Complete research publication
Thematic part : Molecular model simulation.
Registration code of publication: 12-29-1-80
Subsection: Metallurgy.
Publication is available for discussion within permanent
functioning internet-conference: “Butlerov communication ”. http://butlerov.com/readings/
UDC 669.88:537.562. Submitted into editorial office on December 10, 2011 year.
Molecular-dynamics analysis of liquid Niobium with Iron and
Hydrogen impurities structure
© Pastukhov Eduard Andreevich, Vostrjakov Andrey Alexeevich,*
Sidorov Nikolay Ivanovich+ and Chentsov Victor Pavlovich
Laboratory of the metallurgical melts physics chemistry. Institute of metallurgy UrD RAS.
101, Amundsen st. Yekaterinburg, 620016. Russia. Tel.: (343) 267-88-93. E-mail: nik@imet.mplik.ru
_______________________________________________
*Leader of the theme; +Correspondence support
Keywords: short order, molecular dynamics, Niobium, Hydrogen mobility, diffusion, radial distribution
function, melt.
Abstract
Molecular dynamic simulation method is used for estimating of Hydrogen and Iron diffusion factors in
the Niobium melts. Experimental results are compared to literary data on impurities removal from Niobium
melt with Hydrogen applying in the plasma-arc melting as well as vacuum-arc melting processes. Electric
field influence to the Iron removal is estimated.
Introduction
Such properties as infusibility, ability to heat resistance alloys formation as well as magnetic,
corrosion resistance alloys, getter properties, small cross-section capture of the thermal neutrons,
small electron output work allows to consider Niobium as one of perspective metals of future.
Niobium superconductivity at low temperatures increases depending on interstitial impurity removal.
More effective Niobium membranes producing for Hydrogen separation from gases is possible rather
than in the case of Palladium alloys. Besides Niobium alloys are characterized by low net cost. Iron
and Niobium diffusion factors depending on electric field intensity and Hydrogen presence in the
Niobium melt is analyzed in given work using molecular dynamic method. Electron beam melting
(EBM) and plasma-arc melting (PAM) of Niobium melt as well as impurities electro-migration in
Niobium are analyzed as well.
Experimental part
Computer experiment. Molecular dynamic (MD) method simulation is carried out using
microcanonical (NVT) ensemble. The method is used for Iron and Hydrogen ions behavior research in molten
Nb-Fe-H alloy at temperature Т = 3200 К under electric field. Model system was presented by 1000 Niobium,
60 Iron and 10 Hydrogen particles in cubic cell. Periodic boundary conditions have been used in calculations.
Integration of the motion equation is carried out by time steps 1.1·10-15 s using Verlet scheme [1]. The
particles of system have been located randomly in the base MD-cell before simulation start. Inter-particles
potentials were taken from [2, 3] publications. The temperature of system was defined from total kinetic
energy of system. Niobium, Iron impurities and Hydrogen diffusion factors D were calculated basing on
mean square displacement of the model particles using following formula: <R2(t)>) = 6·D·t, where t is
current time.
Short order of the disordered systems is described by the radial distribution function g(r) of atoms
(RDF), which defines any atom location probability on r distance from the given atom. Short order structure
of liquids only pair interaction and outer field influence is taken into account in MD computer simulation.
Interaction between two particles depends only on the interparticle distance in this situation.
Comparison of the liquid Nb structure computer simulation results with experimental data is impossible
due to its absence in published science literature.
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80
MOLECULAR-DYNAMIC ANALYSIS OF LIQUID NIOBIUM WITH IMPURITY…………………._____ 80-83
Results and its discussion
Fig.1 demonstrates g(r) for Nb and Nb-Fe-H melts at 3200 K temperature, obtained by MD
method. It should be noted, that most probable interatomic distance (0.258 nm) in the first
coordination sphere for molten Niobium (curve 1) approximates to the covalent radii sum (0.134 nm)
of Niobium atoms. Small hump is observed
on the g(r) curve for Nb melt on the second
maximum left side. This data comparison to
related values for Niobium crystals (a =
0.3301 nm and Z = 12) proved, that melting
go with considerable short order change, and
hence interatomic bond character as well.
Impurities Fe and H to Nb, as shows curve 2,
lead to considerable decreasing of first
maximum height, its widening and
displacement to the side of lower values of r.
First coordination sphere depends on
dimensions of atoms included into the alloy
content. Niobium atoms have maximal
dimension (0.144nm), minimum – Hydrogen
Fig.1. Radial distribution function g(r) of Nb (1) and
atoms (0.046 nm), mean – Iron atoms (0.126
Nb-Fe-H (2) melts at Т = 3200 К temperature; MDnm). First maximum shift of g(r) to the low
model.
angles side in the Nb-Fe-H system is related
to decreasing of the first coordination sphere radius. Such changing can be explained by considerable
changing of the interatomic interaction forces.
Fig. 2. demonstrates model system with Iron and Hydrogen evolution based on «momentary
snapshots». Several phases of the system developments can be identified during its evolution from
liquid state to state of small number of agglomerated particles. Fig. 2 demonstrates Niobium atoms
migration in melt volume during 3ps time, when atoms agglomerate and form «islets». This process is
stochastic character. Therefore «islets» are different by size and distributed in volume irregularly. Majority of
the primary particles have been agglomerated into large clusters already non spherical form (fig. 2b) at the
final stage of simulation. Since clusters have been formed due to «covering» of formed outer cavities, then
clusters size increasing, seemingly, is related to its surface increasing. It was found, that process time
increasing to t = 5 ps, structure of Niobium–Iron–Hydrogen melt, in the most part have been
forming into elliptic large clusters (fig. 2.) with Iron atoms inside and Hydrogen atoms round it.
Most size cluster, shown on fig. 2b, contains 80% of all atoms in system under simulation.
a)
b)
Fig. 2. Evolution of liquid Niobium with Iron and Hydrogen MD model at T = 3200 K.
a) for time t = 3 ps, b) for time t = 5 ps.
Fig. 3 presents MD model evolution for liquid Niobium with Hydrogen at t = 10 ps and T = 3200 К.
During 10 ps «islets» from Nb atoms became equal size and form structure similar to ordered one. The majority
of clusters to this time are disappeared and 90% of all Nb atoms are located in the clusters with no more than 200
atoms size.
©Butlerov Communications. 2012. T. 29. №1.____________E-mail: jornal.bc@gmail.com_____________________ 81
Complete research publication Pastukhov E.A, Vostrjakov A.A, Sidorov N.I and Chentsov V.P.
As a result, configuration is formed, containing five regularly located Niobium clusters. Possible long range
order in the molten Niobium can be proved also by experimental data on Niobium density in transition from
solid to liquid state [4]: melting jump is absent on density curve.
Simulation shows, that at 10 ps in molten Nb exist clusters, containing only Nb atoms, and Hydrogen
atoms are located among its. Inter-cluster space does not contain Nb atoms; this fact can prove absence of
Niobium-Hydrogen interaction in the melt.
Fig. 3. Evolution of MD model for liquid
Niobium with Hydrogen without Iron
at t = 10 ps and T = 3200 K.
Fig. 4. Dependence of DNb and DFe on Iron (mas. %)
concentration by MD calculation (without Hydrogen
and electric field applying).
Analogously to simulation of Silicon with Oxygen [5], inter-cluster atoms structuring is observed for
liquid Nb in our case. Structuring exists only in Nb without Iron and Hydrogen impurities. Appearance of Fe
and Nb atoms leads to disappearance of rigorous inter-cluster structuring. All these facts prove liquid Niobium
obtaining qualitatively other structure relatively to crystal state at absolute removal of Iron impurities.
Iron and Niobium diffusion factors in the Niobium melt at 3200K temperature with electric
field and without it are calculated basing on computer simulation. As MD simulation results prove,
electric field (600 V/m) applying to Niobium melt decreases Niobium diffusion factor from 4.97∙10-5
to 1.28∙10-5 cm2∙s-1. Electric field intensity increasing
from 600 V/m to 1200 V/m does not lead to DNb
changes. The results of DFe and DNb calculations in
molten Niobium depending on Fe concentration (c) is
illustrated by fig.5.
Diffusion coefficient of Nb decreases
according to Fe − concentration in Niobium
increasing (fig. 4). Hydrogen inducing into Nb-Fe
system leads to decreasing of DNb to value 1.38∙10-5
cm2∙s-1. Electric field increasing from 600 to 1200
V/m does not change value of Niobium diffusion
coefficient 1.38∙10-5 cm2∙s-1.
We carried out calculation of Iron removal rate
Fig. 5. Dependence of log(L,M) at T = 3200 K
from Niobium considering Iron concentration
on Iron impurity concentration decreasing in
decrease at beginning middle and finish stage of
PAM process. Curve 1 – Langmurian (logL)
plasma arc melting process (PAM) with Hydrogen
and curve 2 – data [6].
using experimental data [6]. We calculated
evaporation intensity L(g/cm2) by Langmuir equation for mean Fe concentration for 15, 90 и 150
minutes of melting [6]. It should be noted (fig. 5), that Fe evaporation intensity from Nb melt
according to Langmuir equation coincides with experimental data for PAM [6].
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Vol.29.No.1.P.80-83.
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Communications.
2012
We estimated diffusion layer thickness (x) by equation [7] using experimental dependence CFe
on time [6] and diffusion coefficient DFe, calculated by MD method
 x 
Cx ,t  C0 
,
2 D t 
Fe 

where х is diffusion layer thickness, t – refining time,
C0 and Сх,t – impurities concentration in an initial and refined niobium.
Obtained x values for three above indicated time intervals are equal to: 4.8∙10-2, 1.95∙10-2 and
1.67∙10-2 cm. Diffusion layer thickness is close to data [8] by order of value.
Conclusions
1. Diffusion coefficients for Nab and Fe dependence on Fe content in Nab by molecular dynamic
method are calculated.
2. Evaporation of Fe from liquid Nab is described by Langmuir equation satisfactorily. Proper
calculations for 3200K are in good agreement with experimental data on Fe removal from Nb.
3. Structuring of Nb atoms in liquid Nb-H system is proved by molecular dynamic method.
Structuring disappears with Fe and H atoms appearance between Nb atoms
Acknowledgements
Research is carried out with financial support of Minobrnauka. Government contract
16.552.11.7017. Equipment of CKP «Ural- M» is used.
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