Formation of superabundant vacancies in metal hydrides at high temperatures

Journal of

AND C O M ~ U N D 5 ELSEVIER

Journal of Alloys and Compounds 231 (1995) 35-40

Formation of superabundant vacancies in metal hydrides at high temperatures Yuh Fukai Department of Physics, Chuo University, Kasuga, Bunkyo-ku, Tokyo 112, Japan

Abstract It has been found from X-ray diffraction on several M - H systems under high p, T conditions that a large number of M-atom vacancies amounting to ca. 20 at.% are formed at high temperatures, leading to a vacancy-ordered L12 structure in some f.c.c. hydrides. The energetics of vacancy formation in hydrides suggests that defect-hydrides containing many vacancies are generally more stable thermodynamically than ordinary defect-free hydrides and therefore most phase diagrams of M-H systems reported heretofore are metastable. Keywords: Superabundant vacancies; Metal hydrides

1. Introduction In most M - H systems, H atoms enter interstitial sites of the metal lattice, the structure of which may retain its original form or undergo modification as more H atoms are introduced. The relation between different phases (including a surrounding gaseous H e phase) has been reported for many M - H systems, in the form of phase diagrams or p - x - T relations. Owing to the rapid diffusion of H atoms, processes occurring in M - H systems are generally very fast in comparison with most solid-state reactions or transformations, and lead to a final state in a fairly short time. In an attempt to determine phase relations at higher values of p, x, T, however, it was discovered that in Ni and Pd hydrides a very slow process extending over several hours took place at high temperatures (around 800 °C), causing gradual contraction of the lattice [1]. This lattice contraction was interpreted as being due to the formation of a large number of M-atom vacancies, amounting to ca. 20 at.% In more detailed experiments on the P d - H system [2], it was subsequently observed that a vacancy-ordered structure of L12 type, Pd3VacH n, formed in the lattice-contracted state in the course of cooling from high temperatures. The vacancy concentration in a quenched specimen was determined from the changes in total volume and lattice parameters; it was found to be consistent with this structure. Thus, the formation 0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(95)01834.-4

of superabundant vacancies, which at first appeared unlikely, has attained solid experimental support. The purpose of this paper is to describe the present state of the investigation into superabundant vacancy formation and some of its consequences, including in particular its implications for the constitution of M - H systems in general.

2. Experimental details To make any measurements on metal hydrides at high temperatures, a sample must be placed inside a container impermeable to hydrogen, and the decomposition pressure of the hydride must be sustained by applying high external pressures. In our experiments using a cubic-anvil type press, the sample was a disk of compacted powder, 1 - 2 mm ~b × (0.2-0.3) mm in size, encased in an NaC1 capsule (hydrogen sealant), surrounded by a graphite tube heater, placed at the center of a solid pressure-transmitting medium of 8 mm cube. With this assembly, the temperature could be raised to 1200 °C at a pressure of several gigapascals without any detectable loss of hydrogen. Hydrogenation by high-pressure fluid H 2 was performed by charging an internal hydrogen source, a pellet of LiAIH4, inside the NaC1 capsule. When heated, this decomposes irreversibly at 300400 °C and supplies H 2 to the sample. The sample and

Y. Fukai / Journal of Alloys and Compounds 231 (1995) 35-40

36

LiA1H 4 were separated by thin BN discs to prevent any chemical reaction, In situ X-ray diffraction measurements were taken using a cubic-anvil press MAX80 installed at the

(1) The formation volume of a vacancy can be written in the form

Accumulation Ring of the National Laboratory for High Energy Physics ( K E K ) at Tsukuba. In the energy-dispersive method employed here, diffracted X-rays were energy analyzed by an SSD placed at a fixed angle to the incident beam. More details of the cubic-anvil press MAX80 and the sample cell are given in Refs. [3] and [4] respectively. For quench-recovery experiments, a cubic-anvil press, Oz.Fl, of our laboratory was used.

where v 0 is the atomic volume and AVR is the relaxation volume caused by the average change in the lattice parameter, i.e. AVR/V o = 3(da/dxv)/a, x v being the vacancy concentration in atomic ratio. Previous investigations of f.c.c, metals with large ion cores, i.e. noble metals and transition metals, show that the relaxation volume is always negative, ranging between - 0 . 2 and - 0 . 5 of the atomic volume [5]. (2) The observed temporal variation of the contraction was consistent with the time needed for M-atom vacancies created at the surface to diffuse into the interior of a sample. For Ni, using an approximate expression for the diffusivity of a vacancy in a metal,

3. Results 3.1. Lattice contraction occurring at high temperatures--formation o f superabundant vacancies The temporal variation of the lattice parameter observed in two separate runs for Ni is shown in Fig. 1 [1]. In the course of heating, the lattice parameter increased rapidly as a consequence of hydrogenation, and attained an asymptotic value corresponding to the stoichiometric composition NiH. The gradual lattice contraction that ensued at 800 °C was found to be retained after quenching and decompression to ambient conditions, and even after removal of hydrogen by heating briefly to 400 °C in vacuum. It was only after annealing at 800°C for 15 min that the lattice parameter returned to its original value, Our inference that the lattice contraction was caused by the formation of M-atom vacancies was based on the following considerations, 3.80

i

i

i

I

i

I

i

]

i

i

i

i

i

1

t

[

i

[

3.75 -

*~ 3.703.65-3.60-

E

3.55~~

7sO.,__.._.7c) 800 800 700.'~" r - - ~ 600~t ~ 500~_~ "500 / . . . . 400 / 1 I d"400 1.400 [ ~-400 1.3oo

3.50~ -~(200~ 0 0 ~2~ zoo 16 3.451"t

0

t

1

I

2

i

t

~,~-3oo

t

I

i

,tin1

•

]~L~2

t

t

I

6

t

t

i

I

8

I

(2)

and a known value of the migration energy, e m = 1.1 eV at normal pressure [5], the diffusivity at 800 °C is estimated to be D v = 7 × 10 -8 cm 2 s t, and the time to travel a sample thickness d = 0.2 mm to be t~ = d2/ 2D~ ~ 3 × 103 s. This value agrees fairly well with the observed time scale of the process. Processes caused by diffusion of H atoms are much faster, as actually observed for the initial hydrogenation process in Fig. 1. Similar lattice contractions were observed, when Pd, Mn, Ti dihydride, Zr dihydride, P d - R h and P d - P t alloys were held at high temperatures ( 6 0 0 - 8 0 0 ° C ) i n fluid hydrogen of 5 GPa. 3.2. Concentration o f vacancies produced in the hydride phase

-

vacancies

-

the melting point.

in

metals,

which

amount

to

only

ca.

10

4 at

-

-

4

D v ~ 10 -2 e x p ( - e m/kT) cm 2 s-1

-

=

•

(1)

The concentration of vacancies produced at high temperatures can be estimated, approximately, from the magnitude of the lattice contraction, using a reported value of the relaxation volume of a vacancy. For Ni, from the observed lattice contraction Av/ v o = 3Aa/a o = - 0 . 0 4 0 (Fig. 1) and relaxation volume AVR/V o = --0.22 [6], the vacancy concentration is estimated at Xv = 0.040/0.22 = 0.18! This value is extremely high compared with concentrations of thermal

-

-

Vf=v°+AVR

t r 10

time/h Fig. 1. Temporal variation of the lattice p a r a m e t e r of Ni in the course of heat treatment under a hydrogen pressure of 5 GPa. The temperature at each point is inscribed (in °C) [1].

Lattice contractions of the same order of magnitude were observed in other cases (Pd, Mn, Till1.8, P d - R h and P d - P t alloys in high-pressure fluid H2), indicating that similar amounts of vacancies were produced. More precise determination of the vacancy concentration was made by measuring the total volume and lattice parameter of a quenched specimen [2], i.e. by the method devised by Simmons and Balluffi [7] to

Y. Fukai / Journal of Alloys and Compounds 231 (1995) 35-40

determine the equilibrium concentration of thermal vacancies in metals. In practice, we determined the volume change by measuring the density, and obtained the vacancy concentration from the relation x v = -Ap/po - 3Aa/a o

37

2100 5GPa 500"c 2 o= 4.0°

~

<

(3)

This experiment was perf°rmed f°r Pd" Three small disks (2 mm~b × 0.2 mm), weighing 13 mg in total, were cut out from a sheet of Pd, and used for density measurements after the following treatment. After compression to 5 GPa, samples were heated to 700 °C for hydrogenation to nearly stoichiometric PdH, then maintained there for 3 ih and subsequently quenched and recovered to amb:tent pressure. The recovered samples were heated to 350 °C in vacuo for 3 min for

degassing hydrogen, and quenched. The density was measured using the Archimedean method, using water and an electronic balance of sensitivity 10 ~g. From the observed changes in density and lattice p a r a m e t e r , A p / p o = --0.139 ---+0.029 and A a / a o = 0.014_ 0.001, the vacancy concentration was obtained to be Xv = 18_ 3 at.%. This value is not affected by the possible presence of residual hydrogen atoms in the lattice. Their effect on volume and lattice parameter cancels and their effect on the total weight is negligible. Still another observation which provides a measure of vacancy concentrations was made for Ni [8]. A sample obtained after the heat treatment for vacancy formation described above was then heated in vacuo to 800 °C. Observation by SEM revealed the presence of numerous voids formed by agglomeration of vacancies. The total volume of the voids agreed reasonably well with the estimate from the relaxation volume described above. 3.3. F o r m a t i o n o f a v a c a n c y - o r d e r e d s t r u c t u r e

It is naturally expected that if such a large number of vacancies is created at high temperatures, they must assume some ordered arrangement at lower temperatures. This expectation was verified in our subsequent experiment on Pd [2]. Fig. 2 shows the diffraction pattern taken at 500 °C after heating at 800 °C for 3 h in fluid H 2 of 5 GPa. The diffraction pattern consists of two sets of peaks labeled A and B arising from two coexisting phases. Phase A, having an f.c.c structure with a = 4.069(1) A, is assigned to nearly stoichiometric PdH. Phase B, an f.c.c, structure having a slightly smaller lattice parameter a = 4.016 A, contain,,; additional superlattice reflections with simple-cubic indices (100), (110), (210)and (211). We concluded from symmetry considerations that the only possible structure for this second phase is the L12 (Cu3Au type), Shown in Fig. 3, in which one of

°~

~ I 0-

~

~-.t ~ i = 5=

0 .J,,._

. s00

= "~ ~'~ k,~dk,~_. 10'00 15'00 channel

.

~ ~ ~z \~ 20'00

Fig. 2. X-ray diffraction pattern of Pd hydride measured at 500°C at a hydrogen pressure of 5 GPa, after holding at 800 °C for 3.5 h. Separation into two phases, PdH (A) and a vacancy-ordered phase Pd3WacH4 (B) is clearly visible [2].

Defect- fcc

( M3Vac )

O'M, O; Vacancy ~ ~

'

~

~

~ '

A B

Fig. 3. Vacancy-ordered L12 structure.

the four simple-cubic sublattices constituting the f.c.c. lattice is occupied by vacancies. Our first proposition for the formation of vacancyordered structures in hydrides had been made still earlier. We observed the appearance of superlattice lines having simple-cubic indices in f.c.c. MnH [9] and b.c.c. Fell [4,10], and proposed that a vacancy-ordered L12 structure (Cu3Au-type) was formed in the f.c.c. lattice and a B2 structure (CsCl-type) in the b.c.c. lattice. However, it was only after the formation of superabundant vacancies was established that the origin of superlattice lines came to be fully understood. 3.4. A c c e l e r a t e d d i f f u s i o n o f m e t a l a t o m s

When the diffusion of M atoms proceeds by the vacancy mechanism, as in most metals and probably also in metal hydrides, the diffusivity of M atoms is expressed by the product of the concentration and diffusivity of vacancies, D = XvDv . Thus, the diffusion of M atoms should become much faster as many vacancies are introduced in the hydride phase.

38

Y. Fukai / Journal of Alloys and Compounds 231 (1995)35-40

Evidence for the enhanced mobility of M atoms in a hydrogen atmosphere has been reported for P d - M n [11], P d - R h [12,13], and P d - P t [14] alloys. In H 2 atmosphere, the formation of an ordered structure in Pd3Mn and segregation in P d - R h and P d - P t alloys were found to occur in metastable solid solutions at temperatures where the processes are too slow to be observed in vacuo, In the P d - R h alloy, for example, a miscibility gap exists below 845 °C [15,16], but no evidence of segregation in quenched Pd0.74Ph0.26 alloy was found by R a u b et al. after annealing at 600 °C for i year [15]. By heating in 5.5. M P a of H E gas, however, N o h and coworkers [12,13] obtained strong indications, from hydrogen absorption isotherms, electron microprobe analysis and metallographic examinations, that the phase separation took place in Pd0.sRh0 2 alloy in 4 h. We have recently undertaken a high-pressure experiment to observe the phase separation directly by X-ray diffraction [17]. The sample adopted was a solid solution of Pd0sRh0. 2, quenched from elevated temperatures. In the course of hydrogenation in 5 G P a of fluid hydrogen (as seen in the initial increase in the lattice p a r a m e t e r in Fig. 1), there a p p e a r e d after a few minutes at about 500°C a second phase having a lattice p a r a m e t e r close to that of pure metallic Rh, indicating that the separation into Pd-rich hydride and Rh-rich metal took place. This second phase disappeared on gradual heating to about 550°C after around 10 min. A sample containing these two phases was examined by T E M after quenching to ambient conditions, and precipitates of the second phase were found to be distributed at an average distance of approximately 0.1 txm. F r o m these results, the diffusivity of Rh atoms was estimated to be of the order of D ~ 10 -13 cm 2 s -1 As the ordinary diffusivity in v a c u u m can be estimated from an empirical formula, D ~ ( 0 . 1 - 1 ) e x p ( - 1 7 T m / T ) cm2s -1 (T m is the melting point) [18], to be D ~ 1 0 -17 to 10-18cm2s -1 at 600°C; the observed diffusivity is 4 to 5 orders of magnitude larger. This substantial e n h a n c e m e n t of the diffusivity m a y be explained in terms of extra vacancy formation in the presence of interstitial hydrogen. As the equilibrium vacancy concentration in vacuum is roughly estimated from an empirical formula, Xv ~" l O e x p ( - 9 . 3 T m / T ) [19], to be approximately 10 -s at 600°C, the observed e n h a n c e m e n t of diffusion requires the vacancy concentration of x v ~ 10 -3 to 10 -4. It appears quite reasonable that the vacancy concentration of this magnitude was reached at about 500 °C before it attained its m a x i m u m value of x v ~ 0.2 at higher temperatures. Similar accelerated segregation was also observed in P d - P t alloys by in situ X-ray diffraction under high hydrogen pressures,

4. Discussion

4.1. Mechanism of vacancy formation in hydride phases H e r e we present a qualitative discussion of the formation mechanism of superabundant vacancies in hydrides. Let us recall that in all metals investigated by ion implantation experiments, H atoms are trapped by vacancies, up to six atoms per vacancy, with rather large binding energies (Table 1, compilation in Ref. [20]). This implies that the formation energy of a vacancy in the presence of interstitial H atoms is effectively lowered as m o r e H atoms are trapped by the vacancy, and eventually becomes the formation energy of a VacH 6 complex, e'f = ef ~i = 1 ebi" The values of e'f, also listed in Table 1, show that the decrease in ef in the presence of H atoms is substantial. The lowering of the energy of trapped H atoms nearly compensates for the formation energy of a vacancy. A crude estimate of ef for Ni hydride can be obtained from the results described in Section 3.2. Using an approximate expression [19] -

Xv/(1 - xv) = exp(sf/k) e x p ( - h f / k T ) 10 e x p ( - h f / k T ) (4) and substituting x v = 0.18 and T - - 1 0 7 3 K, we obtain the formation enthalpy of a vacancy h e -~ 0.35 eV. Subtracting pvf ~ 0.30 eV at 5 G P a (vf ~-10 A ), we have ef ~--~0.05eV. Considering the various approximations involved, this value is entirely consistent with the value of e'f given in Table 1. Similar results were also obtained for Pd. Electronic energy calculations on vacancy-ordered hydrides a p p e a r to be quite feasible, and await the efforts of theoreticians. 03

1 Vacancyformation energy in a metal e. hydrogen-vacancy binding energy eb, and formation energy of a VacH6 complex in the presence of interstitial H atoms e'f

Table

Metal

ef

eb

e'f

A1 Ni Cu Pd Fe Zr Mo Ta

0.66 1.55 1.31 ~1.7 1.60 =2.0 3.1 3.1

0.52 O.44,0.28 0.42,0.22 0.23, 0.15

-2.5 -0.45 -0.41 ~0.6 -1.4 =o.3 -2.3 0.6

0.63,0.43

0.28 1.08 0.42

When two values are given for eb, the first is for the first two H atoms and the second is for the 3rd to 6th H atoms trapped by a vacancy.When only one value is given, it is the average of six H atoms trapped by a vacancy. Energies in eV [20].

Y. Fukai / Journal of Alloys and Compounds 231 (1995) 35-40

39

4.2. Superstoichiometric hydrides--Increase in maximum H content in vacancy-ordered hydrides If each M-atom vacancy in a hydride phase retains the same number of adjacent H atoms as an M atom on a regular site, an original hydride MH n will have a composition MVac~Hn(t+~). Hence, the H concentration is increased to 1 + a times the original value. For an f.c.c, structure, the vacancy-ordered L12 structure will have a maximum H concentration Xmax 4/3 for a monohydride, Xmax 8/3 for a dihydride and Xmax 4 for a trihydride. These results compare reasonably well with the composition of superstoichiometric hydrides formed by low-temperature ion implantation ([H]/[Ni] = 1.15 --- 0.07 [21], [H]/[Pd] = 1.32 _+0.07, 1.6 -----0.2 [22], [H]/[Ti] -'= 2.8 --- 0.4 [21] and [H]/[Zr] = 5.0 +--0.8 [21]). Unfortunately, our high-pressure ex=

=

~ ~ ~ ~ ~ ~ ~ ,~ -Q .-E_ ~ ~9

' ~ -~---~

4.3. Implication of defect-hydride formation for the phase diagram of M-I-I systems Our observation of the formation of M-atom vacancies in a number of metal hydrides shows that the phase containing superabundant vacancies (which we call the defect-hydride phase) is more stable thermodynamically than ordinary defect-free hydrides at least under high p, T conditions. We note immediately, however, that high p, T conditions are not essential for stability arguments. High temperatures were necessary to allow vacancy migration in reasonably short times and high pressure was necessary to avoid loss of hydrogen at high temperatures. In addition, the foregoing discussion on the formation mechanism of vacancies in a hydride phase suggests that the internal energy of a defect hydride phase is appreciably lower than that of tile original defect-free hydride. In this connection, :results of our melting expertments may be quoted. We observed for TiHL8 that, on melting, a lattice-contracted phase appeared and coexisted with a melt [23]. This implies that the defect hydride (probably Ti3VacHs) has a higher melting point than the defect-free hydride. Similar observation was also made on Pd0.8Rh0. 2 alloy, where a defectordered phase was found to coexist with a melt. The temperature dependence of the Gibbs free energy of a defect-hydride phase G d, the defect-free hydride G o and the melt Gin, inferred from these observations, is shown schematically in Fig. 4. The implication of these considerations for the

~

Go Gd(Ord.)

G d ( d l s . ) Gm T° ~

=

periments cannot determine the H concentration directly. Most probably, superstoichiometric hydrides were formed under high p, T conditions, but only the vacancies were quenched to ambient conditions while excess H atoms were lost. More effort is needed to make clear the connection between the results of these two types of experimen~t,

x',x

o

"re Tam ~

Temperature

Fig. 4. Temperature dependence of the Gibbs free energy of defectfree hydride G0, defect-ordered hydride Gd(ord), defect-disordered hydride Gd(dis ) and a melt Gm. The melting points of the defect-free phase T°m and defect-hydride phase T~ are also inscribed, as well as the temperature of order-disorder transition T c in defect hydride.

phase diagram of M - H systems is profound. Notice that in practically all cases the phase diagrams of M - H systems have been determined using samples prepared by ordinary methods of hydrogenation, either by absorption from gaseous H 2 or by electrolytic charging, i.e. under conditions where M-atom vacancies are not introduced. The phase diagrams thus obtained are therefore metastable. The equilibrium phase diagram should incorporate defect-hydride phases at finite H concentrations. Indeed, our experiments on the T i - H system at 5 GPa [23] indicated that ~ and e phases originally located near the dihydride composition were shifted to higher H concentrations, probably to 8/3. A similar observation was made on the Z r - H system. Also, we have observed frequently in a number of M - H systems that new hydride phases appear after prolonged heating at high temperatures, and these phases in most cases cannot be properly located in ordinary phase diagrams. For example, they appear as a third phase in the region of a two-phase coexisting field, causing violation of the Gibbs' phase rule. We maintain, in closing, that the phase diagrams of M - H systems reported heretofore are metastable diagrams. They are useful as such, but their metastability should be recognized. Ordinary defect-free hydrides should always tend to approach real stable structures--defect hydrides--whenever M-atom vacancies become available.

Acknowledgments This work is supported by a Grant-in-Aid for General Scientific Research from the Ministry of Education, Science and Culture. The experiments at

40

Y. Fukai / Journal of Alloys and Compounds 231 (1995) 35-40

KEK were performed under the approval of Photon F a c t o r y A d v i s o r y C o m m i t t e e ( P r o p o s a l 92-128, 9 3 G 128, 94G-151). I wish to t h a n k T. K i k e g a w a a n d O.

Shimomura of KEK for their general support. Experim e n t s , n o t explicitly c i t e d in r e f e r e n c e s , h a v e b e e n d o n e b y T. H a r a g u c h i ( M n ) , K. N a k a m u r a ( Z r ) a n d K. Watanabe (Pd-Pt).

References [1] Y. Fukai and N. Okuma, Jpn. J. Appl. Phys., 32 (1993) L1256. [2] Y. Fukai and N. Okuma, Phys. Rev. Lett., 73 (1994) 1640. [3] O. Shimomura, S. Yamaoka, T. Yagi, M. Wakatsuki, T. Tsuji, O. Fukunaga, H. Kawamura, K. Aoki and S. Akimoto, Mater. Res. Soc. Symp. Proc., Vol. 22, Elsevier, Amsterdam, 1984, p. 17. [4] M. Yamakata, T. Yagi, W. Utsumi and Y. Fukai, Proc. Jpn. Acad., 68B (1992) 172. [5] H.J. Wollenberger, in R.W. Cahn and P. Haasen (eds.), Physical Metallurgy, Elsevier, Amsterdam, 1983, p. 1139. [6] O. Bender and P. Ehrhart, J. Phys. F, 13 (1983) 929. [7] R.O. Simmons and R.W. Balluffl, Phys. Rev., 117 (1960) 52. [8] H. Osono, T. Kino, Y. Kurokawa, Y. Fukai and Y. Sakamoto, this issue. [9] Y. Fukai, in M. Doyama, J. Kihara, M. Tanaka and R.

Yamamoto (eds.), Computer Aided Innovation of New Materials II, Elsevier, Amsterdam, 1993, p. 451. [10] Y. Fukai, M.Yamakata and T.Yagi, Z. Phys. Chem., 179(1993) 119. [111 T.B. Flanagan, A.P. Craft, T. Kuji, K. Baba and Y. Sakamoto, Scr. Metall., 20 (1986)1745. [12] H, Noh, T.B. Flanagan, B. Cerundolo and A. Craft, Scr. Metall., 25 (1991) 225. [13] H. Noh, T.B. Flanagan and M.H. Ransick, Scr. Metall., 26 (1992) 353. [14] H. Noh, T.B. Flanagan and Y. Sakamoto, Scr. Metall., 29 (1993) 445. [15] E. Raub, H. Beekskow and D. Menzel, Z. Metallkd., 50 (1959) 426. [16] J. Shield and R. Williams, Scr. Metall., 21 (1987) 1475. [17] K. Watanabe, Y. Fukai, Y. Sakamoto and Y. Hayashi, Scr. Metall., in press. [18] C.P. Flynn, Point Defects and Diffusion, Clarendon, Oxford, 1972, p. 786. [19] M. Doyama and J.S. Koehler, Acta Metall., 24 (1976) 871. [20] Y. Fukai, The Metal-Hydrogen System, Springer, Heidelberg, 1993, p. 181. [21] W. M611er, F. Besenbacher and J. Bottiger, Appl. Phys. A, 27 (1982) 19. [22] S.M. Myers, P.M. Richards, D.M. Follstaedt and J.E. Schirber, Phys. Rev. B, 43 (1991) 9503. [23] K. Nakamura and Y. Fukai, this issue.