The solubility and distribution of hydrogen atoms in ordering alloys

0360 3199/93 $6.00 + 0.00 Pergamon Press Ltd. © 1993 International Association for Hydrogen Energy.

Int. J. Hydrogen Energy, Vol. 18, No. 12, pp. 1001 1008, 1993. Printed in Great Britain.

THE SOLUBILITY AND DISTRIBUTION OF H Y D R O G E N ATOMS IN O R D E R I N G ALLOYS Z. A. MATYSINA,* O. S. POGORELOVA* and S. Yu. ZAGINAICHENKOt *State University, Dnepropetrovsk, Ukraine tMetallurgical Institute, Dnepropetrovsk, Ukraine (Receivedfor publication 10 March 1993) Abstract A theoretical investigation on the solubility of hydrogen in the ordering alloys AB3 with fcc lattice of LI 2 structure has been carried out. It is supposed that hydrogen atoms are located in octahedral, tetrahedral and triangulatical interstitial sites. The equilibrium distribution of hydrogen atoms in different interstitial sites and the kinetics of their redistribution with change of temperature are determined. Comparison of the theoretical results with experimental data on hydrogen solubility in Pd-Pt, Pd-Ni, Fe-V and Ni Fe alloys has been carried out.

a,b F N No, No, N o S T VO, ~0, ~Q

NOMENCLATURE A, B component concentrations Free energy of alloy Number of A, B atoms in alloy (number of lattice sites) Numbers of hydrogen atoms in octahedral O, tetrahedral 0 and triangulatical Q interstitial sites Hydrogen solubility Absolute temperature Energies of hydrogen atoms in O, 0, Q interstitial sites

INTRODUCTION Experimental investigation of the hydrogen solubility S in binary alloys A-B permit us to establish the relationships for the solubility functional dependences on T (temperature), a, b (concentration of matrix atoms) and long-range order ~/[1-12]. The experimental plots of the concentration and temperature dependences of hydrogen solubility in Pd-Pt, Fe-V, P d - N i and N i - F e alloys are shown in Fig. 1. As seen from Fig. 1, these dependences are found to be monotonic, extremal and discontinuous. The discontinuity appearance on the S(T) dependence takes place at the ordering temperature TOand is conditioned by the atomic order-disorder phase transition. It is also known that hydrogen absorption by some metals, e.g. by Pd, Zi and Nb may be considerable. In this case, hydrogen atoms can distribute in interstitial sites of all types: O (octahedral), 0 (tetrahedral) and Q (triangulatical). The volume of triangulatical interstitial sites is smaller than those of O and 0 interstitial sites: VQ < V0 < Vo. So, the arrangement of small hydrogen atoms is quite probable at Q interstitial sites. The authors of Ref. 113]

have pointed out the possibility even of C and B atom disposition in triangulatical interstitial sites of Ni3A1 alloy. It is Liecessary to note that arrangement of interstitial atoms at one or other interstitial site is determined not only by the relation between the volumes of the interstitial sites and of the atoms, but also on the whole by the interaction energies of interstitial atoms with A, B atoms of the structural matrix [14]. For each concrete system, both these factors (volume and energy) or either one of them can promote blocking of some interstitial lattice sites. It is also suggested that at great concentration, hydrogen atoms can be placed at the lattice sites [15] which can stimulate the experimental anomalies in the temperature dependence of hydrogen solubility. If hydrogen atoms can be arranged in interstitial sites of all three types and possibly at lattice sites, then the metal will be a good storage medium for hydrogen atoms. A theoretical investigation on hydrogen solubility in ordering alloys AB 3 with the fcc lattice of LI 2 structure has been carried out [16]. It is supposed that hydrogen atoms are located in interstitial sites of all types: octahedral, tetrahedral and triangulatical. The equilibrium distributions of hydrogen atoms in different interstitial sites and the kinetics of their redistribution with change of temperature are determined. The solubility and equilibrium distribution of hydrogen atoms are determined by minimization of the alloy free energy. The alloy free energy is found by the average energies method, neglecting with correlation, i.e. the hydrogen atom energy in each position is found by summation of the average energies of interaction between hydrogen and the nearest A, B atoms. The interaction between hydrogen atoms is not taken into account.

1001

1002

Z. A. MATYSINA et al. 2500

500

(a) 400

(b)

2000

)

300

1500 o

200

~ 1000

100

500 I

I

I

I

10

20

30

40

20

50

at % Pt in Pd

40

60

80

100

at % V in Fe (c)

0.02

(d) 30--

at % Pt in Pd

20--

,.~ -,~ 0 . 0 1

22.at ~ V m Fe

~

/

10--

100

I

I

300

500

700

I

I

400

800

T(°C)

1200

T(°C)

1.1 (e) .

(f)

..

0.3

0.9 "~ 0.2 0.7 o

0.1

400

I

I

500

600

b

Fe in Ni

I

i

700

T(°C)

300

I

TO

700

900

T(°C)

Fig. 1. Experimental concentration and temperature dependences of hydrogen solubility in Pd-Pt (a, c), Fe-V (b, d), Pd Ni (e) and Ni-F¢ (f) alloys.

FREE ENERGY O F ALLOY The ordered AB3-type binary alloys have two types of octahedral (O t, O2), one type of tetrahedral (0) and two types of triangulatical (Q 1, Q2) interstitial sites. The alloy elementary cell (Fig. 2) contains four lattice sites (one of first type and three of second type), four octahedral interstitial sites (three of Oa type and one of O 2 type), eight tetrahedral interstitial sites (all of 0 type) and 32

triangulaticai interstitial sites (24 of Q t type and eight of Q2 type). So, 11 interstitial sites of all types correspond to each alloy site and 1 IN is the total number of interstitial sites in the alloy, where N is the number of lattice sites. The calculation of the alloy free energy has been carried out by molecular-kinetic theory and also in the model of noninteracting interstitial atoms [14-1. The contribution of the electronic subsystem to the free energy is not taken into account.

HYDROGEN ATOMS IN ORDERING ALLOYS

1003

Numerical values of the V~H,V'~H,V~Henergies for each concrete system can permit us to determine the variational character of the interaction energies for H atomic pairs as a function of interatomic distance within the range 0.41d ~< r ~< 0.5d at the transition of interstitial atoms from Q into 0 interstitial sites and then into O interstitial sites. The calculation of the free energy part dependent on hydrogen concentration gives the following formula: F = --Nol/)Ox -kT Fig. 2. Elementary cell of ordering alloys with the fcc lattice of LI2 structure. Lattice sites and some interstitial sites are marked. O--Sites of first type (cube vertex); (3--sites of second type (face centre of cube); .--interstitial sites: octahedral of O~ type (edge centre of cube), of 02 type (cube centre), tetrahedral of 0 type (tetrahedron centre) and triangulatical of Qt, Q2 type (face centre of tetrahedron).

The energy of a hydrogen atom in the O1, O2, 0, Q1, Qz interstitial sites may be written in the form:

--AD(1)'¢~AH "}- --BDtl)"t~U + 3(P~)v~n .a_ u¢2),,, ~B VBH/, _ - - o(1),,,, - - A UAH + p(l),,,, a B UBH + 2(PtA2)V"AH+ --B D ( 2 ) ' ¢~BnJ, ' t "~

UO----

(1)

No, In No~

-(34N-Nol)ln(~N-No, 1

NQ2VQ2

)

N

+ ~ N In ~ - No~ In No2

+ 2N ln(2N) - N o In N o - (2N - No)ln(2N - No)

+ 2N ln(2N) - No2 In No2 -- (2N -- No2)ln(2N - No2)I ,

vo ~ = 3(p~)v~n _u ~0(2),,,, B V B H /"~ , where: t

r

v~H = V~H(r ), ~t = A, B

(2)

are interaction energies of the AH, BH atomic pairs with the opposite sign for different distances:

./5

(5)

where No,, No2, No, No,, No2 are the numbers of hydrogen atoms in O1, 02, 0, Q1, Q2 interstitial sites, N is the number of A, B atoms in the alloy (the number of lattice sites), k is the Boltzmann constant and T is the absolute temperature. Formula (5) determines the alloy free energy as a function of the Noi, No2 , No, NQI , NQ2 numbers, which are dependent on temperature, alloy composition, longrange order and energetic parameters.

r'=d~-~0.43d,

d r" = x ~ ~ 0.41d,

(3)

between A, B atoms on crystal lattice sites and interstitial atoms in O, 0, Q interstitial sites, d is a parameter of the crystal lattice:

P~) = a + 3q,

Nln ~-

N Q , VQI - -

- (6N - NQ)in(6N - Nol )

Vo2 = 6(P~)VAH + p(B2)/3BH),

r=0.5d,

No2vo~ - Nov o -

+ 6N ln(6N) - No1 In No1

Vo, = 2(P2)VAH + P(al)Van)+ 4(P(A2)VAH+ P(B2)VBH),

UQI

--

P~) = a - ¼rl, P~al)= b - ~rl, P(B2)= b + ¼q,

EQUILIBRIUM DISTRIBUTION OF HYDROGEN ATOMS The minimization of alloy free energy gives the following formulae:

3 No1 = 74N

(4)

are the a priori probabilities of replacement of the first and second types of lattice sites with A and B atoms, respectively, a, b are the A, B component concentrations and q is the long-range order.

1 No: = 74N

D exp 1 + D e x p ~~)O1 ' D exp I)O2 '

! + Dexp~

Z. A. MATYSINA et al.

1004

N o = 2N 1 + Dexp~

D exp

F r o m these formulae at low temperature (T--, 0) and positive energies vo > v o > vo, it is easy to show that:

/)0

D exp

Vo

,

(6)

UQa

N O = N n, N o = 0, NQ = 0

at 0 < N n ~< N,

N O = N, N o = N n -- N, N o = 0

at N ~< N n ~ 3N,

N o = N, N o = 2N, N o = N n -- 3N at 3N ~< N H ~< 1 IN, No=N,

NQ~ =- 6 N

No=2N,

NQ=8N

atNH= llN.

1 + D exp 1)QI' kT D

(11) In the case of

/)Q2 exp k T

T ~ 0

and negative energies vo

< vo <

/)Q, w e have:

NO2 = 2 N

1 + D e x p ~UQ2

N o = N H , N o = 0, N O = 0

at 0 < N H ~< 8N,

N O = 8N, N o = N n -- 8N, N O = 0 at 8N ~< N H ~< 10N, where D = exp - 2 / k T , 2 is the Lagrange factor, which corresponds to the relation: N a = No~ + N o : + N o + NQ~ + NQ2

(7)

and N a is the total number of H atoms in the alloy. In the presence of l l N interstitial sites in the alloy, the N H number can be changed within the limit of: 0 ~< Na ~< l l N .

(8)

Formulae (6) determine the distribution of hydrogen atoms in interstitial sites in dependence on temperature, alloy composition, long-range order and energetic parameters. If the interaction of the AH atom pair is stronger than of the BH atom pair, then at great order (q --* 1) of A, B atom distribution in lattice sites, we shall have, in correspondence with formulae (1)-(3):

N o = 8N, N o = 2N,

N o=N nNo=8N,

No=2N,

Uo

D exp k T 1 + D exp

l)O '

llN.

In accordance with formulae (11) and (12), at very low temperature, hydrogen atoms in the first instance will be located in interstitial sites with deeper potential wells, and as their filling is continued, the hydrogen atoms will be placed into other interstitial sites. The curved plots that represent the dependence of O, 0, Q interstitial site filling by hydrogen atoms on N H number at temperature T ~ 0 in accordance with formulae (11) and (12) will show broken and stepped lines. As temperature is increased, the lines are turned into smooth curves. The plots that demonstrate the hydrogen atom distribution in interstitial sites of disordered AB 3 alloy as a function of hydrogen concentration are shown in Fig. 3. At high temperature (T ~ oo), independently of energetic parameters, such a relationship is corrected: No:No:No=

In the case of a disordered alloy (q = 0) vo = Vol = Vo~, vQ = vo, = Vo~ and formulae (6) and (7) become:

atNa=

(12)

Ivo~l > Ivo~l > Ivol > IVQ~I > IVQ=[.

NO = N

No=N

1 0 N a t 1 0 N ~ < N n~< l l N ,

1:2:8,

(13)

which corresponds to the number of O, 0, Q interstitial sites, i.e. hydrogen atoms will be uniformly distributed in interstitial sites of all types. At N n ~ N, formulae (6) for No~, No2, N o, No1, No2 are simplified: 3

N ° I = 4 N D exp

v°~ N 1 vo = N D exp ,,2 k T ' o2 ~ kT'

Vo

D exp k T N o = 2N

1 + Dexp~

UO N o = 2 N D exp ~ ,

(14)

DO ' UQ1 N UQ2 NO, = 6 N D exp k T ' o~ = 2 N D exp kT"

VQ

D exp k T NQ = 8 N

1 + Dexp~

t~Q '

N n = N o + No + N o •

(9)

SOLUBILITY OF HYDROGEN

(lO)

The hydrogen solubility may be characterized by the number of H atoms that are related to the alloy lattice

HYDROGEN ATOMS IN ORDERING ALLOYS

1005

cal interstitial sites, the formulae for solubility will have the corresponding form:

(a)

So=D

21z z*l z z 4-

Q

3 e x p ~Vo, + e x p ~ - ~Vo~),

i

S o = 8D e x p , ,

,p

SO = 8D 3 exp ~

(17)

(18)

3

vo,

2 1 0

1

0

is

z '~

2

3

4

5

6

7

8

9

10

11

NH

N Co)

.........................

,

~

21z z z lz

--

1

0

,,~

Q

##

i

......................... l

2

3

4

,~5

6

7

8

- - ~ ~.,~ 9

10

11

NH N

Fig. 3. Curves of hydrogen atom distribution in Ox, 02, 0, Q1, Q2, interstitial sites of disordered ABa alloy in dependence on N r d N number at (a) Vo > vo > vQ and (b) vo < vo < re. Solid lines correspond to the case of very low temperature (T --, 0) and dotted lines correspond to the case of slight temperature increase.

cell with N' = ¼N A, B atoms: 3exp

The hydrogen solubility can be considerably increased from N H = 3N to N H = 11N at the expense of hydrogen atom distribution also in triangulatical interstitial sites, as is obvious from equations (15) and (7). The dependence of solubility on temperature even in the case of a disordered alloy is such that its natural logarithm In S* [see equation (16)-I is not a linear function of inverse temperature 1 / T . The value of the nonlinearity of the temperature dependence gives the opportunity to evaluate the packing of interstitial sites of all types by hydrogen atoms. The temperature dependence of S* solubility shows that this function may have an extremum under the condition: O0

vo e x p ~ T +

~o

2v o e x p ~ +

+ 8 exp ~

vQ~ vQ~. + 24 exp ~ + 8 exp kT ](15)

In the case of a disordered alloy, the solubility is determined by:

(

~Q

8vQexp~=0, (21)

which is realized when some energies vo, v o, v o have different signs. If H atoms are distributed in O and Q interstitial sites, then the temperature of the extremum: (22)

+exp vo

s . = 4D exp ~T

(20)

o + S O.

kT~=(Vo-Vo)~n(-8vo/vo),

S=~=D

(19)

Formulae (15)-(19) subject to equations (1) and (4) determine the solubility dependence on temperature, alloy composition, long-range order and energetic parameters in each case. It is obvious from equations (15) and (17)-(19) that: S = So+S

-

+ exp k T ] '

v° +

If hydrogen atoms are located only in octahedral interstitial sites, only in tetrahedral or only in triangulati-

may be real in the case when vo = vo(r) and v o = vQ(r") energies have unlike signs. Such a phenomenon may be fulfilled at the expense of the dependence of the interaction energies for the AH, BH atom pairs on interatomic distance. The change of interatomic distance from r" = 0.41d to r = 0.5d [see formulae (1)-(3)'1 leads to the sign change of VAn, VBn energies. Therefore, in the presence of an extremum on the curve of the S* = S * ( T ) dependence we can come to valuable conclusions about vAa(r), VBa(r) dependences. It is necessary to note that solubility theory, constructed on the configurational method, predicts the appearance of a minimum on the curve of the S * ( T ) dependence with unlike signs of the dissolution heats of

Z. A. MATYSINA et al.

1006

interstitial impurity in A and B metals (a necessary condition, but not sufficient) [17]. This theoretical conclusion is in accordance with the experimental data of hydrogen solubility in Fe-V alloy (Fig. ld). However, in P d - P t and P d - N i alloys, for which the corresponding dissolution heats of hydrogen in Pd, Pt and Pd, Ni metals have unlike signs, the curves of the S* = S*(T) dependence are found to be monotonic (Fig. le, c), and with temperature increase the solubility is decreased. The dependence of hydrogen solubility on composition S * = S*(a) for a disordered alloy is a monotonic function, in accordance with equation (16). The solubility is changed from the value of hydrogen solubility in metal A:

/ 6YAH 4V~H S A = 4 D ~ exp kT + 2 e x p k T - + 8 e x p

3V~rf'~ kT)

at a = 1,

(23)

to the value of hydrogen solubility in metal B:

the arrangement of hydrogen atoms in O and Q interstitial sites (as in all interstitial sites O, 0, Q of all types simultaneously), the solubility has to be increased with appearance of the atomic order ~/ in the alloy. This conclusion corresponds to experimental investigation of hydrogen solubility in N i - F e alloy (Fig. If). The decrease in temperature leads to a discontinuous increase in hydrogen solubility in Ni Fe alloy at ordering temperature To. THE KINETICS O F H Y D R O G E N ATOM REDISTRIBUTION The alloy temperature change gives rise to redistribution of hydrogen atoms into different interstitial sites. Let the alloy temperature decrease abruptly (as with quenching) from T = T1 to T = T2. Suppose also that the redistribution of"slow" A, B atoms does not take place at lattice sites. The kinetic investigation of thermoactivated redistribution of hydrogen atoms is carried out for a disordered alloy at N n ,~ N. The kinetic equations are determined by the following formulae:

/ 6vnn 4vha 3v~n'~ SB = 4D~exp ~ - + 2 exp ~ - + 8 exp k T J

dt = H ° ° at a = 0,

dNo d t = H ° ° - H°°'

dNo

H°°'

(29)

(24) NQ

where v~n = v,n(0.5d), v',n = v,n (0.43d), V:H = v,n(0.41d), = A, B. This is also in accordance with experimental data of hydrogen solubility in P d - P t and Fe-V alloys (Fig. la, b). Let us elucidate the influence of long-range order r/on solubility. It is convenient to investigate separately the functions So(q), So(rl), So(t0 [see equations (17)-(19)] near the temperature of stability loss T', that is, somewhat less than the ordering temperature To. Near temperature T', where r/,~ 1, we expand the So(q), So(q), So(q) functions [see formulae (17)-(19) subject to conditions (1), (4)] into a power series of r/and retain for consideration expansion terms of the series with r/ up to the second power. The calculation results in the following expressions:

I 3 (YAHk~-T -- UBH)2 ] SO = S* 1 + 4 5 q2 ,

(25)

So = S*,

(26)

=

N H - - N O - - N o,

where: 1

Up - - UQ

HQo=N o~exp

kT

1

v,~

Hos=N o~exp

I

'

1

- - UQ

kT

Up - - UO

H°°= 8N°zexp

kT v, -- v o

H°o= 4 N ° z e x p

'

'

kT

'

(30) r = 10-13 s and re, v, are the energies of hydrogen atoms at the peak of the potential barrier in transitions O ~ Q amd 0 ~ Q. It is convenient to rewrite equations (29) for the relative concentrations:

C o=N~°

N n'

C o= N~°

N n'

CQ--

NQ N H"

(31)

They are presented as: 3 (UAH " -- UBH) ,, 2 . 2q SQ = S~ 1 + 16" k2~T2 q j ,

dCo dt- = a2C° + b2C° + C2'

dCo (27)

dt = alC° + blC° + C1'

CQ= 1 - C o - C o, where where the following conventions are introduced: S* = (So),=o, So* - (S0),=o, SQ * - (SQ),=o.

(28)

As was to be expected, we receive S o = S*o for tetrahedral interstitial sites 0, as the examined structure contains only one type of such interstitial sites independent of long-range order. By formulae (20) and (25)-(27), with

a 1=-

~(

vp - vo Vp - vQ~ 8exp~+exP~k~-),

I

bl = - 3 e x p

Up - - DQ

kT

'

(32)

HYDROGEN ATOMS IN ORDERING ALLOYS 1

vv

C t = ~exp

-

~Q

-

kT

1

9¢

a2=-~exp

' -

-

l) O

kT

'

v~, - vo

4exp~+exp

bz=I

v~, - vo" ~

kT

/)O - - /)Q

C 2 = ~ exp

-kT

J' (33)

"

Kinetic equations permit the establishment of the time dependence of concentrations Co, Co, C O• Solutions of these equations may be written as: Co(t ) = G~ ~e x p ( - s l t ) + G~ ) e x p ( - s 2 t ) + Co(T2), Co(t ) = G~ t) exp(--Slt ) + Gto2) e x p ( - s z t ) + Co(T2), CQ(t) = G~ J e x p ( - s l t ) + G~ ) e x p ( - s 2 t ) + Co(T2), (34) where values st, s2 are the roots of the characteristic equation of system (32), and coefficients G~ ), G[1~, G~ ), G~ ), G~2~, G~ ) are determined by the conditions: Co(t ) = Co(Tt),

Co(t ) = Co(Tt), at t = 0,

CQ(t) = Co(T1)

Co(t ) = Co(T2) ,

Co(t) = Co(T2), at t--+ oo.

Co(t) = Co(T2)

It is obvious that:

1007

change if vo > vo > vo, in comparison with the same if Vo < vo < v o (see Fig. 4). This is conditioned by the presence of the triangulatical interstitial sites, of which there are 8 times more than octahedral and 4 times more than tetrahedral interstitial sites. Therefore, from the slope of the curve we might suppose the value and sign of the energetic parameters Vo, vo, v o. Furthermore, the extremal dependence of hydrogen concentration on time Co(t ) may be shown for interstitial sites with an average depth of potential well (that is tetrahedral interstitial sites). The maximum of this dependence will be at the moment: te = - - 1

in(_~i)

'

S 1 -- S 2

from which it follows that the extremum can be when G~I), G~2) have opposite signs. With distribution of hydrogen atoms only in interstitial sites of two types, the extremal dependence of concentrations Co, Co or Co, C o or Co, C o on time do not take place. Therefore, as a result of experiments, the presence of a maximum in the dependence Co(t) points to the distribution of hydrogen atoms in interstitial sites of all types. Values st, s2 characterize the rate of attainment of the equilibrium state by the system. If this rate is great, then the plots of Co(t), Co(t), Co(t) have a considerable slope, while if the attainment of the equilibrium state is too small, then the plots will be smooth. It is important to know the rate of equilibrium state attainment for determination of the conditions for heat treatment of alloys.

6 ~ ) + afro= Co(rl) - Co(T2), G [ " + a [ ~) = Co(T,) - c o ( r g ,

G~' + G~ ) = Co(T,) -- Co(T2). The investigation of equations (34) shows that plots of dependences Co(t), Co(t ), Co(t) have a greater rate of

(a)

Co' Co, Co

CONCLUSIONS The received formulae for the number of hydrogen atoms in interstitial sites O, 0, Q of all types permit us to ascertain the character of hydrogen atom distribution in an alloy at different temperatures and energies of inter-

(b)

Co, Co, Co

1

8/11

0

2/11 0

te

t

0

te

t

Fig.4. Character of the time dependence of hydrogen atom concentrations in O1 -= 02, 0, Q1 - Q, interstitial sites of disordered AB3 alloy at sharp temperature decrease (T1 ~ T2) for cases of(a) Vo > vo > vo and (b) Vo < vo < vQ. Dotted lines show the possible extremal dependence of hydrogen concentration Co(t).

1008

Z, A. MATYSINA et al.

atomic interaction. The arrangement of hydrogen atoms in triangulatical interstitial sites (besides octahedral and tetrahedral) leads to a considerable increase of the hydrogen solubility. The dependence of hydrogen solubility on alloy composition is monotonic. The temperature dependence of hydrogen solubility may have a m i n i m u m if the energies of hydrogen atoms in the interstitial sites O, 0, Q have different signs. The long-range order increases the hydrogen solubility. It is established that the character of the dependence of hydrogen atom concentration in interstitial sites O, 0, Q on time is determined by the relation between the energetic parameters. The criteria are listed at which the dependence of hydrogen concentration in interstitial sites 0 can be extremal. The elucidated regularities of hydrogen solubility are in complete agreement with experimental data for alloys P d - P t , Fe-V, P d - N i and Ni-Fe. REFERENCES 1. C. J. Smithells, Gasy i Metally. Metallurgiya, Moscow (1940). 2. D. P. Smith, Hydrogen in Metals. University Press, Chicago, IL (1948). 3. M. Smialowski, Hydrogen in Steel. Pergamon Press, London (1962).

4. J.D. Fast, Interaction of Metals and Gases. Philips Technical Library, Eindhoven (1965). 5. H. J. Goldschmidt, Interstitial Alloys. Butterworths, London (1967). 6. F. A. Lewis, The Palladium-Hydrogen System. Academic Press, New York (1967). 7. W. M. Mueller, S. P. Blackledge and G. G. Libowitz, Metal Hydrides. Academic Press, New York (1968). 8. O. Kubashewskii, A. Cibula and C. Moore, Gases and Metals. Iliffa, London (1970). 9. I. Fromm and E. Gebhardt, Gases und Kohlenstoffin Metallen. Springer, Berlin (1976). 10. C. J. Smithels, Metals Reference Book. Butterworths, London/Boston (1976). 11. R. A. Andrievskii and Ya. S. Umanskii, Fazy Vnedreniya. Nauka, Moscow (1977). 12. G. Alefeld and J. Vrlkl, Hydrogen in Metals. Springer, Berlin (1978). 13. N. Masahashi, T. Takasugi and O. Izumi, Acta Metall. 36, 1815 (1988). 14. A. A. Smirnov, Teoriya Splavov Vnedreniya. Nauka, Moscow (1979). 15. S.I. Masharov and A. F. Rybalko, Fiz. Met. i Metalloved. 9, 197 (1991). 16. Z. A. Matysina, O. S. Pogorelova and S. Yu. Zaginaichenko, Proc. 9th World Hydrooen Energy Conf., Vol. 2, p. 979, Paris (1992). 17. Z. A. Matysina, M. I. Milyan and S. Yu. Zaginaichenko, J. Phys. Chem. Solids 49, 737 (1988).