**6. 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, 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 Ni64Zr36 (alloy 1, curve 4) и Ni36Zr64 (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 NiZr2 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 NiZr2 composition (curve 1), two first maxima location of a(s) curve corresponds to averaged location of the interference lines for crystal NiZr2 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 ZrH2 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 gij(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 DH varies from 2·10-4 up to 1.2·10-5сm2·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, DH grows

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, 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 Ni64Zr36 (alloy 1, curve 4) и Ni36Zr64 (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

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 NiZr2 composition (curve 1), two first maxima location of a(s) curve corresponds to averaged location of the interference lines for crystal NiZr2 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 ZrH2 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

Partial gij(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 DH varies from 2·10-4 up to 1.2·10-5сm2·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, DH grows

**6. Hydrogen diffusion in the amorphous Ni-Zr alloys** 

icosahedron cluster, which is the basic structural unit of NiZr2 crystal.

contents of Zr and H atoms.

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).

Molecular Dynamic Simulation of Short Order and

(tetra-cavities) and an abrupt increase of DH is observed.

System

**the Zr-Fe melt** 

Hydrogen Diffusion in the Disordered Metal Systems 297

with increase of hydride forming element Zr concentration and H atoms in the MD-model. The activation energy of hydrogen diffusion for amorphous Ni64Zr36 alloy was estimated in the 298-768К temperature interval. A value of Е=0.1еV 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

Partial RDF

Ni64Zr36 0.238 0.270 0.301 Ni36Zr64 0.240 0.261 0.290 Ni64Zr36 < 1H2 > 0.240 0.266 0.310 1.2·10-5 Ni64Zr36 < 2H2 > 0.240 0.26 0.29 1.7·10-4 Ni36Zr64 <1H2 > 0.241 0.265 0.297 8.9·10-5 Ni36Zr64 < 2H2 > 0.230 0.250 0.280 2.1·10-4 Table 2. Short order parameters for amorphous alloy in the Ni-Zr and Ni-Zr-H systems.

**7. Hydrogen and electric field effect to Iron impurities diffusion in** 

radii for Iron and Zirconium (rZr-Fe= 0.29nm, rFe= 0.130nm, rZr= 0.162nm).

intensity applying decreases DFe to 5.23·10-5cm2·s-1 (fig.14).

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 1.1·10-15s 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 gij(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

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, rTa = 0.145nm) and Zr-Zr (0.324nm, rZr=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 (DFe) in the Zirconium melts with Hydrogen linearly depends on electric field intensity (E) and Iron concentration (СFe). Hydrogen diffusion factor negligibly decreases from 2.16·10-4 cm2·s-1 to 1.94·10-4 cm2·s-1, if electric field intensity increases from 900 to 1020 v/m. Hydrogen inducing into system at СFe≈0.1% decreases DFe value from 7.86·10-5 to 6.36·10-5cm2s-1, and electric field 1020 v/m

at 298<sup>К</sup> Ni-Ni Ni-Zr Zr-Zr r, nm r, nm r, nm cm2s-1

DH

Fig. 11. Radial distribution functions gij ( r) of Ni64Zr36 alloy: (а) - no hydrogen; (b) - one hydrogen atom. Partial gij (r): 1,5- general; 2,8 - Ni-Ni; 3,7 - Ni-Zr; 4,6 - Zr-Zr; 9 - H-H. r, nm

0,0 0,2 0,4 0,6 0,8 1,0

**r,nm**

1

9

**b**

7 6 5

8

2

4

**а**

3

Fig. 11. Radial distribution functions gij ( r) of Ni64Zr36 alloy: (а) - no hydrogen; (b) - one hydrogen atom. Partial gij (r): 1,5- general; 2,8 - Ni-Ni; 3,7 - Ni-Zr; 4,6 - Zr-Zr; 9 - H-H.

0,0 0,2 0,4 0,6 0,8 1,0

r, nm

0

0

2

4

6

gij(r)

8

10

12

2

4

**gij(r)**

6

8

with increase of hydride forming element Zr concentration and H atoms in the MD-model. The activation energy of hydrogen diffusion for amorphous Ni64Zr36 alloy was estimated in the 298-768К temperature interval. A value of Е=0.1еV 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 DH is observed.


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