f as indicated. pS2 values were calculated from the equilibrium constants in Table 2.6. The normalized conductivity data for each were fit to a
single exponential function (Eq. (2.33)) and the chemical exchange coefficient kox for
oxidation relaxation curves and kred for corresponding reduction were derived from the
best fit values of τ. Representative conductivity relaxation curves at a range of temperatures are given in Figures 2-28a and b. The decent exponential fits to the data (Figs.
2-28a and c) confirm that a single activation process is limiting the relaxation of conductivity. For a film thickness d = 350 nm and the * DFe results in Figure 2-1 of this chapter,
typical diffusion timescales tdiff can be estimated using t di f f ∼ d 2 /(4DFe ). For the lowest temperature used in the ECR experiments of 390 o C (* DFe ≈ 10-10 cm2 s-1 ), tdiff ∼ 3
s. Diffusion should therefore be on the order of 1000x faster than the observed relaxation process, implying that the observed exponential decay should arise from surface
exchange processes alone.
60
Table 2.8: Electrical conductivity relaxation results for oxidation experiments: initial (pS2 ,i ) and final
(pS2 ,i ) sulfur partial pressure values; surface exchange coefficient kox from exponential fits. These data are
plotted for clearer comparison in Figure 2-28.
T (o C)
log pS2 ,i (atm)
log pS2 , f (atm)
kox (x 10-9 cm/s)
390
-14.6
-13.2
16.5
390
-14.6
-12.6
23.9
390
-14.6
-12.6
7.34
390
-13.2
-11.8
5.75
400
-18.0
-17.0
14.4
400
-18.0
-17.0
19.6
400
-19.0
-17.0
24.9
430
-17.0
-16.0
9.86
450
-16.0
-14.0
14.6
450
-17.0
-16.0
62.2
480
-16.7
-14.7
55.1
490
-11.4
-10.2
164
510
-11.4
-10.2
194
513
-11.0
-10.1
94.7
520
-10.9
-9.8
120
520
-16.0
-14.0
314
520
-16.0
-14.0
124
520
-16.0
-14.0
300
565
-8.7
-8.1
670
567
-10.3
-9.1
832
Table 2.9: Electrical conductivity relaxation results for reduction experiments: initial (pS2 ,i ) and final
(pS2 ,i ) sulfur partial pressure values; surface exchange coefficient kred from exponential fits. These data are
plotted for clearer comparison in Figure 2-28.
T (o C)
log pS2 ,i (atm)
log pS2 , f (atm)
k r ed (x 10-9 cm/s)
400
-17.0
-18.0
23.2
400
-17.0
-18.0
22.0
400
-17.0
-18.0
28.6
513
-10.1
-11.0
63.3
520
-14.0
-16.0
76.8
520
-14.0
-16.0
118
520
-14.0
-16.0
115
565
-8.6
-9.1
418
565
-9.1
-10.3
350
61
% H2S in mix
Electrical resistance relaxation at 565 oC
20
15
10
5
11.5
Resistance (Ω)
5-10% H2S
11
10-15% H2S
15-20% H2S
10.5
10
0
500
1000
1500
2000
Time (s)
Figure 2-27: Electrical resistance relaxation at 565 o C upon three successive changes in H2 S-H2 gas mixture
in the furnace atmosphere, as indicated.
The clearest observation from the tabulated results is an overall trend of increasing k towards higher temperatures, seen more clearly when the data are presented
graphically in Figures 2-28a and b. Ignoring for now the dependence on sulfur partial
pressure, we use this trend to determine an average activation energy for the surface
chemical exchange process Echem of 1.05 ± 0.20 eV for oxidation and 0.79 ± 0.23 eV
for reduction.
The relaxation time should also, in theory, be affected by a chemical driving force, as
has been shown in studies of bulk oxides. [98, 99] This can be defined as the difference
in the equilibrium chemical potentials of sulfur ∆µS in the sample in the inital and final
states. Assuming the ideal gas law and zero activity constant:
pS2 ,i
RT
∆µS =
ln
(2.34)
2
pS2 , f
Tables 2.8 and 2.9 also list the initial and final sulfur partial pressures used in each
experiment. There is no definitive correlation between relaxation time and partial pressures in our data. The uncertainty in each reading is evident by comparing experiments
o
performed at constant temperature. For example,
in Table 2.8 the 390
C measurements
include two results obtained with log pS2 ,i = −14.6 and log pS2 , f = −12.6, yielding
two disparate values of kox = 23.9 × 10−9 and 7.34 × 10−9 cm/s. The other two results
for oxidation at 390 o C were taken using different values of pS2 ,i and pS2 , f ; however,
the resulting values of kox fall between 23.9×10−9 and 7.34×10−9 cm/s. No conclusive
verdict can be reached on the influence of ∆µS from these data. The same is true for
other readings obtained at constant temperature.
In the following section, some of the inaccuracies that may contribute to this uncertainty are discussed in more detail. The ECR technique for pyrrhotite thin films as
described here is judged to be reasonable for obtaining the broad temperature dependence of the oxidation and reduction processes. However, in their present form the
kinetic measurements are too variable and ambiguous to reveal more intricate informa62
(a)
Normalized conductivity: oxidation
(c)
Exchange coefficient: oxidation
Temperature (oC)
600
550
500
450
400 375
-14
Ea, ox = 1.05 ± 0.20 eV
0.8
-15
o
ln(k) (cm.s )
390 C
400 oC
o
480 C
520 oC
565 oC
0.6
0.4
-1
Normalized conductivity
1
-17
ΔPS = 101 atm
-18
Fit:
σ = 1 - exp[-t/τox.]
0.2
-16
2
2
ΔPS = 10 atm
2
-19
0
0
4000
2000
6000
Linear regression
95 % C.I.
1.1
1.2
1.3
Time (s)
(b)
1.4
1.5
1.6
-1
1000/T (K )
Normalized conductivity: reduction
(d)
Exchange coefficient: reduction
Temperature (oC)
600
550
500
450
400 375
-14
400 oC
o
520 C
o
565 C
0.8
Fit:
σ = 1 - exp[-t/τred.]
0.6
0.4
-16
-17
-18
ΔPS = 101 atm
-19
ΔPS = 102 atm
Linear regression
95 % C.I.
0.2
0
0
Ea, red = 0.79 ± 0.23 eV
-15
ln(k) (cm.s-1)
Normalized conductivity
1
2
2
2000
4000
6000
1.1
Time (s)
1.2
1.3
1.4
1.5
1.6
1000/T (K-1)
Figure 2-28: Electrical conductivity relaxation results: (a) representative oxidation relaxation curves (data
points) obtained at different temperatures with best fit exponentials (solid lines). (b) representative reduction
relaxation curves. Chemical exchange coefficients for (c) oxidative sulfur transfer from H2 S to Fe1-x S and (d)
the reverse reductive transfer into the gas phase: individual data and best-fit Arrhenius line with 95 "%"
confidence interval. k values corresponding to the individual curves shown in (a) and (b) are demarcated
with arrows.
tion over secondary effects such as that of the chemical driving force.
Measurement consistency and surface degradation
The inconsistencies in our ECR results, even among results obtained under identical
conditions as discussed above, underscore the high sensitivity of sulfur exchange reaction to the condition of the sample surface. In Figures 2-29a and b, two sets of in
situ resistance measurements are shown that were obtained at 520 o C and 400 o C over
the course of several hours each. Several oxidation/reduction cycles were performed
by switching the sulfur partial pressures between two consistent values as shown and
allowing the sample to equilibrate each time. At first glance, the redox cycling looks
fairly repeatable with little hysteresis, despite a constant upwards drift on the order of
63
50-60 S/hour.
However, in Figure 2-29c we plot some other results obtained at 400 o C on another
sample. This time the conductivity is normalized to the equilibrium conductivity at the
start of each cycle. revealing a consistent attenuation with successive cycles that is suggestive of a history-dependent surface degradation process. For example, the percentage
change in conductance during the first oxidation step "O1" is approximately 1.7%, but
is reduced to only 0.6% for the subsequent reduction step "R1" performed after "O1".
By the fifth cycle "O5", the conductance relaxation has reduced to only 0.4%.
The gradual degradation in the results after repeated cycling on a single sample
rules out sample-to-sample differences to be responsible for the variation in measured
k values; all samples were fabricated and pre-annealed identically. The reason is more
likely to be related to a degradation in the condition of the sample surfaces with time.
Scanning electron microscopy investigations of the Fe1-x S samples after different stages
of experiment revealed the columnar film morphology and grain size to be stable at
high temperature over the course of 12 hours. Moreover, an XPS investigation of a sample subjected to a typical ECR experiment did not expose any atypical surface chemistry, such as increased carbon, oxygen, or other foreign elements. On the contrary, the
carbon and oxygen content of the films was decreased by post-annealing in an H2 S atmosphere after deposition (Fig. 2-26) and subsequently remained stable during further
ECR experiments. Surface contamination can thus be ruled out as an explanation for
the degradation. The as-deposited Fe1-x S films used in this work had a roughness on the
order of 10-20 nm; prolonged annelealing did not measurably change the roughness.
The instability and lack of repeatability observed in these sulfide ECR experiments
are common also in similar work with oxide samples, particularly where thin films
and/or carefully engineered surface chemistry or nanostructuring is involved. [101] For
example, Wang et al. observed the oxygen exchange surface kinetics on La0.6 Sr0.4 Fe0.8 Co0.2 O3
(LSFCO) to degrade after annealing at 900 o C. Here also, no changes in surface chemistry were detected by XPS that could provide an explanation for the degradation in oxygen transfer properties. Conversely, Chen et al. found in another study using epitaxial
lanthanum strontium cobalt oxide (LSCO) that the oxygen exchange activity increased
substantially after annealing. They attributed this to a roughening of the surface, which
introduced surface steps and edges. [105] The surface exchange process for Fe1-x S involves a sulfur atom taking a vacant anion site on the surface; grain boundaries and
surface steps/edges are known to be catalytically active sites for dissociative adsorption. More work is needed to undersand the high sensitivity of ECR experiments to the
surface condition, leading to inconsistent results.
2.5.3
Conclusions
ECR was used to monitor the sulfur surface exchange kinetics for Fe1-x S thin film samples subjected to changes in sulfur partial pressure in buffered H2 S/H2 gas mixtures.
Results can be fit to a single exponential curve, confirming that surface exchange is the
sole rate-limiting process. A clear temperature dependence of the exchange coefficient
k allowed us to determine the activation barrier Echem to sulfur exchange of 1.05 ± 0.20
eV for oxidation and 0.79 ± 0.23 eV for reduction. However, the technique is not sensitive enough to determine the secondary effect of chemical driving force on exchange
kinetics. Moreover, the measurements are history-dependent: multiple redox cycling
leads to an attenuation in the relative resistance change upon subsequent oxidation
or reduction steps. There is no clear explanation for this based on changes in surface
morphology or chemistry, and more work must be done to understand the influence of
surface state on kinetics in more detail.
64
Inconsistencies in ECR measurements
Conductance (x 100 S)
(a)
14.0 520 oC
1 hour
13.8
60 S
Red.
13.6
13.4
~ 4%
change
Ox.
13.2
13.0
0
1.5
1
0.5
2.5
2
3
3.5
4
Time (10 s)
Conductance (x 100 S)
(b)
o
16.5 400 C
< 1% change
Red.
16.4
16.3
Ox.
16.2
0
1
0.5
1.5
2.5
2
3
3.5
4
1.02
O1
t
Normalized conductivity σ /σ
o
Time (10 s)
1.01
O4
1
O3
R3
O2
R2
R1
0.99
0.98
0
2000
4000
6000
8000
Time (s)
Figure 2-29: Drift, stability and repeatability of ECR experiments. (a) conductance measurement for daylong repeated oxidation and reduction cycles at 520 o C. The global drift is on the order of 60 S/hour. There
are also points at which conductance is unstable and jumps suddenly. (b) repeated redox cycling at 400 o C.
The timescale for individual relaxations is longer than for measurements at 520 o C. (c) repeated oxidation
(O1-O4) and reduction (R1-R3) cycles on a different sample at 400 o C. Relative conductivity is obtained
by normalizing results by the equilibrium conductance at the beginning of each cycle; we see a gradual
degradation in the magnitude of the overall change after the first oxidation cycle O1.
2.6
2.6.1
Outcomes
Conclusions
The primary aim of the work described in this chapter was to compare activation barriers Ea and kinetic rates of the unit processes of cation diffusion (bulk) and exchange
of sulfur (surface) in Fe1-x S. The experimentally-determined values of Ea are listed in
Table 2.10. Since the two processes have a similar temperature dependence, there is
65
Surface exchange slower at all temperatures until film is 1000 μm thick
Fe diffusion
S exchange
Faster
Surface
limited
0
Equilibration const. (s-1)
10
Surface
limited
-5
Mixed
10
Diffusion
limited
-10
10
1
Slower
-0.5
10
Film Thickness
(μm)
-1
-1.5
100
-2
1000
-2.5
1000/T (K- 1)
Figure 2-30: Temperature- and film thickness dependence of rate limiting steps. The "equilibration constant" τeq for both processes, as a measure of the kinetic rate, is plotted as a function of both temperature and
also film thickness x. As the film gets thicker from 1 to 1000 µm, the overall rate of both processes becomes
slower. However, since the diffusion rate decreases parabolically with x, a crossover from surface exchange
limited growth to diffusion limited growth would be expected at around x = 100-1000 µm.
no clear transition temperature above which one would be expected to dominate over
the other in controlling the rate of sulfidation of iron. However, we can take an analytical approach to understanding rate-limiiting regimes by considering the "equilibration constant" τeq for each process. This can be thought of as the characteristic time
constant for the given process to occur, assuming an exponential rate R of the form
R(t) = R o exp [−t/τeq ]. For diffusion, we can write τeq = 4D/x 2 , whereas for surface
exchange, τeq = kex /x. In Figure 2-30 we plot the equlibration constant for different
film thicknesses of 1, 10, 100 and 1000 µm. It can be seen that for 1- and 10 µm-thick
films, surface exchange as determined experiementally using ECR is a slower kinetic
process (smaller τeq ), irrespective of the temperature. However, due to the parabolic
dependence of diffusion on film thickness, above 100 µm, the rates become approximately similar, and a crossover would be expected from surface control to bulk diffusion
control in the rate of pyrrhotite growth on iron. Moreover, these basic kinetic rate parameters can be fed into the global kMC and phase field model as described in Chapter
1.
The secondary aim was to understand the influence of the critical magneto-structural
order-disorder transition temperature T N = 315 o C on Fe diffusion in pyrrhotite. This
was studied by two different techniques: first through in situ magnetization measurements of the diffusion-driven, λ magnetic transition and second through tracer diffusion
studies using SIMS. Both studies converged on approximately the same Ea in magnetic
pyrrhotite below T N , which is up to 40% higher than that for non-magnetic pyrrhotite
(Table 2.10). Besides clarifying the effect of T N on diffusion, the results are more practically important in estimating rates of degradation where pyrrhotite forms a passive
layer. For example, assuming a simple extrapolation of the paramagnetic Arrhenius law
66
down to 150 o C would overestimate real diffusivities by up to two orders of magnitude.
2.6.2
Future work
The self-diffusivity of iron was measured here under dry, gaseous conditions in solid
(non-porous) samples. However, real corrosion scales in aqueous conditions could behave markedly differently from this idealized case. It would be of interest to confirm
*
DFe values at temperatures below 300 o C, but under in situ, aqueous conditions. Hightemperature sulfidation and/or corrosion experiments in the range 100-300 o C are required to confirm empirically the rates of both diffusion and surface reaction found here
on pure, dense samples. Such studies are also crucial to validating and improving the
bottom-up passive film mode that serves as the overarching goal of this work.
More work must be done to explain the sensitivity of the ECR technique to surface conditions, and to determine whether fundamentally accurate kinetic rates are measurable
via this method. This would involve repeated oxidation/reduction, with careful surface
analysis using XPS and AFM/STM imaging to understand any surface changes that may
alter the kinetics.
67
Table 2.10: Key activation energies for pyrrhotite growth.
Process
T range (o C)
Technique
Ea (eV)
Fe diffusion
315-700
Literature
0.83 ± 0.03
Fe diffusion
185-315
SIMS
0.83 + αS(T )2
Fe diffusion
180-210
Magnetokinetics
1.10 ± 0.10
Surf. Exch. (ox.)
350-600
ECR
1.05 ± 0.20
Surf. Exch. (red.)
350-600
ECR
0.79 ± 0.23
1
α = 0.41 ±0.06 and S(T ) is the reduced magnetization (= 0 at 0 K).
68
1
Chapter 3
Reactivity: quantification of
electronic band gap and surface
states on FeS2(100)
Synopsis The scanning tunneling microscope (STM) is used to investigate the surface
electronic structure of pyrite, FeS2 , as a model, semiconducting passive layer phase.
The STM allows us to probe controllably the energy levels of FeS2 and quantitatively
evaluate the surface electronic features which affect its charge transfer characteristics,
with respect to a redox species in the environment such as H2 S. The interfacial electronic properties of pyrite are greatly influenced by the presence of electronic states at
the crystal free surface. Scanning tunneling spectroscopy (STS) results are interpreted
using tunneling current simulations informed by density functional theory (DFT). Intrinsic, dangling bond surface states located at the band edges reduce the fundamental
band gap Eg from 0.95 eV in bulk FeS2 to 0.4 ± 0.1 eV at the surface. Extrinsic surface states from sulfur and iron defects contribute to Fermi level pinning but, due to
their relatively low density of states, no detectable tunneling current was measured at
energies within the intrinsic surface Eg . These findings help elucidate the nature of energy alignment for electron transfer processes at pyrite surfaces, which are relevant to
evaluation of electrochemical processes including corrosion. Finally, the broader utility of the methodology developed in this work for reliably interpreting STS results is
discussed. This includes determining the fundamental surface energy band gap for less
commonly-studied semiconductors for use in earth-abundant photovoltaics and other
applications. Portions of this chapter were published in Surface Science. [106] All DFT
calculations in this work were performed by Aravind Krishnamoorthy.
3.1
Background and motivation
At the end of Chapter 3 of this thesis, the kinetics of charge transfer between gaseous
H2 S and pyrrhotite (Fe1-x S) were investigated experimentally by measuring the electrical response of a sample to changes in sulfur chemical potential. This electrochemical
process, a necessary step for the incorporation of sulfur from the environment into a
growing iron sulfide passive layer, can be summarized by the cathodic half-reactions:
H2 S(g) ⇔ S 2− +2H + and 2H + +e− ⇔ H2(g) where the electrons are transferred from the
iron sulfide barrier layer to reduce hydrogen sulfide. The electrical conductivity relaxation experiments in Chapter 3 give a practical, macroscopic measure of reaction rates
that can be used to predict average rates of sulfur transfer. However, they do not provide any mechanistic insight into the physics of interfacial electron exchange between
69
the solid film and molecular redox species.
Chapter goals
In this chapter, we aim to investigate surface reaction in more detail by asking the
question: how do the electronic properties at the surface of an ionic solid affect the
propensity for charge transfer in an electrochemical system? Instead of pyrrhotite, we
investigate the surface of pyrite (FeS2 ) as a model, semiconducting passive film material.
FeS2 was chosen because of its broader interest to the electrochemical community:
other applications including photovoltaics and battery anodes are discussed briefly in
Sections 3.1.4 and 3.4.2. Open questions over the surface electronic structure of pyrite
from the literature partly motivated this work, and the existing amount of data helped
benchmark our experimental and computational results.
The key questions addressed in this chaper are summarized as: (1) can the surface band gap of FeS2 (and by extension, other similar semiconducting materials) be
quantified a priori using STS? (2) how do both intrinsic and extrinsic surface states on
FeS2 (100), as a model passive layer material, affect charge transfer in electrochemical
systems?
3.1.1
Electrochemical charge transfer in semiconductor-absorbate
systems
The theory of charge transfer during surface reactions between solid, semiconducting
materials and molecular adsorbates in corrosion systems is covered in the book Corrosion mechanisms in theory & practice by Marcus et al.. [3] The key points are summarized here to contextualize the remaining work in this chapter. Complex, coupled
electrochemical systems such as a metal-passive layer-electrolyte structure can be reduced to a connected set of energy levels. Under an applied bias (electrode potential),
it is the transfer of electrons across these energy levels which determines the overall
reaction current and therefore rate of metal oxidation during corrosion. Let us imagine
a basic system comprising the three interconnected components of a metal, a passive
layer, and an electrolyte containing a molecular species which can assume a reduced or
oxidized state:
Metal: (e.g. Fe in steel) has a high concentration of mobile charge carriers, typically
O(1023 cm-3 ).
Passive layer: typically semiconducting or insulating, we represent the passive layer
with a conduction band, valence band and Fermi level dependent on level of doping. The volume fraction of defects is typically very high for in situ formed passive
layers, with high concentrations of intrinsic (point) defects and extrinsic defects
(substitutional elements). [32] Charge carrier concentrations are commonly in
the range 1015 -1019 cm-3 .
Redox couple: a molecule in the electrolyte that reacts with the passive layer can be
represented electronically by occupied and unoccupied levels, corresponding to
the reduced and oxidized components of the redox system, respectively. Each level
is depicted as a Gaussian distribution of states, accounting for the uncertainty in
rearrangement energy for the solvation shell around the molecule during a reaction. L represents the energy required to reorganize the shell of H2 O molecules
surrounding a redox species after charge exchange (see Fig. 3-1). The charge concentration of the redox couple is related to the concentration of ions in solution.
For example, a 1 M solution contains 2NA × 10−3 ≈ 1021 ions.cm-3 .
70
We assume that the Fermi levels of each component in the system align at equilibrium. An additional, applied electrochemical potential biases the energy levels depending on the activity of reduced and oxidized species in the electrolyte, aRed and aOx ,
respectively:
E r ed = E rΘed −
RT aRed
ln
zF
aOx
(3.1)
where E r ed is the half-cell reduction potential at a temperature T, E rΘed is the standard
reduction potential, R is the universal gas constant, z is the charge transferred per reaction and F is Faraday’s constant. [3]
Due to the high availability of charge carriers in the metal and electrolyte, and
relative dearth in the passive layer, the potential difference is accommodated across
the passive layer. This leads to potential drops at the metal/passive layer and passive
layer/electrolyte interfaces; the passive layer’s semiconducting band structure is offset
at these interfaces to maintain a constant EF . In other words, charge accumulates or depletes at the passive layer surfaces, resulting in a space-charge layer and band bending
(see detailed introduction to band bending below).
At the metal-passive film interface, we usually assume very rapid charge transfer.
At the passive layer-electrolyte interface, the potential drop can be divided into the
potential dropped within the electrical double layer (Helmholtz layer) of ions in the
electrolyte ∆ϕH and the potential dropped within the semiconducting passive layer
itself ∆ϕSC (Fig. 3-1a). For a constant thickness Helmholtz layer, ∆ϕH is determined
by the pH of the electrolyte. ∆ϕSC similarly depends on the charge carrier concentration
of the passive layer, which determines the Debye length β. For example, considering an
n-type semiconductor with donor concentration N D :
v
u
t ""o kB T
β=
eo2 ND
(3.2)
where " and "o are the relative and vacuum permittivities, respectively; eo is the elementary charge and kB is Boltzmann’s constant. The depth of the resulting space-charge
layer in the passive layer dSC (Fig. 3-1b) can then be written:
dSC
v
t 2e (E − E )
o
FB
=β
kB T
(3.3)
where E is the applied potential and EFB the flat-band potential (no bias). We can therefore see that the width of the space-charge region is potential dependent; in other words,
the passive layer surface compensates for any changes in applied electrode potential.
Band bending For a negative electrode potential η applied to an n-type semiconductor, the EF of the redox couple is lowered relative to that of the passive layer, and free
electrons accumulate at the semiconductor surface until the Fermi levels equilibrate.
This can be represented as a downwards bending of the conduction and valence bands
at the surface (Fig. 3-1a). Conversely, a positive η gives rise to a depletion of electons
at the surface and upwards band bending (Fig. 3-1b). Semiconductor surfaces whose
bands are free to shift up/down in this manner are said to have an "unpinned’" EF .
3.1.2
Surface states
The reactivity of semiconducting materials can be significantly altered by surface states
that are either intrinsic to the crystal termination or arise from the presence of crystalline defects at the surface.
71
72
φ
ΔφSC
Oxide
eη
iDir
2λ
EF, redox
Density of states
E
Valence band
Eg
Distance
EF
VB
CB
iTunn
2λ
Density of states
E
EF, redox
dSC
Conduction band
+
+
+ -- + + + + + + - - - - - - -
(d) Tunneling transfer iTunn (+ve η)
EF
E = e.φ
(b) Band bending at electronic equlibrium
Figure 3-1: Charge transfer in electrochemical (corrosion) systems. (a) Potential distribution across a metal-passive layer-electrolyte couple; most of the potential drop is accommodated at the
interfaces, resulting in the formation of a space charge layer (∆φSC ) in the passive layer. (b) under electronic equilibrium the Fermi level EF is flat, leading to band bending in the passive layer. (c)
negative applied overpotential η : downwards band bending allows direct electron transfer from the passive layer conduction band (CB) to the unoccupied levels in the redox system. (d) positive
η : enough upwards bending can make tunneling transfer through the space charge layer possible.
Distance
VB
EF
CB
ΔφH
Electrolyte
(c) Direct electron transfer iDir (-ve η)
Metal
(a) Potential distribution across passive layer
Intrinsic surface states: The abrupt discontinuation of periodic potential at semiconductor surfaces can impose severe perturbations to the crystal’s electronic structure.
Unless a surface reconstructs to remove dangling bonds and autopassivate, the topmost
atoms’ crystalline orbitals destabilize in the direction of their free atom orbital character
and energy. Binary semiconductors like FeS2 , whose (100) surface does not reconstruct,
are predicted from ligand field models [107] and DFT calculations [108–110] to have
two associated intrinsic surface states: one for the anion dangling bonds and one for
cations. However, the intrinsic surface states have never been experimentally characterized up to this point.
Extrinsic surface states: in reality these states are localized at defects such as anion
or cation vacancies on the surface steps, kinks, dislocations or impurities [111, 112].
However there is evidence to suggest that these types of defects (as well as step edges
or intersecting dislocations) can affect the surface electronic structure over nanometer
distances.
Horizontal charge transfer Adiabatic charge transfer between a redox couple and a
semiconducting passive layer must be horizontal, that is- must occur at the same energy
level. Electrons may be exchanged in either direction: anodic transfer refers to electrons
transferred from the electrolyte, and cathodic transfer in the opposite direction. If we
ignore for the moment the role of surface states, and other potential transfer pathways
such as hopping mechanisms and via bulk, intra-band states, charge exchange with the
bulk bands of the passive layer may occur by two mechanisms: direct exchange and
tunneling. [3]
Direct transfer (see Fig. 3-1a) from the semiconductor requires filled states in the
CB to be higher in energy, i.e. overlap, than the empty states (oxidized species) of the
redox couple. The more negative η is in this scenario, the greater the overlap of electronic states and charge transfer can increase exponentially. This is the fundamental
explanation behind the well known linear Tafel slope on a plot of log(cur r ent) vs. η
for corrosion systems.
Tunneling transfer (see Fig. 3-1b) refers to quantum tunneling of electrons through
the space-charge layer. Thus, the larger the band bending, the smaller the tunneling
distance dT and the greater the probability of tunneling T:
•
˜
16E(Vo − E)
2κd T
exp −
T=
Vo2
h
(3.4)
p
where the coefficient κ describes the dependence on barrier height: κ = 2m∗ (Vo − E),
where V o is the total energy barrier, E is the energy level of the tunneling electron and
m* is the reduced electron mass. Charge transfer at the passive layer surface is therefore
proportional to the density of occupied states of the redox system D(Red) and that of
the empty states within the passive layer CB, D(Ox). By integrating over all energies
above EF where overlapping occupied and empty states may interfere, the tunneling
exchange current i+ is therefore:
i+ = −F
Z
T.D(Ox).D(Red).d E
(3.5)
The size of the band gap and density of electronic states at the surface is therefore
crucial to understanding the propensity for electron exchange. Some oxides that have
a large band gap, e.g. Ta2 O5 (Eg > 3 eV), such levels are not available and they do not
show redox processes even at very positive applied potentials, i.e. would require high
band bending to meet the condition of electron tunneling through the space charge
layer.
73
3.1.3
Scanning tunneling spectroscopy and TIBB
In the work presented in this chapter, the aim was to understand the role of surface
states in determining the surface Eg through quantitative analysis of tunneling spectroscopy (STS) measurements. We adopt the approaches developed in modeling STS
data from semiconductor surfaces that was advanced from the late 1980s by R.M. Feenstra and others. Early work began with the traditional cubic tetrahedrally bonded [113]
and III-V [114] semiconductors, on which band edges and surface-related features could
be determined to within an accuracy of ± 0.03 eV. The concurrent development of tunneling spectrum models based on computations of potential distributions and tunneling
current has helped identify the role of other physical phenomena in experimental STS
spectra, such as tip-induced band bending (TIBB) [115] and surface states [116]. TIBB
greatly affects the STS measurement of unpinned semiconductor surfaces, in which
changes in the tip-induced electric field lead to an unrestricted accumulation or depletion of charge carriers at the surface which act to screen the tip potential. In this case,
the electron chemical potential µe in the sample shifts freely with applied bias, distorting the CB and VB near the surface. However, if surface states are present on the sample,
charges from the bulk bands can fall into them and EF becomes pinned at the level to
which the surface states are occupied. STS spectra of EF -pinned surfaces typically yield
more consistent band onsets and are less affected by localized quantum effects such as
inversion or accumulation currents arising from TIBB.
The large, localized electric field from the proximate tip extends through the vacuum region and into the surface of the pyrite sample. Consequently, a fraction of the
applied potential can be dropped within the sample itself, causing the valence and conduction bands to bend and obscuring the energy scale of the measured STS spectra. A
comprehensive description of TIBB can be found in previous reports [115–118], but the
main points are outlined here for completeness. The contact potential ∆ϕ is defined as
the difference in work function between the metal tip and the semiconductor:
∆ϕ = ϕm − χ − (EC − E F )
(3.6)
where ϕm is the metal work function, χ is the electron affinity of the semiconductor, and
EC and EF are the conduction band minimum and Fermi level of the sample, respectively
(Fig. 3-2a). Even in the absence of applied bias, a non-zero ∆ϕ leads to band bending
and the formation of a depletion region in the sample. For example, a positive ∆ϕ
produces upwards band bending in the semiconductor as the Fermi level aligns with
that of the tip; negative charge correspondingly accumulates at the surface to screen
the potential (Fig. 3-2b). The effect is to shift the energy E of any given state at the
surface by an amount ϕo :
E − E F = eV − ϕo
(3.7)
When EF at the surface is unpinned in this manner, the resulting experimental i(V)
measurement can yield a very wide apparent surface Eg , as the band edges shift with the
sweeping voltage and the onset of tunneling is delayed to more positive (for the CB) or
negative (for VB) voltages (Fig. 3-2c). Such a situation arises on defect-free ZnO(110)
surfaces [119], where the apparent band gap from STS can be larger than the accepted
bulk gap of the material (Fig. 3-2e) , or on GaN(1100) where quantitative Eg determination was not possible [121]. Severe band bending can also introduce large tunneling
currents from local states when the semiconductor EF is pushed into the VB (inversion)
or CB (accumulation) [115, 122]. The presence of intrinsic (dangling bond) surface
states on semiconductors typically limits TIBB by pinning EF (Fig. 3-2d) [116, 123].
These states accumulate charge as they become occupied and effectively screen the
electrostatic potential from the tip, reducing the distortion of STS spectra arising from
TIBB. By analogy, on metallic materials with freely-available conduction band electrons
74
(a) No tunnel contact
TIP
(b) EF alignment
FeS2
Evac
Evac
χ
φtip
Δφ
EF,tip
EC
EF
EV
EF,tip
Δφ
φo
Wtip
E0
E0
(c) No surface states
(d) Surface states
Evac
EF,tip
Δφ+eV
Δφ+eV
EC
EF
EV
EC
EF
EV
(c) ZnO(110) Eapp > Eg, bulk
(d) InN(100) Eapp < Eg, bulk
Figure 3-2: Band bending effects in STS measurement. Schematic energy band diagrams for a n-type pyrite
sample where (a) tip and sample are not in tunneling contact; (b) there is an open circuit tunneling junction.
With a positive contact potential ∆ϕ, an upwards band bending of magnitude ϕo occurs. In addition to the
parameters described in the text: Evac is the vacuum energy level, Eo the ground level, and EV is the valence
band maximum of the semiconductor. W tip is the energy difference between the metal’s Fermi level and the
bottom of the metal valence band, typically ∼8 eV for PtIr tips. EF,tip is the tip Fermi level. All filled states are
shaded in grey. (c) upon applying a positive sample bias V, further upwards tip-induced band bending (TIBB)
occurs if EF is unpinned. However, surface states, e.g. shaded in black in (d), can accommodate enough surface
charge to pin EF and minimize TIBB (after Feenstra et al. [115]). (e) no surface states exist on ZnO(110);
EF remains unpinned and STS measurement gives an overestimate of Eg due to band bending. [119]. (f)
Conversely, extrinsic surface states on InN(110) pin EF and reduce the apparent Eg . [120]
at the surface, the tip potential drops entirely at the surface and does not extend into
the sample. Similarly, extrinsic states (arising from disorder, defects or unintentional
contamination), even at low densities of 0.01 monolayers (3x1014 cm-2 ) or less, can
hold enough charge to significantly affect the magnitude of TIBB and pin EF , e.g. on
InN(110) (Fig. 3-2f) [120]. Below, we rationalize these two competing effects in our
experimental STS spectra by simulating the effect of different surface state features, the
characteristics of which are known from DFT simulations.
75
3.1.4
The FeS2 (100) surface
Applications of FeS2 beyond sulfide corrosion studies Pyrite or FeS2 is a semiconducting mineral for which the electronic structure has been intensively studied in relation to reactivity in geochemical [124–129] and bio-catalytic [130–132] processes, as
well as for photovoltaic (PV) and photoelectrochemical properties [24, 133–136]. Heterostructures of FeS2 and perovskite oxides such as LaAlO3 have recently been proposed
as promising devices for spintronics applications [137]. In the context of PV, low open
circuit voltages (VOC) of < 200 mV (or ∼21% of the widely accepted bulk band gap of
0.95 eV) have been attributed to poor interfacial electronic properties of synthetic FeS2
systems [24].
(100) surface crystallography and electronic properties The crystal structure of
FeS2 (space group Pa3) comprises two interpenetrating cation (Fe2+ ) and anion (S2 2- )
face centered cubic (fcc) sublattices, the latter of which is made up of S2 persulfide
dimers aligned along the cube diagonal direction <111>. Pyrite is a compound, dband semiconductor with an electronic structure that can be qualitatively understood
with the aid of a simple ligand field model [107]. Each Fe2+ ion in the bulk is octahedrally coordinated by S2 2- ions (symmetry group Oh ), creating a strong ligand field
that splits the metal d states into non-bonding, triply degenerate Fe 3d t2g states (dxy ,
dyz and d x 2 − y 2 ) at the top of the valence band (VB). The conduction band (CB) minimum consists of doubly degenerate Fe 3d eg states (dz 2 and d x 2 − y 2 ) hybridized with
S ppσ* orbitals. An indirect, bulk band gap Eg of 0.83-1.01 eV has been measured in
synthetic FeS2 using various optical [138,139], photoconductivity [140,141] and x-ray
absorption/emission spectroscopy studies [142]. At the unreconstructed (100) surface
termination of pyrite, the predominant growth and cleavage face, the symmetry of the
Fe2+ site is reduced from Oh to square pyramidal C4v , leading to a loss of degeneracy
among the Fe 3d t2g and eg states. These further split into two discrete, intrinsic surface
states associated with the Fe dangling bond. Recent density functional theory (DFT) calculations are consistent in identifying these two pronounced surface states to be located
around the VB maximum (Fe-d x 2 character) and at the CB minimum (Fe-d x 2 − y 2 ). The
magnitude of the surface states decays almost entirely to zero beyond approximately
three atomic layers into the bulk [109]. As a result it is theoretically estimated that Eg
at the FeS2 free surface is reduced by up to 0.3-0.4 eV, as compared to the bulk value
(Table 3.1). We define surface Eg as the energy difference between the extrema of the
surface bands that extend into the bulk gap, rather than the gap between empty and
filled surface bands which may exist as discrete states within Eg ; this distinction was
used by Feenstra et al. for investigating states on Ge(111)c(2x8) surfaces [117]. If the
surface states are fully degenerate with the bulk bands (i.e., lie within the fundamental
bulk Eg ) they are not considered in the quantification of the surface Eg . In addition to
the intrinsic surface states on FeS2 (100), computational studies have identified a series
of further surface states that appear within the fundamental surface Eg local to interfacial point defects [108, 109, 132]. We refer to such states as "defect" or "extrinsic" states
to differentiate them from intrinsic surface states. Significant concentrations of neutral
sulfur monomer vacancies V S have been measured by x-ray photoelectron spectroscopy
(XPS) on fractured FeS2 (100) [143–147] as well as in situ ion-bombarded [148] and
annealed [106] growth faces. Indeed, the formation energy ∆Hf for V S is estimated to
be as low as 0.1 eV experimentally [106] and 0.4-0.42 eV computationally [109, 110],
suggesting that up to 20% of surface sulfur sites on FeS2 (100) may be vacant at ambient
temperatures of 298 K, and therefore V S electronic states are prevalent. Moreover, neutral Fe vacancies V Fe on the surface have been imaged at the atomic scale by STM and
shown to comprise a comparably high fraction of the surface [149]. Via DFT, Zhang et al.
predicted a maximum surface Eg of 0.72 eV for stoichiometric (Fe:S = 1/2) FeS2 (100),
but only 0.56-0.71 eV and 0-0.3 eV for sulfur-deficient and sulfur-rich surfaces, respec76
Table 3.1: Calculated bulk band gap Eg , and surface Eg for pristine and defective FeS2 (100). Defective
surface here refers to the presence of a single sulfur vacancy V S in a single 1 x 1 unit surface supercell.
Eg (eV)
Bulk
0.87
1.02
0.86
0.90
Pristine Surface
0.40
0.56-0.71
0.55
0.60
Defective Surface
0.27
N/A
0-0.2
0.0
Ref.
[132]
[110]
[108]
[109]
Table 3.2: Experimental surface Eg measurements by scanning tunneling spectroscopy (STS).
Sample/Surface Type
Natural, fractured in UHV
Natural, fractured in air
Synthetic, as-grown surface
Synthetic, fractured in air
Surface Eg (eV)
0.04
0.20
0.95
0.00
Ref.
[151]
[152]
[50]
[153]
tively. Other authors have theoretically calculated that V S at the surface can reduce the
surface Eg by more than this, even making the surface metallic [109]. Such arguments
have been used, for example, to explain the low resistivity (O(10-1) Ω.cm) of manufactured pyrite thin films for PV applications [150]. Despite this recognition that FeS2 (100)
interfaces are non-stoichiometric, there remains a need to demonstrate experimentally
the effect of defects on the electronic structure.
The scanning tunneling microscope (STM) operating in ultra high vacuum (UHV)
provides a controllable metal-vacuum-semiconductor tunnel junction to probe these
electronic states at the surface. A limited number of STS studies on natural [151,152]and
synthetic [50, 153] FeS2 single crystals have produced inconsistent results, with apparent band gaps ranging from ∼ 0 eV to the accepted bulk value of 0.95 eV (Table 3.2),
and a lack of detailed insight into the nature of the pyrite surface states.
3.2
3.2.1
Methods
Experimental
FeS2 single crystal synthesis High purity single crystals of FeS2 were synthesized by
chemical vapor transport (CVT) in closed quartz ampoules, based on techniques described in Refs. [139, 154]. Raw materials were procured from Alfa Aesar (Haverhill,
MA). A 1:2 stoichiometric mixture of 99.999% pure Fe powder and 99.995% S granules
totaling 4 g – along with ∼0.3 g of 98% pure anhydrous FeBr3 - was sealed in an evacuated, 20 cm long quartz tube and heated to 700o C for 15 days to form polycrystalline
pyrite aggregates. This precursor pyrite was removed, cleaned in acetone and methanol
and resealed in a similar quartz tube with 0.3 g of fresh FeBr3 and a small amount of
solid sulfur to provide a sulfur-rich environment for single crystal growth. The quartz
tube was placed in a temperature gradient from 700 to 550o C, with the polycrystalline
pyrite charge placed at the hot end, and left for up to 30 days. The mechanism of pyrite
growth by CVT is described in Ref. [24]. The resulting crystals were typically cuboidal
in shape with 5-10 mm edge lengths (Fig. 3-3a) and predominant {100} growth faces as
determined by electron backscatter diffraction (EBSD) and single crystal x-ray diffraction (XRD) (Fig. 3-3a). As-grown crystals were checked for phase purity using Raman
spectroscopy (Fig. 3-3b) and were found to be n-type semiconducting, with a donor
concentration N D in the range 1-5 x 1016 cm-3 by Hall measurement at 21o C. In addition, an indirect Eg of 0.9-0.95 eV was detected by optical absorption on FeS2 single
77
(c) Absorption spectrum: optical Eg > 0.9 eV
1000
(200)
800
30 40 50 60 70 80 90 100
2θ
(b) Raman spectroscopy
Intensity (arb.)
344
300
-1
α (cm )
Intensity (arb.)
(a) Single crystal XRD
600
400
380
200
418
350
400
Raman Shift (cm-1)
450
0.7
0.8
0.9
Energy (eV)
1
Figure 3-3: FeS2 single crystal samples. (a) Co-Kα X-ray diffraction (XRD) pattern. (b) Raman spectrum.
(c) Absorption coefficient α measured as a function of photon energy, showing an optical (bulk) band gap Eg
= 0.9-0.95 eV. Inset: photograph of FeS2 single crystals prepared by chemical vapor transport (CVT). Each
square on the background corresponds to 10 x 10 mm2 .
crystals polished down into 200 µm-thick plates (Fig. 3-3c). Absorption measurements
were performed with a Perkins Ellmer LAMBDA 1050 Uv/Vis spectrophotometer.
Scanning tunneling microscopy and spectroscopy Scanning tunneling microscopy
(STM) was carried out using an Omicron VT-AFM system (Omicron Nanotechnology,
GmbH, Germany) under UHV at pressures in the 10-10 Torr range. We used electrochemically etched Pt-Ir tips that were annealed at 150o C for 2 hours under UHV to
remove absorbed H2 O and hydrocarbons prior to taking measurements. Single crystal,
{100} growth faces of FeS2 were investigated by STM subsequent to ex situ cleaning
by the following procedure: sealed quartz tubes containing freshly-grown crystals were
opened in a glove box under a high purity, 95% N2 – 5% H2 environment to control
surface oxidation and were ultrasonically cleaned in acetone and methanol to remove
residual Br2 , which was proposed to be a source of contamination in previous STM
studies of synthetic pyrite [153]. Samples were clamped in a custom made aluminum
stage and transferred to vacuum within < 1 min to minimize exposure to laboratory air.
STM and STS results from samples prepared in this way were compared with similar
data obtained using in situ fractured, synthetic FeS2 single crystals which are known to
have stepped, (100)-oriented faces [155, 156]. The STS results from as-grown and in
situ fractured surfaces were quantitatively indistinguishable.
X-ray photoelectron spectroscopy X-ray photoelectron spectroscopy-valence band
(XPS-VB) spectra were obtained at the U12A beam line of the National Synchrotron
Light Source (Brookhaven National Laboratory, Upton, NY), using a photon excitation
energy of 210 eV. Single crystal growth faces of FeS2 were prepared in a similar fashion
as described above and were cooled in situ under UHV to approximately -170o C before
performing XPS-VB measurements.
78
Table 3.3: Input parameters for tunneling spectroscopy simulations using the SEMITIP program. (a) bulk
Hall measurement on FeS2 single crystals in this work, (b) effective masses optimized from DFT-computed
band structure; (c) contact potential estimated from DFT calculation of work function, supported by experimental evidence in Ref. [24].
Property
Donor concentration (a)
CB effective mass (b)
Heavy hole effective mass (b)
Contact potential (c)
Tip-sample separation
Tip radius
3.2.2
Symbol
ND
mc
mhh
∆ϕ
s
r
Value Used
1x1016
0.09-0.15 me
0.6-2.0 me
1.0-1.2
0.8-1.0
50
Unit
cm-3
N/A
N/A
eV
nm
nm
Computational
Density functional theory (DFT) Density functional theory (DFT) calculations for
this study were carried out by Aravind Krishnamoorthy. The full details on DFT computational methods on the FeS2 system can be found in Refs. [106, 108].
Tunneling current simulation (SEMITIP)
Computations of tunneling current for simulating STS data were carried out using the
full three-dimensional (MultInt3) version of the open-source program SEMITIP v.6,
courtesy of R.M. Feenstra [157]. The program is a Poisson solver that treats the case of a
hyperbolic-shaped tip in tunneling contact with a semiconductor sample. A complete description of the physics involved in the calculations is given in Refs. [115,116,158–160].
Table 3.3 summarizes the key input parameters for tunneling current calculations
that are related to the electronic properties of the tip and sample, and the geometry
of the tunneling simulation. Given the large number of input variables, we found an
efficient approach to modeling proceeded along the following routine: first, all known
variables are assigned their experimentally or computationally measured values. Second, the tip-sample separation distance s and tip radius R were estimated based on
previous literature [115, 122]. Finally, we allocated to the remaining free variables a
physically realistic range of values and performed a sensitivity analysis to optimize the
fits (see Appendix 5). In practice, it was found that only the major semiconductor properties such as donor concentration N D , conduction band effective mass mc and heavy
hole effective mass mhh , along with the contact potential ∆ϕ, had a significant quantitative influence on the model output of tunneling current.
In the tunneling spectrum model, we accounted for the existence of charge accumulating surface states on FeS2 by introducing them explicitly into SEMITIP, either as
a pair of Gaussian-distributed functions (Figure 3-4a), or as a uniform band across a
predefined energy range (Figure 3-4b). For each of these surface state distributions, we
fixed the charge neutrality level EN . Here, EN connotes the energy level below which
states are neutral when filled and positively charged when empty, or, conversely, above
which they are negatively charged when filled and neutral when empty. In the case of
the double Gaussian distribution, the additional variables of centroid energy (the displacements of the states in Energy either side of EN ) and the full width half maximum
(FWHM) of the peaks were assigned optimized values for fitting (see Appendix 5). It is
important to note that surface states in the tunneling model are treated as completely
localized at the surface, i.e., their magnitude does not decay exponentially into the bulk.
Surface states thus affect only the electrostatic potential part of the calculation and are
not included in the computation of tunneling current.
79
Possible surface state distributions in SEMITIP
(a)
(b)
CB
CB
EC
EC
FWHM
EF
EF
EN
EN
Centroid E
EV
VB
VB
EV
Figure 3-4: Distributions of surface states as defined in the SEMITIP program: (a) uniform distribution,
with charge neutrality level EN and (b) double Gaussian distribution, where FWHM is the full width half
maximum of the peaks, and the centroid energy defines their separation either side of EN . Filled states are
shaded in grey. VB and CB refer to the bulk valence and conduction bands respectively.
3.3
3.3.1
Results and Discussion
Current-separation and current-voltage tunneling spectroscopy
STS results were obtained experimentally on single crystal FeS2 (100), measured at various tip-sample separation distances s. Due to the well-known exponential dependence
of tunneling current itunn on s, the onset of detectable tunneling current either side of
0 V bias (nominally the VB and CB edges), which give rise to an apparent surface Eg
in the data, depends on the initial set point tunneling conditions for STS acquisition.
Therefore we normalize the data to the constant tip-sample separation so at which a
consistent "gap"’ of approximately 0.5 eV is visible. However, we explain why the quantification of Eg directly from STS spectra in this manner can be misleading, since it does
not account for the phenomenon of TIBB, as described in Section 3.1.3. Stable STM
images were initially taken at relatively low magnification (500 x 500 nm2 ) to locate
sizeable flat terraces for consistent STS data acquisition (Figure 3-5a). The tip was subsequently scanned over 20 x 20 nm2 , or smaller, atomically-flat areas (Figure 3-5b) to
obtain tunneling spectroscopic information at various set point currents (iset ) and biases
(V set ). The tip was then briefly paused over randomly selected points during which the
feedback loop was turned off for 1 ms to acquire current-separation i(s) or current-bias
i(V) spectra.
The magnitude of the measured tunneling current im as a function of bias voltage
V is affected by the vertical tip displacement at the instant of STS acquisition. This
separation distance s can be related to the setpoint conditions iset and V set through the
simple exponential decay relation i(s) = io ex p(−2κs), where io is a constant and κ is the
vacuum tunnel coefficient, otherwise known as the decay constant. κ is approximated
for one-dimensional tunneling and reasonable V set by [123, 161]:
κ=
v
t 2m 
e
‹ |eVset |
2
B−
+ kq 2
(3.8)
where me is electron mass, B the effective tunneling barrier and kq the parallel wave vector of the tunneling electrons. The decay constant κ for pyrite was determined via i(s)
spectroscopy at a range of different setpoint biases. Figure 3-6a shows the i(s) response
at V set = -1.4 V (main image) and V set = 0.4, 1.2 and 2.0 V (inset), each averaged over
approximately 20 measurements at different points on the FeS2 sample surface. The
magnitude of κ over the range -2V ≤ V ≤ 2V varied linearly from approximately 0.3
Å-1 at large bias to 0.5 Å-1 near 0 V, and was symmetric for negative and positive bias
80
Square pyramidal FeS2(100) surface imaged by STM
z (nm) (b)
+4
(a)
z (pm)
+25
0
Fe
S
-4
0
-25
100 nm
0.5 nm
-8
-50
Figure 3-5: Scanning tunneling spectroscopy (STM) images of the as-grown FeS2 (100) surface: (a) showing large atomic terraces with step edges oriented along the <100> direction. Tunneling conditions: V set =
- 1.5 V, iset = 0.5 nA. Scanning tunneling spectroscopy (STS) was performed on selected 20 x 20 nm2 flat
areas, (b). Fe atoms are resolved on the FeS2 (100) surface. The inset figure displays an atomic model for
comparison, with one unit cell of Fe atoms outlined by the dashed square. Tunneling conditions: V set = 0.2
V, iset = 4 nA.
(Figure 3-6b). The average effective tunneling barrier B, calculated using Eq. (3.8) and
assuming k=0, was 1.2 eV. This corresponds to the average work function between the
metallic tip and the pyrite sample at the tunnel junction.
Figure 3-7a displays a series of individual i(V) spectra taken at four different values of s, where the set point V set = 1.5 V and iset = 200 pA was arbitrarily chosen
as the reference separation so . The other values of s were calculated relative to so using the exponential decay relation for tunneling with the experimentally-determined
κ from i(s) spectroscopy. At more positive s (larger tip-sample separation), the measured current around 0 V becomes very small and the Eg appears larger, up to approximately 1.7 eV for s = so + 1.8 Å. To correct for the exponential decay in transmission
coefficient for tunneling, the i(V) data are normalized in Figure 3-7b to a constant
tip-sample separation distance by converting the measured current im to “distance corrected current” is = im e x p [2κ(V ) s], where s = 0 at the reference separation distance
so . Separation distance-normalized data are displayed with a logarithmic current scale
to enable discrimination among spectra. The four curves overlap consistently, indicating
that throughout the tunneling set point range used in this work the tunneling spectra
give a true representation of the tunneling response without metallic behavior due to
point contact at very small s, or anomalously insulating behavior at large s. Further, we
normalize the data to normalized conductance (di/dV ) /(i/V ) (Figure 3-7c) which is
known to approximate the DOS in semiconducting or metallic samples [113]. We calculated (d i/d V )by numerical differentiation from the i(V) response. To correct for the
well-known divergence of the direct conductance (i/V) at small values of i, i/V was
broadened to i/V using a Gaussian distribution described previously [114].
A first approximation of surface Eg from the i(V) response is 0.5 eV, obtained by
taking the average voltage separation between the CB and VB current onsets at 1 pA
current, which is approximately the instrument resolution or "noise floor" below which
current is not reliably measured in the STM used for this study (Figure 3-7b). Nevertheless, the direct quantification of surface Ebg in this manner does not account for the
possible occurrence of TIBB, as described in Section 3.1.3.
81
Determine decay constant κ:
0
(a)
i =o i exp(-2κs)
Experimental i(s)
-0.4
ln(i) (nA)
i (nA)
-0.2
-0.6
-0.8
-1
0
1.2
-2
-4
-6
2
2
2.0V
1.2V
0.4V
6
4
Δs (Å)
4
s (Å)
6
8
(b)
2κ (Å
-1
)
1
0.8
0.6
0.4
-2
1
-1
0
Sample Bias (V)
2
Figure 3-6: Current-separation spectroscopy: (a) Tunneling current i as a function of tip-sample separation
s at a set point bias of -1.4 V (solid line). A fitted exponential function i = io ex p (−2κs) with decay constant
κ = 0.80 Å-1 is overlaid on the experimental data (open circles). Inset: experimental data for 0.4, 1.2 and
2.0 V biases, plotted on a log scale. (b) κ variation across the bias range used in this work. The dashed lines
are to guide the eye, and do not represent a fit to the data.
3.3.2
Simulated tunneling spectra based on DFT-calculated DOS
We interpret the underlying electronic structure in our measured STS results on FeS2
by simulating the tunneling spectra using an explicit calculation of the electrostatic potential across the tip-vacuum-pyrite system, followed by a full numerical integration of
the resulting tunneling current. Using DFT as a guide for the position and distribution
of intrinsic and defect-related surface states, we explored several different configurations of surface electronic structure as the input for the tunneling spectra computations
and optimized the fit to the experimental STS data in each case. We first compare the
DFT-calculated DOS for pyrite with the valence band spectrum of a synthetic sample,
measured using synchrotron x-ray photoelectron spectroscopy (Figure 3-8). A prominent, Fe 3d-related band and the broad, hybridized Fe 3d and S 2p states between 1-7
eV below EV [107,162] are clearly visible in both the experimental and theoretical data,
indicating a general correlation which justifies the use of this DFT data in guiding our
analysis.
To investigate the origin of the apparent 0.5 eV surface Eg in the STS results we considered the calculated DOS in energy region surrounding the bulk band gap (approximately EV - 0.5 eV ≤ E ≤ EV + 1.5 eV) and present here the results for four different
simulated electronic structures, which could conceivably give rise to the experimental
tunneling spectra. These four models are based on DFT calculations for the bulk crystal (Figure 3-9a), a pristine (stoichiometric) surface (Figure 3-9d,g), and a defective
surface containing both charge neutral V Fe and V S (Figure 3-9j). For the purposes of
simulating the tunneling current as a function of bias, each of these characteristic DOS
distributions was converted to a simplified representation with inputs for the bulk valence and conduction bands and the requisite surface states. The computed tunneling
82
(c)
|current| (pA)
(b)
so-1.2Å
800
400
0
-400
-800
Raw i(V) data
1.7 eV
so
so+0.9Å
so+1.8Å
0.5 eV
Distance corrected
i(V)/exp[-2κ.s]
102
101
1 pA noise floor
100
Normalized conductance
(di/dV)/(i/V)
(arb units)
(a)
current (pA)
Precise Eg not quantifiable straight from i(V) curves
-2 -1.5 -1 -0.5 0 0.5 1
Sample Bias (V)
1.5 2
Figure 3-7: Current-voltage spectroscopy: (a) Tunneling current-voltage i(V) curves measured on FeS2 (100)
with varying tip-sample separations s. so corresponds to a tunneling set point of V set = 1.5 V and iset = 200 pA.
(b) the same i-V data normalized to constant tip-sample separation, plotted on a logarithmic i axis to facilitate
comparison. (c) normalized conductance (di/dV ) /(i/V )as a measure of local density of states (DOS). An
estimate of surface band gap Eg width using the instrument resolution of 1 pA is ∼0.5 eV.
Fe-3d states at valence band edge
DOS (arb. units)
XPS hν = 210 eV
DFT calculated
Iron
Sulfur
Total
-10
-5
0
E-EV (eV)
5
Figure 3-8: Pyrite valence band: Experimental valence band spectrum obtained using synchrotron x-ray
photoelectron spectroscopy (XPS) at photon energy hυ = 210 eV (top) compared against DFT-computed
density of states for FeS2 (100) (bottom), also showing partial DOS contributions from iron and sulfur. The
dashed line marks the valence band edge.
current that resulted from the different simulated DOS representations was compared
to the experimental STS results from Figure 3-7.
The four theoretical electronic structures that were matched to the experimental
data can be described in more detail as:
1. FeS2 bulk-like density of states as calculated by DFT (Figure 3-9a). In the simpli83
fied STS model, the VB and CB extrema are separated by an assumed bulk band
gap of 0.95 eV and no surface states exist (Figure 3-9b).
2. Pristine FeS2 (100) surface density of states, including intrinsic surface states arising from Fe dangling bonds (Figure 3-9d). In the theoretical tunneling spectra
input (Figure 3-9e), a double Gaussian distribution of surface states is included,
straddling the VB and CB edges. The density of surface states is set to 6.8 x 1014
cm-2 .eV-1 , consistent with the density of Fe dangling bonds at the unreconstructed
(100) surface. The charge neutrality level EN is fixed exactly halfway between the
VB maximum and CB minimum, while the FWHM and centroid energies of the
surface states were optimized within a reasonable range to provide the closest
match to experiment. In this model, the intrinsic surface states can accumulate or
deplete in charge depending on the applied bias, and thus serve to screen the tip
potential, but do not produce itunn . Eg is still 0.95 eV at the surface.
3. Pristine FeS2 (100) surface density of states, similar to that described in Model
(2), but we now postulate that intrinsic surface states are homogeneously connected to the bulk VB and CB. Therefore, surface states are not explicitly defined
in this model, but rather the bulk Eg in the input is decreased from 0.95 to 0.5
eV, to approximate the tunneling contribution of intrinsic surface states (Figure
3-9h). It is important to note that no surface states were explicitly defined in the
computations employing this model so no EF pinning would be expected. We include the gray, double Gaussian states in Figure 3-9vh merely to draw the eye to
how they effectively reduce the surface Eg .
4. Defective FeS2 (100) surface density of states. The surface Eg is reduced to 0.5 eV
by the intrinsic surface states, as in Model (3), but we also include defect states
from V Fe and V S with 12.5% surface coverage each, i.e. density of 8.5 x 1013
cm-2 .eV-1 (Figure 3-9j). In this theoretical tunneling spectrum model, the defect
states form a broad band across the width of the reduced Eg and only contribute
free charge to screen the tip potential, without contributing further tunneling
current (Figure 3-9k).
The results for the four different tunneling spectra simulations are presented adjacent to their corresponding DOS graphs in Figure 3-9. Together with each simulated
curve we also show the same, repeated experimental STS result obtained using set point
tunneling conditions of V set = 1.5 V and iset = 200 pA, equivalent to the reference tipsample separation of so in Figure 3-7. As expected, the first model of bulk-like density
of states (Figure 3-9c), which excludes any surface states, gives a poor fit to the experimental results. In the absence of available free charge at the surface to pin EF , the
semiconductor bands are free to shift with the applied bias, and the CB (VB) edge is
dragged to higher (lower) energies with increasing positive (negative) bias. The apparent surface Eg width is therefore > 0.95 eV. The second model (Figure 3-9f) with
surface-localized, non-tunneling intrinsic states seems to approximate the experimental
result better, but still does not reliably capture the small size of the zero tunnel current
region, nominally corresponding to Eg , which is 0.3-0.5 eV larger than the experimental STS results would suggest. A parametric sensitivity study was conducted, and no
adjustment of the relative surface state positions or widths produced a fit better than
that shown in Figure 3-9f, as quantified by minimizing the root mean squared (RMS)
difference between the simulated and experimental results (see Appendix 5). We conclude that the effect of these intrinsic surface states extends beyond a simple screening
of the tip potential distribution, as they are defined in the tunneling spectrum model.
Consequently, close replication of the experimental spectra can instead be achieved by
defining a narrower forbidden energy region Eg in the model input, simulating the case
where significant tunneling current originates from the surface states when the bias
is swept across biases in the range of approximately 0.4 V and below. In Figure 3-9i
84
85
(j)
(g)
(d)
(a)
0
EV
0.5
1
E - EV (eV)
Intrinsic & defect SS
CB
Screen potential
Tunneling
0.5 1 1.5
E - EV (eV)
(k) E = 0.5 eV
g
(h)
(e)
VB
Eg = 0.95 eV
1.5 -0.5 0
Tunneling from intrinsic SS
Intrinsic SS screen tip
EC
Bulk-like states
(b)
-500
0
-500
-2
0
500 (l)
(i)
(f)
500 (c)
-1
0
1
Sample Bias (V)
Experiment
STS Model
2
Figure 3-9: Modeling tunneling spectroscopy with surface states: (Left column) density of states (DOS) calculated by density functional theory (DFT) with (middle column) their corresponding,
simplified analogs used in tunneling spectroscopy modeling. The shaded regions correspond to surface states (SS’s) that either just screen tip potential (black) or, alternatively, contribute to
the tunneling current (grey) in the tunneling spectra model input. (Rightmost column) the output from each tunneling spectrum model (solid line) is displayed alongside the same, repeated
experimental scanning tunneling spectroscopy (STS) result (open circles), corresponding to a tip-sample separation of so as described in the main text. (a), (b) and (c): bulk-like electronic
structure with band gap Eg = 0.95 eV and no SS’s. (d), (e) and (f) include intrinsic SS’s at the FeS2 (100) surface, bordering the band edges but not contributing to tunneling current (itunn ) within
the fundamental, bulk Eg . (g), (h) and (i): the intrinsic SS’s now mediate tunneling and the band gap is reduced to 0.5 eV. (j), (k), and (l) correspond to a FeS2 (100) surface with reduced Eg of 0.5
eV containing 12.5% iron point defects (V Fe ) and sulfur monovacancies (V S ).
-0.5
Density of States (arb. units)
Progressively add computed surface states into STS model to match experimental result
Current (pA)
Intrinsic surface states connected; extrinsic form discrete band
1.5
Energy (eV)
(a)
(b)
(c)
1
0.5
Defect State
0
-0.5
L
Γ
X
K
L L
Γ
X
K
L L
Γ
X
K
L
k point
Figure 3-10: Density functional theory (DFT)-computed band structures for (a) bulk FeS2 , (b) a 4-layer
surface slab with (100) termination, where we show in the red region the additional bands arising from
intrinsic surface states, and (c) the same surface slab but containing a single sulfur vacancy V S in the topmost
layer. The single band coming from the defect is highlighted with a bold, blue line.
the intrinsic surface states are included continuously with the VB and CB in this manner, i.e., the Eg for the simulation is reduced now to only 0.5 eV. This input produces
simulated tunneling currents that match the experiment much better around the zero
current region. However, the best fit to the experimental data was achieved when we
further include a broad, distributed band of defect states that simulate a 12.5% concentration of both V Fe and V S , at the surface (Figure 3-9l). In the model these defect
states do not mediate electron tunneling but their effect on the simulated spectrum is
to reduce the effect of TIBB by screening the tip potential. Physically, we interpret this
to mean that the defect surface states that exist within Eg are too dilute and sparsely
distributed to contribute significantly to tunneling and thus further reduce Eg . Nevertheless, their presence sufficiently affects the tunneling spectra through EF pinning. To
help understand the lack of measured tunneling current from inter-band defect states,
in Figure 3-10 we compare the band structure of bulk FeS2 alongside that of a pristine
(100) surface and a defective (100) surface containing a 12.5% concentration of V S ,
as calculated by DFT. The additional, intrinsic surface state bands - highlighted in red
in Figures 3-10b,c - form a dense network of states that overlap continuously with the
bulk VB and CB. By comparison, the V S defect state is manifested in a single, isolated
band 0.2-0.3 eV below EC . Moreover, we see the minimum energy point on this defect
band clearly dips down at the L point of the Brillouin zone. During the tunneling process, the perpendicular wave vector for the electron k⊥ is relatively small compared to
those from intrinsic surface bands, where the empty-state minimum is very flat across
the entire k point range shown. Together, these facts suggest the tunneling from intrinsic surface states would be much stronger than for the defect states, explaining why we
observe the intrinsic surface states directly in the experimental tunneling spectra, but
the defect states have a more subtle effect.
In order to quantify the width of the surface Eg from the experimental data, a sensitivity analysis of Model (4) was performed with the range 0.3 ≤ Eg ≤ 0.6 as the input.
The results plotted with logarithmically displayed current in Figure 3-11 indicate a best
fit to experimental tunneling current can conceivably be achieved with Eg = 0.4 ± 0.1
eV. The close match between the experimental and the simulated tunneling spectrum
results suggest that the presence of dangling bond surface states on the FeS2 (100) free
surface leads to a reduction in Eg by ∼0.5 eV over the accepted bulk Eg of 0.95 eV. These
86
Surface Eg = 0.4 ± 0.1 eV
8
10
0.3 eV
Expt.
Model
6
Tunneling current (pA)
10
0.4 eV
4 0.5 eV
10
0.6 eV
2
10
0
10
-2
-1
0
1
Sample Bias (V)
2
Figure 3-11: Fitting to experimental surface Eg . Comparison of experimentally measured tunneling currentvoltage i(V) spectrum (open circles, V set = 1.5 V and iset = 200 pA) , with defective FeS2 (100) surface Model
(4) and four different magnitudes of Eg as listed beside each curve: 0.3, 0.4, 0.5 and 0.6 eV. The absolute values
on the tunneling current scale are arbitrary and the curves have been separated by a uniform multiplication
of the current data for ease of comparison. We have omitted showing the experimental and modeled data
below a current of 1 pA which is the instrument resolution for experimental data acquisition.
intrinsic surface states form continuous bands connected to the bulk electronic states
and therefore offer available energy levels into which and from which electron tunneling can occur in the presence of the biased probe tip. In contrast, surface states arising
from distributed point defects do not contribute to electron tunneling during STS, but
instead provide states across a broad range of energies within the fundamental surface
Eg that can accrue additional charge from the bulk. This acts to pin the Fermi level
and moderate the amount of TIBB during STS. By accounting for both of these surface
contributions in tandem, the theoretical model most accurately replicates the experimental STS data. The requirement for such a seemingly high surface defect concentration of 12.5% in the model raises the question of whether this is realistic for a pristine
FeS2 (100) surface. The existence of a vacant site at one in every eight surface-bound
sulfur sites, with a correspondingly similar density of vacant iron sites, would imply
one cation and one anion vacancy per four surface unit cells. As we have already discussed, there is a large body of XPS evidence suggesting that up to 20% of pristine pyrite
surfaces can comprise V S , even at ambient temperatures of 298 K, including our work
in parallel to this study [106]. Likewise, high concentrations of surface V Fe have been
imaged on pyrite by STM [149]. It is probable that the synthetic samples used in the
current work contain a significant concentration of V Fe , given the sulfur-rich conditions
of single crystal synthesis. Therefore the assumption of 12.5% as an average for both
types of ionic point defect seems plausible. In addition, the effect of extrinsic (S-Br)2defects - a known source of impurity in CVT-grown pyrite [163] - has not been considered in our analysis. Although the surface states associated with these defects would be
localized at the defects themselves, there is evidence to suggest that vacancies (as well
as other defects such as step edges, substitutional dopants and intersecting dislocations)
can affect the electronic structure at nanometer distances through the redistribution of
87
Delocalized defect state
Figure 3-12: Visualization of FeS2 (100) surface charge q surrounding a single sulfur point defect (V S )
located at the arrow. We show only the difference in q between the defective and defect-free surfaces, i.e.
∆q (VS − S). Positive and negative 0.014 e/Å3 isosurfaces are colored in red and blue, respectively. Unit cell
edges are shown as dashed lines; one defect in this area corresponds to a V S concentration of 12.5%.
surface charge [164–166]. Figure 3-12 displays the charge density difference between a
supercell of four unit cells of FeS2 (100) containing a charge-neutral V S defect and that
of the perfect host, with an isosurface of 0.014 e/Å3 . The delocalized positive and negative charge resulting from the V S defect is distributed over almost the entire 2 x 2 unit
cell area of the simulation, equivalent to approximately 10.8 x 10.8 Å2 on the surface.
This extent of delocalization would suggest that the charge from a density of only 12.5%
V S on the surface could affect the experimental tunneling spectroscopy measurement,
regardless of the exact location that the probe tip is placed during the data acquisition.
3.4
3.4.1
Outcomes
Conclusions
An accurate, quantitative assessment of the surface electronic structure of semiconducting pyrite, FeS2 (100), is necessary for understanding the behavior of pyrite in a wide
range of applications, including geochemical, bio-catalytic, and corrosion processes, as
well as pyrite’s photovoltaic and photoelectrochemical properties. While scanning tunneling spectroscopy is an ideal tool for this purpose, the analysis is complicated by the
well-known effect of tip-induced band bending, the presence of intrinsic surface states,
and the additional effects of defect states associated with native ionic vacancies and
other defects. We performed systematic STS measurements on synthetic FeS2 single
crystals at different tip-sample separations and demonstrated that the apparent surface
band gap is consistently 0.4 ± 0.1 eV, or ∼0.55 eV smaller than the widely-accepted
bulk band gap of 0.95 eV for pyrite. By basing our tunneling current simulations on
methodically varied, simplified DFT-calculated electronic structures, we link the origin
of this reduction in Eg to the presence of intrinsic surface states from Fe dangling bonds
at the free surface termination. The electronic bands arising from the intrinsic surface
states overlap continuously with the bulk bands. In addition, the experimental tunneling spectra results can be modeled most accurately if a second distribution of surface
states arising from cation and anion vacancies is incorporated into the tunneling current simulations. These defect states do not contribute significantly to overall tunneling
current but have an influence on the tunneling spectra by accumulating charge at the
pyrite surface, which screens the tip potential during measurement and pins the Fermi
88
Surface states affect photovoltaic performance
Into
crystal
(100) Free
surface
Figure 3-13: Low surface bandgap implications for PV. A smaller surface band gap may lower overall pyrite
solar cell open circuit voltage and therefore performance by supplying a connected set of energy levels into
which excited states can thermalize before being usefully extracted. Image from Ref. [167].
level. Our findings confirm the influence of both intrinsic and defect surface states on
the electronic structure of pyrite. The presence of a reduced band gap on the surface, as
well as the existence of defect states within the band gap, has implications for electronic
processes such as charge transfer during electrochemical redox reactions.
3.4.2
Implications for other applications of FeS2 , e.g. PV
One of the several motivations for this work, outside the central scope of this thesis,
was the applicability of FeS2 to photovoltaic (PV) solar cells. In a paper written by Lasic, Armiento et al., to which the author of this thesis contributed, an attempt was made
to explain the low open circuit voltage (OCV) of pyrite devices, which have not exceeded
0.2 V (out of a potential 0.95 V maximum as dictated by the bulk Eg ). [167] One argument was that the surface states responsible for the lowered surface Eg are connected
directly to bulk bands in pyrite. Any photoexcited carriers could then thermalize into
lower energy levels at interfaces, before being usfully extracted (Figure 3-13).
Since this work was published, another group advanced a theory for a conductive
inversion layer at the FeS2 (100) surface, essentially comprising positively-charged surface states. [168] The authors suggested this would be consistent with our STS measurements in this work, and provided evidence that surface states can be passivated,
offering hope that pyrite devices with OCV > 0.5 V may one day be feasible.
3.4.3
Future work
The next step in improving the methodology for quantifying surface band gaps and surface states directly from scanning tunneling spectroscopy is to modify the SEMITIP code
for a direct input of DFT data. Such a collaboration was discussed with Prof. Feenstra,
the author of SEMITIP, but this was not pursued further during this thesis. However,
the next generation of code should allow direct input of first-principles calculated surface density of states, rather than the relatively coarse, parabolic band inputs currently
allowed by the program. Moreover, the code as it stands at the time of writing cannot
compute tunneling current from surface states. The next version should be able to deal
with tunneling from predicted, charged states that also pin the Fermi level.
89
(a) MoS2: facile STM over large areas
z (pm)
50
0
20 Å
-50
3.2 Å
(c) Preliminary STS inconclusive
-2.5V, 1nA
MoS2 Bulk Crystal
MoS2 Single Layer
[di/dV] / [i/V]
(arb. units)
(b) MoS2 basal plane
-2
-1
0
1
Sample Bias (V)
2
Figure 3-14: Preliminary investigations on bulk and 2-dimensional MoS2 . (a) stripped MoS2 offers highquality surfaces for scanning tunneling microscopy. (b) higher-magnification image, showing Mo atoms in
hexagonal arrangement. (c) an initial study to compare the surface band gap of multilayered ("bulk") vs.
single layer MoS2 was inconclusive; however the methodology for STS quantification outlined in this chapter
offers a systematic way to further investigate this and other, similar open questions.
Experimentally, we hope that the methodology outlined in this chapter will be used and
improved by other researchers to test other interesting materials with poorly-characterized
surface electronic properties. For example, as part of a collaboration with the Palacios
group of the Department of Electrical Engineering at MIT, the author made some preliminary measurements of the MoS2 surface to compare the surface band gap of singlelayered versus multi-layered samples. Figure 3-14 presents some initial findings; the
surface is very conducive to imaging by STM. However, the collected STS data was inconclusive without further analysis using a similar technique to that described in this
chapter. The surface Eg of both multi- and single-layered MoS2 was found to be close to
the known bulk value of 1.2 eV. Many other chalcogenide and other rare semiconducting surfaces should be convenient for such coupled experimental and computational
analysis of their surface electronic structure.
90
Chapter 4
Stability: dynamics of point
defect formation, clustering and
pit initiation on the pyrite
surface
Synopsis The collective behavior of point defects formed on the free surfaces of ionic
crystals under redox conditions can lead to initiation of local breakdown by pitting.
Here, we controllably generated sulfur vacancies on single crystal FeS2 (100) through
in vacuo annealing, and investigated the resulting evolution of surface chemistry using
synchrotron x-ray photoelectron spectroscopy (XPS). By measuring the S 2p photoemission signal intensity arising from sulfur defects as a function of temperature, the
enthalpy of formation of sulfur vacancies was found to be 0.1 ± 0.03 eV, significantly
lower than the reduction enthalpy of bulk FeS2 . Above 200 o C, the created sulfur vacancies together with preexisting iron vacancies condensed into nm-scale defect clusters,
or pits, on the surface, as evidenced by scanning tunneling microscopy (STM). We provide a mechanistic description for the initiation of pits that requires concerted behavior
of both the sulfur and iron vacancies, and validate this model with kinetic Monte Carlo
(kMC) simulations. The model probes realistic length and time scales, providing good
agreement with the experimental results from XPS and STM measurements. Our results mechanistically and quantitatively describe the atomic scale processes occurring
at pyrite surfaces under chemically reducing environments, important in many natural and technological settings, ranging from its role as a passivating film in corrosion
to its potential use as a photovoltaic absorber in solar energy conversion. Portions of
this chapter were published in Electrochimica Acta [169]. The kMC simulations were
developed by Aravind Krishnamoorthy.
4.1
Background and motivation
As we have seen in Chapters 2 and 3, a stable passive layer can hinder ion or electron
transport to/from the metal, and suppress charge transfer at the surface. However, the
inherent protectiveness of a passive layer relies on this physicochemical barrier remaining intact. Passive films can break down due to chemical, electrochemical or mechanical
stimuli, resulting in more rapid, localized corrosion that accelerates equipment failure.
Localized degradation of the barrier layer can expose bare metal to the corrosive environment. In many cases, the metal will quickly re-passivate. However, in some instances
a failure to re-passivate will result in the formation of a stable pit, which can rapidly
91
expand due to localized galvanic corrosion (the exposed, small area becomes anodic
relative to the surrounding passivated metal). In the extreme case, a pipe wall may be
compromised well before the expected service life of the structure. On stressed components, a pit may serve as the nucleation site for a critical crack. Aggressive anions in
the environment such as chloride Cl- are known to promote pitting, as will be discussed
in Section 4.1.2 below. Certain theoretical approaches have been developed to predict
passivity breakdown, such as the point defect model (PDM) of Macdonald et al. which
asserts that pitting is a deterministic process that can be modeled by individual, atomistic processes such as point defect formation and condensation. [32] Despite this, local
corrosion rates are often non-linear and highly unpredictable.
4.1.1
Chapter goals
In this chapter, we aim to understand: (1) the dynamic process of pit nucleation in
ionic passive films at the atomic scale, by studying the surface of pyrite as a model
system and (2) whether the reported off-stoichiometry in polycrystalline pyrite can be
attributed to easily-reducible surfaces. Both these aspects are introduced in more detail
in the following Sections 4.1.2 and 4.1.3:
4.1.2
Passivity breakdown by pitting
The first and foremost motivation for this study was to uncover the atomic-scale mechanism behind vacancy condensation into nanometer-scale imperfections that could serve
as nuclei for the localized breakdown of ionic passive layers, i.e. pitting. There is experimental evidence that vacancy condensation both at the metal-passive layer interface
(Figure 4-2a and b) and the passive layer-electrolyte interface (Figure 4-2c) can lead
to the localized breakdown of passivity. Various mechanistic theories and models have
been proposed to describe this process [170], the most comprehensive of which is the
Point Defect Model (PDM) which serves as the key, non-empirical framework guiding
the development of a multiscale model in this project. The PDM has been developed to
successfully account for the critical breakdown parameters (critical breakdown voltage,
V c , and induction time, tind ) for single breakdown sites on the surface, for the distributions in these quantities, and for their pH- and chloride concentration-dependencies.
The PDM also provides the first, mechanistically-based explanation of the role of alloying elements in the inhibition of passivity breakdown and hence localized corrosion.
Despite a long-standing correlation of global environmental variables to corrosion rates,
microscopic mechanisms of passivity and breakdown are not quantitatively understood.
Consequently, localized corrosion and the associated macroscopic failure are typically,
but incorrectly, identified as being stochastic in nature. However, passivity breakdown
is not a matter of chance, but occurs for a well-defined, mechanistic reason, i.e. a deterministic process. A schematic illustrating some of the proposed causes of pitting is
shown in Figure 4-1, with a brief description of each provided in the caption. Below
we briefly review some of the motivations for the study of surface point defects in this
chapter:
Aggressive anions and point defects. Chloride is the most commonly observed and
well-known pitting agent, although other halides and SO4 2− can also have an accelerating effect on localized corrosion. [3] While the presence of chloride ion is known
to lead to localized attack, preferentially at structural and chemical discontinutities in
the barrier layer such as grain boundaries and inclusions [171], the key mechanism
responsible for the X − induced pitting is still debated. Two broad, descriptive models
account for the action of X − on locally degrading the oxide film: the PDM suggests that
anions absorb into oxygen vacancy sites at the oxide surface, leading to the creation of
cation vacancies in the oxide (Figure 4-1a). [170] This increase in cation point defect
92
Proposed pitting mechanisms
(a)
(b)
(c)
Figure 4-1: Proposed mechanisms of passivity breakdown and pitting. (a) Halide ions X − preferentially
adsorb at inhomogeneites in the barrier layer such as nanopits and vacant lattice sites, leading to the creation
of cation vacancies. The Point Defect Model (PDM) postulates that the resulting, enhanced metal vacancy
flux to the alloy interface cause voiding. (b) enhanced dissolution at surface defects can lead to blistering and
rupture due to film growth stresses σ, to expose bare metal. (c) If the metal does not repassivate, a stable
pit may grow. Hydrolysis of cations enhances local acidity, attracting more negatively-charged X − ions and
propagating further pitting. Large pits may serve as nucleation sites for more catastrophic failure modes, e.g.
stress corrosion cracking (SCC).
concentration in turn leads to enhanced vacancy flux in localized channels in the oxide
barrier layer; if the rate of metal vacancy accumulation at the metal interface cannot
be matched by absorption into the metal, macroscopic voids may form at the interface.
These cavities can subsequently chemically or mechanically destabilize the overlaying
film, creating a pit on the nanometer scale.
Surface imperfections as initiation sites. Open questions remain over halide-defect
association as described above. However what is clear is that surface imperfections
serve as initiation sites for localized corrosion. Microstructural or micro-chemical inhomogeneities in the passive film itself are known to play an important role in pitting, and
even in the absence of aggressive anions these can lead to differential rates of dissolution which nucleate metastable pits. [172]
Modeling pitting: realistic length- and timescales. Both on metals and on ionic
passive films, clustering of point defects (vacancies) is thought to be necessary for pit
initiation, the rate-controlling step in overall pitting corrosion [110]. This process has
been observed on pure metals [173] and alloys. [174] On the other hand, understanding the surface pitting mechanism on ionic passive films has been a challenge, experimentally limited to only few successfully studied systems such as Ni-O, Ni-OH and
Cr2 O3 , [175, 176] and without a concerted modeling and experimental demonstration
at the atomic scale. Even insimpler systems such as pure metals and semiconductors,
where surface pitting is relatively better understood, modeling of surface degradation
is generally limited to the use of empirical kinetic parameters. Matching simulated time
scales to experimental ones has remained challenging and has lacked experimental val93
Metal-barrier interface
(a)
Barrier-electrolyte interface
(c)
(b)
Figure 4-2: Nanopits formed by vacancy agglomeration. (a) Scanning tunneling microscopy (STM) images
of vacancy condensation to form nanocavities at intermetallic-oxide interfaces, leading to spallation of the
passive layer. [179] (b) nanopits formed by localized dissolution (vacancy formation) at NiO surfaces, as
recorded by electrochemical STM [175].
idation of model results. [177, 178]
4.1.3
FeS2 surface chemistry and non-stoichiometry
The second motivation for this investigation, which is complementary to the first, regards the unresolved non-stoichiometry of pyrite surfaces, which cannot be explained
based on defect chemistry of the bulk material. Native point defect concentrations in
bulk FeS2 are generally low (O(106 ) cm3 ) at room temperature. [135] On the other
hand, anionic vacancies, specifically sulfur vacancies denoted as V S , are expected to
be far more prevalent at free surfaces, with calculated formation enthalpies as low as
0.4 eV. [109, 134] This has led to difficulties in obtaining surfaces with low intrinsic
defect concentrations in nanocrystalline pyrite precursors and films. [133, 150] Sulfur
deficiency is typically put forward as a source of non-ideal electronic and optical properties in synthetic FeS2 . However, there remains a need to experimentally quantify the
formation energy of V S on the surface to understand whether these defects are indeed a
significant source of off-stoichiometry in pyrite surfaces. As described in Chapter 4, the
crystal structure of pyrite is NaCl-type cubic, with Fe2+ at the cation site and S22− dimers
at the anion site, aligned along the cube diagonal <111>. The (100) surface of FeS2 is
unreconstructed and is the most stable surface, as shown by low energy electron diffraction (LEED) [151,156] and scanning tunneling microscopy (STM). [149,181] The sulfur
S 2p x-ray photoemission peak of pyrite, when accessedusing soft x-ray synchrotron radiation, reveals highly detailed information about the different binding environments
of sulfur inthe near-surface region. In addition to the dimer S22− signal from the crystal bulk, pyrite’s S 2p photoelectron spectrum distinguishes two additional, surfacelocalized and coordinately reduced sulfur environments at more negative binding energies. [143, 145, 146, 148] Quantification of these surface-localized defect environments
enables further understanding of the two open areas summarized above.
94
4.2
4.2.1
Methods
Experimental
Samples Single crystal pyrite samples were synthesized by chemical vapour transport (CVT) in the presence of Br as a transport agent, described in Chapter 4. Growth
faces were identified to be primarily (100) by electron back-scattered diffraction (EBSD;
ZeissSupra-55 scanning electron microscope). Phase purity of the single-crystalline synthesized pyrite was confirmed using Raman spectroscopy and X-ray diffraction. We note
that the synthesis of FeS2 single crystals was performed under a high partial pressure of
sulfur. Although the pyrite phase has a stoichiometric ratio of Fe/S = 0.5 in the bulk in
ambient conditions, such sulfur-rich growth conditions are expected to favor the incorporation of iron vacancies in the bulk, consistent with previous calculations of defect
formation energies as a function of sulfur chemical potential. [108, 135] After cooling
the as-synthesized crystals at ∼ 5 o C/min under sulfur-rich conditions inside quartz
tubes, a non-equilibrium high concentration of V Fe remainedquenched within the bulk
FeS2 . We propose this quenched-in iron deficiency to be the source of mobile iron vacancies near/on the surface under the reducing environment (i.e., under a low chemical
potential of sulfur) during our subsequent experiments. Elevated temperatures assist in
the migration of V Fe to the surface from the bulk that has become supersaturated, as
the bulk evolves toward thermal equilibrium with a lower vacancy concentration. The
role of such iron vacancies on the surface is discussed in more detail in Section 4.3.2.
Soft x-ray photoelectron spectroscopy (s-XPS)
Synchrotron x-ray photoelectron spectroscopy (XPS) was performed at Brookhaven National Lab (Upton, NY) at the U12A beamline of the National Synchrotron Light Source
(NSLS), in order to deduce the temperature dependence and the formation enthalpy
of surface defects. The radiation source was tuneable, monochromatized soft x-rays in
the energy range 100-600 eV with a resolution ∆E/E of 2 x 102 –103 and spot size of 1
mm2 on the sample surface. The base pressure in the vacuum chamber remained below
1010 Torr for the duration of the experiment. Clean single crystal FeS2 samples with
(100)-oriented growth faces larger than 5 x 5 mm2 were prepared by ultrasonication
in acetone then methanol in an inert atmosphere glove box, before being mounted in a
mechanical sample clamp (Figure 4-3). During transfer into the UHV environment, the
samples were limited to <5 min air exposure to minimize surface oxidation and other
contamination. We did not observe any secondary peaks from sulfates or other oxidation
products. [144] Controllable, in situ heating between 120-330 o C at steps of 30 o C was
achieved using a resistively-heated coil placed behind the sample. The heating apparatus and sample stage were cooled collectively by flowing liquid N2 through the manipulator, which was attached to the sample via a large copper block. Each in situ annealing
cycle lasted 150 min, which was adequate for the pyrite surface to reach equilibrium
with the UHV base pressure; subsequently, the sample was allowed to cool to approximately -170 o C for XPS measurements in order to quench in the surface chemistry and
also minimize phonon broadening of the XPS signal. S 2p photoemission spectra were
obtained at excitation energies of 210, 350 and 500 eV with an energy resolution of 100
meV and pass energy of 10 eV. Peak fitting of the S 2p XPS spectra was carried out using
CasaXPS Version 2.3.16. Shirley background subtraction was applied to all spectra and
individual components were fit with 95% Gaussian-5% Lorentzian peak distributions,
unless otherwise specified
Scanning tunneling microscopy (STM)
Scanning tunneling microscopy (STM) images were collected in order to visualize the
evolution of surface defects at elevated temperatures. An STM system (Omicron VT95
(a) XPS sample holder
(c) Sample clamp dimensions
Screw for T.C.
12 mm
4 mm
20 mm
(b) FeS₂ sample in vice
(d) Side view
3.5 mm
3.2 mm
25 mm
Figure 4-3: XPS sample clamp for FeS2 crystals.(a) circular holder for synchrotron x-ray photoelectron
spectroscopy (s-XPS) equipment. (b) custom-built aluminium sample clamp, showing FeS2 single crystal with
(100) face exposed. (c and d) sample holder design schematics with approximate dimensions.
STM; Omicron Nanotechnology, GmbH, Germany) was used under UHV conditions below 109 Torr. Electrochemically etched PtIr tips were annealed in the chamber at 150
o
C to clean them prior to taking measurements. FeS2 samples used for STM/STS were
synthesized and prepared in a manner similar to that described above for the XPS experiments. STM images were subjected to a global flattening procedure and horizontal
noise removal using SPIP 4.8.4 software from Image Metrology (Denmark).
4.2.2
Computational
Density functional theory (DFT)
DFT calculations of the FeS2 (100) surface for this work were made by Aravind Krishnamoorthy. Details can be found in Refs. [108, 182]
kinetic Monte Carlo (kMC)
Kinetic Monte Carlo (kMC) simulations were performed on a model of the pyrite (100)
surface to understand the processes responsible for the experimentally observed timeevolution of the surface defect structure under non-equilibrium conditions. The kMC
was formulated by FWH and Aravind Krishnamoorthy, and coded by Aravind Krishnamoorthy. A full description is available in Ref. [182]. Briefly, we modeled a small set
of elementary processes that were able to reproduce the experimentally-observed defect phenomena, including sulfur and iron vacancy formation. and vacancy diffusion
diffusion processes.
The probability of each process occuring, J, was given by the Arrhenius equation:
J = ν exp (−Ea /kB T ), where ν is the attempt frequency and Ea the activation barrier.
The two processes described above were subjected to geometrical constraints based on
the FeS2 (100) surface. It is worth mentioning briefly that the activation energy for surface V S formation was based on the value of 0.1 eV obtained from the XPS experiments
in this work.
96
Table 4.1: XPS core level shift (CLS) for S 2p peak, relative to the bulk pyrite dimer signal B, and full width
half maximum (FWHM) of fitted S 2p peaks (B, S, M and HE) used for quantification.
CLS (eV) / FWHM of fitted S 2p components
Excitation Energy
B
S
M
HE
210 eV
0.00 / 0.77 ±
0.03
-0.64 ± 0.03 /
0.65 ± 0.02
-1.23 ± 0.04 /
0.55 ± 0.02
+1.75 ± 0.02 /
1.7 ± 0.30
350 eV
0.00 / 0.63 ±
0.01
-0.65 ± 0.05 /
0.53 ± 0.01
-1.25 ± 0.05 /
0.57 ± 0.02
+1.80 ± 0.10 /
2.2 ± 0.20
500 eV
0.00 / 0.78 ±
0.02
-0.67 ± 0.02 /
0.77 ± 0.02
-1.26 ± 0.02 /
0.60 ± 0.03
+1.80 ± 0.20 /
2.3 ± 0.30
4.3
Results and Discussion
We first demonstrate how the surface of FeS2 evolves under the reducing conditions
of the ultra-high vacuum environment and increasingly high temperature, through the
initial formation of sulfur monovacancies and the migration to the surface of iron vacancies that were supersaturated in the bulk crystal. At a sufficiently high temperature
of ∼ 240 o C, vacant cation and anion siteswere observed to coalesce into pits of < 100
nm in lateral dimension and of either exactly one-half or one lattice parameter depth.
We employed the kMC model to substantiate our propoesed atomistic mechanism for
this phenomenon at realistic time and length scales.
4.3.1
Evolution of pyrite surface structure and chemistry
We examined the formation of individual and clustered point defects on the (100) surface of pyrite under successive reduction at increasing temperatures in the UHV environment. The approach to gather element-specific signatures around an x-ray absorption
site included analysis of core holes that result from core-level ionization and x-ray absorption. Figure 4-4 shows a series of four S 2p spectra taken on single crystal FeS2 (100)
to illustrate the effects of varying the annealing temperature (210 o C and 330 o C, as labeled), as well as the source excitation energy (350 eV in Fig. 4-4a and b; 210 eV in Fig.
4-4c and d. The experimental data were deconvoluted by peak fitting into three doublet
components, consistent with the well-established S 2p features of pyrite. [128,145–148]
Here, we adopt the nomenclature introduced by Andersson et al. [148] for the features
B, S and M, as described below. The spin-orbit splitting 2p3/2 peak was fixed for each
component at 1.18 eV above the corresponding 2p1/2 peak, with an intensity ratio of
1:2 for the doublet pairs. Further constraints used in peak fitting are listed explicitly in
Table 4.1. Feature B (“Bulk”), distinguished by a 2p3/2 peak centered at 162.8 eV binding energy (BE), is ascribed to the signal from bulk sulfur S22− dimers (see Fig. 4-5b).
Feature S (“Surface”) has a core level shift (CLS) of -0.65 ± 0.05 eV BE relative to B and
represents surface S22− dimers (Fig.4-5c). Finally, feature M (“Monomer”) is at a CLS of
-1.25 ± 0.05 eV BE relative to B and is related to the monomer defect (or monovacancy)
species S 2− at the surface (Fig. 4-5d) which is of primary interest for this work.
Quantifying the temperature dependence of proportion of the M contribution in
the S 2p spectrum enabled us to identify the sulfur vacancy formation enthalpy on
the pyrite surface, as described below. An additional singlet peak, which we refer to
as the ‘high energy’ (HE) peak was fit to each spectrum at 1.8 ± 0.2 eV above the
main B peak, with a 70% Gaussian-30% Lorenztian distribution. Previous reports of the
FeS2 (100) S 2p photoemission have either explicitly or implicitly dealt with a similar
feature. For example, Nesbitt et al. fit a single peak in their work and attributed it to
97
98
HE
S
M
165 164 163 162
Binding Energy (eV)
B
161
160
HE
167
166
330oC
B
S
165 164 163 162
Binding Energy (eV)
hν = 210 eV
(d)
210oC
hν = 210 eV
(c)
M
161
160
Figure 4-4: S 2p photoelectron spectra of FeS2 (100) at excitation energies hν of (a, b) 350 eV and (c, d) 210 eV after annealing in ultra-high vacuum at 210 o C and 330 o C, respectively. The
recorded XPS data points are shown as dots and solid lines mark the enveloping curve from peak fitting. Three features, labeled B, S and M are fit to the experimental data. Components S and M
grow in intensity from 210-330 o C and are more prominent when probed with the lower 210 eV excitation energy, consistent with the surface localization of these features.
166
330 C
o
hν = 350 eV
(b)
210 C
o
hν = 350 eV
(a)
167
Intensity (arb. units)
Monomer defects (M) form under high temperature, reducing environment
Intensity (arb. units)
Three types of surface sulfur binding environment: B, S, M
(a)
(100) surf.
(b)
(c)
(d)
S
M
B
B
001
Fe
010
S
VS
Figure 4-5: Atomic model of the FeS2 (100) surface as viewed side-on. (a) with highlighted sulfur atoms
corresponding to x-ray photoelectron spectroscopy features denoted as: (b) Bulk ‘B’ sulfur binding environment with 3 Fe-S bonds and 1 S-S bond, (c) surface ‘S’ environment with one fewer Fe-S bond, and (d)
monomer ‘M’ with an adjacent sulfur vacancy and hence no S-S bond.
polysulfides (Sn2− ) [143], Mattila et al. stipulated the additional signal in this region
to arise from the effect of the core hole [146], and Andersson et al. fitted their pyrite
S 2p peaks with asymmetric tails towards higher binding energies to account for this
contribution. [148] In our work, we did not observe the high-energy tail of the S 2p
spectra to change significantly during the course of the annealing experiments from
120-350 o C. As the experiments were conducted under reducing UHV conditions we
dismiss the possibility of surface Sn2− contributing to the signal. We therefore postulate
that the fitted HE component is generated by the core hole effect in pyrite, and we used
systematic fitting parameters to remove the influence of this peak on the quantification
of the other components B, S and M. The total intensity (area) of the HE peak was
constrained to be 10% of the total S 2p signal and variation of this constraint by ± 5%
had no quantitative effect on the relative proportions of the B, S and M features fitted on
each spectrum. The surface sensitivity of XPS is related to the inelastic mean free path
λ of the emitted photoelectrons. To minimize λ, the incident photon energy is chosen
such that the kinetic energy of the excited photoelectron is of the order 40-50 eV [46].
For the S 2p peak at a BE of ∼ 160 eV this corresponds to an x-ray excitation energy
hν of 200-210 eV. Hence the spectra in Fig.4-4c and d obtained using hν = 210 eV
originate from the top 4.5 ± 1 Å (2-3 sulfur layers) while those in Fig. 4-4a and b at hν
= 350 eV are attributable to the top 11 ± 1 Å (4-5 sulfur layers). For the other excitation
energy used in this work, hν = 500 eV, the estimated is 14 ± 1 Å (5-6 sulfur layers).
At the 500 eV photon energy, the surface sulfur species of interest to this work have
relatively weak signal as compared to the bulk species B; therefore we do not include
the 500 eV XPS results in further discussion. Features S and M are most prominent in
Fig. 4-4c and d which were obtained using 210 eV excitation energy, indicating that
these signals arise from the 1-2 atomic layers of pyrite closest to the (100) free surface
of the crystal.The proportion of M as a fraction of the total S 2p signal, denoted as [M],
increases with increasing annealing temperature up to 330 o C. This trend is consistent
with the formation of surface monomer defects as the sample surface is increasingly
chemically reduced. In the intermediate temperature region between 120-240 o C, [M]
increased consistently with temperature (Fig. 4-6).
To estimate the formation enthalpy of sulfur monomer vacancies, [M] in the most
surface-sensitive measurement (hν = 210 eV) was quantified as a function of temperature. We assume the following simple defect reaction to form electronically neutral
vacancies under UHV annealing:
99
1
×
×
FeS2 ⇔ Fe×
Fe + SSi + VSii + S2,(g)
2
(4.1)
where the conventional Kröger-Vink notation [183] is used andthe subscripts Si and
Sii refer, in no particular order, to the two adjacent sulfur sites on any given anion dimer.
Although the formal oxidation state of the newly formed sulfur monomer site (Sii here)
should be S1- , it is understood this configuration relaxes to the more stable S2 by electron
transfer from an adjacent cation, leaving the vacant site electronically neutral. [110,
143] We write the Gibbs free energy change of the defect formation reaction in Eq. (4.1)
as ∆G f = ∆H f − T ∆S f , where ∆H f and∆S f are the enthalpy and entropy of vacancy
formation, respectively. The sulfur vacancy concentration at a given temperature T can
then be written:
ª
§
∆G f
|VS | = pS12 . exp −
2
kB T
(4.2)
where kB is Boltzmann’s constant, pS2 is the equilibrium partial pressure of sulfur gas,
and we assume the activities of the solid to be unity. Finally, we note that a given change
in [M] can be used as anestimate for change in [V s ], if we apply the reasonable assumption that the only defect species contributing to the increase in [M] is the monomer
vacancy, V s .
Figure 4-6 shows the results for the increase in relative contribution attributed to
M, as ln[M] vs. 1/T, in the annealing temperature range of 120-240 o C. We present
only the data obtained with 210 eV XPS excitation energy, which gives the most surface sensitive results. From the slope of the straight-line fit and Eq. (4.2) we infer the
formation enthalpy ∆H f to be 0.1 ± 0.03 eV. Our estimated error in ∆H f is the difference between maximum and minimum slope fits obtained from systematic variations in
software-generated quantification of S 2p peak fits (including sensitivity to the selection
of the HE fitted component, giving rise to the error bars), and does not reflect experimental error associated with the sample, equipment or measurement. The optimal peak
fit for each component was first chosen so as to minimize the total root mean squared
error between fitted data and experimental data. Error bars were then generated by methodically varying the peak positions of the M and S components relative to the position
of B, across the ranges listed in Table 4.1; we believe this gives a reasonable quantitative estimate of fitting error. However, in this quantification we neglect any clustering
of defects at lower temperatures that would effectively suppress the value of [M], as
discussed in more detail below. This is reasonable given the high resolution achieved in
our STM images, which suggest that these surfaces are not likely to have many small
clusters at the lower temperatures. As a result, the calculated ∆H f may only slightly
underestimate thetrue activation enthalpy for vacancy formation.
Upon annealing to higher temperatures (240 o C - 330 o C) we observed a noticeable deviation from the Arrhenius behavior of [M] that is seen in Figure 4-6. Figure
4-7a shows that the percentage of M reached a maximum at around 240 o C and then
dropped by ∼ 3-4% of the total S 2p signal, before leveling off to a roughly constant
value for temperatures above 270 o C. Furthermore, the total signal arising from the S
component increased in this temperature range up to 270 o C, by a roughly equivalent
amount (∼10%) to M, then leveled to a consistent value of around 43% of the total
S 2p signal between 270 - 330 o C (Fig. 4-7b). Such non-Arrhenius behavior of [M]
and [S] imply a more complicated phenomenon than the otherwise logical hypothesis
that surface-localized sulfur dimers (S) are converted directly to monomers (M) by the
thermally-assisted breaking of the sulfur-sulfur bonds; in such a case we would expect
any increase in M signal to be matched by a corresponding drop in S. We will revisit the
mechanisms that could explain such a non-monotonic change in sulfur monovacancies
via later description of kMC simulations. However, the model underlying such computational simulations is informed by direct observation of the surface reconstruction of
100
Arrhenius growth in [M] at low temperatures
T ( oC)
3.6
240
200
160
120
3.4
ln [M]
3.2
3
2.8
f
ΔH = 0.1 ± 0.03 eV
2.6
2
2.2
2.4
- 1) x 10 -3
1/T (K
2.6
Figure 4-6: Sulfur monomer vacancy concentration [M] as a percentage of total S 2p photoelectron spectrum signal vs. inverse temperature. The dashed line is the best linear fit to the data, and error bar generation
is discussed in the text. ∆H f is calculated from the slope of this line, assuming the Arrhenius relationship in
Eq. (4.2).
Non-monotonic defect formation at higher T’s
30
(a)
%M
25
20
15
210 eV
300 eV
500 eV
10
200
45
250
300
o
Annealing T ( C)
350
250
300
o
Annealing T ( C)
350
(b)
%S
40
35
30
25
200
Figure 4-7: Proportion of the M and S components of the S 2p photoelectron spectra on FeS2 (100) at
200-330 o C, measured using three different excitation energies: 210, 350 and 500 eV. (a) The fraction of the
total signal represented by M increased upto 270 o C then dropped and stayed approximately constant, (b)
The fraction of total signal represented by S also increased up to 270 o C but then remained unchanged to
330o C . The dashed lines connecting the data points are shown as a guide for the eye.
101
Nucleation and growth of surface vacancy pits by scanning tunneling microscopy
25oC
z (nm)
+0.25
(a)
220oC
z (nm)
+0.5
(d)
0.0
0.0
-0.25
-0.5
300oC
(g)
z (nm)
+2.0
EXPERIMENTAL
0.0
30 nm
50 nm
+0.25
(b)
50 nm
-1.0
-0.5
+0.1
(e)
-2.0
+0.4
(h)
0.0
0.0
0.0
-0.1
10 nm
10 nm
-0.4
-0.2
10 nm
-0.25
0.0
SIMULATED
(c)
10 nm
-0.8
0.0
(f)
10 nm
-0.25
0.0
(i)
10 nm
-0.25
-0.25
Figure 4-8: Scanning tunneling microscopy (STM) images of single crystal FeS2 (100) surfaces (a, b) prior
to any in situ annealing in ultra high vacuum, (d, e) after three hours of in situ annealing at 220 o C, and (g, h)
after three hours at 300 o C. The surface morphology of atomically-flat terraces at room temperature changes
underannealing due to the formation of vacancy clusters. In addition, originally straight terrace edges, visible
in the bottom left corner of (a), develop into wavy lines, e.g. as indicated by the white arrow in (d). All STM
data were collected at room temperature using tunneling conditions in the range ± (1-2) V and 200-1000 nA.
The bottom row of images (c, f, i) display the results of kinetic Monte Carlo (kMC) simulations performed at
the same temperatures of (c) 25 o C, (f) 220 o C and (i) 300 o C for comparison with the experimental images.
The activation barrier values used in these kMC simulations are from Ref. [182].
pyrite, which we address next.
Scanning tunneling microscopy (STM) images of single crystal pyrite (100) surfaces
both at room temperature and after in situ annealing to 220 o C and to 300 o C for > 150
min (Fig. 4-8) provided further details on the behavior of defects underlying the results
in Figure 4-7. For comparison, we include predictions from our temperature-dependent
kMC simulations of point defect formation and clustering. These simulated results are
discussed in more detail in the following section. The initial surface condition of the FeS2
single crystals consisted of multiple atomically-flat, featureless (100) terraces (Fig. 4-8a
and b).
After annealing at 220o C in UHV, we observed two notable changes in surface morphology: first, the straight ledges separating atomic terraces became wavy, with small incursions into the terrace (Fig. 4-8d). Second, there appeared multiple small, irregularlyshaped depressions on the surface of flat terraces that arose from the agglomeration of
surface anion and cation vacancies (Fig. 4-8e), henceforth referred to as vacancy clusters or ‘pits’. At 220 o C we observed a dispersion of cluster sizes (widths) from smaller
than 1 nm to ∼ 10 nm (Fig. 4-8e). Following annealing at 300 o C, these grew to form
a more homogeneous spread of clusters with lateral dimensions consistently between
5-10 nm (Fig. 4-8g, h and i). As described in Section 4.2.1,we believe the source of
the observed iron vacancies (V Fe ) to be supersaturated V Fe remaining in the bulk after crystal synthesis under high sulfur chemical potential S. During annealing in the
low S experimental conditions in UHV, iron vacancies migrate to the surface to equi102
librate a stoichiometric bulk rid from V Fe . This process effectively ‘provides’ cation vacancies to the surface, leading to a situation similar to the dissolution of metal cations
into liquid electrolytes in contact with a passive film. [184, 185] Similar surface vacancy clusters have been observed on metals containing supersaturated vacancies from
quenching [173,186,187], non-stoichiometric oxides such as CeO2 [188,189] and also
natural pyrrhotite Fe1-x S that have been subjected to heating under vacuum. The pits
exhibited a curved, non-faceted morphology that can be rationalized by comparison
to the curved terrace steps observed by Rosso et al. on conchoidal fracture surfaces of
FeS2 . [151] Normal to the free surface of the crystal, the depth of the defect clusters
also changed between 220-300o C , as seen in the image height histograms of Figure
4-9. After in situ annealing treatment at 220 o C, there existed a bimodal distribution of
pit depths, with the majority of pixels at the nominal surface level (normalized to 0 nm
on the scale shown) and a subset located at a depth of approximately 0.25 nm. After in
situ annealing at 300 o C, the pit depth distribution broadened and the mean depth of
the minor peak in the histogram is shifted to approximately 0.55 nm. The line traces in
Figures 4-9a, b and c provide more detail on the depth of pits: at 220 o C the surface pits
were consistently 2.7 ± 0.1 Å deep whereas at 300o C the majority of pits have a depth
of 5.4 ± 0.1 Å. Given the lattice parameter of pyrite of 5.41 Å [162], these pit depths
correspond to one half and one full lattice parameter, respectively.
4.3.2
Mechanism of vacancy formation and coalescence
The growth of defect clusters as evidenced by our STM results, along with the XPS
results presented in Figures 4-6 and 4-7, lead us to propose a mechanism involving three
distinct phenomena occurring in tandem during the in situ reduction of the FeS2 (100)
surface, as visualized in Fig. 4-10.
1. Formation of isolated S monovacancies (V S ) and surface-ward migration of V Fe
from the bulk, giving rise to increasing signals of sulfur species M and S, respectively;
2. surface diffusion of V S and V Fe , followed by the stochastic clustering of small
numbers of vacancies;
3. growth of vacancy clusters, which are more stable geometric features for the reduced surface compared to dispersed point defects, due to a reduced formation
energy for sulfur vacancies at step edges.
The proposed mechanism was cast into our kMC model. The last row of images in
Figure 4-8 shows the successive formation and growth of surface pits after simulated
annealing for 4 h. The model reproduces the flat, nearly featureless surface at ambient
temperatures (Fig. 4-8c), while a series of pits with average lateral dimension of 1 x 1
nm2 becomes visible at 220o C (Fig. 4-8f) and larger pits on the order of 2 x 2 nm2 at
300o C (Fig. 4-8i). For a complete discussion of the kMC results, the reader is referred
to Ref. [182].
Below, we discuss in more detail the three phenomena that account for this pit
initiation mechanism:
1. Formation of sulfur and iron vacancies at and near the surface: Elemental sulfur is highly volatile in comparison to iron, with a melting temperature of 115 o C
at 1 atm pressure. We therefore assume sulfur sublimes from pyrite and is dynamically removed from the sample surface under vacuum until the pyrite equilibrates
with the ambient sulfur chemical potential, dictated by the chamber pressure of
109 -1010 mbar. We also noted the importance of iron vacancies in our model. The
corresponding appearance of V Fe near the surface is indicated by the growth of
the S feature of the XPS S 2p spectra while the surface is increasingly reduced.
103
Evolution of vacancy pit depth with temperature
“M”
(a)
z (nm)
0.2
200 oC
0
-0.2
-0.4
-0.6
0
(b)
z (nm)
0.2
4
16
8 12
x (nm)
001
“S”
010
240 oC
0
2.7 Å step
-0.2
-0.4
-0.6 0 5
(c)
0.2
10 15 20
x (nm)
300 oC
z (nm)
0
5.4 Å step
-0.2
-0.4
-0.6
10
0
20
Fe
x (nm)
(d)
% of pixels
o
300 C
-0.8
VS
VFe
0.25 nm
o
220 C
-1
S
0.55 nm
-0.6
-0.4
-0.2
0
0.2
0.4
Figure 4-9: Pits are one half- or one lattice parameter deep. (a-c) line traces taken across representative
surface features observed in scanning tunneling microscopy (STM) scans at 200, 240 and 300 o C. Inset in
each graph are STM images of the nanopits, with grey arrows indicating each line trace. The ball-and-stick
atomic diagram next to each graph depics a side-on view of the surface at the pit edges. In (a), we observed
single monomers or very small nanopits that could not be resolved on the atomic scale. By 240 o C in (b) the
measured pit depth is exactly one-half of a pyrite lattice parameter, or 2.7 Å. Finally, in (c) the step height
has grown to a full lattice parameter of 5.4 Å. (d) shows height (z-axis) histograms of STM images obtained
after annealing at 220o C (and at 300o C bimodal distributions of pit depths are observed at both annealing
temperatures; however the average pit gdepth is ∼0.25 nm in the former case and ∼ 0.55 nm in the latter.
Figure 4-5 illustrates how six new S binding environments would accompany the
introduction of a single V Fe in the second atomic layer from the (100) surface
(NB: only 4 S sites are shown in the plane of the graphic). Since Fe loss through
evaporation into vacuum is unlikely at the relatively low annealing temperatures
compared to the melting point T m of iron (300o C < 0.2 T m ), the increaseof V Fe
requires an alternative explanation. It is known that the formation enthalpy of
the V Fe in pyrite increases by up to 1.42 eV as the environment changes from
sulfur-rich to one deficient in sulfur. [108] This large change implies that the sizable number of V Fe defects originally present in the pyrite crystal during synthesis
104
Atomic processes in pitting mechanism
S2 (g)
(b)
(a)
(d)
(c)
001
010
Fe2+
VFe
Formation
S22-
VS
Diffusion
Figure 4-10: Illustration of atomic processes involved in the proposed mechanism of pit formation and
growth on pyrite (100). (a) Formation of surface sulfur monovacanciesVSthrough evaporation into vacuum.
(b) Diffusion of V S to a pit site. (c) Agglomeration of vacancies on the iron and sulfur sublattices by diffusion,
leading to theinitiation and growth of the pit. Presence of an initiated pit (as depicted in this fig-ure) is not
a necessary precursor to the process in (c). (d) Iron vacancies, denotedas V Fe , that are already present in the
bulk migrate to the surface during annealing.(e) V S formation at under-coordinated sites surrounding pits
has lower formation enthalpy as compared to isolated vacancy formation process in (a).
kMC result replicates M defect formation
0.4
[M]
0.3
0.2
0.1
0
KMC
XPS (210 eV)
200
240
280
320
Temperature (°C)
Figure 4-11: kinetic Monte Carlo simulation results. Simulated values of the sulfur monomer vacancy concentration [M] on the pyrite surface as a function of annealing temperature, obtained by kinetic MonteCarlo
simulations (kMC) and indicated by the blue zone. The width of predicted [M] indicated by this blue band
is given by variation in kMC energy barrier values over the range described in Ref. [182]. Values of [M]
experimentally determined from our XPS measurements (Fig. 4-7) are shown for comparison.
in sulfur-rich conditions are not stable in the sulfur-deficient conditions encountered during the annealing process. In order to equilibrate the bulk under these
experimental conditions, the oversaturated V Fe point defects migrate from bulk
towards the free surface at high temperatures to annihilate. In providing iron vacancies to the surface, coincidentally in this work, the situation is analogous to
the dissolution of metal cations from the passive film in liquid electrolytes. [184]
2. Diffusion of sulfur and iron vacancies on the surface: the generation of incursions into pre-existing atomic terrace edges (Fig. 4-8d) and the nucleation of
105
small vacancy clusters on top ofterraces (e.g., as seen in Fig.4-8e), requires the
diffusion of both V Fe and V S across the surface. When two or more vacancies encounter each other stochastically, a small cluster is formed which is more stable
relative to the dispersed individual vacancies. STM imaging by Rosso et al. has
recorded surface diffusion of iron vacancies on natural single crystals of FeS2 at
room temperature over time scales of minutes, so diffusive processes are expected
to occur with low energy barriers. [149] In the kMC model in this work, a higher
barrier was taken for diffusion of vacant surface sites away from the pits compared
to diffusion of vacancies towards the pits, simulating the trapping of vacant sites
by the initiated pits.
3. Growth of pits: Once a stable pit nucleates, the reduced coordination of sulfur
atoms at the newly-created step edges of pits reduces the formation energy for
vacancies at these sites, and accelerates the growth of pits. Indeed, our DFT calculations showed that ∆H f for individual V S at a step edge of a pit could be up
to ∼ 40% lower than that on an atomically-flat surface. This type of dependence
of defect formation on the local atomic configuration has also been observed in
sulfide inclusions in pitting corrosion. [190]
The formation and expansion of surface vacancy clusters in this manner provides
an explanation for the surprisingly low ∆H f for sulfur vacancies of around 0.1 eV that
we measured using XPS below 240 o C (Fig. 4-6), as compared to recent theoretical
predictions in the range of 0.4-1.44 eV. [108,109,134] Upon raising the temperature to
greater than 240 o C, the effect of growing the vacancy clusters is to maintain the XPS
signal intensity from M at a roughly constant value. This is because the removal of a
sulfur atom from the step edge of a vacancy cluster, while growing the cluster, does not
result in the creation of an adjacent monomer M site on the surface structure; therefore
the M signal intensity does not increase in the S 2p spectrum.
4.4
4.4.1
Outcomes
Conclusions
We have investigated the evolution of surface chemistry and morphology on synthetic
pyrite single crystals as a function of annealing temperature in reducing conditions, in
order to visualize and quantify the mechanisms leading to pit initiation on the surface.
The formation enthalpy for sulfur vacancies was found to be tobe 0.1 ± 0.03 eV from the
exponential temperature dependence of the sulfur monomer vacancy (V S ) binding environment detected in the S 2p photoelectron spectra. However, at higher temperatures
above 200 o C, the sulfur vacancy concentration decreased and deviated from Arrhenius
behavior, concurrent with the initiation of nanometer-scale surface pits. The depths of
these pits were exactly one-half or one FeS2 lattice parameter, as imaged by STM. To explain this behavior, we propose a mechanism involving the simultaneous formation and
migration of vacancies at the surface, with facilitated vacancy formation and agglomeration at step edge sites surrounding pits. A simple kinetic Monte Carlo simulation with
thermally activated reactions was used to validate the proposed mechanism. We note
two important implications of these findings. First, the observed, concerted agglomeration of point defects from both cation and anion sublattices to initiate nanoscale pits has
broad consequences for ionic solids in reducing environments. The dynamics of surface
point defects observed under controlled reducing environments offer an atomistic level
description of the incipient stages of pit formation in passive films, as postulated in models of surface degradation such as the Point Defect Model. Second, the relatively low
defect formation energy that we measure for sulfur vacancies confirms the high chemical reducibility of the FeS2 surface, often linked to poor electronic and electrochemical
properties in synthetically grown pyrite.
106
4.4.2
Future work
Having observed the formation of surface nanopits by reducing FeS2 in UHV at high
temperatures, it would be of interest to study in situ pitting nucleation at lower temperatures (< 100 o C) but under electrochemical conditions, for example in model corrosive
solutions and/or under an applied electrode bias. The ideal instrument would be an
electrochemical STM, to investigate whether the same atomic processes as described in
this chapter apply when a high temperature gradient combined with chemical driving
force is replaced by an electrochemical one.
Separately, it would be interesting to study the reactivity of surface defects and defect
clusters towards molecules such as H2 S and H2 O, building on the work by Guevremont
et al. [126] and others. [127] Since the publication of the work described in this chapter, Andersson et al. have reported the formation of monomers on the FeS2 (100) surface
under energetic ion bombardment, suggesting that the surface chemical activity can be
altered greatly by sputtering. [191] However, their assessment of surface reactivity assumes that many monomer defects form individually, dispersed across the surface. As
we have shown here, vacancies at elevated temperatures can cluster and reduce the
number of dangling bonds available to catalyze heterogeneous reactions. A concerted
experimental and computational approach could help understand the reactivity of real
pyrite surfaces in aggressive, electrochemical environments. Experimentally, temperature programmed desorption (TPD) would be a good tool to study the adsorption and
reactive properties of surface defects on pyrite.
Acknowledgements
We gratefully acknowledge support provided by BP Plc. through the BP-MIT Center for
Materials and Corrosion Research. We thank S. Yip (MIT), R. Woollam, Steven Shademan and Sai P. Venkateswaran (BP) for discussions on pitting mechanisms in H2 S, P.
Lazic, R. Armiento and G. Ceder (MIT) for discussions on relevance of these results
to PV performance of pyrite, Klas Andersson (formerly of Stockholm University, Sweden) for discussions on pyrite surface chemistry and XPS, and R. Sun (MIT) and M.
Kabir (IISER-Pune) for verification of some of the point defect formation energycalculations. We thank D. Mullins and P. Albrecht at Oak Ridge National Laboratory for the
use of the U12A beamline (BrookhavenNational Laboratory) for XPS measurements.
The U12a beamline is supported by the Division of Chemical Sciences, Geosciences,and
Biosciences, Office of Basic Energy Sciences, U.S. Departmentof Energy, under contract
DE-AC05-00OR22725 with Oak Ridge National Laboratory, managed and operated by
UT-Battelle, LLC. Use of the National Synchrotron Light Source, Brookhaven National
Laboratory, was supported by the U.S. Department of Energy, Office of Science, Office
of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886. We thank the National Science Foundation for providing the computational resources for this project
through the Texas Advanced Computing Center under Grant No.TG-DMR120025.
107
108
Chapter 5
Conclusions
5.1
Summary of activation barriers
This thesis explored the bulk and surface defect chemistry of the two stable Fe-S phases
pyrrhotite and pyrite, to understand the governing mechanisms behind their protectiveness as passive layers formed on steels under sulfidizing conditions. A key goal was
to measure activation barriers Ea , the fundamental descriptor of kinetic rates, for the
processes depicted in Figure 1-7a. To that end, a summary of the activation barriers of
interest is given in Table 5.1.
Table 5.1: Summary of experimentally determined activation barriers Ea in eV for key unit processes
investigated in the course of this work. Bold entries are contributed from the experiments described in this
thesis; those marked "N/A" were either not measured, or could not be found in the literature.
Process
Temp. (o C)
Pyrrhotite Fe1-x S
Pyrite FeS2
Chapter 2: Growth
Bulk Fe diffusion * DFe
0.83
αS(T )2
170-700
(a)
+
N/A
Bulk S diffusion * DS
> 500
7.9 (b)
2.1 (c)
Surface S exchange (ox.)
350-600
N/A
Surface S exchange (red.)
350-600
1.05 ± 0.20
0.79 ± 0.23
N/A
Chapter 3: Reactivity
Bulk band gap Eg, bulk
25
0.30-0.80 (d)
0.95
Bulk band gap Eg, surf
25
N/A
0.40 ± 0.10
Chapter 4: Stability
0.10-0.20 (e)
Surface Fe diffusion *DFe, surf
25
Fe surface vacancy ∆H v,Fe
100-300
N/A
N/A
S surface vacancy ∆H v,S
100-300
N/A
0.10 ± 0.03
(a) α = 0.41 ± 0.06 and S(T ) is the reduced magnetization (= 0 at 0 K), (b) Ref. [40], (c) Ref. [192], (d)
Refs. [52, 193], (e) Ref. [149]
109
5.2
Contributions
With reference to Table 5.1 and to supplement the "Outcomes" from each of Chapters
2, 3 and 4, the key scientific questions and corresponding contributions of this thesis
are summarized below:
What are the rate limiting mechanisms in the growth of Fe1-x S on iron? Pyrrhotite
scale growth occurs by Fe diffusion from the metal to the surface of the passive layer,
where Fe combines with S transferred from molecular form such as in H2 S in the environement. Both Fe diffusion and heterogeneous surface exchange of S have a similar
activation energy of ∼1 eV. Hence, regardless of temperature (or electrochemical potential), the sulfidation of iron should always commence with linear kinetics, controlled
by the surface reaction. However, since the diffusive transport depends on the square
of film thickness, eventually diffusion will become the limiting process in scale growth,
marked by a transition to parabolic time dependence. From our studies on phase-pure
pyrrhotite thin film and bulk samples, this transition should occur when the film has
grown to approximately 100-1000 µm thickness.
Does the order-disorder transition in Fe1-x S have an effect of iron diffusivity? Iron
self diffusivity * DFe in pyrrhotite had not been systematically studied below the known
order-disorder transition at T N = 315 o C. Above T N , iron atoms are paramagnetic and
cation vacancies are consequently randomly arranged in the lattice. * DFe in the paramagnetic regime follows an Arrhenius trend with an average activation energy Ep =
0.83 eV. However, below T N iron atoms spontaneously magnetize, imposing a driving
force for Fe vacancy ordering that results in a series of complex ordered superstructures at low temperature. The effect of spontaneous magnetization is to increase the
Fe vacancy migration barrier. Hence the activation enregy Em for self-diffusion below
T N has a magnetic dependence of the form: Em = E p + αS(T )2 , where S is the reduced
magnetization of pyrrhotite and α is a constant ∼0.4. Therfore, extrapolation of the
paramagnetic trend to lower temperatures would overestimate real diffusivitites in this
material, by up to 100 times at 150 o C.
How can we quantitatively assess surface electronic structure via scanning tunneling spectroscopy (STS)? The probability of charge transfer between a solid and
adsorbate is ultimately dictated by the availability of electronic states at the correct
energy levels. FeS2 is a good example of a semiconducting material in which unsaturated "dangling" bonds at the surface introduce additional states to those present in the
bulk. A seemingly ideal tool to confirm the existence of surface states experimentally is
STM; however, the inherent electronic properties of the surface are easily distorted by
the very high proximate electric field of the tip, frequently leading to misinterpretation
of values such as surface band gap Eg . This thesis contributes a systematic methodology for quantifying the surface electronic strucutre by matching simulated tunneling
current predictions to experimental results from the STM. This approach is extendible
to other semiconducting materials with similar characteristics, such as other transition
metal chalcogenides.
What role do surface states play in charge transfer on FeS2 (100)? Using the technique outlined above, the (100) surface of FeS2 is confirmed to contain intrinsic surface
states (SS’s) arising from Fe and S dangling bonds. These sit on the edges of the valence
and conduction band, respectively, and have the effect of reducing the surface band gap
from 0.95 to 0.4 eV. Since the surface states form continuous bands with the bulk states,
charge cannot localize at intrinsic SS’s and they do not pin the Fermi level EF . However,
extrinsic surface states from surface point defects and adsorbates sit discretely within
110
the surface Eg and do pin EF . The implications for electrochemical reactions such as oxidation during corrosion are that horizontal charge transfer can occur at smaller overpotentials η via surface states than would be predicted if the bulk electronic structure were
evaluated alone. In considering a generalized passive film model, this finding highlights
the need to differentiate carefully between bulk and surface electronic structure.
What are the atomic-scale dynamics of point defects on destabilized ionic passive
film surfaces? According to the Point Defect Model of Macdonald et al. (see Chapter 1),
pitting is a deterministic process in which the breakdown of passivity is controlled on
the microscopic scale by the interactions of point defects at the metal-passive layer and
passive layer-electrolyte interfaces. The formation of cavities at these interfaces requires
vacancies on both the anion and cation sublattice to coalesce, via vacancy formation
and diffusion processes. We show on a model FeS2 (100) surface that under reducing
conditions at elevated temperatures, vacancies can condense into pit-like features which
effectively comprise single atomic steps into the surface. While not necessarily potential
pit initiation sites per se, their characterization allow us to formulate a real-time and
predictive model of the dynamics and interactions of point defects at the surface as it
destabilizes under reducing conditions.
Can surface vacancies account for reported polycrystalline FeS2 off-stoichiometry?
The formation of vacancies in bulk pyrite is calculated to be energetically costly; however, the surface of pyrite is found to readily forgo sulfur, and this has been proposed as
one reason for the observed off-stoichiometry in polycrystalline FeS2 prepared by high
temperature methods such as sulfurization. The distinct binding energies of surface S
atoms that are either bound to another S or adjacent to a vacancy, thereby allowing us
to quantify the formation of vacancies with increasing temperature. A very low formation enthalpy ∆H f = 0.1 eV for sulfur vacancies implies that the surface is indeed very
susceptible to losing sulfur to the atmosphere at even mild temperatures > 100 o C. Such
facile vacancy formation suggests that the pyrite surface in situ is constantly in flux vacancies easily form but are also reactive sites for further sulfidation. More generally,
these findings are critical to the fabrication of synthetic pyrite for photovoltaic or other
applications where homogeneity and/or full stoichiometry are important.
5.3
Outlook and perspectives
This thesis began with the hypothesis that a multiscale model for passive layers can
be constructed via a "bottom-up" approach, that is, by studying the elementary physical chemistry at the surface and in the bulk of the ionic materials that comprise the
passive film, and determining the key unit processes governing film growth, reactivity
and stability. None of the experimental contributions outlined above were realized under authentic sour corrosion conditions or even laboratory simulated ones. Instead, the
majority of the work was carried out under either ultra high vacuum (UHV), i.e. where
sensitive ion- and electron- detection equipment can operate, or high-temperature, gas
environments. Therefore, we must ask to what extent these fundamental studies advance the overarching goal of constructing the universal passive film model introduced
in Chapter 1. The problem of the vacuum gap, which asks how practical it is to extend
discoveries made under highly-controlled, low pressure conditions to the "real-world"
environment, is not unique to the investigations described in this thesis. However, it is
still greatly important to understand these microscopic events on surfaces free of contaminants in order to gain insight into behavior on the fundamental level. To accomplish a fully non-empirical, predictive tool for electrochemical systems we must start
by studying ionic point defects on clean surfaces and in pure materials before adding
111
further complexity in the form of microstructure, liquid interfaces, applied stresses and
so on.
Nevertheless, the further advancement of these ideas necessitates bridging this gap to a
more realistic environment, for example with in situ aqueous studies on the iron sulfide
phases of interest. The structure and bonding of water at surfaces is central to all electrochemical reactions in water-based electrolytes. Therefore some of the further studies
suggested in the individual experimental Chapters 2-4 involve the introduction of water: is diffusion and therefore film growth more rapid in porous iron sulfide films formed
in solution? In what way does an electrical double layer affect the inherent reactivity of
the surface? Can this be modeled accurately from first principles by density functional
theory? Would a pyrite surface imaged by electrochemical STM in a corrosive solution,
and under an applied bias, undergo surface destabilization that can still be described
by the basic vacancy dynamics described here? These constitute a small set of the questions that must be answered if we are to achieve a comprehensive passive film model
that has real-world applicability.
Let us end with a perspective on the two practical drivers of this project: the simulation
of microscopic events as a predictive tool, and as a platform to design more robust
materials for service in aggressive conditions. As outlined in Chapter 1, the study of
passive films on metals has an almost 300-year old history, and it would be a haughty
overstatement to suggest this work is anything but a minor contribution to our overall
understanding of the field. However, we have outlined a basic methodology by which
the study of local phenomena at the basic level of materials - atoms and electrons can be fashioned into a larger-scale, descriptive model that can serve both these end
goals. Through novel insights into the rate-limiting mechanisms of surface reactions and
diffusion, and continued advances in computing power, we can forsee the ability one
day to predict the integrity of the materials in our vast network of energy infrastructure
down to the sub-nanometer scale. While humbled by this lofty goal, it is exciting to
consider what is possible through our knowledge of these materials on the fundamental
level.
112
Appendix A
Pourbaix diagrams for the
Fe-H2S-H2O system
The calculations in this Appendix give rise to the two Pourbaix diagrams shown in Figure
1-3 in Chapter 1. The standard Gibbs free energies (∆G of ) and enthalpies (∆H of ) of
the species involved in constructing the thermodynamic stability diagrams are listed in
Table A.1, referring to reference conditions of 25 o C and 1 atm pressure.
H2 S dissociation
The H2 S activity input to the thermodynamic stability diagrams must account for the
dissolution of H2 S gas in the local aqueous environment:
H2 S(g)
KH2 S/H2 S
⇔ H2 S(aq)
(A.1)
with a corresponding solubility constant:
KH2 S(aq) /H2 S(g) =
aH2 S(aq)
γH2 S.pH
(A.2)
2S
where:
• γH2 S is the fugacity coefficient of H2 S which can vary between 0.4-1.0. [20]
• pH2 S is the partial pressure of H2 S in the system.
Aqueous H2 S can proceed to dissociate in two partial steps (Equations A1.3 and A1.4
followed by Equations A1.5 and A1.6):
Kd,1
H2 S(aq) ⇔ H + + HS −
Kd,1 =
aH + aHS −
aH2 S(aq)
Kd,2
HS − ⇔ H + + S 2−
Kd,2 =
aH + aS 2−
aHS −
(A.3)
(A.4)
(A.5)
(A.6)
In the diagrams here, the value of γH2 S = 1 is used. The H2 S gas-aqueous solubility
constant expression determined experimentally by Suleimenov et al. [197], Equation
113
Table A.1: Thermodynamic data for species in H2 S-H2 O-Fe system.
Species
H
+
(aq) G
∆G of (kJ/mol)
∆H of (kJ/mol)
0.00
0.00
[194]
H2 S(g)
-33.3
H2 S(aq)
-27.9
H2 O(l)
-237.1
H2(aq)
17.7
O2(aq)
16.5
Fe (s)
0
2+
-20.6
[194]
-39.7
[194]
-241.80
[194]
[194]
[194]
[194]
(aq)
-91.5
Fe3+ (aq)
-17.2
Fe2 O3 (s)
-743.5
Fe3 O4 (s)
-1017.4
Fe(OH)2 (s)
-492.0
Fe(OH)3 (s)
-705.5
FeSm (s) Mackinawite
-93.3
-92.0 *
FeSp (s) Pyrrhotite
-114.5
-101.7
FeS2 (s) Pyrite
-160.1
Fe
FeHS
Reference
-92.3
[194]
[194]
[194]
[194]
[194]
[194]
[195]
[194]
-171.5
[194]
+
-104.3
-152.7 *
[196]
Table A.2: Input parameters.
Temperature (o C)
25
ptotal (atm)
1
pH2 S (atm)
0.01
-3
a Fe2+ (mol.dm )
1.8x10-4 (10 ppm)
a Fe3+ (mol.dm-3 )
1.0x10-6
pH2 (atm)
1.0
pO2 (atm)
1.0
114
Table A.3: Fe-H2 O Reactions and reversible potentials.
No. Reaction
Erev or pH
+
O
O2 + 4H + 4e ⇔ 2H2 O
E r ev(O) = E roev(O) −
2.3RT
4F
log (a
H
2H + + 2e− ⇔ H2
E r ev(H) = E roev(H) −
2.3RT
2F
log (a
−
1
4
H+ )
(pH2 )
2
H+ )
−
2.3RT
2F
log (a
Fe2+ )
−
2.3RT
2F
log (a
Fe3+ )
Fe(OH)2 + 2H + + 2e− ⇔ Fe + 2H2 O
E r ev(3) = E roev(3) −
2.3RT
2F
log (a
2
H+ )
4
Fe3 O4 + 2H2 O + 2H + + 2e− ⇔ 3Fe(OH)2
E r ev(4) = E roev(4) −
2.3RT
2F
log (a
2
H+ )
5
6Fe2 O3 + 4H + + 4e− ⇔ 4Fe3 O4 + 2H2 O
E r ev(5) = E roev(5) −
2.3RT
4F
log (a
4
H+ )
6
Fe3 O4 + 8H + + 2e− ⇔ 3Fe2+ + 4H 2 O
E r ev(6) = E roev(6) −
2.3RT
2F
log
E r ev(6) =
2.3RT
4F
Fe
2+
+ 2e ⇔ Fe
E r ev(1) =
E roev(1)
2
Fe
3+
+ 2e ⇔ Fe
E r ev(2) =
E roev(2)
3
1
7
8
9
−
−
+
2Fe2 O3 + 12H + 4e ⇔ 4Fe
2Fe
Fe
3+
2+
−
2+
+ 3H2 O ⇔ Fe2 O3 + 6H
+ 6H2 O
+
+ 2H2 O ⇔ Fe(OH)2 + 2H
pH =
+
E roev(6)
−
1
1
1
1
1
(a Fe2+ )3
(aH + )8
(a Fe2+ )4
log (a
12
H+ )
− 21 .log(K8 .a2Fe3+ )
pH = − 21 .log(K8 .a Fe2+ )
(A.7). yields the aqueous H2 S activity for a given partial pressure input for the reference
temperature T = 298 K.
l o g(KH2 S(aq) /H2 S(g) ) = −634.27 + 0.2709T − 0.11132 × 10−3 T 2 −
16719
− 261.9log T
T
(A.7)
Fe-H2 O equilibrium reactions
The reactions demarcating the equilibrium between different species in the Fe-H2 OH2 O system are taken from Ref. [14]. Table A.3 lists the expected water-iron reactions
along with the reversible oxygen and hydrogen evolution reactions. The column on
the far right explicitly shows the reversible electrode potential, or constant pH line, for
each reaction. The standard reversible electrode potential E roev(n) for a given reaction n
is calculated here by evaluation of the Gibbs free energy of the reaction ∆G r(n) under
standard conditions of 25 o C, 1 atm pressure and unit activities, in turn estimated by the
sum of the Gibbs free energies of formation of product species minus reactant species:
E roev(n) = −
∆G r(n)
zF
=−
i
Š
1 X€
pr od.
∆G f
− ∆G rf eac t.
zF m=0
(A.8)
Mackinawite, FeSm
Mackinawite has been proposed to form on bare iron or steel via the sequential chemisorption of SH- ions and the following anodic discharge reactions. [20]
−
Fe(s) + H2 S + H2 O ⇔ FeSH ads
+ H3 O+
−
+
FeSH ads
⇔ FeSH ads
+ 2e−
The species FeSH+ can be incorporated directly into the growing layer of mackinawite via:
115
Table A.4: Mackinawite-Fe-H2 O system equilibrium reactions.
No. Reaction
10
Erev , pH or K
+
FeSm + 2H + 2e ⇔ Fe + H2 S(aq)
−
+
2.3RT
2F
log (a
2
H+ )
log (a
2
2
H2 S ) (aH + )
log (a
2
3
H2 S ) (aH + )
11
Fe2 O3 + 2H2 S(aq) + 2H + 2e ⇔
2FeSm + 3H2 O
E r ev(11) =
−
2.3RT
2F
12
Fe3 O4 + 3H2 S(aq) + 2H + + 2e− ⇔
3FeSm + 4H2 O
E r ev(12) = E roev(12) −
2.3RT
2F
13
FeSm + 2H + ⇔ Fe2+ + H2 S(aq)
pH = − 12 log
14
Fe(OH)2 + H2 S(aq) ⇔ FeSm +
2H2 O
K14 =
−
aH2 S
E r ev(10) = E roev(10) −
E roev(11)
€a
Fe2+ aH2 S
1
1
Š
K13
1
aH2 S
Table A.5: Pyrrhotite-Fe-H2 O system equilibrium reactions.
No. Reaction
Erev or pH
+
aH S
20
−
FeS p + 2H + 2e ⇔ Fe + H2 S(aq)
E r ev(20) = E roev(20) −
2.3RT
2F
log (a+2)2
21
Fe2 O3 + 2H2 S(aq) + 2H + + 2e− ⇔
2FeS p + 3H2 O
E r ev(21) = E roev(21) −
2.3RT
2F
log (a+ )2 (a1
Fe3 S4 + 2H + + 2e− ⇔ 3FeS p +
H2 S(aq)
E r ev(22) = E roev(22) −
2.3RT
2F
log (a+2)2
22
23
FeS p + 2H + ⇔ Fe2+ + H2 S(aq)
pH = − 12 .log
€a
Fe2+ aH2 S
H
H
2
H2 S )
aH S
H
Š
K23
Assume mackinawite → pyrrhotite in solid state reaction
+
−
FeSH ads
⇔ FeS1−x(aq) + xSH(aq)
+ (1 − x)H +
However, for the purposes of a simplified stability diagram, we can assume a series of overall equilibrium mackinawite formation reactions such as a direct, solid state
reaction (i.e. electrochemical reaction, No. 10 in Table A.4) or solution-phase precipitation (i.e pure chemical reaction, No. 13 in A.4). Other possible formation reactions of
mackinawite are also listed in Table A.4.
Pyrrhotite, FeSp
It is assumed that pyrrhotite forms by direct, solid-state transformation from mackinawite. Since FeSp is the more thermodynamically stable phase, this reaction will occur spontaneously under all conditions in which mackinawite initially forms and greigite/pyrite are unstable. Therfore addition of FeSp to the consideration of a Fe-H2 S-H2 O
system Pourbaix diagram will necessarily displace macknawite. In reality, sluggish kinetics of the solid state transformation can "stabilise" mackinawite to long times observed
in experiment and in the field, especially at low temperatures and H2 S partial pressures,
illustrating the major shortcoming of overreliance on thermodynamic stability diagrams
for corrosion product prediction. The other equilibrium reactions involving pyrrhotite
are listed in Table A.5.
Pyrite, FeS2
The reactions involving pyrite used for construction of the final stability diagram (incorporating all the considered Fe-S phases) are listed in Table A.6.
116
Table A.6: Pyrite-Fe-H2 O system equilibrium reactions.
No. Reaction
Erev
+
(aH2 S )2 (a Fe2+ )
24
FeS2 + 4H
2H2 S(aq)
+
E r ev(24) = E roev(24) −
2.3RT
2F
log
25
FeS2 +4H + +4e− ⇔ Fe+2H2 S(aq)
E r ev(25) = E roev(25) −
2.3RT
4F
log
E r ev(26) =
−
2.3RT
2F
log
E r ev(27) = E roev(27) −
2.3RT
2F
log (a+2)2
aH2 S
+ 2e
−
⇔ Fe
+
2+
26
2FeS2 + 3H2 O + 2H + 2e
Fe2 O3 + 4H2 S(aq)
27
FeS2 + 2H + + 2e− ⇔ FeSm +
H2 S(aq)
28
29
30
−
⇔
E roev(26)
+ )4
(aH
(aH2 S )2
+ )4
(aH
(aH2 S )4
+ )2
(aH
aH S
H
FeS2 + 2H + + 2e− ⇔ FeS p +
H2 S(aq)
E r ev(28) = E roev(28) −
2.3RT
2F
log (a+ )2
FeS2 +4H + +e− ⇔ Fe3+ +2H2 S(aq)
E r ev(29) = E roev(29) −
2.3RT
F
log
E r ev(30) =
2.3RT
4F
+
3FeS2 + 4H + 4e
2H2 S(aq)
−
⇔ Fe3 S4 +
117
E roev(30)
−
H
log
(aH2 S )2 (a Fe3+ )
+ )4
(aH
(aH2 S )2
+ )4
(aH
118
Appendix B
Chemical Vapor Deposition of
Fe-S
B.1
Motivation
A chemical vapor deposition (CVD) system was set up to fabricate thin films of pyrrhotite
(Fe1-x S), with the primary objective of using them for tracer diffusion studies. To this
end, we aimed to make high-purity films supported on non-ferrous substrates that
would simulate a thin pyrrhotite corrosion scale on the order of several hundreds of
nanometers thick. Besides pyrrhotite phase purity, it was desirable to investigate a film
growth technique that could allow control over stoichiometry and that produced samples with low surface roughness. A set of samples fabricated via CVD were used in
initial diffusion studies for this thesis, the results of which are presented in Appendix
3. The work described here constitutes an initial, empirical investigation into the effects of deposition parameters (substrate temperature, precursors, flow conditions) on
film chemistry and morphology. In this appendix, we describe the setup of a homemade
CVD system and the fabrication of different iron sulfide films through the use of combinations of various substrates and organic Fe and S precursors, and as a function of
substrate temperature. Finally, we introduce the "template stripping" technique that
was used to make Fe-S samples with atomically-flat smoothness. Several potential applications of combined CVD/template stripping approach facilitated by this work include:
• deposition of ultrathin Fe-S (or other similar sulfides e.g. Ni-S, Co-S, etc.);
• atomically-flat, polycrystalline samples for STM studies;
• surface patterning: surface plasmonics with chalcogenides.
B.2
Methods: CVD setup and apparatus
A schematic of the CVD apparatus is shown in Figure B-1a, along with a photograph
of the equipment in Figure B-1b. The entire system was constructed in a fume hood to
avoid any exposure to toxic precursors. The flow of inert gas (Ar or N2 -5% H2 ) through
the system was controlled electronically by Omega FMA-series mass flow controllers
(MFCs). The various iron and sulfur precursors used in this work are described in Figure
B-2: iron (III) acetylacetonate (Fe(acac)3 ), iron pentacarbonyl (Fe(CO)5 ), di-tert butyl
disulfide (TBDS), tert butyl methyl-sulfide (TBMS) and hydrogen sulfide (H2 S). Liquid
precursors were kept in glass vials. Stainless steel tubes, connected to the gas lines
via 14 -inch Swagelok fittings, passed through a rubber bung in the vial to carry the
precursor vapor into the furnace. The inlet gas tube was not submerged beneath the
119
liquid; due to the relatively high vapor pressures it was sufficient to simply have the gas
passing through the vial containing the liquid precursors. When the solid iron precursor
Fe(acac)3 was used, approximately 20 g of powder was placed in a stainless steel tube,
which was wrapped in heating coils powered by an automatic temperature controller
to achieve the desired setpoint. The substrate was placed on an 10 o inclined Al2 O3
holder in a quartz tube placed inside a Thermo Scientific Lindberg Blue M Mini-mite
tube furnace. Homemade stainess steel compression fittings served as gas inlet/outlet
seals to the quartz tube. The temperature variation from the front to back ends of the
tube inside the furnace was up to 200 o C. The actual temperatures measured uisng
a thermocouple at various positions along the furnace are shown in Figure B-1c, for
furnace setpoint temperatures of 300-600 o C. The deposition temperatures reported
henceforth refer to this calibration. Finally, the exhaust was scrubbed by bubbling at
the surface of a bleach solution before being sent up the stack of the fume hood.
Various substrates were used, including polished, 5 x 5 mm2 SiO2 (y-cut) and MgO(100)
(both from MTI Corp., Richmond CA), cleaved Muscovite Mica sheets and NaCl crystals
(both from SPI supplies, West Chester PA) and cut, soda-lime glass slides (VWR Int.,
Radnor PA). In a typical deposition run, the substrate was placed in the furnace in the
desired position and heated under flowing inert gas. Five minutes prior to the start of
the deposition, the vessels containing the Fe and S precursors were flushed with inert
gas at the desired flow rate to remove any residual oxygen. The liquid precursor flow
during flushing was diverted directly to the exhaust. To begin deposition, a three way
valve was switched to redirect the liquid precursor into the furnace.
B.3
Results
Table B.1 lists a range of conditions used in several prior CVD syntheses of iron sulfides by other authors. Generally, the target composition was FeS2 for applications in
photovoltaic adsorbers. In the following, we describe the phase composition, purity
and morphology of sample deposited using different precursors and under the range of
conditions outlined in Table B.2. First, a combination of Fe(acac)3 and TBDS was used,
producing iron disulfide (FeS2 ) films with substantial carbon contamination. To mitigate this, we switched to Fe(CO)5 as an iron source. Finally, to produce monosulfide
(Fe1-x S) films, we switched TBDS for TBMS and finally H2 S, both of which contain a
single sulfur atom as opposed to a S-S dimer.
Fe(acac)3 and TBDS: mostly FeS2
The initial setup we used was similar to that described by Berry et al., using Fe(acac)3
and TBDS sources. [198] Figure B-3 shows the phase identification and SEM micrographs of as-deposited films using this setup, as evidenced by Raman spectroscopy (Fig.
B-3a) and x-ray diffraction (Fig. B-3b)a. Pyrite has Raman peaks at 337 and 370 cm-1
while marcasite is characterized by resonances at 321 and 384 cm-1 . Pyrrhotite (Fe1-x S)
has no Raman resonance. At a substrate temperature of 280 o C, the predominant phases
present were pyrite and marcasite (both FeS2 . Increasing the substrate temperature to
400 o C increased the volume fraction of marcasite relative to pyrite. At lower temperatures, the deposition of the disulfide phases is facilitated by the pre-existence of a
sulfur-sulfur bond in the TBDS. To obtain pure pyrite films, the as-deposited samples
were post annealed in sealed and evacuated quartz tubes containing a small amount of
sulfur powder, removing any trace of metastable marcasite phase. Finally, at higher temperatures beyond 400 o C, the stability limit for FeS2 is reached and increasing amounts
of pyrrhotite were deposited. At 600 o C, pyrrhotite was the only iron sulfide phase observed.
120
(a) Schematic of original CVD apparatus
MFC’s
Fe(acac)
150oC
O-ring
seals
Furnace 300-600oC
MFC 1
MFC 2
MFC 3
Vent
Ar
Mesh to mix Substrate holder Exhaust
gases
Scrubber
inclined 10o
d-TBDS
50oC
(b) CVD apparatus without heating coils for precursors
MFC’s
Precursors
Furnace
Exhaust
(c) Temperature variation across furnace
Measured temperature (oC)
700
Tset = 600 oC
600
Tset = 500 oC
500
Tset = 400 oC
400
Tset = 300 oC
300
200
100
0
2
4
6
8
10
12
14
Sample position (inches from gas inlet)
Figure B-1: Home-made Chemical Vapor Deposition (CVD) system: (a) schematic drawing of setup for
solid iron (III) acetylacetonate (Fe(acac)3 ) and liquid di-tert-butyl disulfide (d-TBDS) sources. (b) photograph
of setup in fume hood, indicating the position of the components drawn in the schematic. (c) the furnace
temperature was not uniform; the graphs shows the variation as a function of position from the gas inlet of
the furnace tube, for furnace set temperatures of 300, 400, 500 and 600 o C.
Carbon contamination from Fe(acac)3
However, the use of Fe(acac)3 and TBDS as precursors led to the contamination of the
samples with carbon. Figure B-4 indicates the amount of carbon measured in the films as
a function of substrate temperature, as measured by electron dispersive spectrometry
(EDS) in a JEOL Supra 55 SEM. The amount of carbon deposited increases approximately linearly with increasing temperature up to ∼ 30 at% at a substrate temperature
of 550 o C. We believe the source of the carbon to be Fe(acac)3 , since it is a large, complex molecule containing fifteen carbon atoms and only six oxygens; hence the removal
121
IRON PRECURSORS
SULFUR PRECURSORS
(a) Iron(III) acetylacetonate
(c) (Di)tert-butyl disulfide [TBDS]
[Fe(acac)3]
H 3C
H 3C
CH3
S
S
H 3C
CH3
CH3
Straw-colored liquid.
Harmful to aquatic life.
(d) Tert-butyl methylsulfide
[TBMS]
Red, air stable solid.
Harmful if swallowed.
H 3C
H 3C
S
CH3
H 3C
(b) Iron pentacarbonyl [Fe(CO)5]
Straw-colored liquid.
Flammable, low toxicity.
(e) Hydrogen sulfide [H2S]
1
3
S
1
H
4
H
4
Straw-colored liquid.
Pungent gas.
Very toxic, highly flammable.
Highly toxic, highly flammable.
0
Figure B-2: Description and safety information for Fe and S precursors: (a) and (b) iron precursors.
Fe(CO)5 is toxic and requires special handling precautions; however, it is easier to control vapor flow in CVD.
(c-e) sulfur precursors. TBDS is useful for making FeS2 because it already contains a sulfur-sulfur dimer bond.
TBMS dissociates at elevated temperatures to leave an HS- reactive radical. H2 S is the cleanest S source of
all (no carbon).
Table B.1: CVD of Fe-S phases by other authors.
Fe source
S source
Substrate
T (o C)
P (Torr)
Phase
Ref.
Fe(acac)3
TBDS
Glass, Si
300 + A a)
760
Py.
[198]
Fe(CO)5
TBDS
Various
580
38
Py.
Fe(CO)5
TBDS
FeS2
475
Fe(CO)5
TBDS
Glass
475
Cp2 Fe
b)
Fe(CO)5
C3 H6
Pyrex
410
H2 S/S
Glass
140
c)
[199]
d)
[200]
38
Py.
38
Py., Po.
[201]
38/760
Po.
[202]
760
Py.
[203]
Py = pyrite; Po = pyrrhotite; a) A = post anneal in S2 at 500 o C; b) Cp = η-C2 H5 ; c) cold-walled reactor; d)
epitaxial pyrite.
122
123
Temp.
(o C)
160
0
0
Type
Fe(acac)3
Fe(CO)5
Fe(CO)5
Iron source
5-30
30
300
Flow
(sccm)
H2 S
TBMS
TBDS
Type
25
25
50-60
Temp.
(o C)
Sulfur source
350
50-180
200
Flow
(sccm)
N2 - 5% H2
Ar (400)
Ar (500)
Carrier gas
(sccm)
375-550
400-500
300-600
Substrate
T (o C)
Fe1-x S
Fe1-x S, Fe
FeS2 ,
Fe1-x S
Phases
Table B.2: Chemical Vapor Deposition conditions for Fe-S phases: literature.
20-100
20-100
100-500
Deposition rate
(nm/hr)
Best quality and purity
Fe deposits < 450 o C
C contamination > 300 o C
Remarks
(a) Fe(acac)3 and TBDS precursors: Raman spectroscopy
321
Intensity (arb. units)
384
Pyrrhotite
o
600 C
1 μm
337 370
432
Marcasite + Pyrite
400oC
Pyrite + Marcasite
o
280 C
Pyrite
o
Annealed S2 500 C
300
350
400
450
-1
Raman Shift (cm )
250
(b) X-ray diffracion of as-deposited and S2-annealed samples
Intensity (arb. units)
*
*
†
*
*
† *
*
†
* Pyrite
† Marcasite
*
*
*
As-grown CVD
o
280 C
o
Annealed in S2 500 C
20
30
40
50
60
70
Cu-kα 2Θ
Figure B-3: Iron sulfide films deposited from Fe(acac)3 and TBDS: (a) Raman spectroscopy and corresponding scanning electron microscope (SEM) images for samples deposited at 600, 400, 280 o C and a
pyrite film post-annealed in sulfur vapor at 500 o C. (b) Cu-kα x-ray diffraction patterns for as-grown marcasite/pyrite and post-annealed pure pyrite films.
of carbon through reaction to carbon monoxide or dioxide is not 100% efficient.
Pyrrhotite (Fe1-x S) films with monosulfide precursors
With Fe(CO)5 serving as the iron precursor, the sulfur precursor was changed to TBMS
(Fig. B-2d) to avoid the pre-existing S-S bond such as in TBDS, which would encourage
the formation of the disulfide phases. TBMS is a volatile but low-toxic liquid that could
be kept at room temperature during deposition. Fe(CO)5 , on the other hand is toxic and
pyrophoric liquid that requires special handling (see Appendix 4 for MSDS). Fe(CO)5 is
very volatile and dissociates readily at temperatures as low as 150 o C, and therefore had
to be maintained in an ice bucket at 0 o C to avoid excessive metallic iron deposition.
Nevertheless, as evidenced by the XRD results in Figure B-5, some pure iron phase
was deposited in films at temperatures below 450 o C. Finally, to increase the sulfide
partial pressure and ensure full reaction of the precursors, the TBMS was exchanged
for N2 - 4% H2 S gas. All films deposited in the range 300-500 o C with Fe(CO)5 / H2 S
124
Carbon contaminaton from Fe(acac)3
Carbon content (at%)
40
30
20
10
0
400
500
600
200 300
Substrate temperature (oC)
Figure B-4: Carbon contamination in Fe-S films from Fe(acac)3 : as measured by electron dispersive spectroscopy (EDS), as a function of substrate temperature during deposition.
Fe(CO)5 and TBMS precursors: pyrrhotite/iron films
Intensity (arb. units)
*
*†
*
*
*
Hex. Fe1-xS
Metallic Fe
** *
**
*
*
*
*
*
†
*
†
**
30
*
40
200 nm
450oC
†
†
400oC
*
†
†
300oC
50
60
70
Cu-k α 2Θ
80
90
Figure B-5: Iron sulfide films deposited from Fe(CO)5 and TBMS: Cu-kα x-ray diffraction patterns for
films deposited at 300, 400 and 450 o C with decreasing metallic Fe content; corresponding scanning electron
microscopy (SEM) images of the as-deposited film surfaces.
were pure pyrrhotite. Moreover, this combination of precursors also offers the "cleanest"
way to deposit FeS: i.e. without any source of carbon or other likely contamination.
The downside is the toxicity of the precursors; beyond Fe(CO)5 , hydrogen sulfide is an
extremely toxic gas that requires special precautions and handling.
In Figure B-6 we show SEM micrographs of the top surface from samples deposited
using Fe(CO)5 / H2 S on glass (Fig. B-6a), muscovite mica (Fig. B-6b and c) and NaCl
(Fig. B-6d). The choice of substrate had little obvious effect on the morphology of the
as-deposited Fe1-x S; in all cases the grains were roughly equiaxed with sizes between
several hundreds of nm and one µm. Finally, the exact stoichiometry of the films could
not be measured due to their thickness being on the order of 100-1000 nm. The signal
from conventional chemical composition techniques, e.g. EDS, was not strong enough
to give adequate counting statistics and distinguish the Fe:S ratio within the Fe1-x S composition of 0 ≤ x ≤ 0.125.
125
Fe(CO)5 and H2S precursors:
(a) Glass substrate
(b) Mica substrate
1 μm
(b) Mica substrate
3 μm
(d) NaCl substrate
1 μm
200 μm
Figure B-6: Iron sulfide films deposited from Fe(CO)5 and H2 S: scanning electron microscopy (SEM)
images of films deposited on (a) glass slide, (b and c) mica, (d) NaCl(100) substrate.
Template stripping for atomically-smooth surfaces
The root-mean squared (RMS) roughness of as-deposited films using Fe(CO)5 / H2 S precursors (Fig. B-7a) was on the order of 50+ nm, as measured by atomic force microscopy
(AFM). Given the original motivation of the CVD project to produce thin film samples
for tracer diffusion studies, a surface roughness of this order (i.e. greater than the target
tracer deposit thickness of 10 nm) was not conducive to obtaining accurate diffusion
profiles. Therefore we explored ways to make the films smoother. By vastly reducing the
Fe precursor flow such that the overall deposition rate was just a few nm per hour, the
films could be fabricated with RMS roughness < 10 nm. However, this approach was
impractical for making samples with total thickness of 100 nm or more. Therefore we
employed the template stripping technique, which has been used to make "ultrasmooth",
patterned metal films for surface plasmonics [204] or flexible electrodes [205] or TiO2
for various applications. [206] The procedure is outlined in Figure B-7c: the as-grown
film is coated with an epoxy resin, onto which a glass piece is pressed to remove air
bubbles. The epoxy is left to set for the requisite time, before removing the original
substrate using the edge of a razor blade. Due to the low surface energy and chemical
incompatibility of the substrates (oxide substrates to sulfide films), the CVD film preferentially adheres to the epoxy, exposing the side grown directly onto the polished or
atomically-flat, cleaved substrate surface (Fig. B-7b). This technique worked well on a
variety of substrates. An alternative that was also attempted was to deposit on NaCl
crystals, and wash away the NaCl using distilled water after supporting the FeS film on
a glass slide with epoxy. Although also successful, this technique was not as clean as the
oxide substrate version.
126
(b) Smooth side
(a) As-deposited surface
2 μm
(c) Template stripping process
Grow film on
flat substrate
Strip from substrate
Coat with high
with razor blade
temperature epoxy
Figure B-7: Template stripping for ultrasmooth sulfide surfaces. Scanning electron microscopy (SEM)
images of (a) as-deposited surface (Fe(CO)5 / H2 S) and (b) template stripped (inverted) surface, as grown
on polished SiO2 . (c) schematic of the template stripping process.
127
128
Appendix C
Diffusivity measurements using
thin film samples
Before turning to bulk, natural samples to obtain the diffusivity measurements in this
work, we carried out preliminary tests using synthetic thin film Fe1-x S samples, fabricated by either chemical vapor deposition (CVD) or sputter deposition. Shown in Figure
C-1, iron self-diffusivity values measured from thin film samples were inconsistently low
as compared to data from literature or from our bulk samples measured in this work,
and hence were not reported in the main text of this paper. Below, we briefly report
how the films were fabricated, describe the diffusion measurement results, and discuss
the likely sources of the disparate results.
Chemical Vapor Deposition of Fe1-x S films
CVD films were grown on soda lime glass pieces according to the procedure outlined in
Appendix 2, using Fe(CO)5 and H2 S as precursors. As-deposited films were on the order
of 300-700 nm thick. In order to obtain flat surfaces for SIMS analysis, we employed
the template stripping technique. [204, 206] The as-grown film was coated in a hightemperature epoxy (stable up to 350 o C), and covered with another glass piece, slightly
larger than the substrate size. After curing, the glass piece was removed with a razor
blade, and the film preferentially adhered to the cured epoxy, stripping cleanly off the
original growth substrate and revealing a surface conforming to the substrate’s original
topography. Various polished substrates such as MgO(100), SiO2 , Si and soda lime glass
were experimented with; soda lime glass was found to give satisfactory results at the
lowest cost. The x-ray diffraction (XRD) pattern of a typical CVD template stripped film
is shown in Figure
Sputter deposition of Fe1-x S films
Sputter deposited films were made according to the procedure outlined in Chapter 2.
The XRD pattern is shown in Figure
Thin film diffusion measurements: results and discussion
Both CVD and sputtered film samples were coated in 10 nm of 57 Fe using thermal evaporation. Annealing runs to produce diffusion profiles were performed by holding the
samples in heated nitrate salt baths held at the desired temperature. Samples were
vacuum-sealed in quartz tubes during immersion in salt baths. SIMS analysis to obtain
diffusion profiles of the annealed samples was as described in the main text. To fit the
data, we used the thin film diffusion solution to Fick’s second law [70]:
129
Full Fe self-diffusion results from Ch. 2 and for thin films
Temperature (oC)
-5
10
900 700
500
400
300
200
150
-10
10
Literature
Fryt *
log[*D
Fe
-
1
] (cm 2 s )
0.94 eV
Condit **
Linear reg.
-15
10
-20
10
0.5
This work
Bulk crystal
Model fit
CVD
Sputtered
1
1.5
2
2.5
-1
1000/T (K )
Figure C-1: Iron self-diffusivity * DFe measurements obtained from thin film, chemical vapor
(CVD) and sputter deposited samples (triangles), alongside the literature data and bulk sample measurements discussed in the main text. Our thin film measurements fall up to 3-4 orders of
magnitude lower than the bulk sample results. We attribute the discrepancy to oxide formation
from residual oxygen during annealing runs, which binds the 57 Fe deposit as iron oxide and hence
reduces the extent of interdiffusivity (discussed in the text below).
C(x, t) =

‹
Co
a−x
a+x
er f p
+ er f p
2
2 Dt
2 Dt
(C.1)
where Co is the concentration at the surface, a is the original deposit thickness, and D
is diffusivity. In the limit of a very thin film, a Gaussian approximation to Eq. (C.1) can
be given:
x2
C(x, t) = p
exp −
4Dt
4πDt
N
(C.2)
Figure C-3 shows selected results from thin film profile measurements. For CVD samples
(Figures C-3a), we used Eq. (C.2) to fit the results. In Figure C-3b we re-plot the data
as C vs. x2 , obtaining a straight line from which diffusivity D was calculated. For the
sputter deposited samples, we fit the results using Eq. (C.1).
The results of our thin film diffusion experiments are presented in Figure C-1, alongside the literature values and the bulk sample results, as discussed in the main text.
Although the slope, i.e. activation energy Q, is consistent with the bulk sample result in
the ordered regime below T N , the thin film diffusion coefficients are shifted down by 3-4
orders of magnitude. This difference cannot be explained on the basis of difference in
stoichiometry alone (which would only account for approx 10x difference: see Figure 1b
130
XRD of thin film samples
(100)
(110)
Intensity (arb. units)
(101)
(102)
(004)
(200)
CVD
Sputtered
30
40
50
Cu-k α 2 Θ
60
70
Figure C-2: X-ray diffraction of thiin films for ECR experiments. (a) Cu-kα x-ray diffraction
(XRD) scans for chemical vapor (CVD) and sputter deposited films, with hexagonal pyrrhotite
reflections indicated. (b) scanning electron microscope (SEM) of sputtered film top surface, after
post-annealing treatment (inset: 60 o tilted view). (c) pole figure XRD scans confirm the high
(100) texture of the sputtered samples.
in the main text). Still, a very low iron vacancy concentration would be expected after
annealing due to the high volume of pure 57 Fe deposit relative to Fe1-x S in the interdiffused region, that would put * DFe values on the lower limit of the stoichiometric effect.
We postulate a further reason for the vastly reduced diffusion coeffieicents: oxidation of
the 57 Fe deposit from residual oxygen during annealing. The quartz tubes used to seal
the samples during diffusion runs in salt baths were evacuated to ∼ 10-3 Torr, and the
sample surface after annealing typically turned from metallic silver to a blue tinge. We
performed a control test using a sample annealed under a dynamic flowing atmosphere
of 1% H2 S-N2 , where the amount of available oxygen was practically nil. The results
are presented in Figure C-4, for two samples (original 57 Fe deposit thickness = 30 nm)
annealed at 185 o C. Despite being held for a much shorter time of 5 days compared to
25 days, the sample annealed in the H2 S furnace had a completely flat [57 Fe] profile,
indicating that all the deposit had fully diffused through the specimen. Upon removing
the sample from the furnace after 5 days, the surface was found to still be metallic silvery in color. Conversely, even after 25 days in the quartz vial, the other sample showed
a much lesser extent of diffusion. Moreover, the surface coloration evolved into a blue
lustre, indicative of iron oxide formation at the surface.
In conclusion, we believe two compounding factors lead to an underestimate of * DFe
from our measurements on thin film samples annealed in evacuated quartz vials. First,
the residual oxygen in the vials reacted with the 57 Fe deposit surface and tied it up as
oxide, preventing rapid interdiffusion with the pyrrhotite substrate. Second, the lack of
available sulfur in the atmosphere to react with the deposit meant that vacancies in the
samples were "flooded" with Fe, making the samples highly iron-rich. Since Fe diffusion
in Fe1-x S occurs via a vacancy-exchange mechanism, removing vacancies would have an
additional effect on reducing measured diffusion coefficients. After these initial trials
with thin film samples, we decided to utilize bulk natural crystals (giving the results
outlined in the main text) rather thanto further pursue thin films annealed under dynamic, H2 S-containing environments. The reason was that for thin tracer deposits of
10’s of nm, the required annealing times to achieve measureable diffusion profiles became impractically short (on the order of seconds). For bulk samples, a much thicker
131
(a)
(b)
Diffusion profiles for CVD films
0.35
-1
CVD FILMS
0.3
CVD FILMS
-1.5
o
Annealed at 250 C
3600s
Annealed at 250 oC
-2
ln[ Fe]
36000s (10 hrs)
0.2
57
511440s (>5 days)
57
[ Fe]
0.25
0.15
-2.5
-3
0.1
-3.5
0.05
0
0
(c)
Fit to Gaussian diffusion solution
40
80
120
Depth (nm)
-4
200
160
(d)
Diffusion profiles: constant temperature
0
0.2
0.4
0.6
4
2
x 2 (nm x 10 )
0.8
1
Diffusion profiles: constant anneal time
0.8
SPUTTER DEPOSITED FILMS
0.8
0.7
o
% Fe
57
0.6
0.5
0.6
Fit D = 1.6 x 10-15
Fit D = 1.1 x 10-15
Fit D = 1.4 x 10-15
57
360 s
1200 s
3600 s
36000 s
% Fe
0.7
0.4
Annealed 1 hour
0.5
275 oC
300 oC
315 oC
Fit D = 3.5 x 10-16
Fit D = 1.1 x 10-15
Fit D = 1.4 x 10-15
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
SPUTTER DEPOSITED FILMS
Annealed at 300 C
20
40
60
Depth (nm)
80
0
0
100
Figure C-3: Representative diffusion profiles of
50
Depth (nm)
100
57
Fe in thin film Fe1-x S, measured by secondary
ion mass spectrometry (SIMS) for: (a, b) chemical vapor deposited (CVD) samples annealed at
250 o C for different lengths of time as indicated, fit to the Gaussian solution in Eq. (C.2); (c) sputter deposited samples annealed at 300 o C for different times, fit with the thin film error function
solution in Eq. (C.1); (d) sputter deposited films annealed for 1 hour at different temperatures,
as displayed.
depost of tracer can be made, allowing more reasonble annealing experiments on the
order of minutes-hours.
132
Surface oxidation of thin films reduces diffusion
1
185 oC 25 days
Quartz vial
0.6
185 oC 5 days
H2S furnace
[
57
Fe]
0.8
0.4
0.2
0
0
20
40
60
80
100
x (nm)
Figure C-4: Oxidation of samples annealed in quartz vials.
57
Fe diffusion profiles measured for
two identically-produced Fe1-x S samples annealed at 185 C inside an evacuated quartz vial, or
under a dynamic H2 S-bearing envionment, as indicated. The quartz vial sample turned a blue
lustre, whereas the furnace annealed sample retained its original silvery metallic surface.
o
133
134
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