J. CHEM. SOC'. F'ARADAY TRANS., 1994, 90(6), 899-903 High-temperature Diffusion of Hydrogen and Deuterium in Palladium Takeshi Maeda, Shizuo Naito," Masahiro Yamamoto, Mahito Mabuchi and Tomoyasu Hashino Institute of Atomic Energy, Kyoto University, Uji, Kyoto 61I, Japan The diffusivity of hydrogen and deuterium in palladium has been measured at temperatures between 773 and 1373 K and at hydrogen and deuterium concentrations less than lop4 H/Pd and D/Pd (atomic ratio). The mea- sured diffusion coefficients for hydrogen (DH)and deuterium (D,) showed Arrhenius behaviour. The depen- dence of the ratio DD/D, on temperature has been explained by a model of diffusion in which a hydrogen atom in an octahedral site of the palladium lattice can jump into the adjacent octahedral site only when local deforma- tion of the palladium lattice assists the jump.The palladium-hydrogen system has long attracted interest and has been the most extensively studied of all the metal- hydrogen systems.' This is primarily because palladium can absorb a large amount of hydrogen and the hydrogen atoms in palladium have high mobility; also, in the palladium-hydrogen system reliable experimental data such as accurate solubility and diffusivity can easily be obtained from measurements of the rate of absorption of gaseous hydrogen by solid palladium with simpler surface treatments than in other metal- hydrogen systems. Nevertheless, there remains some uncertainty in the details of the measured diffu- sion coefficients and of the model to be applied to the diffu- sion of hydrogen in palladium.The measured diffusion coefficients for hydrogen (D,) are in good agreement.6 'However, there have been fewer mea- surements of difTusion coefficients for deuterium (0,) and the agreement between the reported values at high ternperat~res'*'~is not good enough to form a basis for a diffusion model. Models of hydrogen diffusion in metals, especially those applicable to low-temperature diffusion, have been extensively discussed.3-5911-l4 Despite a variety of models presented, no conclusion has been reached as to which is the most appropriate for describing the high-temperature diffusion of hydrogen in fcc palladium. A clue to the most appropriate model may be the follow- ing: the pre-exponential factor of the measured D, is of the same order of magnitude as that calculated from the Debye temperature of palladi~rn~,'~ and the values of the measured ratio DD/D, at high temperatures are larger than the classical value i.e.the ratio is rather isotope independent 1/,/2,77"7'0 compared with the classical case. We thus consider a model in which the motion of palladium atoms, rather than the vibration of a hydrogen atom, plays a key role in the diffusi- vity. Then, to calculate D, and D, from the model, we need, if we apply rate theory,' 'pl 5.16 partition functions and conse- quently energy levels of hydrogen and deuterium in palla- dium. However, the available energy levels obtained experimentally' '9'' and the~retically'~ 22 are insufficient for calculating the partition functions and it is difficult to find the analytical expression for the energy levels.We therefore employ the partition functions that can reproduce the mea- sured solubility of hydrogen and de~terium.~.~.~~-~~ In this study we measure the diffusivity and solubility of hydrogen and deuterium in palladium. We next consider a model of diffusion and obtain, using rate theory, an expres- sion for the diffusion coefficient. The partition functions appearing in the diffusion coefficient are determined from the solubility data. The diffusion coefficient is then computed and compared with the measured one. Finally, we show that the model considered can be successfully applied to the diffusion of hydrogen in palladium at high temperatures.Applicability of other models is also briefly discussed. Experimental The diffusion coefficient was obtained from measurements of the rate of absorption of gaseous hydrogen by palladium. The details of the apparatus and procedures for measurements were identical to those described previo~sly.~~~~~ The specimen was a spherical, polycrystalline sample of palladium of diameter 15 mm and had a nominal purity of 99.9%. It was heated to 1173 K in a vacuum chamber for 4 h until the ambient pressure reached 1 x lop7Pa. Before each measurement the specimen was heated to a temperature 50 K higher than that at which the measurement was made. The absorption rate was measured in the temperature range 773-1373 K and at hydrogen pressure 6.7 Pa.This pressure corresponds to hydrogen concentrations less than 1 x H/Pd (atomic ratio) in this temperature range. The hydrogen pressure, and consequently the hydrogen concen-tration, should be as small as possible to measure the tracer diffusion ~oefficient,',~ which is simpler to interpret than the chemical diffusion coefficient and, also, the hydrogen pressure should be as large as possible to reduce the effect of disso-ciative adsorption of hydrogen molecules onto the surface of the specimen, which is necessarily involved in the measured absorption rate and becomes large as the pressuredecrease^.^^.^^ (The details of the procedure for separating this effect from the measured absorption rate have been described in ref.9, 27 and 30.) By choosing the pressure to be 6.7 Pa the absorption rate was found to be limited only by diffusion of hydrogen into the palladium bulk. We could thus obtain the diffusion coefficient by comparing the amount of absorbed hydrogen obtained experimentally with that com- puted from the solution of the diffusion equation together with its boundary c~ndition.~~.~~ To determine the partition functions involved in the expression for the diffusion coefficient, we obtained the solu- bility from the amount of hydrogen absorbed when the absorption rate became negligibly small. Results and Discussion Experimental Results Fig. 1 shows the Arrhenius plots of the measured diffusion coefficients, D, and D,, together with those reported in the literature.*-" The measured values of D, and D, fell on straight lines.The measured D, almost coincided with that reported by Katsuta et aL8 It was impossible to observe the upward deviations from the straight lines and some hysteresis on cooling as reported by Gol'tsov et al." for temperatures above ca. 950 K; below ca. 950 K their data are in agreement with those in the present study. Extrapolation of the mea- sured values of D, to room temperature reproduced the J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 .-v) N E--. Q 1o-8 -'\ I I I I I I I 0.8 1.o 1.2 1.4 103 KIT Fig. 1 Arrhenius plots of the diffusion coefficients DH and D,. (0) D, and (a)D,, this study; (--) Gol'tsov et al." (upper line: DH and lower line: D,; the result of their measurements is shown here only for heating); (.* .) Katsuta et a1.* for D, and (-. -) Powell and Kirkpatrick' (upper line: D, and lower line: OD).The thick solid line has been computed using eqn. (1). For details see the text. reported values of DH.6*7From Fig. 1 we can obtain graphi- cally the activation energies: 219 meV for hydrogen and 215 meV for deuterium and the pre-exponential factors : 2.8 x lod7m2 s-l for D, and 2.4 x lop7m2 s-l for D,. These values are in general agreement with those report- ed.5-1 0,31-34 Fig. 2 shows the temperature dependence of the measured ratio DD/DH together with those rep~rted.~*~*'*"*~'-~~ The measured values agreed with those of Gol'tsov et ~1 for.~ temperatures below ca.950 K, where they observed neither the deviations nor the hysteresis. The data of Jost and Widmann31 show lower values than those in the present study and the values of Powell and Kirkpatrick' are, to a lesser extent but systematically, smaller than those reported. General agreement, however, is good, allowing for the com- parison of DD/DH,which is more critical than the comparison of quantities such as solubility. The values obtained experi- mentally are larger than the classical value 1/,/2 and unlikely to approach it even at high temperatures. The large values at low temperatures are, as will be mentioned later, due mainly to the difference in the zero-point energies of hydrogen and deuterium.Model of Diffusion of Hydrogen in Palladium As systematic discussions have been presented for models of diffusion of hydrogen in metal^^^^*''-^^ we are here con- cerned with finding among them a model that can be applied, with minor modifications, to the diffusion of hydrogen in pal- ladium at high temperatures. A characteristic of the measured D, is that its pre-exponential factor is 2.8 x lo-' m2 s-l, which compares with the values 4.3 x lop7m2 s-l calculated from the Debye temperature (274 K) and the distance (0.27 nm) between the 2000 1000 500 300 I I I 1 1 1.5 I Q 1.o 0.5 I I I 0 1 2 3 4 103 KIT Fig. 2 Temperature dependence of DJDH. (@) Present study and (--) reported N umbers on the dashed lines refer to references.The result of Gol'tsov et al." is shown only for T < 950 K. The thick and thin solid lines have been computed using eqn. (1) and (2), respectively. For details see the text. Note that the scale of the inverse temperature axis has been compressed compared with that in Fig. 1. adjacent octahedral (0)sites of the palladium lattice (Fig. 3). The value 2.8 x lo-' m2 s-l, however, is considerably smaller than the value 1.3 x m2 s-l calculated from the Einstein temperature (800 K) of hydrogen in palladium. This indicates that the hydrogen atom cannot jump over the fixed potential of the palladium lattice with the frequency of vibra- tion of the hydrogen atom. Another characteristic is that the measured ratio DD/DH has values larger than those expected from the classical value l/J2 at high temperatures (Fig.2); the diffusion coefficient is rather isotope independent. At high temperatures the jump of the hydrogen atom from one site to another over the fixed potential barrier would lead to DD/DH x 1/J2.5J1 Both these characteristics imply, as a model of high-temperature diffusion of hydrogen in palladium, the jump of ~ the hydrogen atom assisted by the local deformation of the palladium lattice. In this model the hydrogen atom can only make the jump from one site to another by jumping over the potential barrier when the palladium lattice is deformed. Here, we assume that the change in the electronic state of the palladium-hydrogen system is much faster than the motions n Fig.3 Diffusion path for hydrogen in the palladium lattice. Circles: palladium atoms, 0:octahedral sites, S: saddle points, T: tetrahedral site and dotted line: a possible diffusion path. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 of the palladium and hydrogen nuclei and the change in the motion of the hydrogen nuclei is faster than that of the palla- dium nuclei, although the validity of this assumption has not yet been proved for paliadi~rn.~*'~ The jump process is shown schematically in Fig. 4. Although models that incorp- orate tunnelling of the hydrogen atom through the potential barrier into the jump rate have been propo~ed,'~.~~we cannot apply them directly to the interpretation of the experi- mental results because they include the tunnelling probabil- ity, which is difficult to estimate for the locally deformed palladium lattice.We note here that, according to the present model, the pre-exponential factor may be smaller than that calculated from the Debye temperature because coincidence of two uncorrelated vibrations of palladium atoms in direc- tions perpendicular to each other is needed to cause the local deformation that permits the jump of the hydrogen atom.12 The diffusion coefficient can now be formulated on the basis of the model described above. Using rate theory15 we can write it in the form where d' is a constant, v is the effective jump frequency,f&, andfH(i, are the partition functions for the hydrogen atom in the activated state and at the 0 site (Fig.3), respectively, and E~ is the activation energy for diffusion. Eqn. (1) resembles the familiar form of the diffusion coefficient, but the following should be noted. First, v is usually taken to be the frequency with which the hydrogen atom passes through the activated state along its diffusion path.15 In the present model, however, we assume v to be the frequency of occurrence of the local deformation of the palladium lattice, and therefore to be independent of hydrogen isotopes, for the following reason. The hydrogen atom in the activated state is on a rather flat potential-energy surface along the diffusion path as can be expected from the result of the first-principles20*2' and molecular-dynamics14 calculations and has a lifetime prob- ably longer than that of the local deformation of the palla- dium lattice.Thus, if the hydrogen atom in the activated state always succeeds in making the jump, v corresponds to the frequency of occurrence of the local deformation and not to the vibrational frequency of the hydrogen atom in the acti- vated state. Secondly, the activation energy is the energy needed to make a configuration of the locally deformed palla- dium lattice with the hydrogen atom in it. Thirdly,fi(i, has the same degree of freedom asfH(i). Eqn. (1) is often used in w Fig. 4 Schematic diagram of the jump of the hydrogen atom in the palladium lattice. The hydrogen atom (H) is self-trapped in the 0 site (a)jumps over the potential barrier lowered by the local deformation of the palladium lattice (b)into the adjacent 0 site and again is self-trapped (c).901 the f~rm"*'~*'~ In this form the partition functionf&, has one less degree of freedom thanf&i,. To compute eqn. (1) and compare it with the measured values of D, we next need to determinef&i, andfH,i,. Partition Functions for Hydrogen in Palladium Partition FunctionfH(j) The partition function for the hydrogen atom in the 0 site is written, if the energy levels Enx,n,,n,of the hydrogen atom vibrating in the x, y and z directions with the quantum numbers n, ,nyand n, are given, as Enx,ny, ",measured with inelastic neutron scattering (INS)'7*1 indicate harmonic oscillation of the hydrogen atom with anharmonicity. It seems difficult to obtain from the measured Enx,ny, n, the analytical expression for Enx, that permits cal- ny, n, culation of the Enx,ny,n,beyond those measured, i.e.beyond 190 meV. The first-principles calculation20,2' suggests that the analytical expression for Enx,ny, n, is difficult to obtain because of the great complexity of the potential-energy surface for the hydrogen atom and the resulting delocal- ization of the hydrogen atom beyond one 0 site. Fortunately, however, both the experimental and the calculated results show that the values of the ratio of En=,ny, n, -Eo, o, for deu- terium to that for hydrogen lie around 0.67.'8,'9Taking this fact into account we try to find the Enx,ny,nzsuch that .fH(i) computed from eqn.(3) reproduces the measured solubilities of hydrogen and deuterium, as described below. The relationship between the hydrogen pressure pH and the hydrogen concentration 8, (H/Pd, atomic ratio) is, for small 8, ,given by' 5727 PH = kHuh (4) (5) where k' is a constant,f,,,, is the partition function for hydro- gen molecules in the gas phase, and E, is the heat of solution per hydrogen atom and is assumed to be the same for hydro- gen and deuterium. fH(g) and fD(g) can readily be calcu-lated.2.'5.16*27.28 We consider fH(i, and fDci, that are determined by the Enx,ny, n, of harmonic oscillators of hydro- gen and deuterium whose energy-level spacings hw, and haD are related by hoD/hoH # 1/,/2.Fig. 5 shows the comparison of the values of kD/kH computed using these Enx, with theny, n, experimental results. The experimental values are shown only for those obtained in this study and those of Lasser and because their measurements are the most systematic and because most reported values3,23-26 are in good agree- ment with each other. The thick solid line has been computed using fH(i) and fD(i) for three-dimensional isotropic harmonic oscillators with h~,= 69 meV and hwD= 47 meV,17*'8i.e. hwD/hwH = 0.68, which is slightly smaller than 1/42. The thin solid line shows the values computed for the model used by Rush et a/.' i.e. the three-dimensional isotropic harmonic oscillators with anharmonicity, whose energy levels are given =by Enx,ny.n,hw(nx +ny+n, +3/2) +p(n: +n: +nf +n,+n,, +n, + 3/2), nx, n,,, n, = 0, 1, 2, ...with h(oH= J2hwD = 50 meV and PH (the magnitude of the J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 TIK 2000 1000 500 300 4 I r Y 2 0 0 1 2 3 4 103 KIT Fig. 5 Temperature dependence of kdk,. (0)Present study and (- -) Lasser and The thick solid line has been computed for f&) with houhwf, = 0.68 and the thin solid line for fH(i) with the energy levels given by Rush et a/.' 'For details see the text. anharmonicity) = 2pD = 9.5 meV. Fig. 6 shows the Arrhenius plots of the same k, and k, as those in Fig. 5. From Fig. 5 and 6 we find the solubility can be well repro- duced by f&) and f&) computed for the harmonic oscillators with ho,,/h~~,= 0.68.We will use these fH(i) and fD(i) to compute D, and D,. The value hwD/ho, = 0.68 compares well with those obtained experimentally18 and expected from the cal~ulations'~-~~ and with the value 0.65 introduced to explain the isotope effect for the solubility of hydrogen and deuterium in palladium24 although doubt over the used value 0.65 has been rai~ed.~ TIK 2000 1000 500 300 loio I I I I 10' I 1 1 I 0 1 2 3 4 lo3 KIT Fig. 6 Arrhenius plots of k, and k,. (0)k, and (0)k,, present study; (--) Lasser and Powellz6 (lower line: k, and upper line: kD).The solid lines correspond to those in Fig. 5. Partition Functionf&,) The hydrogen atom in the 0 site jumps into the adjacent 0 site through the tetrahedral (T) site'3*'4*20,21*23 as shown in Fig.3. A saddle (S) point comes between the 0 site and the T site. The diffusion path for the hydrogen atom is thus O-S-T-SO. We assume the activated state to be the state of the hydrogen atom occupying some point near the T site. Since we are dealing with the model of hydrogen diffusion assisted by the local deformation of the palladium lattice and it is difficult to determine unambiguously the potential energy at the S point, it does not seem to be of crucial importance to fix the point for the activated state strictly at the S point. We assume the hydrogen atom in the activated state to be a three-dimensional harmonic oscillator with two identical vibrations in the directions perpendicular to the diffusion path and one slower vibration along it.The energies of the vibrations will be determined when eqn. (1) is computed and compared with the experimental result. Comparison of the Experimental and Calculated Results Fig. 1 shows the comparison of the measured D, and DD with the computed values. The thick solid lines represent the values of eqn. (1) computed using the following partition functions:fH(i) computed for the three-dimensional isotropic harmonic oscillator with ho, = 69 meV and hoD/ho, = 0.68 and fk,, computed for the strongly anisotropic three-dimensional harmonic oscillator with hof, = 1.82hwH for the two directions perpendicular to the diffusion path, Aof, = 0.02hoH for the remaining direction and hoD/ho, = 0.68.The values hof, = 0.02hoH and hof, = 1.82hoH indicate that the hydrogen atom in the activated state is on a rather flat energy surface along the diffusion path and in a relatively steep potential well perpendicular to it, respectively. The acti- vation energy for diffusion has been found to be ed = 195 meV for both hydrogen and deuterium, which is different from the values 219 meV for hydrogen and 215 meV for deu- terium obtained graphically from Fig. 1. This difference comes from the fact that in eqn. (1) the zero-point energies of the vibrations of the hydrogen and deuterium atoms have been included in fH(i), fDCi), f&(i) and fb, and not in Ed. The results of the computations using other models are not shown in Fig.1 because the difference in the results calculated for different models cannot be clearly distinguished in Fig. 1. Fig. 2 shows the comparison of the measured ratio DJD, with the computed ratio. DD/DHincreases beyond unity as the temperature decreases. This is due to the difference in the zero-point energies of the vibrations of the hydrogen and deuterium atoms and to the values of hof, and hob for the activated state" that are larger than those of ho, and Am, for the 0 site. The thick solid line has been computed for the same fH(i), fqi,, f&i, and as those used in Fig. 1. The values of hof,and hob have been chosen so that they repro- duce the values of DD/DH obtained in this study and by Volkl .~~et ~1 The result of Powell and Kirkpatrick' can be repro- duced by choosing the values of hof, and hob.A line almost identical to the thick solid line, which for clarity is not shown in Fig.2, has been obtained by using for fH(i) andfqi, the energy levels given by Rush et a1.,'* i.e. ha, = ,/2ho, = 50 meV and BH = 28, = 9.5 meV and for f&i) and f&i) the energy levels of three-dimensional harmonic oscillators with hok = 2.57h0, for the two directions, hof, = 0.03h0, for the remaining direction and hoh/hwf, = 0.68. The thin solid line shows eqn. (2) computed using for f&) and f&) the energy levels of two-dimensional harmonic oscillators with ha$, = 2.25hwH and AoD/ho, = 0.68. The values of hof, etc. have been chosen so that the experimental result at high tem- peratures could best be reproduced, but the computed values J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 903 approaches 1/J2 as the temperature increases, We can see 5 Y. Fukai, The Metal-Hydrogen System, Springer, Berlin, 1993. the following from the comparison of the three computations above (the solid line, the line almost identical with the solid line and the thick solid line in Fig. 2): the model of diffusion described by eqn. (1) gives a possible explanation of the ratio DD/D, observed at high temperatures as well as at low tem- peratures whereas eqn. (2) can only poorly reproduce the 6 7 8 9 H. K. Birnbaum and C. A. Wert, Ber Bunsenges. Phys. Chem., 1972, 76, 806. J. Volkl and G. Alefeld, in Hydrogen in Metals I, ed. G. Alefeld and J.Volkl, Springer, Berlin, 1978. H. Katsuta, R. J. Farraro and R. B. McLellan, Acta Metall., 1979,27, 11 11. G. L. Powell and J. R. Kirkpatrick, Phys. Reo. B, 1991,43,6968. experimental results, especially those at high temperatures. Similar behaviour of DD/DH has been observed for hydro- gen and deuterium in fcc nickel and ~opper'~,~~ and Katz et ~1.'~have explained it in terms of anharmonicity. The values of haHthey used, however, were 116 meV for nickel and 138 meV for copper, which are larger than the value 88 meV 10 11 12 13 V. A. Gol'tsov, V. B. Demin, V. B. Vykhodets, G. Ye. Kagan and P. V. Gel'd, Phys. Metals Metallog., 1970, 29, 195. K. W. Kehr, in Hydrogen in Metals I, ed. G. Alefeld and J. Volkl, Springer, Berlin, 1978. H. Kronmiiller, G.Higelin, P. Vargas and R. Lasser, Z. Phys. Chem. NF, 1985,143,161. M. J. Gillman, Phil. Mag. A, 1988,58, 257. obtained by INS3' and considerably larger than the value 69 meV for palladi~m.'~~'~ It can be shown from numerical cal- culations that the values of DJDH larger than 1/,/2 are obtained more easily for larger values of ha,; the values 116 meV and 138 meV are large enough to reproduce, without having recourse to eqn. (l), the ratio DD/DH observed at high temperatures in terms of the anharmonicity by using eqn. (2), which corresponds to the model used by Katz et all6 Eqn. (1) is capable of reproducing the nickel result by using the value ho, = 88 meV obtained by INS. Thus, the model described by eqn. (1) explains the observed D, and DD for nickel better than other models such as that described by eqn.(2). However, more experimental and theoretical investi- gations are necessary to discuss D, and DD for a wider range of the fcc metals. 14 15 16 17 18 19 20 21 22 23 24 25 Y. Li and G. Wahnstrom, Phys. Rev. B, 1992,445,14528, S. Glasstone, K. J. Laidler and H. Eyring, The Theory of Rate Processes, McGraw Hill, New York, 1941. L. Katz, M. Guinan and R. J. Borg, Phys. Reo. B, 1971,4, 330. W. Drexel, A. Murani, D. Tocchetti, W. Kley, I. Sosnowska and D. K. Ross, J. Phys. Chem. Solids, 1976,37, 1135. J. J. Rush, J. M. Rowe and D. Richter, Z. Phys. B, 1984,55, 283. L. R. Pratt and J. Eckert, Phys. Reu. B,1989,39, 13170. C. Elsasser, PhD Thesis, Universitat Stuttgart, 1990. C. Elsasser, K. M. Ho, C. T. Chan and M. Fahnle, J.Phys: Condens. Matter, 1992,4, 5207. B. M. Klein and R. E. Cohen, Phys. Rev. B,1992,4S, 12405. E. Wicke and G. H. Nernst, Ber. Bunsenges. Phys. Chem., 1964, 68,224. J. D. Clewley, T. Curran, T. B. Flanagen and W. A. Oates, J. Chem. SOC., Faraday Trans. I, 1973,69,449. W. A. Oates and T. B. Flanagan, J. Chem. SOC., Faraday Trans. I, 1977, 73,407. 26 R. Lasser and G. L. Powell, Phys. Rev. B, 1986,34, 578. Conclusion 27 28 S. Naito, J. Chem. Phys., 1983,79, 3113. S. Naito, T. Hashino and T. Kawai, J. Chem. Phys., 1984, 81, The measured diffusion coefficients for hydrogen and deute- rium in palladium showed Arrhenius behaviour in the tem- perature range 773-1373 K. A model of diffusion in which the hydrogen atom can jump from one 0 site into the adja- cent 0 site assisted by local deformation of the palladium lattice well describes the behaviour of the high-temperature diffusion of hydrogen and deuterium in palladium. 29 30 31 32 33 3489. S. Naito, M.Yamamoto and T. Hashino, J. Phys: Condens. Matter, 1990, 2, 1963. T. Maeda, S. Naito, M. Yamamoto, M. Mabuchi and T. Hashino, J. Chem. SOC., Faraday Trans., 1993,89,4375. W. Jost and A. Widmann, 2. Phys. Chem. B, 1940,45,285. G. Bohmholdt and E. Wicke, 2. Phys. Chem. NF, 1967,56, 133. H. Ziichner and N. Boes, Ber Bunsenges. Phys. Chem., 1972,76, 783. 34 J. Volkl, G. Wollenweber, K. H. Klatt and G. Alefeld, 2. Natur- References forsch., A, 1971,26,922. F. A. Lewis, The Palladium Hydrogen System, Academic, London, 1967. E. Wicke and H. Brodowsky, in Hydrogen in Metals 11,ed. G. Alefeld and J. Volkl, Springer, Berlin, 1978. R. Lasser, Tritium and Helium3 in Metals, Springer, Berlin, 35 36 37 H. Eyring, Trans. Faraday SOC., 1938,34,41. W. Eichenauer, W. Loser and H. Witte, 2. Metallk., 1965, 56, 287. J. Eckert, C. F. Majkzrak, L. Passell and W. B. Daniels, Phys. Rev. B,1984,29,3700. 1989. T. B. Flanagan, Annu. Rev. Mater. Sci., 1991,21,269. Paper 3/06593F; Received 3rd November, 1993