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Study of hydrogen diffusion in ZrNi alloys by 181Ta perturbed angular correlation spectroscopy
Journaf of the Lea-Cordon
Metak, 1.29 (1987)
STUDY OF HYDROGEN PERTURBED ANGULAR P. BOYER?
213 - 221
213
DIFFUSION IN Zr-Ni ALLOYS BY l8’Ta CORRELATION SPECTROSCOPY*
and A. BAUDRY*
Centre d *Etudes Nucldaires de Grenoble, DRF-Service de Physique, Magndtisme et Diffusion par Interactions Hyperfines, 85 X, 38041 Grenoble CWex (France) (Received May 7,1986)
Summary
The diffusion of hydrogen in the crystallized hydride ZrzNiHs.s has been studied by perturbed angular correlation (PAC) spectroscopy using rslTa as a probe in substitution for zirconium. The temperature dependence of the quadrupole relaxation of the rslTa spins between 200 K and 470 K could be properly described by assuming the jump probability of hydrogen atoms to result from the coexistence of two thermally activated processes. The values obtained for the activation energies and pre-exponential frequency factors of both processes suggest that diffusion is dominated by a tu~elling mechanism for T< 300 K and by a “classical” over-barrier jump m~h~ism for T>370K.
1. Introduction
For technological reasons much attention has been paid to the hydrides of intermetallic compounds in recent years. An important class of such compounds is formed by binary alloys in which a strongly hydrogen attracting transition element is combined with a metal which displays no or very little attraction [l]. The ~te~et~lic compounds ZrNi and Zr?Ni belong to this class, and the kinetics of hydrogen absorption in both crystalline and amorphous samples of these alloys has been extensively investigated [2 - 41. Moreover, the interstitial positions of hydrogen in various hydrides of ZrNi are known from the data of neutron diffraction experiments [ 5,6]. However, to our knowledge, there is no study regarding hydrogen diffusion in hydrogenated Zr-Ni alloys. The aim of the work presented in this paper
*Paper presented at the international Symposium on the Properties and Applications of Metal Hydrides V, Maubuisson, France, May 25 - 30,1986. $Universit& Scientific, Technologique et Medicale de Grenoble. Centre National de la Recherche Scientifique. 0 Elsevier Sequoia/Printed in The Netherlands
214
is to study the diffusion of hydrogen in a ZrlNiH, hydride by using a local method such as the perturbed angular correlation (PAC) on the “‘Ta nucleus.
2. Sample preparation and experimental conditions Polycrystalline ZrzNi prepared from high purity metals (99.95% Zr; 99.9% Ni) and containing 1.5 at.% Hf substituted for Zr, was hydrogenated under low hydrogen pressure (700 Torr) at 250 “C. Under such conditions the hydride Zr,NiH, with x = 4 could be obtained within about 20 h. The hydride was found to be a single homogeneous phase which retains the Cl6 CuAlrtype structure of Zr,Ni with parameters of the unit cell corresponding to an additional volume of 2.68 A3 (H atom)-‘. A sample (about 100 mg) of composition Zr2NiH3.s was irradiated for 3 h in a thermal neutron flux to obtain the 18rHf activity suitable for PAC experiments. The irradiated material was put in a quartz tube sealed under air so as to vary the temperature over a sufficiently large range without significantly changing the hydride composition. The PAC experiments were performed with a four-detector spectrometer on the 133 - 482 keV cascade of the 181Tanucleus fed by /3decay from ‘*lHf. The coincidence spectra between y rays emitted in cascade with a time separation t (0 < t < t,,, 2 lo- ’ s) in directions separated by an angle 8 = 90” or MO’, were recorded with a time resolution of 450 ps. The timedependent modulation factor G,(t) of the angular correlation between the y rays was calculated from an appropriate combination of the coincidence spectra. This modulation results from the coupling of the intermediate spin level of the lslTa cascade with the hyperfine field produced by the close environment of the probe nucleus. In non-magnetic materials, pure quadrupole modulation spectra are expected to be observed, as the result of the coupling of the quadrupole moment of the intermediate nuclear level with the electric field gradient (e.f.g.) generated by the non-cubic charge distribution around the nucleus. The theoretical expression for the quadrupole modulation corresponding to the interaction between a r~domly-orients static e.f.g. and the I = 512 spin level of “ITa is G?t(t) = s20(77)
+
5
S2n(‘?)
exPi--6f,(r7)&$)
~~~%d~)vQt~
(1)
n=l
This expression represents a mixture of three oscillating functions with amplitudes S2,(~) and frequencies v, = fn(q)vQ respectively, superposed on a time-independent contribution S,,(r)). The interaction is characterized as usual by the quadrupole frequency vQ and the asymmetry parameter 77of the e.f.g. tensor. The exponential term in the sum of eqn. (1) accounts for the existence of a quadrupole frequency distribution which is assumed to be properly represented by a Iorentzian shape with a relative width 6. Rather large values of S are expected in disordered systems such as non-stoichiometric hydrides.
215
Fluctuations in the e.f.g. produced by atomic diffusion give rise to a relaxation of the angular correlation as a result of the progressive depolarization of the nuclear spins with the time elapsed between the emission of two successive y rays. In most cases, this relaxation can be characterized to a good approximation by an unique relaxation constant h and an exponentially decaying “damping” factor must be introduced into the modulation which can be expressed as follows: G2(t) = e-ht GSt(t)
(2)
A simple relation exists between h and the jump frequency w of the diffusing atoms in both extremely slow (w 4 fnva) and fast (o 9 ~~~~) diffusion regimes. In these asymptotic conditions h = w and X a < ~6 > w-’ respectively. In practice, numerical calculations based on a stochastic relaxation model [7] show that such asymptotic relations remain valid within a few per cent for large ranges of jump frequencies, i.e. o S 10’ s-l and w > lo9 s-l respectively for ‘slTa PAC spectroscopy [S]. Consequently, a single-diffusion mechanism obeying an Arrhenius law such as w = w. exp(--E,/hT) is expected to be represented by a log X us. l/T plot consisting of two straight lines with opposite slopes. In the intermediate range corresponding to jump frequencies of the same order as the spin-precession frequencies we are able to observe with the rglTa probe, ie. 10’ - lo9 s-i, the spindepol~ization rate is very high and one observes a flat maximum in the values of h. However, no qu~titative significance should be attached to the values of the spin-relaxation constant in this region, as is clearly seen from the results of numerical calculations performed within the stochastic model: the pronounced damping of the perturbation factors cannot be properly reproduced with a unique time-decaying exponential term as in eqn. (2).
3. Results and discussion Examples of lslTa PAC modulation factors measured in polyc~st~line ZrzNiH,_s are presented in Fig. 1. The temperature range investigated extends from 190 K to 450 K. At T < 190 K, the modulation pattern corresponds to a static interaction and can be fitted to expression (1) - corrected from time resolution effects -with the quadrupole parameters vQ = 7.7 + 0.1 MHz, q = 0.70(2). A rather large (6 = 0.16) distribution of quadrupole frequencies is observed, which is an indication of some degree of randomness in the occupation of interstitial sites by hydrogen atoms. It is interesting to compare these values with the quadrupole parameters measured in ZrzNi which are vQ = 15.6 f 0.1 MHz (6 = 0.02) and q = 0.84(2). This comparison clearly indicates that the e.f.g. tensor is very sensitive to the presence of hydrogen in the vicinity of the r81Taprobe.
216
G211I 1.00 t
(4
O’
0.73
R
0.50 0.25
0.00
lllns ”
10.
0.
IO.
20.
30.
10.
50.
60,
70.
80.
@I
0.15
0.25
Il.00
IOns 20.
30.
LO.
50.
60.
70.
(cl
Fig. 1. lslTa PAC quadrupole spectra in ZrzNiHa 8: (a) at 209 K, (b) at 365 K and (c) at 404 K. The full lines represent the results of best-fit procedures using eqns. (1) and (2) as theoretical expressions for the modulation factors.
When the temperature is raised, a “damping” characteristic of spin relaxation effects appears in the modulation factor which can be satisfactorily fitted to the expression (2) at all temperatures. Simultaneously, the quadrupole frequency remains practically constant below 300 K and then
217
displays a rather fast decrease towards the value vg = 1.6 MHz observed for T > 420 K. As expected [9], the quadrupole frequency starts to fall when the correlation time characteristic of the spin relaxation process, which is also the mean time elapsed between two successive jumps of a hydrogen atom, becomes comparable with the period of the spin precession. The values of the PAC relaxation constant X are plotted against l/T in Fig. 2. This plot clearly does not correspond to a relaxation mechanism represented by a single Arrhenius law in the whole temperature range investigated . A first ~te~retation consists of assuming that fluctuations occurring in the pro~n-d~~sion barrier height are responsible for the ~ymmet~ observed in the temperature dependence of the spin relaxation constant. Such a model has been successful in explaining the results of PAC experiments in disordered ionic conductors [lo]. Spin relaxation data from NMR experiments in disordered systems including hydrides could also be satisfactorily interpreted by assuming the existence of a distribution of activation energies [ 111. The values of the relaxation constant plotted in Fig. 2 are effectively well reproduced by assuming the existence of a distribution characterized by a mean activation energy E, = 0.23 eV and a relative width u = 23%. However, the pre-exponential factor of the mean jump frequency stands at 3 X 10” T’ and is smaller by about three orders of magnitude than the frequency v. = lOI s-l of th e hy d rogen atom ~brations. Furthermore, the value obtained for the quad~pole frequency co~esponding to the ~uctuat~g e.f.g. is unreasonnably low (0.23 MHz). Then, although the existence of fluctuations in the barrier which controls the diffusion of hydrogen atoms could not be completely excluded, this model does not allow us to account for the lslTa spin relaxation in Zr,NiH,.s. Alternatively, the behaviour of the lslTa spin relaxation constant is quite well reproduced over the full range of temperatures investigated - excluding the region between 300 K and 370 K for reasons previously mentioned - by assuming the relaxation results from two competing thermally activated processes. The full hydrogen jump frequency is then given by the sum w = wol exp(-E&T) + oo2 exp(--E&T) with I& = 0.11 f 0.01 eV, w o1 = 1.7 X 10” s-’ and Ed = 0.38 + 0.04 eV, oo2 = 1.8 X lOI s-l. The first ?h(d) I
2
3
i 4
+(10-3K-') 5
Fig. 2. Plot of the quadrupole relaxation constant h of the lsiTa spins in ZrZNiH3.s against l/T. Straight lines represent Arrhenius law with activation energies Es = 0.1 eV and E, = 0.3 eV in the low- and high-temperature regions respectively.
218
process, characterized by a much lower activation energy and by an anomalously small pre-exponential frequency factor, predominates at low temperatures and could be associated with a subbarrier diffusion mechanism involving tunnelling effects. The activation energy _& is comparable with the energy associated with the localized vibrations of hydrogen in ZrzNi [12]. From the values of the Arrhenius parameters given above, it can be seen that both diffusion processes display identical jump probabilities for T = 335 K. Let us note that a similar behaviour resulting from the coexistence of two jump mechanisms is encountered for the diffusion of hydrogen in other metallic lattices such as, for example, niobium where the crossing point for the jump probab~ities stands at T= 250 K [13 J. The fitting procedure of the X( l/T) data leads to a mean square value (vi> = (1.7 MHz)* for the fluctuating quadrupole frequency. This value is smaller than the value expected from the whole amplitude of the variation observed for the quadrupole frequency with temperature. This is an indication that the relaxation is not exclusively produced by atomic jumps between equivalent first-neighbour positions around the ‘*ITa probe. A significant contribution of hydrogen jumps involving more distant sites to the relaxation of the rslTa spins should actually result in a lowering of the mean-square value of the fluctuating quadrupole frequency which enters the expression of the relaxation constant in the fast diffusion regime. By using the simplest model for describing the tunnelling process the pre~xponenti~ factor wol observed at low temperatures can be written as follows [ 141 ool = voexp .- a (2mU)1’2a i i This expression is the product of the frequency v. of proton vibrations by the transparency coefficient of the potential barrier between two neighbour hydrogen sites. The quantities U and a are the height and width of the barrier respectively. By taking for zi the value of the activation energy deduced from the high-temperature PAC relaxation data, i.e. tr = 0.38 eV, an estimation of the barrier width from eqn. (3) gives a - 0.4 8. This value should be compared with the distance between hydrogen neighbour sites. Unfo~unately, no data are yet available concerning the ~terstiti~ positions occupied by hydrogen in Zr,Ni hydrides. We can, however, try to get some information on this point from simple geometrical considerations. From a detailed examination of the structure of ZrzNi it is clear that hydrogen atoms occupy tetrahedral interstitial sites. The positions of the different hydrogen sites as indicated in Fig. 3, the H-H distances and the radii of the tetrahedral holes have been calculated by using the values of the lattice parameters measured for Zr2NiH,., (a = b = 6.8307 A, c = 5.7026 A) and the atomic positions reported for Zr&i [X5]. We used the values 1.25 A and 1.60 A for the atomic radii of zirconium and nickel respectively. The results of such c~culations are given in Table 1. Owing to the values obtained for the hole radii which are higher than those observed
219
Fig. 3. Atomic arrangement in Zr2Ni viewed along the z axis, with tetrahedral interstitial sites possibly available for occupation by hydrogen shown as &id symboIs: 8, a sites; A, b sites; *, c sites; 0, d sites.
TABLE 1 Hole sizes and H-H nearest- and next-nearest neighbour distances for hydrogen in interstitial sites in ZrzNiH3,s Site (as designated in Fig. 1)
Coordination
Number 0 f sites per Zr atom
H-H distance (‘Q
Hole radius 6)
nearest neighbour 4Zr
0.52
a-b
1‘425
0.54
a-e a-d b-c
3.29 2.96 1.05
4
0.47
b-d b-b’ c-c’
1.31 2.11 1.41
2
0.42
d-d’
1.26
0.5
(l,2,4,6f 1
4Zr (1,2,3,4) 3Zr (3’, 2Zr (l’,
+ 1Ni 4’, 5’ + I) + 2Ni 3’ + I, I’)
next-nearest neighbour
2.38 2.57
- 0.39 8) in many stable hydrides, any one of the tetrahedral sites is able to accommodate hydrogen. However, according to the criterion which fixes the minimum distance between hydrogen atoms at about 2.1 A [IS], a and b sites could not be occupied simultaneously. Because of the same criterion, the full occupation of b sites precludes occupation of c and/or d sites. As occupation limited to a or b sites does not allow us to obtain hydrogen concentrations higher than x = 2, it may be reasonably concluded that the formation of the hydride Zr2NiH3.s requires occupation of some combination of a, b, c and d sites, with a less probability for the latter owing to the weak affinity of nickel for hydrogen. This conclusion does not contradict the results of neutron spectroscopy which indicate different environments for (0.37
220
the hydrogen atoms in Z&NiH,s and ZrNiH,_s [lo]. In the latter compound, the proton is encountered in four- and five-coordinated sites with “mixed” environments (3Zr f 1Ni and 3Zr + 2Ni respectively) {17], Within the predictions of the geometrical model, the proton is expected to be able to diffuse easily through the face shared by two adjacent tetrahedra in ZrZNiH3.s IThe value estimated for the tunnelling barrier of the proton is then quite realistic if compared with the distance of 1 - 1.4 A between such neighbouring sites. For temperatures lower than 300 K, he. T 5 on, tunnelfing diffusion may be interpreted in a more sophisticated way with a phonon-assisted tunnelling model as developed by Flynn and Stoneham [Ml. The fit of the PAC relaxation data to the expression af the atomic jump frequency calculated by these authors for a multiphonon process gives an activation energy of 0.13 eV and a tunnelling matrix element J = 240 meV, In conclusion, the **ITa spin-relaxation data are consistently interpreted by using a thermally activated tunnelling model for the diffusion of hydrogen atoms in crystallized ZrzNiH,.s below 300 K. At high temperatures, the diffusion takes place predominantly from over-barrier atomic jumps. In our opinion, an interesting field of investigations is open concerning hydrogen diffusion in Zr-Ni intermetallic compounds. PAC experiments on deuterated ZrzNi, as well as on amorphous hydrides of this alloy, are in progress. Acknowledgments Thanks are due to Dr. L. Billard for his collaboration in calculating hydrogen site positions. References 1 R. M. van Essen and K. II. J. Busehow, J. Less-Common iWet., 64 (1979) 217. 2 F. I-I. M. Spit, J. W. Drijver and S. Radelaar, Scripta Met&, 14 (1980) 1071. 3 K. Aoki, A. Horata and T. Masumoto, Proc. 4th Znt. Conf. on Rapidly Quenched Met&, Sendai, August 1081, Japan Institute of Metals, Sendai, 1982, p. 1649, 4 K. Aoki, M. Kamachi and T. Masumoto, J. Non-Cryst. Solids, 61 (1984) 679, 5 D. G. Westlake, J. Less-Common Met., 75 (1930) 177. 6 D. G. WestIake, H. Shaked, P. R. Mason, B. R. M&art, M. H. Mueller, T. Matsumoto and Ail.Amano, J. Less-Common Met., 88 (1982) 17. 7 H. Winkler and E. Gerdau, 2. Phys., 262 (1973) 263. 8 A. Baudry and P. Boyer, Proc. 7th Conf. on Hyperfine Interactions, Bangalore, India, 1986, Hyperfine Interactions, to be published. 9 0. de 0. Damasceno, A. L. de Oliveira, J, de Oliveira, A. Baudry and P. Bayer, Solid State Commlm., 53 (1935) 363. 10 A. Baudry, P. Boyer and A. L. de Oliveira, J. Fhys. Chem, Solids, 43 (1982) 871. 11 J. Shinar, Proc. ht. Symp. on the Properties and Applicator of Metal Hydrides ZV, Eilat, Israel, 1984 in J. Less-Common Met., 104 (1984) 87. 12 H. Kaneko, T. Kajitani, M. Hirabayashi, M. Ueno and K. Suzuki, J. Less-Common
Met., 89 (1983) 237.
221 13 A. Seeger, Hyperfine Zntemct., 17 - 19 (1984) 63. 14 V. G. Grebinnik, I. I. Gurevich, V. A. Zhukov, A. P. Manych, E. A. Meleshko, I. A. Muratova, B. A. Nikol’skii, V. I. Selivanov and V. A. Suetin, Sov. Phys.-JETP, 41 (1976) 777. 15 M. E. Kirkpatrick, D. M. Bailey and J. F. Smith, Acta Crystallogr., 15 (1962) 252. 16 A. C. Switendick, Sandia Lab. Rep. 78-0250, 1978. 17 A. V. Irodova, V. A. Somenkov, S. Sh. Shil’shtein, L. N. Padurets and A. A. Chertkov, Sov. Phys.-Crystallogr., 23 (1978) 591. 18 C. P. Flynn and A. M. Stoneham, Phys. Rev. B, 1 (1970) 3966.
Metak, 1.29 (1987)
STUDY OF HYDROGEN PERTURBED ANGULAR P. BOYER?
213 - 221
213
DIFFUSION IN Zr-Ni ALLOYS BY l8’Ta CORRELATION SPECTROSCOPY*
and A. BAUDRY*
Centre d *Etudes Nucldaires de Grenoble, DRF-Service de Physique, Magndtisme et Diffusion par Interactions Hyperfines, 85 X, 38041 Grenoble CWex (France) (Received May 7,1986)
Summary
The diffusion of hydrogen in the crystallized hydride ZrzNiHs.s has been studied by perturbed angular correlation (PAC) spectroscopy using rslTa as a probe in substitution for zirconium. The temperature dependence of the quadrupole relaxation of the rslTa spins between 200 K and 470 K could be properly described by assuming the jump probability of hydrogen atoms to result from the coexistence of two thermally activated processes. The values obtained for the activation energies and pre-exponential frequency factors of both processes suggest that diffusion is dominated by a tu~elling mechanism for T< 300 K and by a “classical” over-barrier jump m~h~ism for T>370K.
1. Introduction
For technological reasons much attention has been paid to the hydrides of intermetallic compounds in recent years. An important class of such compounds is formed by binary alloys in which a strongly hydrogen attracting transition element is combined with a metal which displays no or very little attraction [l]. The ~te~et~lic compounds ZrNi and Zr?Ni belong to this class, and the kinetics of hydrogen absorption in both crystalline and amorphous samples of these alloys has been extensively investigated [2 - 41. Moreover, the interstitial positions of hydrogen in various hydrides of ZrNi are known from the data of neutron diffraction experiments [ 5,6]. However, to our knowledge, there is no study regarding hydrogen diffusion in hydrogenated Zr-Ni alloys. The aim of the work presented in this paper
*Paper presented at the international Symposium on the Properties and Applications of Metal Hydrides V, Maubuisson, France, May 25 - 30,1986. $Universit& Scientific, Technologique et Medicale de Grenoble. Centre National de la Recherche Scientifique. 0 Elsevier Sequoia/Printed in The Netherlands
214
is to study the diffusion of hydrogen in a ZrlNiH, hydride by using a local method such as the perturbed angular correlation (PAC) on the “‘Ta nucleus.
2. Sample preparation and experimental conditions Polycrystalline ZrzNi prepared from high purity metals (99.95% Zr; 99.9% Ni) and containing 1.5 at.% Hf substituted for Zr, was hydrogenated under low hydrogen pressure (700 Torr) at 250 “C. Under such conditions the hydride Zr,NiH, with x = 4 could be obtained within about 20 h. The hydride was found to be a single homogeneous phase which retains the Cl6 CuAlrtype structure of Zr,Ni with parameters of the unit cell corresponding to an additional volume of 2.68 A3 (H atom)-‘. A sample (about 100 mg) of composition Zr2NiH3.s was irradiated for 3 h in a thermal neutron flux to obtain the 18rHf activity suitable for PAC experiments. The irradiated material was put in a quartz tube sealed under air so as to vary the temperature over a sufficiently large range without significantly changing the hydride composition. The PAC experiments were performed with a four-detector spectrometer on the 133 - 482 keV cascade of the 181Tanucleus fed by /3decay from ‘*lHf. The coincidence spectra between y rays emitted in cascade with a time separation t (0 < t < t,,, 2 lo- ’ s) in directions separated by an angle 8 = 90” or MO’, were recorded with a time resolution of 450 ps. The timedependent modulation factor G,(t) of the angular correlation between the y rays was calculated from an appropriate combination of the coincidence spectra. This modulation results from the coupling of the intermediate spin level of the lslTa cascade with the hyperfine field produced by the close environment of the probe nucleus. In non-magnetic materials, pure quadrupole modulation spectra are expected to be observed, as the result of the coupling of the quadrupole moment of the intermediate nuclear level with the electric field gradient (e.f.g.) generated by the non-cubic charge distribution around the nucleus. The theoretical expression for the quadrupole modulation corresponding to the interaction between a r~domly-orients static e.f.g. and the I = 512 spin level of “ITa is G?t(t) = s20(77)
+
5
S2n(‘?)
exPi--6f,(r7)&$)
~~~%d~)vQt~
(1)
n=l
This expression represents a mixture of three oscillating functions with amplitudes S2,(~) and frequencies v, = fn(q)vQ respectively, superposed on a time-independent contribution S,,(r)). The interaction is characterized as usual by the quadrupole frequency vQ and the asymmetry parameter 77of the e.f.g. tensor. The exponential term in the sum of eqn. (1) accounts for the existence of a quadrupole frequency distribution which is assumed to be properly represented by a Iorentzian shape with a relative width 6. Rather large values of S are expected in disordered systems such as non-stoichiometric hydrides.
215
Fluctuations in the e.f.g. produced by atomic diffusion give rise to a relaxation of the angular correlation as a result of the progressive depolarization of the nuclear spins with the time elapsed between the emission of two successive y rays. In most cases, this relaxation can be characterized to a good approximation by an unique relaxation constant h and an exponentially decaying “damping” factor must be introduced into the modulation which can be expressed as follows: G2(t) = e-ht GSt(t)
(2)
A simple relation exists between h and the jump frequency w of the diffusing atoms in both extremely slow (w 4 fnva) and fast (o 9 ~~~~) diffusion regimes. In these asymptotic conditions h = w and X a < ~6 > w-’ respectively. In practice, numerical calculations based on a stochastic relaxation model [7] show that such asymptotic relations remain valid within a few per cent for large ranges of jump frequencies, i.e. o S 10’ s-l and w > lo9 s-l respectively for ‘slTa PAC spectroscopy [S]. Consequently, a single-diffusion mechanism obeying an Arrhenius law such as w = w. exp(--E,/hT) is expected to be represented by a log X us. l/T plot consisting of two straight lines with opposite slopes. In the intermediate range corresponding to jump frequencies of the same order as the spin-precession frequencies we are able to observe with the rglTa probe, ie. 10’ - lo9 s-i, the spindepol~ization rate is very high and one observes a flat maximum in the values of h. However, no qu~titative significance should be attached to the values of the spin-relaxation constant in this region, as is clearly seen from the results of numerical calculations performed within the stochastic model: the pronounced damping of the perturbation factors cannot be properly reproduced with a unique time-decaying exponential term as in eqn. (2).
3. Results and discussion Examples of lslTa PAC modulation factors measured in polyc~st~line ZrzNiH,_s are presented in Fig. 1. The temperature range investigated extends from 190 K to 450 K. At T < 190 K, the modulation pattern corresponds to a static interaction and can be fitted to expression (1) - corrected from time resolution effects -with the quadrupole parameters vQ = 7.7 + 0.1 MHz, q = 0.70(2). A rather large (6 = 0.16) distribution of quadrupole frequencies is observed, which is an indication of some degree of randomness in the occupation of interstitial sites by hydrogen atoms. It is interesting to compare these values with the quadrupole parameters measured in ZrzNi which are vQ = 15.6 f 0.1 MHz (6 = 0.02) and q = 0.84(2). This comparison clearly indicates that the e.f.g. tensor is very sensitive to the presence of hydrogen in the vicinity of the r81Taprobe.
216
G211I 1.00 t
(4
O’
0.73
R
0.50 0.25
0.00
lllns ”
10.
0.
IO.
20.
30.
10.
50.
60,
70.
80.
@I
0.15
0.25
Il.00
IOns 20.
30.
LO.
50.
60.
70.
(cl
Fig. 1. lslTa PAC quadrupole spectra in ZrzNiHa 8: (a) at 209 K, (b) at 365 K and (c) at 404 K. The full lines represent the results of best-fit procedures using eqns. (1) and (2) as theoretical expressions for the modulation factors.
When the temperature is raised, a “damping” characteristic of spin relaxation effects appears in the modulation factor which can be satisfactorily fitted to the expression (2) at all temperatures. Simultaneously, the quadrupole frequency remains practically constant below 300 K and then
217
displays a rather fast decrease towards the value vg = 1.6 MHz observed for T > 420 K. As expected [9], the quadrupole frequency starts to fall when the correlation time characteristic of the spin relaxation process, which is also the mean time elapsed between two successive jumps of a hydrogen atom, becomes comparable with the period of the spin precession. The values of the PAC relaxation constant X are plotted against l/T in Fig. 2. This plot clearly does not correspond to a relaxation mechanism represented by a single Arrhenius law in the whole temperature range investigated . A first ~te~retation consists of assuming that fluctuations occurring in the pro~n-d~~sion barrier height are responsible for the ~ymmet~ observed in the temperature dependence of the spin relaxation constant. Such a model has been successful in explaining the results of PAC experiments in disordered ionic conductors [lo]. Spin relaxation data from NMR experiments in disordered systems including hydrides could also be satisfactorily interpreted by assuming the existence of a distribution of activation energies [ 111. The values of the relaxation constant plotted in Fig. 2 are effectively well reproduced by assuming the existence of a distribution characterized by a mean activation energy E, = 0.23 eV and a relative width u = 23%. However, the pre-exponential factor of the mean jump frequency stands at 3 X 10” T’ and is smaller by about three orders of magnitude than the frequency v. = lOI s-l of th e hy d rogen atom ~brations. Furthermore, the value obtained for the quad~pole frequency co~esponding to the ~uctuat~g e.f.g. is unreasonnably low (0.23 MHz). Then, although the existence of fluctuations in the barrier which controls the diffusion of hydrogen atoms could not be completely excluded, this model does not allow us to account for the lslTa spin relaxation in Zr,NiH,.s. Alternatively, the behaviour of the lslTa spin relaxation constant is quite well reproduced over the full range of temperatures investigated - excluding the region between 300 K and 370 K for reasons previously mentioned - by assuming the relaxation results from two competing thermally activated processes. The full hydrogen jump frequency is then given by the sum w = wol exp(-E&T) + oo2 exp(--E&T) with I& = 0.11 f 0.01 eV, w o1 = 1.7 X 10” s-’ and Ed = 0.38 + 0.04 eV, oo2 = 1.8 X lOI s-l. The first ?h(d) I
2
3
i 4
+(10-3K-') 5
Fig. 2. Plot of the quadrupole relaxation constant h of the lsiTa spins in ZrZNiH3.s against l/T. Straight lines represent Arrhenius law with activation energies Es = 0.1 eV and E, = 0.3 eV in the low- and high-temperature regions respectively.
218
process, characterized by a much lower activation energy and by an anomalously small pre-exponential frequency factor, predominates at low temperatures and could be associated with a subbarrier diffusion mechanism involving tunnelling effects. The activation energy _& is comparable with the energy associated with the localized vibrations of hydrogen in ZrzNi [12]. From the values of the Arrhenius parameters given above, it can be seen that both diffusion processes display identical jump probabilities for T = 335 K. Let us note that a similar behaviour resulting from the coexistence of two jump mechanisms is encountered for the diffusion of hydrogen in other metallic lattices such as, for example, niobium where the crossing point for the jump probab~ities stands at T= 250 K [13 J. The fitting procedure of the X( l/T) data leads to a mean square value (vi> = (1.7 MHz)* for the fluctuating quadrupole frequency. This value is smaller than the value expected from the whole amplitude of the variation observed for the quadrupole frequency with temperature. This is an indication that the relaxation is not exclusively produced by atomic jumps between equivalent first-neighbour positions around the ‘*ITa probe. A significant contribution of hydrogen jumps involving more distant sites to the relaxation of the rslTa spins should actually result in a lowering of the mean-square value of the fluctuating quadrupole frequency which enters the expression of the relaxation constant in the fast diffusion regime. By using the simplest model for describing the tunnelling process the pre~xponenti~ factor wol observed at low temperatures can be written as follows [ 141 ool = voexp .- a (2mU)1’2a i i This expression is the product of the frequency v. of proton vibrations by the transparency coefficient of the potential barrier between two neighbour hydrogen sites. The quantities U and a are the height and width of the barrier respectively. By taking for zi the value of the activation energy deduced from the high-temperature PAC relaxation data, i.e. tr = 0.38 eV, an estimation of the barrier width from eqn. (3) gives a - 0.4 8. This value should be compared with the distance between hydrogen neighbour sites. Unfo~unately, no data are yet available concerning the ~terstiti~ positions occupied by hydrogen in Zr,Ni hydrides. We can, however, try to get some information on this point from simple geometrical considerations. From a detailed examination of the structure of ZrzNi it is clear that hydrogen atoms occupy tetrahedral interstitial sites. The positions of the different hydrogen sites as indicated in Fig. 3, the H-H distances and the radii of the tetrahedral holes have been calculated by using the values of the lattice parameters measured for Zr2NiH,., (a = b = 6.8307 A, c = 5.7026 A) and the atomic positions reported for Zr&i [X5]. We used the values 1.25 A and 1.60 A for the atomic radii of zirconium and nickel respectively. The results of such c~culations are given in Table 1. Owing to the values obtained for the hole radii which are higher than those observed
219
Fig. 3. Atomic arrangement in Zr2Ni viewed along the z axis, with tetrahedral interstitial sites possibly available for occupation by hydrogen shown as &id symboIs: 8, a sites; A, b sites; *, c sites; 0, d sites.
TABLE 1 Hole sizes and H-H nearest- and next-nearest neighbour distances for hydrogen in interstitial sites in ZrzNiH3,s Site (as designated in Fig. 1)
Coordination
Number 0 f sites per Zr atom
H-H distance (‘Q
Hole radius 6)
nearest neighbour 4Zr
0.52
a-b
1‘425
0.54
a-e a-d b-c
3.29 2.96 1.05
4
0.47
b-d b-b’ c-c’
1.31 2.11 1.41
2
0.42
d-d’
1.26
0.5
(l,2,4,6f 1
4Zr (1,2,3,4) 3Zr (3’, 2Zr (l’,
+ 1Ni 4’, 5’ + I) + 2Ni 3’ + I, I’)
next-nearest neighbour
2.38 2.57
- 0.39 8) in many stable hydrides, any one of the tetrahedral sites is able to accommodate hydrogen. However, according to the criterion which fixes the minimum distance between hydrogen atoms at about 2.1 A [IS], a and b sites could not be occupied simultaneously. Because of the same criterion, the full occupation of b sites precludes occupation of c and/or d sites. As occupation limited to a or b sites does not allow us to obtain hydrogen concentrations higher than x = 2, it may be reasonably concluded that the formation of the hydride Zr2NiH3.s requires occupation of some combination of a, b, c and d sites, with a less probability for the latter owing to the weak affinity of nickel for hydrogen. This conclusion does not contradict the results of neutron spectroscopy which indicate different environments for (0.37
220
the hydrogen atoms in Z&NiH,s and ZrNiH,_s [lo]. In the latter compound, the proton is encountered in four- and five-coordinated sites with “mixed” environments (3Zr f 1Ni and 3Zr + 2Ni respectively) {17], Within the predictions of the geometrical model, the proton is expected to be able to diffuse easily through the face shared by two adjacent tetrahedra in ZrZNiH3.s IThe value estimated for the tunnelling barrier of the proton is then quite realistic if compared with the distance of 1 - 1.4 A between such neighbouring sites. For temperatures lower than 300 K, he. T 5 on, tunnelfing diffusion may be interpreted in a more sophisticated way with a phonon-assisted tunnelling model as developed by Flynn and Stoneham [Ml. The fit of the PAC relaxation data to the expression af the atomic jump frequency calculated by these authors for a multiphonon process gives an activation energy of 0.13 eV and a tunnelling matrix element J = 240 meV, In conclusion, the **ITa spin-relaxation data are consistently interpreted by using a thermally activated tunnelling model for the diffusion of hydrogen atoms in crystallized ZrzNiH,.s below 300 K. At high temperatures, the diffusion takes place predominantly from over-barrier atomic jumps. In our opinion, an interesting field of investigations is open concerning hydrogen diffusion in Zr-Ni intermetallic compounds. PAC experiments on deuterated ZrzNi, as well as on amorphous hydrides of this alloy, are in progress. Acknowledgments Thanks are due to Dr. L. Billard for his collaboration in calculating hydrogen site positions. References 1 R. M. van Essen and K. II. J. Busehow, J. Less-Common iWet., 64 (1979) 217. 2 F. I-I. M. Spit, J. W. Drijver and S. Radelaar, Scripta Met&, 14 (1980) 1071. 3 K. Aoki, A. Horata and T. Masumoto, Proc. 4th Znt. Conf. on Rapidly Quenched Met&, Sendai, August 1081, Japan Institute of Metals, Sendai, 1982, p. 1649, 4 K. Aoki, M. Kamachi and T. Masumoto, J. Non-Cryst. Solids, 61 (1984) 679, 5 D. G. Westlake, J. Less-Common Met., 75 (1930) 177. 6 D. G. WestIake, H. Shaked, P. R. Mason, B. R. M&art, M. H. Mueller, T. Matsumoto and Ail.Amano, J. Less-Common Met., 88 (1982) 17. 7 H. Winkler and E. Gerdau, 2. Phys., 262 (1973) 263. 8 A. Baudry and P. Boyer, Proc. 7th Conf. on Hyperfine Interactions, Bangalore, India, 1986, Hyperfine Interactions, to be published. 9 0. de 0. Damasceno, A. L. de Oliveira, J, de Oliveira, A. Baudry and P. Bayer, Solid State Commlm., 53 (1935) 363. 10 A. Baudry, P. Boyer and A. L. de Oliveira, J. Fhys. Chem, Solids, 43 (1982) 871. 11 J. Shinar, Proc. ht. Symp. on the Properties and Applicator of Metal Hydrides ZV, Eilat, Israel, 1984 in J. Less-Common Met., 104 (1984) 87. 12 H. Kaneko, T. Kajitani, M. Hirabayashi, M. Ueno and K. Suzuki, J. Less-Common
Met., 89 (1983) 237.
221 13 A. Seeger, Hyperfine Zntemct., 17 - 19 (1984) 63. 14 V. G. Grebinnik, I. I. Gurevich, V. A. Zhukov, A. P. Manych, E. A. Meleshko, I. A. Muratova, B. A. Nikol’skii, V. I. Selivanov and V. A. Suetin, Sov. Phys.-JETP, 41 (1976) 777. 15 M. E. Kirkpatrick, D. M. Bailey and J. F. Smith, Acta Crystallogr., 15 (1962) 252. 16 A. C. Switendick, Sandia Lab. Rep. 78-0250, 1978. 17 A. V. Irodova, V. A. Somenkov, S. Sh. Shil’shtein, L. N. Padurets and A. A. Chertkov, Sov. Phys.-Crystallogr., 23 (1978) 591. 18 C. P. Flynn and A. M. Stoneham, Phys. Rev. B, 1 (1970) 3966.