**1. Introduction**

280 Molecular Dynamics – Theoretical Developments and Applications in Nanotechnology and Energy

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Yang, Q.&Zhong, C. (2006). Understanding Hydrogen Adsorption in Metal-Organic

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655-658.

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.

Unlike crystal alloy, where interstice volumes are presented discretely only by tetrahedron and octahedron cavities, small and big interstice cavities distribution in an amorphous alloy is close to Gaussian function (Polukhin and Vatolin, 1985, Polukhin et.al, 1984, 1986). Thus Hydrogen energy distribution function form in the amorphous alloys cavities is close to the main RDF peak which is approximated by Gaussian function. Inter-cavities transitions are strongly correlated, and the stationary states contribution to the Hydrogen atoms motion is negligible.

Amorfizator-elements (Si, B, C, etc.) insertion into the amorphous metals reduces number of large cavities (octahedrons) providing most energetically favourable Hydrogen migration path. It reduces metal absorption ability, as well as hydrogen diffusion motion intensity, reducing Hydrogen permeability.

Amorphous alloys absorption ability of hydrogen is defined by number and size of cavities for hydrogen insertion, as well as the hydride forming elements (Ti, Zr, Hf, etc.) content in an alloy. Hydrogen diffusion factor in the amorphous alloys depends on its concentration.

Crystal and amorphous Palladium alloys are widely used in membranes for high pure Hydrogen producing. Literary data analysis shows possibility of filtering alloys production for hydrogen based on less expensive metals: V, Nb, Zr, Ta, etc., characterized by high Hydrogen solubility, which defines alloy Hydrogen permeability by diffusion factors as well as Palladium. Negative effect of these elements hydrides formation should be inhibited

Molecular Dynamic Simulation of Short Order and

in MD model by the well-known formula:

factor s(k) is defined by following equation:

**(experiment)** 

experiment data (Vatolin et.al, 1989).

4000С from amorphous specimen.

Hydrogen Diffusion in the Disordered Metal Systems 283

determines location probability any atom at r distance from the chosen atom and described

*r rN*

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

> <sup>4</sup> ( ) () 1 () 1 , *rm N Sin kr s k <sup>g</sup> <sup>r</sup> r dr L kr*

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.

> 3 0 <sup>4</sup> ( ) *rm <sup>N</sup> <sup>Z</sup> <sup>g</sup> r r dr L*

Molecular dynamics calculation had been done using microcanonical (NVE) ensemble.

using had been considered in details by authors (Polukhin & Vatolin, 1985).

**3. Hydrogen in amorphous and recrystallized Fe-Ni-Si-B-C-P alloy** 

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

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

Hydrogen permeability of the amorphous and recrystallized Fe based (Fe77.333Ni1.117Si7.697 B13.622C0.202P0.009) alloy membrane (25 micron thickness) was researched by stationary stream method (Pastuchov et.al, 2007). Recrystallized alloy was prepared by vacuum annealing at

Molecular Hydrogen injection to input side of degasified specimen at maximal acceptable temperatures (300°С for amorphous and 400°С for recrystallized specimens) didn't lead to

*g r*

3 0

Where k is wave vector, k = (4 Sin 2Ө)/λ and rm is RDF attenuation radius.

Coordination number had been calculated by following formula:

3 2 ( ) () , <sup>4</sup> *N L*

<sup>2</sup>

3

(3)

(4)

(5)

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.

#### **2. 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.

$$r\_i(k+1) = 2r\_i(k) - r\_i(k-1) + \frac{F\_i(k) \text{(\Delta t)}^2}{m} \tag{1}$$

Where ri – radius-vector of particle, m - its mass, Fi – 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 pi - 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 <sup>2</sup> ( ) *ir t* by the major of steps.

$$D = \frac{1}{6t} < r\_i^2(t) > ,\tag{2}$$

Where <r2(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

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

Therefore research of an electric field intensity affect to the impurity elements transport

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

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

<sup>2</sup> ( )( ) ( 1) 2 ( ) ( 1) *<sup>i</sup>*

Where ri – radius-vector of particle, m - its mass, Fi – 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 pi - 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

> 1 <sup>2</sup> () , <sup>6</sup>

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

*m* (1)

*D rt <sup>i</sup> <sup>t</sup>* (2)

( ) *ir t* by the major

*Fk t rk rk rk*

*i ii*

calculated from mean square displacement of the particles in model <sup>2</sup>

Where <r2(t)> – mean square displacement of Hydrogen atoms at t – time.

impurities removal from Zr and Ta in plasma-arc melting in the Hydrogen presence.

researches as well.

previous (k-1)-steps.

of steps.

properties in the liquid metals is very urgent.

**2. Molecular dynamics calculation method** 

determines location probability any atom at r distance from the chosen atom and described in MD model by the well-known formula:

$$\log(r) = \frac{(\Delta N)L^3}{4\pi r^2 \Delta r N},\tag{3}$$

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:

$$s(k) = 1 + \frac{4\pi N}{L^3} \prod\_{0}^{r\_m} [g(r) - 1] \frac{\sin(kr)}{kr} r^2 dr \,\tag{4}$$

Where k is wave vector, k = (4 Sin 2Ө)/λ and rm 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:

$$Z = \frac{4\pi N}{L^3} \int\_0^r g(r)r^3 dr\tag{5}$$

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).

### **3. 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 (Fe77.333Ni1.117Si7.697 B13.622C0.202P0.009) alloy membrane (25 micron thickness) was researched by stationary stream method (Pastuchov et.al, 2007). Recrystallized alloy was prepared by vacuum annealing at 4000С from amorphous specimen.

Molecular Hydrogen injection to input side of degasified specimen at maximal acceptable temperatures (300°С for amorphous and 400°С for recrystallized specimens) didn't lead to

Molecular Dynamic Simulation of Short Order and

ЕescEcap.

2 – recrystallized alloy)

written as

where VT + Vr

Hydrogen Diffusion in the Disordered Metal Systems 285

value 2.71013 sm-2s-1 at 3750C (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 2000C, low increase Hydrogen streams observed in reality. Its decrease begins after 2000C. Such behavior is proper namely for the traps with activation energies of escape and capture

Fig. 2. Stationary Hydrogen stream (J) dependence on temperature. (1 – amorphous alloy,

Penetrating stream decreasing in amorphous specimen for temperature interval from 2000 C up to 3000 C most probably is related to surface processes. Since penetrating stream is three orders less than incident stream to input surface (Vf 1016cm-2s-1), balance of streams is

Vf = VT + Vr (6)

 Vr = VfCi/Cmax and VT = bi·exp(-Ei/RT)Ci (7) are streams of ion-induced reemission and thermal desorption on input side. Term Ci is Hydrogen concentration in no-violated alloy structure near input surface, bi – pre-exponent factor. Maximal obtainable concentration in near-surface layer Cmax at room temperature

noticeable output stream increase. At 10 torr Hydrogen pressure the stream achieved 3.81012 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 1250C for amorphous and 2000С 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.

Fig. 1. Atoms radial distribution for amorphous (Fe77.3 Ni1.1Si7.7B13.6C0.2P0.009) alloy with Hydrogen ( <Н2> ) and Hydrogen absence (1 - 2750C; 2 - 3000 + <H2>; 3 - 4250C; 4 - 4250C + <H2>; 5 - 4500C; 6 - 4750C +<H2>; 7 - 5500C; 8 - 5750C +<H2>).

Hydrogen stream stabilization has different nature in amorphous and recrystallized specimens. But both situations are characterized by rapid increase of output stream with characteristic 3060s stabilization times.

Amorphous membrane is characterized by very elongated hydrogen output with 6000s stabilizing time after rapid output increase at temperatures from 1250 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 1250С and achieves maximum 3.31013 sm-2s-1 value at 200°С. Subsequent heating demonstrates anomalously sharp decrease. Second specimen follows to classic Arrhenius dependence with activation energy 17.9 kj/mol and maximum stream

noticeable output stream increase. At 10 torr Hydrogen pressure the stream achieved 3.81012 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

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 1250C for amorphous and 2000С for crystal specimens. Most impotent difference between two states of the researched alloy is observed as non-monotonic output stream increase at

Fig. 1. Atoms radial distribution for amorphous (Fe77.3 Ni1.1Si7.7B13.6C0.2P0.009) alloy with Hydrogen ( <Н2> ) and Hydrogen absence (1 - 2750C; 2 - 3000 + <H2>; 3 - 4250C; 4 - 4250C +

Hydrogen stream stabilization has different nature in amorphous and recrystallized specimens. But both situations are characterized by rapid increase of output stream with

Amorphous membrane is characterized by very elongated hydrogen output with 6000s stabilizing time after rapid output increase at temperatures from 1250 C up to 225°C. Hydrogen stream dependence on inverse temperature is illustrated by fig.2. The

The stream increases from 1250С and achieves maximum 3.31013 sm-2s-1 value at 200°С. Subsequent heating demonstrates anomalously sharp decrease. Second specimen follows to classic Arrhenius dependence with activation energy 17.9 kj/mol and maximum stream

<H2>; 5 - 4500C; 6 - 4750C +<H2>; 7 - 5500C; 8 - 5750C +<H2>).

dependence isn't monotonous and has maximum in 200°C region.

characteristic 3060s stabilization times.

discharge is most stable.

temperature expansion in amorphous state.

value 2.71013 sm-2s-1 at 3750C (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 2000C, low increase Hydrogen streams observed in reality. Its decrease begins after 2000C. Such behavior is proper namely for the traps with activation energies of escape and capture ЕescEcap.

Fig. 2. Stationary Hydrogen stream (J) dependence on temperature. (1 – amorphous alloy, 2 – recrystallized alloy)

Penetrating stream decreasing in amorphous specimen for temperature interval from 2000 C up to 3000 C most probably is related to surface processes. Since penetrating stream is three orders less than incident stream to input surface (Vf 1016cm-2s-1), balance of streams is written as

$$\mathbf{V\_{f}} = \mathbf{V\_{T}} + \mathbf{V\_{r}} \tag{6}$$

where VT + Vr

$$\mathbf{V\_{r} = V\_{i}C\_{i}/C\_{\text{max}}} \quad \text{and} \quad \mathbf{V\_{T} = \ b\_{i} \exp(-\mathbf{E\_{i}}/RT)\mathbf{C\_{i}}} \tag{7}$$

are streams of ion-induced reemission and thermal desorption on input side. Term Ci is Hydrogen concentration in no-violated alloy structure near input surface, bi – pre-exponent factor. Maximal obtainable concentration in near-surface layer Cmax at room temperature (when thermal desorption is negligible) is estimated as 1018 at/cm3 (Grashin et.al, 1982, Sokolov et.al, 1984). In assumption, that С2 – concentration n on output side much less than Ci, for stationary penetrating stream, we obtain following expression

$$\mathbf{J} = \mathbf{A} \cdot \exp(-\mathbf{E\_d}/\mathbf{RT}) / \left(\mathbf{1} + \mathbf{B} \cdot \exp(-\mathbf{E\_i}/\mathbf{RT})\right) \tag{8}$$

Molecular Dynamic Simulation of Short Order and

(1- amorphous alloy, 2- recrystallized alloy).

Hydrogen desorption.

**crystal silicon** 

development.

in recrystallized alloy is less than in amorphous one Ei

Hydrogen Diffusion in the Disordered Metal Systems 287

Fig. 4. Temperature Hydrogen concentration dependence at input side of membrane

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

explained by surface reconstruction and changing of the passivation layer to the

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

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

**4. Hydrogen effect to the short order structure for liquid, amorphous and** 

cr < Ei

am . This fact could be

where Ed – diffusion activation energy. The rates of diffusant capture and release are equal in stationary state and do not affect to stationary stream intensity. Thus equation (8) doesn't include interaction parameters of Hydrogen with traps. Approximation results are displayed by solid curves at fig. 3. Energy values Edam = 40.8, Ei am = 86.7 kj/mol for amorphous, and Еdcr = 71.2, Ei cr = 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 Cmax , used in calculation does not any effect to activation energies, but affects only to pre-exponent factors.

Fig. 3. Stable (stationary) Hydrogen stream through amorphous membrane.

Surface processes and correlation of Ed and Ei values define stationary stream temperature dependence. Concentration Cam for an amorphous alloy has Сmax value up to 175°С temperature and penetration rate is defined by diffusion, at that stream increases. Following temperature increase leads to exponential Ci concentration decrease, and Ed<Ei correlation leads to stream decreasing. Input Ccr concentration for recrysallyzed alloy decreases in all temperature interval (fig. 4, curve 2), and Еd > Ei relation leads to classic Arrhenius dependence

$$\mathbf{J} \approx \exp(\mathbf{-}\mathbf{E}\_a/\mathbf{RT})\tag{9}$$

where Ea=Ed-Ei ~ 19.6 kj/mol in our calculation, that is close to Еа = 17.9 kj/mol, obtained experimentally.

(when thermal desorption is negligible) is estimated as 1018 at/cm3 (Grashin et.al, 1982, Sokolov et.al, 1984). In assumption, that С2 – concentration n on output side much less than

where Ed – diffusion activation energy. The rates of diffusant capture and release are equal in stationary state and do not affect to stationary stream intensity. Thus equation (8) doesn't include interaction parameters of Hydrogen with traps. Approximation results are

Concentration calculation on input membrane side by (6) and (7) equations accounting thermodesorption activation energies is illustrated by fig. 4. Parameter Cmax , used in calculation does not any effect to activation energies, but affects only to pre-exponent

J = A·exp(-Ed/RT)/(1 + B·exp(-Ei/RT)) (8)

cr = 51.7 kj/mol for crystal specimens give good agreement

am = 86.7 kj/mol for

Ci, for stationary penetrating stream, we obtain following expression

displayed by solid curves at fig. 3. Energy values Edam = 40.8, Ei

Fig. 3. Stable (stationary) Hydrogen stream through amorphous membrane.

Surface processes and correlation of Ed and Ei values define stationary stream temperature dependence. Concentration Cam for an amorphous alloy has Сmax value up to 175°С temperature and penetration rate is defined by diffusion, at that stream increases. Following temperature increase leads to exponential Ci concentration decrease, and Ed<Ei correlation leads to stream decreasing. Input Ccr concentration for recrysallyzed alloy decreases in all temperature interval (fig. 4, curve 2), and Еd > Ei relation leads to classic Arrhenius

 J exp(-Ea/RT) (9) where Ea=Ed-Ei ~ 19.6 kj/mol in our calculation, that is close to Еа = 17.9 kj/mol, obtained

amorphous, and Еdcr = 71.2, Ei

with experiment data.

factors.

dependence

experimentally.

Fig. 4. Temperature Hydrogen concentration dependence at input side of membrane (1- amorphous alloy, 2- recrystallized alloy).

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 Ei cr < Ei am . This fact could be explained by surface reconstruction and changing of the passivation layer to the Hydrogen desorption.

### **4. 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.

Physics-chemical properties of computer models (containing thousands atoms) for amorphous Silicon, could be described in terms of empiric potentials (Tersoff, 1986, Stillimger & Weber, 1985).

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:

$$\varphi = 2 \arcsin\left(\frac{r\_2}{2r\_1}\right) \tag{10}$$

Molecular Dynamic Simulation of Short Order and

Hydrogen Diffusion in the Disordered Metal Systems 289

Fig. 5. RDF of the Si-Si (1) and Si-H atoms (2) for crystal Silicon with Hydrogen at 278К.

Fig. 6. RDF of the Si-Si (1) and Si-H atoms (2) for amorphous Silicon with Hydrogen at 278К.

Experimental data analysis obtains, that, in certain approximation, there is one metastable equilibrium configuration of atoms with coordination number 4 in the c-Si и 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 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

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

Physics-chemical properties of computer models (containing thousands atoms) for amorphous Silicon, could be described in terms of empiric potentials (Tersoff, 1986,

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

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

2arcsin

Experimental data analysis obtains, that, in certain approximation, there is one metastable equilibrium configuration of atoms with coordination number 4 in the c-Si и 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

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

2 1

(10)

2 *r r*

character (Z=6.4).

reconstruction.

(Pastukhov, 2008).

formula:

Stillimger & Weber, 1985).

а-Si is practically absent.

lattice node.

Fig. 5. RDF of the Si-Si (1) and Si-H atoms (2) for crystal Silicon with Hydrogen at 278К.

Fig. 6. RDF of the Si-Si (1) and Si-H atoms (2) for amorphous Silicon with Hydrogen at 278К.


Molecular Dynamic Simulation of Short Order and

Fig. 7. Partial RDF in an amorphous Pd-H – system.

Fig. 8. Partial RDF for amorphous Pd-Si (15 at.%)-H alloy.

Hydrogen Diffusion in the Disordered Metal Systems 291


Table 1. Short order parameters for crystal (c-Si), liquid (l-Si) and amorphous Silicon (a-Si). (Pastukhov et.al, 2003, Gordeev et.al, 1980).
