**5. 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 1.8·10-15s time steps. Short order structure analysis of the amorphous Pd materials (Sidorov & Pastukhov, 2006) and Pd-Si (15 ат.%) with Hydrogen had been carried out using partial functions *gij (r)* of Pd-Pd, Pd-Si and Pd-H pairs (Pastukhov et.al, 2009) (fig. 7 and 8).

Second peak of *gij(r)* curve for Pd-H (fig. 7) has change symmetry shoulder in comparison with *gij(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 (г = 2r0); b) two Pd atoms trough через two Pd atoms (r = 1.732r0); c) two Pd atoms through three Pd atoms (r = 1.633r0). 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 *gij(r)* for amorphous Palladium with Hydrogen obtains information about short order reforming of metal. Second peak differences of *gij(r)* for Pd-Pd and Pd-H indicate strong Hydrogen affect to Palladium matrix structure.

numb. Z

(1700К) 6,4 103,9±26,8 6,4·10-5

(Si-Si) 0.450 (Si-H) 0.218

(Si-Si) 0,380 (Si-H) 0.215/0.27

**5. Hydrogen diffusion in the amorphous Pd-Si alloy** 

Pd-Si and Pd-H pairs (Pastukhov et.al, 2009) (fig. 7 and 8).

Hydrogen affect to Palladium matrix structure.

1 2 3 4 5 6 7

(300K) 0.241 4.6 106.3±21 2.294

4,2

4

Table 1. Short order parameters for crystal (c-Si), liquid (l-Si) and amorphous Silicon (a-Si).

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 1.8·10-15s time steps. Short order structure analysis of the amorphous Pd materials (Sidorov & Pastukhov, 2006) and Pd-Si (15 ат.%) with Hydrogen had been carried out using partial functions *gij (r)* of Pd-Pd,

Second peak of *gij(r)* curve for Pd-H (fig. 7) has change symmetry shoulder in comparison

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 (г = 2r0); b) two Pd atoms trough через two Pd atoms (r = 1.732r0); c) two Pd atoms through three Pd atoms (r = 1.633r0). 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 *gij(r)* for amorphous Palladium with Hydrogen obtains information about short order reforming of metal. Second peak differences of *gij(r)* for Pd-Pd and Pd-H indicate strong

0.240 0.386 4,2 106 2.10

(φSi-Si) 180 (φSi-H) 90

(φSi-Si) 110 (φSi-H) 90

Mean angle inter-bonds φ Diff. factors D, cm2/s

> DSi 1.94·10-5 DH 4.83·10-4

> > DSi

2.45·10-6 2.33

Density ρ, g/cm3.

2.10

RDF Peaks positions,

r1 r2

Diamond 0,236 0,384 4

(calculation) 0,25 0,355; 0,42 6,3

(Si-Si) 0,250 (Si-H) 0.15

(Si-Si) 0,231 (Si-H) 0.15

(Pastukhov et.al, 2003, Gordeev et.al, 1980).

Nm. Coord.

Silicon phases structure

White Tin

Liquid Si

a-Si

a-Si, (298K) Our data MD-model

а-Si+H, (298K) Our data MD-model

c-Si+H, (298K) Our data MD-model

with *gij(r)* curve for Pd-Pd.

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

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

Molecular Dynamic Simulation of Short Order and

lead to different time mode of Hydrogen diffusion.

Hydrogen Diffusion in the Disordered Metal Systems 293

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 DSi = 4.93·10-6 cm2·s-1, but DSi = 2.53·10-6 cm2·s-1 with Hydrogen presence. There are different energy zones in an amorphous system, which

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 volume changing in 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).

0

constant energy E0 - Eg, (if energy distribution is Gaussian).

equal to 26kj/mol independently on Hydrogen concentration.

energy interstices, that are large faces polyhedrons.

depending on its concentration increase.

decreases diffusion mobility.

activation energy decrease.

Pd83Si17 alloy.

1 \* 0 0 0

*<sup>E</sup> D D*

*DD C*

exp

1 2

*RT*

Here D0\* - pre-exponent factor, E0- mean activation energy, equal to difference between mean Hydrogen energy, calculated, from energy distribution function and saddle point

Hydrogen diffusion factors are calculated from equation (11) dependent on its concentration for amorphous Pd83Si17 alloy at T=298K temperature. It was obtained, that DH increases

For example DH value is 7.85·10-6cm2·s-1 at Т=298К and СН(Н/Ме)=10-3 for amorphous

Basing on DH temperature dependence, diffusion activation energy value was estimated as E0 = 18.9 kj/mol. It should be noted, that for crystal alloy activation energy is higher. It's

According to Richards theory (Richards, 1983), there is Hydrogen probability to occupy low

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

On the other hand, Hydrogen atoms location in the higher energy interstices leads to

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.

(1 ) exp ,

(11)

*C RT*

Partial RDF for Si-Si indicates to preferential Silicon atoms distribution relatively each other in the second coordination sphere, i.e. Palladium atoms cover Silicon atoms by the first coordination shell (fig. 8).

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.

Fig. 9. Structure factor for amorphous Pd-Si with Hydrogen obtained by MD – model calculation.

Mixed type micro-groupings occurred, in Рd85Si15 alloy, are formed with most presence of BCC and FCC polyhedron type. Particles number does not exceed 13-14 in one cluster.

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.

Calculated diffusion factors values for Pd-H system were: DH = 18.8·10-6 cm2·s-1, DPd = 3.4·10-6 cm2·s-1, and DH = 6.67·10-6 cm2·s-1, DPd = 2.0·10-6 cm2·s-1 for amorphous Pd-Si-H alloy.

Partial RDF for Si-Si indicates to preferential Silicon atoms distribution relatively each other in the second coordination sphere, i.e. Palladium atoms cover Silicon atoms by the first

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

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.

structures of Pd-H, Si-H - types presence (Ivanova et.al,, 1994, Avduhin et.al, 1999).

Fig. 9. Structure factor for amorphous Pd-Si with Hydrogen obtained by MD – model

regular 2.71Å leg (Pd-Pd) base triangle (Polukhin, 1984)

Mixed type micro-groupings occurred, in Рd85Si15 alloy, are formed with most presence of BCC and FCC polyhedron type. Particles number does not exceed 13-14 in one cluster.

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

Calculated diffusion factors values for Pd-H system were: DH = 18.8·10-6 cm2·s-1, DPd = 3.4·10-6 cm2·s-1, and DH = 6.67·10-6 cm2·s-1, DPd = 2.0·10-6 cm2·s-1 for amorphous Pd-Si-H alloy.

Separately chosen Pd, Si and H atoms motion in our model is different by its character.

coordination shell (fig. 8).

calculation.

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 DSi = 4.93·10-6 cm2·s-1, but DSi = 2.53·10-6 cm2·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 volume changing in 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).

$$\begin{aligned} D &= D\_0^1 \frac{\partial}{\partial C} \left\{ (1 - C)^2 \exp\left(\frac{\mu}{RT}\right) \right\}, \\ D\_0^1 &= D\_0^\* \exp\left(\frac{E\_0}{RT}\right) \end{aligned} \tag{11}$$

Here D0\* - pre-exponent factor, E0- mean activation energy, equal to difference between mean Hydrogen energy, calculated, from energy distribution function and saddle point constant energy E0 - Eg, (if energy distribution is Gaussian).

Hydrogen diffusion factors are calculated from equation (11) dependent on its concentration for amorphous Pd83Si17 alloy at T=298K temperature. It was obtained, that DH increases depending on its concentration increase.

For example DH value is 7.85·10-6cm2·s-1 at Т=298К and СН(Н/Ме)=10-3 for amorphous Pd83Si17 alloy.

Basing on DH temperature dependence, diffusion activation energy value was estimated as E0 = 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.

Molecular Dynamic Simulation of Short Order and

0

1

2

a(s)

3

4

5

Hydrogen Diffusion in the Disordered Metal Systems 295

0 20 40 60 80 100 120

S,nm-1

0 20 40 60 80 100 120

4

5

6

s,nm -1

Fig. 10. Amorphous Ni-Zr alloys structure factors with hydrogen and without:

a) Ni36Zr64(1), Ni36Zr64+1H(2), Ni36Zr64+2H(3); b)Ni64Zr36(4), Ni64Zr36+1H(5), Ni64Zr36+2H(6).

0

1

2

a(s)

3

4

3

a

3

1

b

2
