Molecular Dynamic Simulation of Short Order and Hydrogen Diffusion in the Disordered Metal Systems

Main concepts of Hydrogen permeability (HP) mechanism for the pure crystal metals are already stated. There are well-founded theoretical models and numerous experimental researches. As far as disordered systems (in which Hydrogen solubility is much more, than in crystal samples) are concerned, such works appear to be comparatively recent and rare. Particularly, they are devoted to Hydrogen interaction of with amorphous structures. Deficiency of similar researches is caused by thermo-temporal instability of amorphous materials structure and properties.

by the other metals additives.In the plasma-arc (PAM) and electron beam (EBM) refining melting of the Nb, Zr, Ta, etc. metals, the necessity of impurity elements (especially hydrogen and iron) transport research in such melts arises.Electric and magnetic fields affect to liquid metal and its impurities during melting have been indicated in the number of researches as well.
Therefore research of an electric field intensity affect to the impurity elements transport properties in the liquid metals is very urgent.
Amorphous and liquid systems based on Fe, Pd, Zr, Ta, Si with and without Hydrogen researches are presented in this work.Short order structure experimental results and molecular dynamics simulations are considered.Partial structure factors, radial distribution function of atoms, its mean square displacement and diffusion factors are calculated.Hydrogen concentration affect to its mobility and short order parameters in the system are analyzed.Electric field intensity affect to liquid metals are compared with literary data on impurities removal from Zr and Ta in plasma-arc melting in the Hydrogen presence.

Molecular dynamics calculation method
Molecular dynamics method (MD) had been primary proposed in (Alder & Wainwright, 1959).The method allows particles real-time motion analysis using classic equations.So far it's the only numeric method for dens medium dynamic research.Generally accepted nowadays MD calculation scheme is the following.A system consisting of several hundred particles with the given interparticle interaction potential is considered.Classic equations of the particles motion are numerically resolved using Verlet algorithm (Verlet, 1976).It calculates i-particle coordinate on the following (k+1)-step by coordinates on given k-and previous (k-1)-steps.

() ( ) (1 ) ( )(1 ) i ii i
Fk t rk rk rk m Where r i -radius-vector of particle, m -its mass, F i -resultant force and Δt -time step.Velocity doesn't take part in calculation.Other algorithms of motion path calculation are considered in (Polukhin & Vatolin 1985).Periodic boundary conditions are used in motion equation solution, i.e. if some particle with p i -momentum exits through cube face, then other particle with the same momentum enters through opposite face symmetric relatively plane in the center of cube.Interaction in the MD models is defined as the pair interaction potentials resultant force in the pair approximation models.Temperature of system is defined basing on its total kinetic energy.Diffusion factors are calculated from mean square displacement of the particles in model 2 () i rt by the major of steps.(2) Where <r 2 (t)> -mean square displacement of Hydrogen atoms at t -time.
Disorder systems short order is characterized by of radial distribution function of atoms g (r) (RDF) and its Fourier transform -structure factor s(k). Radial distribution function RDF Where ∆N ─ number of particles in a spherical layer thickness ∆r on r distance from the chosen particle: L ─ cube edge length of basic cell and N ─ number of its particles.Structure factor s(k) is defined by following equation: Where k is wave vector, k = (4  Sin 2Ө)/ and r m is RDF attenuation radius.
Minimum k value in the MD -experiment is inversely proportional to main cube edge and calculations for smaller k, have not physics sense.Final configuration for RDF in our calculation was chosen its constant value.This condition needs no less than 10000 steps.
Coordination number had been calculated by following formula: Molecular dynamics calculation had been done using microcanonical (NVE) ensemble.The particles of system were randomly distributed in the basis MD -cell.Interpartial potentials and its numerical value factors had been taken from works of (Varaksin & Kozjaychev, 1991, Zhou et.al, 2001, Rappe et.al, 1992).General questions of this method using had been considered in details by authors (Polukhin & Vatolin, 1985).

Hydrogen in amorphous and recrystallized Fe-Ni-Si-B-C-P alloy (experiment)
Experimental researches of Hydrogen absorption affect to structure and physical-chemical properties of transition metals (Palladium and Iron) alloys are presented by works (Pastukhov et.al, 1988).This researches indicated, that Hydrogen absorption leads to considerable shift of structure relaxation start and finish to the higher heating temperature interval.This process provokes significant modification of the amorphous (Iron based) material strength properties and leads to increased embrittlement.All mentioned changes are adequately displayed on the atoms distribution curves (fig.1), obtained from diffraction experiment data (Vatolin et.al, 1989).
Hydrogen permeability of the amorphous and recrystallized Fe based (Fe 77.333 Ni 1.117 Si 7.697 B 13.622 C 0.202 P 0.009 ) alloy membrane (25 micron thickness) was researched by stationary stream method (Pastuchov et.al, 2007).Recrystallized alloy was prepared by vacuum annealing at 400 0 from amorphous specimen.
Molecular Hydrogen injection to input side of degasified specimen at maximal acceptable temperatures (300° for amorphous and 400° for recrystallized specimens) didn't lead to noticeable output stream increase.At 10 torr Hydrogen pressure the stream achieved 3.8•10 12 sm -2 /s value.Hydrogen medium glow discharge had been used in order to delete the specimen passivation layer.Hydrogen ions, formed in glow discharge, simply penetrate to the specimen bulk (Lifshiz, 1976).We observed significant penetrating stream in this procedure.All researches have been carried out at 2 torr Hydrogen pressure, when the discharge is most stable.
Temperature dependences of the stable (stationary) Hydrogen stream had been defined for amorphous and recrystallized specimens.Lower limit of the researched temperature interval was defined as reliable stream registration possibility which had been stated as 125 0 C for amorphous and 200 0 for crystal specimens.Most impotent difference between two states of the researched alloy is observed as non-monotonic output stream increase at temperature expansion in amorphous state.Hydrogen stream stabilization has different nature in amorphous and recrystallized specimens.But both situations are characterized by rapid increase of output stream with characteristic 3060s stabilization times.Amorphous membrane is characterized by very elongated hydrogen output with 6000s stabilizing time after rapid output increase at temperatures from 125 0 C up to 225°C.Hydrogen stream dependence on inverse temperature is illustrated by fig. 2. The dependence isn't monotonous and has maximum in 200°C region.
The stream increases from 125 0 and achieves maximum 3.3•10 13 sm -2 s -1 value at 200° .Subsequent heating demonstrates anomalously sharp decrease.Second specimen follows to classic Arrhenius dependence with activation energy 17.9 kj/mol and maximum stream value 2.7•10 13 sm -2 s -1 at 375 0 C (fig. 2).Amorphization of the alloys leads to considerable free volume increasing, which increases Hydrogen permeability, solubility and diffusion.Special attention should be directed to the Hydrogen permeability changing (by order) effect with comparatively low solubility increase.This effect is explained by competition from amorphization-elements, which occupy large Bernal polyhedron-cavities, first of all in the high amorphization-elements concentration region (Polukhin et.al, 1997)."Overextended" stream yield to the stationary value evidently related to reversible diffusant capture (Herst,1962).Thus Hydrogen escape probability from the traps increases faster than capture probability.It was experimentally showed, that at temperature increase up to 200 0 C, low increase Hydrogen streams observed in reality.Its decrease begins after 200 0 C.Such behavior is proper namely for the traps with activation energies of escape and capture Е esc E cap .Penetrating stream decreasing in amorphous specimen for temperature interval from 200 0 C up to 300 0 C most probably is related to surface processes.Since penetrating stream is three orders less than incident stream to input surface (V f 10 16 cm -2 s -1 ), balance of streams is written as are streams of ion-induced reemission and thermal desorption on input side.Term C i is Hydrogen concentration in no-violated alloy structure near input surface, b i -pre-exponent factor.Maximal obtainable concentration in near-surface layer C max at room temperature (when thermal desorption is negligible) is estimated as 10 18 at/cm 3 (Grashin et.al, 1982, Sokolov et.al, 1984).In assumption, that 2 -concentration n on output side much less than C i , for stationary penetrating stream, we obtain following expression where E d -diffusion activation energy.The rates of diffusant capture and release are equal in stationary state and do not affect to stationary stream intensity.where E a =E d -E i ~ 19.6 kj/mol in our calculation, that is close to Е а = 17.9 kj/mol, obtained experimentally.Diffusion activation energies related to specimens structure, obviously.Excess free volume presence in the amorphous alloy provides less energy consumption for the Hydrogen atom jumps from one interstice to another.Besides some part of interstices may perhaps be wrong Bernal cavities, i.e. be deformed.Thermodesorption activation energy in recrystallized alloy is less than in amorphous one E i cr < E i am .This fact could be explained by surface reconstruction and changing of the passivation layer to the Hydrogen desorption.

Hydrogen effect to the short order structure for liquid, amorphous and crystal silicon
Due to its semiconductor properties, Silicon had been found wide application in the recent microelectronics and electronic technique.Hydrogen has been generally recognized to play impotent function in the different complex formation in the amorphous Silicon.Attention to the Hydrogen behavior in Silicon is explained by its affect to physicalchemical properties, which gives opportunity of new materials with necessary properties development.
Hydrogen diffusion in crystal Si was researched by TBMD (tight binding molecular dynamics) method (Panzarini. & Colombo, 1994).The model considered single Hydrogen atom in 64-atoms super-cell of Silicon.On the TBMD data the authors supposed, that Hydrogen diffusion mechanism in crystal Silicon acts according to Arrhenius low, and there are not other "anomalous" mechanisms but, for example, the single skips.Amorphous Silicon short order structure had been researched in the works of (Pastukhov et.al, 2003, Gordeev et.al, 1980).It had been found, that amorphous Silicon retains covalent bond type with coordination number Z=4.2, in difference with melt, where the bond has metallic character (Z=6.4).
The data of experimentally estimated values for Hydrogen diffusion factors in amorphous Si are limited, and published results are not in good agreement.The experimental research data on amorphous Silicon Hydrogen permeability are presented in the work (Gabis, 1997).
For Hydrogen transfer through amorphous Silicon film the author used model, where besides diffusion, low rate of the processes on surface, as well as capture and temporal keeping of the Hydrogen diffusing atoms in traps had been taken into consideration.It's the author's opinion that Hydrogen transfer related to local bonds Silicon-Hydrogen reconstruction.
We used interparticle potential (Tersoff, 1986) and MD method to calculate structure parameters and diffusion factors of Si and H in crystal, amorphous and liquid Silicon (Pastukhov, 2008).
Calculations had been carried out for system, containing 216 Silicon and 1 Hydrogen atoms in basic cube using periodic boundary conditions.Cube edge length had been had been taken according to experimental density system under consideration at 298К temperature.Molecular dynamic calculation results are presented on fig.5, 6 and in table 1. Valent angles mean values were found from first and second coordination sphere radii using following formula: Experimental data analysis obtains, that, in certain approximation, there is one metastable equilibrium configuration of atoms with coordination number 4 in the c-Si a-Si materials with Hydrogen as well as without it.First peak sharpness of intensity curve (fig.6) indicates comparatively large ordering in а-Si.First and second maxima of RDF curve practically coincide.Differences are observed in consequent part of curves.Third maximum of RDF for а-Si is practically absent.
Computer calculations for Si-H model found, that Hydrogen diffusion mechanism in crystal Si with n -conductivity type is realized by electro-neutral Hydrogen atoms migration through tetrahedral interstices according to the same principle as screened proton diffusion in the amorphous transition metals (Vatolin et.al, 1988).However Hydrogen atom moving path trough matrix nodes accompanied by Si-Si bond breakage due to Si atom 0.05nm shift from the node occupied and formation of chemical bond Si-H and free Si bond, left in the lattice node.

Hydrogen diffusion in the amorphous Pd-Si alloy
Model system (Pastukhov et.al, 2009), used in MD method for Hydrogen behavior research in the amorphous Pd-Si alloy at Т=300К temperature, was presented by 734 Palladium particles, 130 Silicon particles and 8 Hydrogen particles in the cubic cell with 2.44869nm edge length.Motion equation integration was carried out with 1.8·10 -15 s time steps.Short order structure analysis of the amorphous Pd materials (Sidorov & Pastukhov, 2006) and Pd-Si (15 а .%)with Hydrogen had been carried out using partial functions g ij (r) of Pd-Pd, Pd-Si and Pd-H pairs (Pastukhov et.al, 2009) (fig.7 and 8).
Second peak of g ij (r) curve for Pd-H (fig.7) has change symmetry shoulder in comparison with g ij( r) curve for Pd-Pd.
Refer to (Herst, 1962), distances, related to second g(r) peak are formed by 3 types of contact: a) two Pd atoms through Pd atom ( = 2r 0 ); b) two Pd atoms trough ч two Pd atoms (r = 1.732r 0 ); c) two Pd atoms through three Pd atoms (r = 1.633r 0 ).More easy Hydrogen affected turns contact of Pd-Pd atoms, realized by b) -type.Amorphous Palladium structure changes, due to Hydrogen presence, are caused by re-distribution of formed distances to its increasing (right sub-peak of RDF second peak).Observed second peak splitting inversion of g ij (r) for amorphous Palladium with Hydrogen obtains information about short order reforming of metal.Second peak differences of g ij (r) for Pd-Pd and Pd-H indicate strong Hydrogen affect to Palladium matrix structure.The effects observed in MD -model allow assumption about micro-grouping presence, which are identified as stable hydride structures, indicating to high degree of dissipative structures of Pd-H, Si-H -types presence (Ivanova et.al,, 1994, Avduhin et.al, 1999).
Hump, observed close to 3.44nm -1 (fig.9) on our calculated and experimental (Polukhin 1984) structure factor curves for amorphous state with Hydrogen as well as its absence, hasn't so far interpretation.Authors (Polukhin & Vatolin, 1985) have shown by statistic geometry method, that most often Voronoy-polyhedrons occurred in the amorphous metals are recognized as polyhedrons with 12, 13, 14, 15 coordination numbers for given sties-atom.Amorphous Pd-Si alloy structure model is supposed to consist from Palladium microgroupings, characterized by distorted triangle pyramid form with 2.5Å leg (Pd-Si) and regular 2.71Å leg (Pd-Pd) base triangle (Polukhin, 1984) Separately chosen Pd, Si and H atoms motion in our model is different by its character.
As MD model calculation show, not only Silicon atoms can affect Hydrogen mobility, but Hydrogen itself can change considerably diffusion of the other components of alloy.For example, Pd-Si system without Hydrogen has D Si = 4.93•10 -6 cm 2 •s -1 , but D Si = 2.53•10 -6 cm 2 •s - 1 with Hydrogen presence.There are different energy zones in an amorphous system, which lead to different time mode of Hydrogen diffusion.Therefore low of defunding particle energy change in the amorphous metals should be statistic nature and be defined by the cavities type distribution type.Due to little part of the octahedron cavities, three types of diffusion process are possible in the amorphous metals.That are octahedron-octahedron, octahedron-tetrahedron-octahedron, octahedronoctahedron, tetrahedron-tetrahedron. Due to v o l u m e c h a n g i n g i n the hydrogenization process for crystal is similar to that for amorphous alloys (Kircheim et.al, 1982), this fact indirectly proves, that hydrogen occupies similar Bernal polyhedrons (tetrahedrons and octahedrons).Interstice diffusion factors in disordered material can be calculated as temperature and concentration function with hydrogen energies distribution and constant saddle point energy according to Kircheim formalism (Kircheim et.al, 1985).
12 0 1* 0 00 ( 1) exp , exp Here D 0 * -pre-exponent factor, E 0 -mean activation energy, equal to difference between mean Hydrogen energy, calculated, from energy distribution function and saddle point constant energy E 0 -E g , (if energy distribution is Gaussian).
Hydrogen diffusion factors are calculated from equation (11) dependent on its concentration for amorphous Pd 83 Si 17 alloy at T=298K temperature.It was obtained, that D H increases depending on its concentration increase.
Basing on D H temperature dependence, diffusion activation energy value was estimated as E 0 = 18.9 kj/mol.It should be noted, that for crystal alloy activation energy is higher.It's equal to 26kj/mol independently on Hydrogen concentration.
According to Richards theory (Richards, 1983), there is Hydrogen probability to occupy low energy interstices, that are large faces polyhedrons.
Due to Hydrogen concentration increase, it occupies low energy interstices forcing H atoms to overcome higher energy potential barriers.Thus it neutralizes one of the factors, which decreases diffusion mobility.
On the other hand, Hydrogen atoms location in the higher energy interstices leads to activation energy decrease.
Described mechanism does not affect to diffusion, due to most part of Hydrogen atoms, absorbed by metal, have been found in low energy interstices (which are traps for H atoms). Sharp diffusion factor increase takes place only after traps saturation by Hydrogen.

Hydrogen diffusion in the amorphous Ni-Zr alloys
Computer calculation of the amorphous Ni-Zr and Ni-Zr-H alloys structure and properties are presented by fig. 10, 11 and table 2. The model system unlike (Pastukhov et.al, 2009(Pastukhov et.al, , 2010) ) contained 640 (360)particles of nickel, 360 (640) particles of zirconium and 1(2) particles of hydrogen in the cubic cell.The movement equations integrating were carried out by time steps of 1.1・10 -15 s.General structure factors for Ni 64 Zr 36 (alloy 1, curve 4) Ni 36 Zr 64 (alloy 2, curve 1), with Hydrogen and without it are presented on fig.10.All curves have diffused interferential maxima proper to amorphous state, which indicates, that amorphous state is saved with Hydrogen absorption at low as well as at high hydrate-forming element and Hydrogen concentration in an alloy.Increasing the number of H -atoms in a MD model for 1-alloy initially results in structural factor peaks displacement to the low dispersion vectors (S) and in main peak height (h) increasing.Then the displacement vice versa results in the high S-and low h-values.It testifies to the quantity of H-atoms affects to amorphous alloys structure.All peaks of a(s) became more relief, oscillations extend to higher scattering vectors.The authors (Sadoc et.al, 1973, Maeda & Takeuchi 1979) proved, that icosahedrons type of atoms packing is dominating in amorphous metals structure, where high polyhedron concentration with coordination number 12 takes place.The main structural factor maximum height and form of the bifurcated second peak are determined by contacting polyhedrons quantity and their type of bond (Brine & Burton, 1979).The amorphous alloy short order therefore can be described with the help of a coordinating icosahedron cluster, which is the basic structural unit of NiZr 2 crystal.
Hydrogen in such a structure can be located in numerous tetra-cavities, formed by Ni and Zr atoms (Kircheim et.al, 1988).For 2 -alloy, that is close to NiZr 2 composition (curve 1), two first maxima location of a(s) curve corresponds to averaged location of the interference lines for crystal NiZr 2 compound.Hydrogen atom including in the MDmodel (curve 2) leads to strong diffusion and height decreasing of relatively good resolved structure factor peaks due to Hydrogen penetration into numerous cavities of the amorphous structure.Hydrogen atoms probably form with Zr some kind of quasi crystal ZrH 2 lattice ( Sudzuki et.al, 1987).This assumption reveals in a better resolution of short and long diffraction maxima (3, 6 curves) of structure factors for alloys with high contents of Zr and H atoms. Partial g ij (r) radial distribution functions of model systems and short order parameters are presented in Fig. 11 and in the table 2. For all low and zero hydrogen alloys, the shortest inter-atomic distance of Ni-Ni pair remains constant (0.240nm), decreasing up to 0.230nm when H increases up to two atoms.Inter-atomic distances of N-Zr and Zr-Zr pairs considerably decrease with growth of Zr and H concentration.We note that rNi-Ni and rZr-Zr are close to Ni and Zr atoms diameters (0.244 nm and 0.324 nm) correspondently, and the distance between Ni-Zr atoms is somewhat less than the sum of the Ni and Zr atoms radii, that is confirmed by diffraction experiment results (Buffa et.al, 1992).This fact confirms bond formation between these elements due to hybridization of vacant 3d -electron band of Ni and 4d-band of Zr Hafiuer et.al, 1993).Calculated diffusion coefficients of hydrogen for amorphous Ni-Zr-H alloys are presented in the Table 2.The value of D H varies from 2·10 -4 up to 1.2·10 -5 m 2 ·s -1 , in the same limits, as diffusion coefficients of H atoms in an icosahedron TiNiZr alloy (Morozov et.al, 2006).As it follows from the Table 2,    The activation energy of hydrogen diffusion for amorphous Ni 64 Zr 36 alloy was estimated in the 298-768К temperature interval.A value of Е=0.1 V was obtained.This result on H atoms diffusion may be explained by various energy position (Richards, 1983, Kircheim et.al, 1988) in the disordered materials.Deep potential wells acts like traps (octa-cavities) and are occupied by hydrogen initially.Then hydrogen occupies interstices with high energy values (tetra-cavities) and an abrupt increase of D H is observed.

Hydrogen and electric field effect to Iron impurities diffusion in the Zr-Fe melt
Iron and Zirconium diffusion factor dependence on electric field intensity and Hydrogen presence in the molten Zirconium had been analyzed in the terms of molecular dynamics (MD) method.Model system for research of Iron and Hydrogen ions behavior in the Zr-Fe-H melt at Т=2273К temperature and electric field presence contained 516 Zirconium particles, 60 Iron particles and 1Hydrogen particle in cubic cell with a=2.44195 nm cube edge.Integration of the motion equation was carried out by 1.1·10 -15 s time steps.Interparticle potentials and its parameters had been taken from (Varaksin & Kozyaichev, 1991, Zhou et.al, 2001).Calculation results of impurities migration in the molten Zirconium are compared to experimental data (Lindt et.al, 1999, Ajaja et.al, 2002, Mimura et.al, 1995).Partial radial distribution functions g ij (r) for Zirconium-Iron melt are presented on fig.12.Most probable inter-atomic distance in first coordination sphere is close to sum of atomic radii for Iron and Zirconium (r Zr-Fe = 0.29nm, r Fe = 0.130nm, r Zr = 0.162nm).
This results comparison to computer simulation data for Ta-Fe melt (Pastukhov et.al, 2010, Vostrjakov et.al, 2010) reveals sufficiently close character of the radial distribution function for large dimension atoms, namely Ta-Ta (0.29 nm, r Ta = 0.145nm) and Zr-Zr (0.324nm, r Zr =0.162nm).Iron and Zirconium diffusion factors in the Zirconium melt in the presence, as well as absence of electric field and Hydrogen at 2273K had been calculated by means of MD method (fig.13 and 14).Diffusion factor of Iron (D Fe ) in the Zirconium melts with Hydrogen linearly depends on electric field intensity (E) and Iron concentration ( Fe ).Hydrogen diffusion factor negligibly decreases from 2.16•10 -4 cm 2 •s -1 to 1.94•10 -4 cm 2 •s -1 , if electric field intensity increases from 900 to 1020 v/m.Hydrogen inducing into system at Fe ≈0.1% decreases D Fe value from 7.86•10 -5 to 6.36•10 -5 cm 2 s -1 , and electric field 1020 v/m intensity applying decreases D Fe to 5.23•10 -5 cm 2 •s -1 (fig.14).
Calculation results of D Fe changing in dependence on E value had been compared to evaporation constant rate for the Fe-ions from Zr, calculated by equation (Pogrebnyak et.al, 1987, Vigov et.al, 1987) Fig. 12. Partial radial distribution functions g ij (r) for Zr-Fe melt at 2273К, calculated in terms of MD model.

/ 2 () exp
where -ion vibration frequency (10 13 •s -1 ), Fe -impurity concentration, -Fe evaporation heat, I -first ionization potential (V/Å), E -electric field intensity, W -electron exit work, q -ion charge.Values of , I, W, R had taken in electron-volt, E -in volt per angstrom.Diffusion factor D directly depends on rate (k) and time (t) evaporation of main metal (Kuznetsov et.al, 1968).The log k and log D Fe on Е dependences (fig.15) are relatively similar.
Thus assumption is possible, that limiting factor of Fe removal from the Zr melt is diffusion of Fe.The Hydrogen is considered as light intrusion impurity into metals with different cell type.Therefore Hydrogen diffusion is significant problem in researching of high temperature metals refining.Impurities have less action upon Incoherent diffusion.Therefore this kind of diffusion becomes dominating at high temperature (Maximov et.al, 1975).
We had compared Hydrogen diffusion factors in Ta at 3400K (Pastukhov et.al, 2010) and in Zr at 2273K (Ajaja et.al, 2002).This values are 1,7 10 -5 and 5,01 10 -4 cm 2 ·s -1 respectively.The authors (Maximov et.al, 1975) explain such difference due to Hydrogen diffusion activation energy (E a ) dependence on atomic metal mass, its Debye frequency, modulus of elasticity and volume change at Hydrogen addition.Calculated values of Е а for different metals (Flynn et.al, 1970) are in quantity agreement with experimental data.Temperature dependence D H at high temperatures is described in the term of theory (Flynn et.al, 1970).(Shmakov et.al, 1998) calculated D H in Zirconium at 2273K without electric field influence as 3.862·10 -4 cm 2 ·s -1 , which low differ from our calculated value D H =5.01•10 -4 cm 2 •s -1 .We have estimated diffusion layer thickness (x) by ( 13) equation (Flynn et.al, 1970).
Calculation were carried out basing on Fe -experimental time -dependence (Mimura et.al, 1995).Value of Fe we calculated by MD -method.
In the equation 0 and (х,t) are impurity concentrations in initial and refined Zirconium (Flynn et.al, 1970) and t is time of refining.Calculated (x) value is equal 7•10 -2 cm.By the order of value it's close to data on Silicon borating (Filipovski et.al, 1994), which is 1.6-1.8•10 -2 cm.It should be noted, that zone thickness of Zirconium shell interaction with molten Uranium is 0.2•10 -2 cm (Belash et.al, 2006).
We carried out calculation of Iron removal rate (G) from Zirconium by Iron concentration decrease during matched time intervals of plasma-arc-melting (PAM) with Hydrogen basing on the experimental data of (Mimura et.al, 1995)

Hydrogen and electric field effect to Iron impurities diffusion in Ta-Fe melt
Hydrogen and Iron atoms radial distribution functions and diffusion constants had been found by MD method in the Tantalum melt at 3400K in the presence and absence of outer electric field (fig.16).
The model system was presented by 486 tantalum, 1 iron and 1hydrogen atoms in a cubic cell of 2.13572 nanometers cube edge length.Computer experiment data have found short order of Ta-Fe-H system at 3400K is close to Tantalum structure: first maximum at R Ta-Ta ≈ 0.29 nm corresponds to Tantalum atom radius ≈ 0.292 nm.All RDF maxima diffusion is observed at electric field and Hydrogen in the Ta-Fe system.This fact may indicate liquid transition to more disordered structure.
Unusual kind of RDF curve for Ta-H atoms pairs obtained at electric field 1020v/m intensity (fig.17): first maximum of the curve is bifurcated, besides first sub-peak at r 1 = 0.22nm corresponds to one of most probable distance Ta-H and second sub-peak at r 2 = 0.24nm corresponds to Ta-Fe without electric field.
Dynamics and local structure of the close to Hydrogen surrounding for the ternary interstitial alloy should depend on Hydrogen concentration, temperature and solvent structure short order.There is no conventional opinion about Hydrogen location in such systems.Since the Hydrogen atom radius is 0.032 nm, it can occupy octahedron (0.0606 nm), as well as tetrahedron (0.0328 ) (Geld et.al, 1985) location.System Ta -H particularity is that starting from the concepts of geometry, distance between Tantalum atom and octahedron interstice centre in Tantalum cell more, than Ta (0.146nm) and (0.032nm) radii sum.Distance Ta -H remains less than equilibrium distance, and Hydrogen not always occupies interstice centre.At the same time, distance from the octahedron interstice centre to the second neighbors, R 2 =a/√2=0.234nm is more than Tantalum plus Hydrogen distance.That leads to Hydrogen atoms shift from octahedron centre to whatever neighbor of Tantalum atom.
Dynamics and local structure of the close to Hydrogen surrounding for the ternary interstitial alloy should depend on Hydrogen concentration, temperature and solvent structure short order.There is no conventional opinion about Hydrogen location in such systems.Since the Hydrogen atom radius is 0.032 nm, it can occupy octahedron (0.0606 nm), as well as tetrahedron (0.0328 ) (Geld et.al, 1985) location.System Ta -H particularity is that starting from the concepts of geometry, distance between Tantalum atom and octahedron interstice centre in Tantalum cell more, than Ta (0.146nm) and (0.032nm) radii sum.Distance Ta -H remains less than equilibrium distance, and Hydrogen not always occupies interstice centre.
At the same time, distance from the octahedron interstice centre to the second neighbors, R 2 =a/√2=0.234nm is more than Tantalum plus Hydrogen distance.That leads to Hydrogen atoms shift from octahedron centre to whatever neighbor of Tantalum atom.
Hydrogen shift from geometric centre of octahedron position during heating of researched system is possible.According to computer experiment data, distance between nearest Tantalum and Hydrogen atoms changes at electric field and Hydrogen presence, but Ta-Fe remains constant (table 4).7.·10 -4 cm 2 s -1 , which some less, than Iron diffusion constant increase: from 1.3·10 -5 to 1.5·10 -4 cm 2 s -1 .Thus, Hydrogen increases Iron atoms mobility more than electric field.This fact is in god agreement with Ta-H and Ta-Fe bonds strength.

Conclusion
Amorphous and liquid systems structure for Fe, Pd, Zr, Ta, Si with presence and absence of Hydrogen atoms had been researched by means of x-rays diffraction and molecular dynamic methods.Strong affect of H atoms to amorphous matrixes Fe-Ni-Si-b-C-P, Pd-Si and Ni-Zr structure had been obtained.
Observed RDF changing at Hydrogen presence had been revealed in better resolution of the close and distant maxima could indicate to stable hydride bonds like Pd-H, Si-H, Zr-H formation.
Calculated by MD model Hydrogen diffusion constants increase on H concentration and hydride forming element presence in alloy (system Ni-Zr-H).Not only amorphous alloy component (Pd-Si-H) affects to H atoms mobility, but Hydrogen atoms can considerably change other components (Si) diffusion.Refining processes of the liquid high-melting metals, like Zr, Ta, containing Fe impurities can be analyzed by MD method for PAM and EBM melting technologies.The method gives opportunity to estimate limiting stage of process, electric field affect and Hydrogen presence in system to Fe diffusion constant in the melts.
The researches had been carried out with financial support of Minobrnayka.Federal contract 16.552.11.7017, science equipment of CKP "Ural-M" had been used.
www.intechopen.comMolecularDynamic Simulation of Short Order and Hydrogen Diffusion in the Disordered Metal Systems 283 determines location probability any atom at r distance from the chosen atom and described in MD model by the well-known formula:

Fig. 3 .
Fig. 3. Stable (stationary) Hydrogen stream through amorphous membrane.Surface processes and correlation of E d and E i values define stationary stream temperature dependence.Concentration C am for an amorphous alloy has max value up to 175° temperature and penetration rate is defined by diffusion, at that stream increases.Following temperature increase leads to exponential C i concentration decrease, and E d <E i correlation leads to stream decreasing.Input C cr concentration for recrysallyzed alloy decreases in all temperature interval (fig.4, curve 2), and Е d > E i relation leads to classic Arrhenius dependence J  exp(-E a /RT) (9)
Fig. 5. RDF of the Si-Si (1) and Si-H atoms (2) for crystal Silicon with Hydrogen at 278К.
Fig. 7. Partial RDF in an amorphous Pd-H -system.

Fig. 9 .
Fig. 9. Structure factor for amorphous Pd-Si with Hydrogen obtained by MD -model calculation.Mixed type micro-groupings occurred, in d 85 Si 15 alloy, are formed with most presence of BCC and FCC polyhedron type.Particles number does not exceed 13-14 in one cluster.

Fig. 13 .
Fig. 13.Dependencies of D Fe and D Zr on Iron concentration at 2273К (MD -calculation).
Thus equation (8) doesn't include interaction parameters of Hydrogen with traps.Approximation results are displayed by solid curves at fig. 3. Energy values E d am = 40.8,Eiam=86.7 kj/mol for amorphous, and Е d cr = 71.2,Eicr=51.7 kj/mol for crystal specimens give good agreement with experiment data.Concentration calculation on input membrane side by (6) and (7) equations accounting thermodesorption activation energies is illustrated by fig.4.Parameter C max , used in calculation does not any effect to activation energies, but affects only to pre-exponent factors.

Table 2 .
Short order parameters for amorphous alloy in the Ni-Zr and Ni-Zr-H systems.

Table 3 .
Dependences of L and G on mean residual Iron content in Zirconium for PAM process.C Fe -mean Iron concentration: initial (15min.),middle (90min.),and final (165min.)stage of melt.

Table 4 .
Partial inter-atomic distances in the Ta-Fe by MD calculation.