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181Ta perturbed angular correlation study of hydrogen duffusion in hafnium hydride
Solid State Communications, Vol. 53, No. 4, pp. 363-368, 1985. Printed in Great Britain.
0038-1098/85 $3.00 + .00 Pergamon Press Ltd.
181Ta PERTURBED ANGULAR CORRELATION STUDY OF HYDROGEN DIFFUSION IN HAFNIUM HYDRIDE O. de O. Damasceno, A.L. de Oliveira, J. de Oliveira Universidade Federal de Minas Gerais, Departamento de Fisica, C.P. 702, Pampulha, 30.000 Belo-Horizonte, Brazil and A. Baudry* and P. Boyer** Centre d'Etudes Nucl~aires de Grenoble, DRF/Laboratoire Interactions Hyperfines, 85 X - 38041 Grenoble Cedex, France
(Received 18 September 1984 by E.F. Bertaut) The quadrupole coupling parameters of the 181Ta probe were measured by Perturbed Angular Correlation spectroscopy in the f.c.c, phase of hafnium hydride (HfI-ll.~). Spin relaxation phenomena associated with the hydrogen diffusion are observed above 100°C. The activation energy deduced from the temperature dependence of the quadrupole relaxation constant is in agreement with the values previously observed by ~H NMR spectroscopy. No significant perturbation of the hydrogen diffusion due to the presence of Ta substitutional impurity is detected. I. INTRODUCTION BECAUSE OF THEIR potential interest for technological applications, the hydrides of the type MHx (0 ~< x <~ 2) formed by I V - B transition metals (Ti, Zr, Hf) have been extensively studied. The phase diagrams and the changes in the crystal structure with the hydrogen concentration have been recognized for a long time in these systems [ 1]. On the other hand, a number of works have been specially devoted to the important problem of hydrogen diffusion in these non-stoichiometric hydrides. In particular, several studies of the proton and/or deuteron spin relaxation have been carried out by NMR spectroscopy for different hydrogen concentrations [ 2 - 5 ] . The aim of this paper is to show that a spin precession technique such as the Perturbed Angular Correlation (PAC) of the two gamma rays emitted successively in the 133 keV-482 keV cascade of the 18XTanucleus can provide valuable informations concerning hydrogen diffusion in I V - B metal hydrides. In a 181Ta PAC experiment the I = 5/2 intermediate level of the nuclear cascade is used as a spin probe to investigate the local properties of the material one is interested in. The precession of the spins in static magnetic fields or electric field-gradients is readily observed by this technique [6]. In addition, the angular correlation of ~'-rays is very sensitive to the relaxation of the nuclear spins produced by fluctuating hyperfine *Centre National de la REcherche Scientifique **Universit~ Scientifique et M6dicale de Grenoble
fields [7]. Such fluctuations can result from random atomic motions occurring in the close environment of the probe. Typically, atomic motions corresponding to jump frequencies within the range 107-10 l° s -1 are readily observed by 181Ta PAC spectroscopy. Some recent experiments performed in oxygen-ion conductors such as stabilized zirconia have clearly demonstrated that the PAC technique can be a valuable microscopic tool to study atomic diffusion in solids [8]. Moreover, let us point out a specific aspect of this technique which is able to provide unique information about the behaviour of hydrogen in the presence of a substitutional impurity in hydrogenated metals and alloys. At the present time, the number of PAC experiments conducted on hydrogenated materials is quite limited. Let us mention however that relaxation phenomena were observed about IO0°C by Damasceno [9] in a preliminary work on HfH1.65 by 181Ta PAC Spectroscopy. Recently, a paper by Heidinger et al. reported the existence of relaxation effects in 18~Ta PAC spectra relative to hydrogenated HfVz alloys [10]. The relaxation was nicely observed for an hydrogen concentration of 40 at. % in the temperature range 100-200 K. However, because of the possible existence of structure fluctuations associated with a tetragonalorthorhombic transition occurring in this temperature region, the relaxation could not be confidently attributed to hydrogen motions in the probe surroundings. Let us mention also the X81TaPAC study of the face-centered tetragonal phase Zrl-ll.97 by Rasera et al. [ 11 ]. In this almost stoichiometric hydride purely static quadrupole spectra are observed between room 363
364
HYDROGEN DIFFUSION IN HAFNIUM HYDRIDE
temperature and 588 K. in agreement with the slow diffusion of hydrogen indicated by ~tt NMR results. In the experiments described herein the ~s~Ta PAC technique is applied to hatnium hydride in its facecentered cubic phase. Neutron diffraction studies have shown this fluorite-type structure to be highly defective, with the hydrogen atoms partially occupying the intersticial sites of tetrahedral symnletry in the cubic lattice [12].
gradient (efg) tensor generated by non-cubic charge distribution. Tire theoretical expression of (72(t) for a quadrupole interaction between a randomly-oriented static electric-field-gradient and a I - 5/2 intermediate spin-level can be written as follows 3
G~t(t) - S2o(rD + ~ S2n(T~)exp(-- 6fn(rl)uqt ) rt=l
× cos l . t ; , ( n ) . ~ t l . 1I. EXPERIMENTAL CONDITIONS The polycrystalline material used in our experiments was of commercial origin (Ugine Kubhnann). The X-ray diffraction spectrum recorded at room temperature displayed the characteristic lines of a pure f.c.c, phase (6 phase) with a lattice parameter a = (4.703 -+ 0.001) A. This value is very close to the value a = (4.702 -+ 0.012) A reported by Espagno et al. for the composition HfHL64 [13]. The material was irradiated for 3 mn in a thermal neutron flux o f ~ 1013 n.cm -2 s -I in order to produce the requisite 181Hf activity from iS°HI(n, "y)lsl tlf reaction. The 133 keV- 482 keV cascade of the '8~Ta daughter nucleus is fed by/3-decay from the parent nucleus through a long-lived (~ 17/as) level. Therefore, as free electrons are readily available in hafiaium hydride, any eventual perturbation produced by the beta desintegration in the outer electronic shells of the tantalum atom is expected to be ruled out before the two successive "),-rays are detected. In a PAC experiment one observes coincidence events, each one corresponding to the detection successively of the first "y-ray of the cascade in a given direction, and the second 3,-ray after a time t at an angle 0 from the direction of the first one. The coincidence spectrum recorded for a given angle 0 appears as a time-decaying exponential function which is modulated by the precession of the spins of the intermediate level in the hyperfine field (spin precession method). This time-dependent modulation, conventionally called perturbation factor of the angular correlation, contains the whole information about the interaction(s) between the spin probe and the hyperfine field(s). In our experiments, the time-dependent perturbation factor G2(t) of the ~8~Ta cascade was extracted from an appropriate combination of the coincidence spectra recorded with a three-detector spectrometer for two different angles (90 ° and 180 °) between the directions of emission of the two successive radiations. In non-magnetic materials such as hafnium hydrides, pure quadrupole spectra are observed as the result of the coupling of the large quadrupole moment ((2 = -- 2.5 b) of the intermediate nuclear level with the electric field-
Vol. 53, No. 4
(I)
This expression includes a time-independent term $20 and three ternrs which are oscillating functions of time. Each oscillating term is characterized by its magnitude S2n and frequency (fnUO) which depend on the asynmretry of tire efg tensor. As usual, this tensor is completely determined if the values of the quadrupole frequency u# and the asymmetry parameter r/are known. The exponential factor in the sum accounts for the possible existence of a quadrupole frequency distribution which is assunred to be correctly described by a Lorentzian shape with a relative width 6. A nonvanishing value of 6 can be associated either with a significant concentration of defects and/or impurities in the material under study, or with a disordered arrangement or atoms in the probe surroundings. In the presence of fluctuating efg's the initial alignment of the spins in the intermediate level which gives rise to the gamma-gamma angular correlation phenomenon tends to be destroyed with the passage of time. The disalignment of the spins results in a damping of the perturbation factor with time. Although the relaxation of the spins in PAC experiments cannot be in general completely described by an unique relaxation time [14, 15], it is observed that in most circumstances this damping effect can be satisfactorily reproduced by a single decaying exponential factor. The perturbation factor can hence be expressed as follows G2(/) = exp(-- Xt) GS2t(t),
(2)
where GS2t(t) is given by equation (1). The damping rate is determined by the relaxation constant X of the nuclear spins. If the relaxation is produced by atomic diffusion, a simple relation exists between X and the jump frequency w of the diffusing atoms in both extremely slow (w ~ f~uq) and fast (w >>j'~uQ) diffusion regimes. In these asymptotic conditions X oc w and X oc (u~)w -l respectively. In practice, numerical calculations based on a stochastic relaxation model show that such asymptotic relations remain valid within a few percents for large ranges of jump frequencies, i.e. w ~< l0 s s -1 and if ~ 109 s -1 respectively for 181Ta PAC spectroscopy [ 16]. In the intermediate range corresponding to jump frequencies of the same order as the spin-precession frequencies we are able to observe with the 181Ta probe,
Vol. 53, No. 4
365
HYDROGEN DIFFUSION IN HAFNIUM HYDRIDE Gt.b
i.e. 108--109 s -1 , the spin-depolarization rate is very high and one observes a flat maximum in the values of k. However, no quantitative significance should be attached to the values of the spin-relaxation constant in this particular region, as it 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 an unique time-decaying exponential term as in equation (2).
1.00
0.'~
0.50
0.25
'
i
t
0.00 I II )~,, 0.
1.00
II0.
.
40.
.
.
"/0.
l0
G t. I ' ~.
Ill. RESULTS AND DISCUSSION Examples of experimental time-dependent perturbation factors measured at various temperatures in HfH;.64 and fitted to theoretical G2(t) functions after correction for finite time resolution (~ 0.8 ns fwhm) effects, are presented in Fig. 1. At room temperature, the PAC spectrum does not display any damping of the perturbation factor with time and is then characteristic of a static quadrupole coupling. However, the experimental data do not correctly fit to a single static GS2t(t) function. One is then led to consider them as resulting from the superposition of several GS2t(t) functions corresponding to distinct efg's at the 181Ta site. As clearly shown in Fig. la, the room-temperature data can be correctly interpreted by assuming the existence of two efg's in almost equivalent proportions. The two components of the whole perturbation factor are determined by the following parameters
v01 v02
= (3.9 + 0.26)MHz
'171 ~ 1
= (5.70 + 0.50)MHz
r/2 ,-~ 1
with rather large relative widths of the frequency distributions (/51 ~/52 ~ 0.25). This indicates the existence of important variations in the static charge configuration around the probe. Such variations are to be expected in a highly defective structure such as that of HfH1.64in which approximately as much as 20% of the hydrogen sites are vacant. On this point, let us mention the relatively small width (/5 = 0.08) of the quadrupole frequency distribution observed in ZrH1.97 [ 11 ], which is a clear indication for a smaller disorder in the hydrogen sublattice when the di-hydride composition is approached. The PAC spectra obtained in the temperature range 90-120°C still retain the features of a twocomponent perturbation factor, at the same time when some damping characteristic of the existence of relaxation effects starts to occur. Beyond 120°C, all the PAC patterns can be nicely fitted to a G2(t) function which corresponds to a unique time-fluctuating quadrupole interaction with an asymmetry parameter r / ~ 0.30 (Fig. l b, c, d).
i O.
1.00
|0.
I ZO.
I __~ 30. ~0.
50.
GO.
j (t)~e
70.
~--
" i 0.
1.00
,~
0.75
.
i 10.
I 20.
I 30.
I ~0.
1
J t t )he
_
~0.
60.
70.
50.
60.
10.
d
0.
10.
20.
30.
~0.
Fig. 1. ~8~TaPerturbed Angular Correlation spectra obtained in HfH1.64 at oroom temperature (a), 131°C (b), 180°C (c) and 240 C (d). The full lines are the results of best fit procedures using equations (1) and (2) as the theoretical expressions of the perturbation factors. The evolution of the quadrupole frequency with temperature is plotted on Fig. 2. Below 120°C, the data correspond to the averaged quadrupole frequency deduced from the results given by the two-site fitting procedure. On Fig. 2 is also plotted the intensity G~T(0) at w -- 0 of the Fourier transform of the experimental spectra. For static interactions this quantity is essentially related to the "hard-core" term $2o of the perturbation factor (see equation (1)) which varies from 0.20 for an
366
HYDROGEN DIFFUSION IN HAFN1UM HYDRIDE
Wo(MHz),
(3~T(0) o,
\'
0.2
6
V 0.1
y
,.',
"',÷
/
2 0
i
1.5
I
i
2
I
I
2.5
3
+ (I0-3K-I)
Fig. 2. Plot against 1/T of the quadrupole coupling frequency vO and the value of the Fourier transform of the perturbation factor G2(t) at zero frequency for the lalTa probe in HfH1.64.
(arb.units)
e
0.!
Vol. 53, No. 4
proton) to jump randomly upon the vertices of a cube around the probe. The perturbation factor was calculated for various jump frequencies through a fulldiagonalization process of the Blume's relaxation matrix, and then fitted to equation (2) [16]. The behaviour observed simultaneously for both quantities uO and G~r(O) as the temperature is raised in Htltl.64 is therefore characteristic of the existence of spin-relaxation effects. In particular, the fast decrease of the quadrupole frequency is closely related to the relaxation phenomenon as it corresponds to a slowing down of the precession rate of the 181Ta spins when faster and faster changes in the orientation of the efg tensor occur. In addition, the uO vs. 1/Tplot suggests that the quadrupole frequency does not go down to zero at high temperatures, but rather tends toward a limit value of ~ 1.3 MHz. This observation is consistent with the fact that hydrogen diffusion can induce changes in the magnitude as well as in the orientation of the efg tensor. In effect, if the strength of the quadrupole interaction is allowed to change from a stochastic state to another in such a way that the cubic symmetry for the efg tensor is broken, the quadrupole frequency could never be averaged to zero even though the jump frequency between the different stochastic states becomes much higher than the precession frequency of the spins. By the other hand, some contribution to this residual electric fieldgradient due to the presence of defects and/or impurities in the sample cannot be discarded. The observed values of the relaxation constant X are plotted against 1/T in Fig. 4. If the relaxation of the
,k (ns-1) 0.1
100
10
1
W
Fig. 3. Plot of the calculated quadrupole coupling frequency u0 and Fourier transform of G2(t) at zero frequency against the jump frequency W for a point charge (e.g. a proton) jumping upon the vertices of a cube centered on the 18~Ta site. The values indicated on the figure are the results of numerical calculations using the Blume's stochastic model for describing the spin relaxation. axial efg tensor (r/= 0) to 0.258 for r / = 1. As shown in Fig. 3, these diagrams could be qualitatively reproduced from numerical calculations performed by using the Blume's stochastic model for describing the spin relaxation [ 14]. In these calculations a time-fluctuating efg tensor was generated by allowing a point-charge (e.g. a
0.01
0.001 1.5
+
1 2
I
t>
2"5~(10-::1K-1)
Fig. 4. Plot against lIT of the quadrupole relaxation constant X of the lS~Ta spins in HfHL64. Open circles and triangles correspond to experiments performed with a time resolution of 3 ns and 0.8 ns respectively. 181Ta spins is produced by hydrogen self-diffusion, X is expected to be practically proportional to the frequency w of the protons jumps at low temperatures. Assuming w to be described by an Arrhenius law
Vol. 53, No. 4
HYDROGEN DIFFUSION IN HAFNIUM HYDRIDE
w = Woexp (-- E / k T ) , the value of the activation energy can be straight deduced from the low-temperature part of the X(1/T) plot. By using the data obtained between 100 and 180°C, we calculated an activation energy E = 0.43 + 0.05 eV. This result is about 20 percent lower than the value determined by Weaver (0.55 -+ 0.05 eV) from 1H and 2D NMR experiments in HfHx.7 [4]. On the other hand, aH NMR relaxation experiments conducted by do Nascimento et al. [19] on a sample of our material indicate values of 0.49 eV (from Tx) and 0.46 eV (from 7"2) for the activation energy of H diffusion. We have good reasons to believe the activation energy deduced from our PAC experiments to be underestimated. In effect, it can be seen from the results of calculations using the Blume's stochastic approach for describing the spin relaxation that the X(w) relation progressively deviates from the linearity observed for very low diffusion rates as the jump frequency raises [16]. In the Arrhenius plot we observe therefore an "apparent" activation energy which is smaller than the "true" value deduced from the asymptotic data corresponding to extremely slow diffusive motions. Hence, the activation energy as determined from PAC data was estimated to be underevaluated by about 10 percent. We may then conclude that a quite good agreement exists between the activation energies of proton jumps observed by either 181Ta PAC or 1H NMR spectroscopy. The minimum value of the 1H spin-lattice relaxation time observed at T ~ 340°C in HfH1.7 [4] corresponds to the well-known relation ( C O T c ) m i n " " 1, where co is the Larmor pulsation of the protons and r e the spin correlation time. In high-temperature 1H NMR experiments, one observes dipole interactions only and ~'e is then related to the individual jump frequency through the relation ze = 1/2w. From the NMR data reported in Weaver's paper the temperature at which one should expect relaxation effects to occur in PAC experiments can be easily estimated. Considering that in practice the lSlTa probe does not allow to measure confidently relaxation times longer than 5 t0 -7 s, we obtain a temperature of ~ 100°C, in good agreement with our observations. The absence of any detectable influence of the Ta substitution impurity on local motions of hydrogen atoms may be thought as a rather surprising fact. However, it must be remembered that recent observations made by quasielastic neutron spectroscopy in hydrogenated niobium indicate a rather small trapping effect on hydrogen due to substitutional V or Cr impurities [17]. By the other hand, a fast H-motion around the substitutional V-atom in hydrogenated Nbl-xVx alloys had to be assumed by Matsumoto [18] in order to explain the motional narrowing observed on the
367
NMR-proton line below the room-temperature. It was proposed that such a rapid motion takes place between 24 equivalent positions around the V impurity, without breaking of the V - H pairs. If one assumes a similar situation to occur in the vicinity of the Ta-impurity in HfHx, no contribution to the electric field-gradient experienced by the 181Ta probe is expected from the rapidly moving first-neighbour H atoms at high temperatures. At the same time, an important variation of the efg tensor should occur at low temperatures, as soon as the jump rate of Ta-trapped hydrogen atoms would slow down below the lower limit (~ 107 s-1) detectable by 181Ta PAC spectroscopy. Moreover, relaxation effects associated with the slqwing-down of Ta-trapped H motions should be observed on the PAC spectra. Experiments performed at 77 K and 4.2 K do not indicate any significant change in the PAC patterns compared with the room-temperature data. In particular, no variation of the quadrupole frequency distribution is observed. These observations demonstrate that within the time scale of 181Ta PAC spectroscopy the configuration of hydrogen atoms around the probe does not change - that is, remains static and disordered - between 4.2 K and 300 K. However, the true configuration of hydrogen atoms in the vicinity of the Ta site can be hardly deduced from the quadrupole coupling data. Actually, as it is clear from the calculations performed in HfV2Hx compounds by Heidinger et al. [10], no confident estimation of the electric field-gradient in transition metal hydrides can be reasonably made at the present time. In conclusion, it may be claimed that 181Ta is a suitable microscopic probe for the observation of hydrogen diffusion in hafnium and zirconium hydrides. Consequently, the application of 181Ta PAC spectroscopy to the study of a variety of hydrogenated systems, especially crystallized and amorphous metallic alloys with hafnium and zirconium, seems to be promising. Acknowledgements - This work was undertaken during the stage of one of us (P. Boyer) in the Departamento de Fisica of the Universidade Federal de Minas Gerais, Belo Horizonte, Brazil. This stage was supported by CNRS (Centre National de la Recherche Scientifique, France), CNPq (Centro National de Pesquisas, Brazil) and FINEP (Financiadora de Estudos e Projetos, Brazi!L REFERENCES 1. 2. 3.
W.M. Mueller, J.P. Blackledge & G.G. Libowitz, Metal Hydrides, Academic Press, New-York (1968) Chap. 7 and 8. C. Korn & D. Zamir,J. Phys. Chem. Solids 31, 489 (1970) E.F. Khodosov & N.A. Shepilov, Phys. Stat. Sol. (b)47,693 (1971).
368 4. 5. 6.
7. 8. 9. 10. 11. 12.
HYDROGEN DIFFUSION IN HAFNIUM HYDRIDE H.T. Weaver,J. ofMag. Res. 15, 84 (1974). K.R. Doolan, P.P. Narang & J.M. Pope, J. Phys. F: MetalPhys. 10, 2073 (1980). H. Frauenfelder & R.M. Steffen in Alpha-, Betaand Gamma-ray Spectroscopy, K. Sieg Bahn ed., North-Holland Publ. Co., Amsterdam (1965) p. 997. A. Abragam & R.V. Pound, Phys. Rev. 92, 943 (1953). A. Baudry, P. Boyer & A.L. de Oliveira, J. Phys. Chem. Solids, 43, 871 (1982). O. de O. Damasceno, Thesis, Belo Horizonte (1975). R. Heidinger, P. Peretto & S. Choulet, Solid State Commun. 47,283 (1983). R.L. Rasera, G.K. Shenoy, B.D. Dunlap & D.G. Westlake, J. Phys. Chem. Solids 40, 75 (1979). S.S. Sidhu, Leroy Heaton & D.D. Zauberis, Acta Cryst. 9, 607 (1956).
13. 14. 15. 16. 17. 18. 19.
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L. Espagno, B. Azou & P. Bastien, Compt. Rend. 250, 4352 (1960). M. Blume in Hyperfine Structure and Nuclear Radiations, E. Matthias and D.A. Shirley eds., North-Holland, Amsterdam (1968) p. 911. H. Winkler & E. Gerdau, Z. Physik, 262, 363 (1973). A. Baudry & P. Boyer (Unpublished). A. Magerl, J.J. Rush, J.M. Rowe, D. Richter & H. Wipf, Phys. Rev. B,27,927 (1983).
T. Matsumoto,J. Phys. Soc. Japan, 42,1583(1977). V.M. do Nascimento, J. Pedro Donoso, H. Panepucci, A.L. de Oliveira & O. de O. Damasceno, Communication at the 36th meeting of the Sociadade Brasileira Para o Progresso da Ciencia, Sgo Paulo (1984).
0038-1098/85 $3.00 + .00 Pergamon Press Ltd.
181Ta PERTURBED ANGULAR CORRELATION STUDY OF HYDROGEN DIFFUSION IN HAFNIUM HYDRIDE O. de O. Damasceno, A.L. de Oliveira, J. de Oliveira Universidade Federal de Minas Gerais, Departamento de Fisica, C.P. 702, Pampulha, 30.000 Belo-Horizonte, Brazil and A. Baudry* and P. Boyer** Centre d'Etudes Nucl~aires de Grenoble, DRF/Laboratoire Interactions Hyperfines, 85 X - 38041 Grenoble Cedex, France
(Received 18 September 1984 by E.F. Bertaut) The quadrupole coupling parameters of the 181Ta probe were measured by Perturbed Angular Correlation spectroscopy in the f.c.c, phase of hafnium hydride (HfI-ll.~). Spin relaxation phenomena associated with the hydrogen diffusion are observed above 100°C. The activation energy deduced from the temperature dependence of the quadrupole relaxation constant is in agreement with the values previously observed by ~H NMR spectroscopy. No significant perturbation of the hydrogen diffusion due to the presence of Ta substitutional impurity is detected. I. INTRODUCTION BECAUSE OF THEIR potential interest for technological applications, the hydrides of the type MHx (0 ~< x <~ 2) formed by I V - B transition metals (Ti, Zr, Hf) have been extensively studied. The phase diagrams and the changes in the crystal structure with the hydrogen concentration have been recognized for a long time in these systems [ 1]. On the other hand, a number of works have been specially devoted to the important problem of hydrogen diffusion in these non-stoichiometric hydrides. In particular, several studies of the proton and/or deuteron spin relaxation have been carried out by NMR spectroscopy for different hydrogen concentrations [ 2 - 5 ] . The aim of this paper is to show that a spin precession technique such as the Perturbed Angular Correlation (PAC) of the two gamma rays emitted successively in the 133 keV-482 keV cascade of the 18XTanucleus can provide valuable informations concerning hydrogen diffusion in I V - B metal hydrides. In a 181Ta PAC experiment the I = 5/2 intermediate level of the nuclear cascade is used as a spin probe to investigate the local properties of the material one is interested in. The precession of the spins in static magnetic fields or electric field-gradients is readily observed by this technique [6]. In addition, the angular correlation of ~'-rays is very sensitive to the relaxation of the nuclear spins produced by fluctuating hyperfine *Centre National de la REcherche Scientifique **Universit~ Scientifique et M6dicale de Grenoble
fields [7]. Such fluctuations can result from random atomic motions occurring in the close environment of the probe. Typically, atomic motions corresponding to jump frequencies within the range 107-10 l° s -1 are readily observed by 181Ta PAC spectroscopy. Some recent experiments performed in oxygen-ion conductors such as stabilized zirconia have clearly demonstrated that the PAC technique can be a valuable microscopic tool to study atomic diffusion in solids [8]. Moreover, let us point out a specific aspect of this technique which is able to provide unique information about the behaviour of hydrogen in the presence of a substitutional impurity in hydrogenated metals and alloys. At the present time, the number of PAC experiments conducted on hydrogenated materials is quite limited. Let us mention however that relaxation phenomena were observed about IO0°C by Damasceno [9] in a preliminary work on HfH1.65 by 181Ta PAC Spectroscopy. Recently, a paper by Heidinger et al. reported the existence of relaxation effects in 18~Ta PAC spectra relative to hydrogenated HfVz alloys [10]. The relaxation was nicely observed for an hydrogen concentration of 40 at. % in the temperature range 100-200 K. However, because of the possible existence of structure fluctuations associated with a tetragonalorthorhombic transition occurring in this temperature region, the relaxation could not be confidently attributed to hydrogen motions in the probe surroundings. Let us mention also the X81TaPAC study of the face-centered tetragonal phase Zrl-ll.97 by Rasera et al. [ 11 ]. In this almost stoichiometric hydride purely static quadrupole spectra are observed between room 363
364
HYDROGEN DIFFUSION IN HAFNIUM HYDRIDE
temperature and 588 K. in agreement with the slow diffusion of hydrogen indicated by ~tt NMR results. In the experiments described herein the ~s~Ta PAC technique is applied to hatnium hydride in its facecentered cubic phase. Neutron diffraction studies have shown this fluorite-type structure to be highly defective, with the hydrogen atoms partially occupying the intersticial sites of tetrahedral symnletry in the cubic lattice [12].
gradient (efg) tensor generated by non-cubic charge distribution. Tire theoretical expression of (72(t) for a quadrupole interaction between a randomly-oriented static electric-field-gradient and a I - 5/2 intermediate spin-level can be written as follows 3
G~t(t) - S2o(rD + ~ S2n(T~)exp(-- 6fn(rl)uqt ) rt=l
× cos l . t ; , ( n ) . ~ t l . 1I. EXPERIMENTAL CONDITIONS The polycrystalline material used in our experiments was of commercial origin (Ugine Kubhnann). The X-ray diffraction spectrum recorded at room temperature displayed the characteristic lines of a pure f.c.c, phase (6 phase) with a lattice parameter a = (4.703 -+ 0.001) A. This value is very close to the value a = (4.702 -+ 0.012) A reported by Espagno et al. for the composition HfHL64 [13]. The material was irradiated for 3 mn in a thermal neutron flux o f ~ 1013 n.cm -2 s -I in order to produce the requisite 181Hf activity from iS°HI(n, "y)lsl tlf reaction. The 133 keV- 482 keV cascade of the '8~Ta daughter nucleus is fed by/3-decay from the parent nucleus through a long-lived (~ 17/as) level. Therefore, as free electrons are readily available in hafiaium hydride, any eventual perturbation produced by the beta desintegration in the outer electronic shells of the tantalum atom is expected to be ruled out before the two successive "),-rays are detected. In a PAC experiment one observes coincidence events, each one corresponding to the detection successively of the first "y-ray of the cascade in a given direction, and the second 3,-ray after a time t at an angle 0 from the direction of the first one. The coincidence spectrum recorded for a given angle 0 appears as a time-decaying exponential function which is modulated by the precession of the spins of the intermediate level in the hyperfine field (spin precession method). This time-dependent modulation, conventionally called perturbation factor of the angular correlation, contains the whole information about the interaction(s) between the spin probe and the hyperfine field(s). In our experiments, the time-dependent perturbation factor G2(t) of the ~8~Ta cascade was extracted from an appropriate combination of the coincidence spectra recorded with a three-detector spectrometer for two different angles (90 ° and 180 °) between the directions of emission of the two successive radiations. In non-magnetic materials such as hafnium hydrides, pure quadrupole spectra are observed as the result of the coupling of the large quadrupole moment ((2 = -- 2.5 b) of the intermediate nuclear level with the electric field-
Vol. 53, No. 4
(I)
This expression includes a time-independent term $20 and three ternrs which are oscillating functions of time. Each oscillating term is characterized by its magnitude S2n and frequency (fnUO) which depend on the asynmretry of tire efg tensor. As usual, this tensor is completely determined if the values of the quadrupole frequency u# and the asymmetry parameter r/are known. The exponential factor in the sum accounts for the possible existence of a quadrupole frequency distribution which is assunred to be correctly described by a Lorentzian shape with a relative width 6. A nonvanishing value of 6 can be associated either with a significant concentration of defects and/or impurities in the material under study, or with a disordered arrangement or atoms in the probe surroundings. In the presence of fluctuating efg's the initial alignment of the spins in the intermediate level which gives rise to the gamma-gamma angular correlation phenomenon tends to be destroyed with the passage of time. The disalignment of the spins results in a damping of the perturbation factor with time. Although the relaxation of the spins in PAC experiments cannot be in general completely described by an unique relaxation time [14, 15], it is observed that in most circumstances this damping effect can be satisfactorily reproduced by a single decaying exponential factor. The perturbation factor can hence be expressed as follows G2(/) = exp(-- Xt) GS2t(t),
(2)
where GS2t(t) is given by equation (1). The damping rate is determined by the relaxation constant X of the nuclear spins. If the relaxation is produced by atomic diffusion, a simple relation exists between X and the jump frequency w of the diffusing atoms in both extremely slow (w ~ f~uq) and fast (w >>j'~uQ) diffusion regimes. In these asymptotic conditions X oc w and X oc (u~)w -l respectively. In practice, numerical calculations based on a stochastic relaxation model show that such asymptotic relations remain valid within a few percents for large ranges of jump frequencies, i.e. w ~< l0 s s -1 and if ~ 109 s -1 respectively for 181Ta PAC spectroscopy [ 16]. In the intermediate range corresponding to jump frequencies of the same order as the spin-precession frequencies we are able to observe with the 181Ta probe,
Vol. 53, No. 4
365
HYDROGEN DIFFUSION IN HAFNIUM HYDRIDE Gt.b
i.e. 108--109 s -1 , the spin-depolarization rate is very high and one observes a flat maximum in the values of k. However, no quantitative significance should be attached to the values of the spin-relaxation constant in this particular region, as it 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 an unique time-decaying exponential term as in equation (2).
1.00
0.'~
0.50
0.25
'
i
t
0.00 I II )~,, 0.
1.00
II0.
.
40.
.
.
"/0.
l0
G t. I ' ~.
Ill. RESULTS AND DISCUSSION Examples of experimental time-dependent perturbation factors measured at various temperatures in HfH;.64 and fitted to theoretical G2(t) functions after correction for finite time resolution (~ 0.8 ns fwhm) effects, are presented in Fig. 1. At room temperature, the PAC spectrum does not display any damping of the perturbation factor with time and is then characteristic of a static quadrupole coupling. However, the experimental data do not correctly fit to a single static GS2t(t) function. One is then led to consider them as resulting from the superposition of several GS2t(t) functions corresponding to distinct efg's at the 181Ta site. As clearly shown in Fig. la, the room-temperature data can be correctly interpreted by assuming the existence of two efg's in almost equivalent proportions. The two components of the whole perturbation factor are determined by the following parameters
v01 v02
= (3.9 + 0.26)MHz
'171 ~ 1
= (5.70 + 0.50)MHz
r/2 ,-~ 1
with rather large relative widths of the frequency distributions (/51 ~/52 ~ 0.25). This indicates the existence of important variations in the static charge configuration around the probe. Such variations are to be expected in a highly defective structure such as that of HfH1.64in which approximately as much as 20% of the hydrogen sites are vacant. On this point, let us mention the relatively small width (/5 = 0.08) of the quadrupole frequency distribution observed in ZrH1.97 [ 11 ], which is a clear indication for a smaller disorder in the hydrogen sublattice when the di-hydride composition is approached. The PAC spectra obtained in the temperature range 90-120°C still retain the features of a twocomponent perturbation factor, at the same time when some damping characteristic of the existence of relaxation effects starts to occur. Beyond 120°C, all the PAC patterns can be nicely fitted to a G2(t) function which corresponds to a unique time-fluctuating quadrupole interaction with an asymmetry parameter r / ~ 0.30 (Fig. l b, c, d).
i O.
1.00
|0.
I ZO.
I __~ 30. ~0.
50.
GO.
j (t)~e
70.
~--
" i 0.
1.00
,~
0.75
.
i 10.
I 20.
I 30.
I ~0.
1
J t t )he
_
~0.
60.
70.
50.
60.
10.
d
0.
10.
20.
30.
~0.
Fig. 1. ~8~TaPerturbed Angular Correlation spectra obtained in HfH1.64 at oroom temperature (a), 131°C (b), 180°C (c) and 240 C (d). The full lines are the results of best fit procedures using equations (1) and (2) as the theoretical expressions of the perturbation factors. The evolution of the quadrupole frequency with temperature is plotted on Fig. 2. Below 120°C, the data correspond to the averaged quadrupole frequency deduced from the results given by the two-site fitting procedure. On Fig. 2 is also plotted the intensity G~T(0) at w -- 0 of the Fourier transform of the experimental spectra. For static interactions this quantity is essentially related to the "hard-core" term $2o of the perturbation factor (see equation (1)) which varies from 0.20 for an
366
HYDROGEN DIFFUSION IN HAFN1UM HYDRIDE
Wo(MHz),
(3~T(0) o,
\'
0.2
6
V 0.1
y
,.',
"',÷
/
2 0
i
1.5
I
i
2
I
I
2.5
3
+ (I0-3K-I)
Fig. 2. Plot against 1/T of the quadrupole coupling frequency vO and the value of the Fourier transform of the perturbation factor G2(t) at zero frequency for the lalTa probe in HfH1.64.
(arb.units)
e
0.!
Vol. 53, No. 4
proton) to jump randomly upon the vertices of a cube around the probe. The perturbation factor was calculated for various jump frequencies through a fulldiagonalization process of the Blume's relaxation matrix, and then fitted to equation (2) [16]. The behaviour observed simultaneously for both quantities uO and G~r(O) as the temperature is raised in Htltl.64 is therefore characteristic of the existence of spin-relaxation effects. In particular, the fast decrease of the quadrupole frequency is closely related to the relaxation phenomenon as it corresponds to a slowing down of the precession rate of the 181Ta spins when faster and faster changes in the orientation of the efg tensor occur. In addition, the uO vs. 1/Tplot suggests that the quadrupole frequency does not go down to zero at high temperatures, but rather tends toward a limit value of ~ 1.3 MHz. This observation is consistent with the fact that hydrogen diffusion can induce changes in the magnitude as well as in the orientation of the efg tensor. In effect, if the strength of the quadrupole interaction is allowed to change from a stochastic state to another in such a way that the cubic symmetry for the efg tensor is broken, the quadrupole frequency could never be averaged to zero even though the jump frequency between the different stochastic states becomes much higher than the precession frequency of the spins. By the other hand, some contribution to this residual electric fieldgradient due to the presence of defects and/or impurities in the sample cannot be discarded. The observed values of the relaxation constant X are plotted against 1/T in Fig. 4. If the relaxation of the
,k (ns-1) 0.1
100
10
1
W
Fig. 3. Plot of the calculated quadrupole coupling frequency u0 and Fourier transform of G2(t) at zero frequency against the jump frequency W for a point charge (e.g. a proton) jumping upon the vertices of a cube centered on the 18~Ta site. The values indicated on the figure are the results of numerical calculations using the Blume's stochastic model for describing the spin relaxation. axial efg tensor (r/= 0) to 0.258 for r / = 1. As shown in Fig. 3, these diagrams could be qualitatively reproduced from numerical calculations performed by using the Blume's stochastic model for describing the spin relaxation [ 14]. In these calculations a time-fluctuating efg tensor was generated by allowing a point-charge (e.g. a
0.01
0.001 1.5
+
1 2
I
t>
2"5~(10-::1K-1)
Fig. 4. Plot against lIT of the quadrupole relaxation constant X of the lS~Ta spins in HfHL64. Open circles and triangles correspond to experiments performed with a time resolution of 3 ns and 0.8 ns respectively. 181Ta spins is produced by hydrogen self-diffusion, X is expected to be practically proportional to the frequency w of the protons jumps at low temperatures. Assuming w to be described by an Arrhenius law
Vol. 53, No. 4
HYDROGEN DIFFUSION IN HAFNIUM HYDRIDE
w = Woexp (-- E / k T ) , the value of the activation energy can be straight deduced from the low-temperature part of the X(1/T) plot. By using the data obtained between 100 and 180°C, we calculated an activation energy E = 0.43 + 0.05 eV. This result is about 20 percent lower than the value determined by Weaver (0.55 -+ 0.05 eV) from 1H and 2D NMR experiments in HfHx.7 [4]. On the other hand, aH NMR relaxation experiments conducted by do Nascimento et al. [19] on a sample of our material indicate values of 0.49 eV (from Tx) and 0.46 eV (from 7"2) for the activation energy of H diffusion. We have good reasons to believe the activation energy deduced from our PAC experiments to be underestimated. In effect, it can be seen from the results of calculations using the Blume's stochastic approach for describing the spin relaxation that the X(w) relation progressively deviates from the linearity observed for very low diffusion rates as the jump frequency raises [16]. In the Arrhenius plot we observe therefore an "apparent" activation energy which is smaller than the "true" value deduced from the asymptotic data corresponding to extremely slow diffusive motions. Hence, the activation energy as determined from PAC data was estimated to be underevaluated by about 10 percent. We may then conclude that a quite good agreement exists between the activation energies of proton jumps observed by either 181Ta PAC or 1H NMR spectroscopy. The minimum value of the 1H spin-lattice relaxation time observed at T ~ 340°C in HfH1.7 [4] corresponds to the well-known relation ( C O T c ) m i n " " 1, where co is the Larmor pulsation of the protons and r e the spin correlation time. In high-temperature 1H NMR experiments, one observes dipole interactions only and ~'e is then related to the individual jump frequency through the relation ze = 1/2w. From the NMR data reported in Weaver's paper the temperature at which one should expect relaxation effects to occur in PAC experiments can be easily estimated. Considering that in practice the lSlTa probe does not allow to measure confidently relaxation times longer than 5 t0 -7 s, we obtain a temperature of ~ 100°C, in good agreement with our observations. The absence of any detectable influence of the Ta substitution impurity on local motions of hydrogen atoms may be thought as a rather surprising fact. However, it must be remembered that recent observations made by quasielastic neutron spectroscopy in hydrogenated niobium indicate a rather small trapping effect on hydrogen due to substitutional V or Cr impurities [17]. By the other hand, a fast H-motion around the substitutional V-atom in hydrogenated Nbl-xVx alloys had to be assumed by Matsumoto [18] in order to explain the motional narrowing observed on the
367
NMR-proton line below the room-temperature. It was proposed that such a rapid motion takes place between 24 equivalent positions around the V impurity, without breaking of the V - H pairs. If one assumes a similar situation to occur in the vicinity of the Ta-impurity in HfHx, no contribution to the electric field-gradient experienced by the 181Ta probe is expected from the rapidly moving first-neighbour H atoms at high temperatures. At the same time, an important variation of the efg tensor should occur at low temperatures, as soon as the jump rate of Ta-trapped hydrogen atoms would slow down below the lower limit (~ 107 s-1) detectable by 181Ta PAC spectroscopy. Moreover, relaxation effects associated with the slqwing-down of Ta-trapped H motions should be observed on the PAC spectra. Experiments performed at 77 K and 4.2 K do not indicate any significant change in the PAC patterns compared with the room-temperature data. In particular, no variation of the quadrupole frequency distribution is observed. These observations demonstrate that within the time scale of 181Ta PAC spectroscopy the configuration of hydrogen atoms around the probe does not change - that is, remains static and disordered - between 4.2 K and 300 K. However, the true configuration of hydrogen atoms in the vicinity of the Ta site can be hardly deduced from the quadrupole coupling data. Actually, as it is clear from the calculations performed in HfV2Hx compounds by Heidinger et al. [10], no confident estimation of the electric field-gradient in transition metal hydrides can be reasonably made at the present time. In conclusion, it may be claimed that 181Ta is a suitable microscopic probe for the observation of hydrogen diffusion in hafnium and zirconium hydrides. Consequently, the application of 181Ta PAC spectroscopy to the study of a variety of hydrogenated systems, especially crystallized and amorphous metallic alloys with hafnium and zirconium, seems to be promising. Acknowledgements - This work was undertaken during the stage of one of us (P. Boyer) in the Departamento de Fisica of the Universidade Federal de Minas Gerais, Belo Horizonte, Brazil. This stage was supported by CNRS (Centre National de la Recherche Scientifique, France), CNPq (Centro National de Pesquisas, Brazil) and FINEP (Financiadora de Estudos e Projetos, Brazi!L REFERENCES 1. 2. 3.
W.M. Mueller, J.P. Blackledge & G.G. Libowitz, Metal Hydrides, Academic Press, New-York (1968) Chap. 7 and 8. C. Korn & D. Zamir,J. Phys. Chem. Solids 31, 489 (1970) E.F. Khodosov & N.A. Shepilov, Phys. Stat. Sol. (b)47,693 (1971).
368 4. 5. 6.
7. 8. 9. 10. 11. 12.
HYDROGEN DIFFUSION IN HAFNIUM HYDRIDE H.T. Weaver,J. ofMag. Res. 15, 84 (1974). K.R. Doolan, P.P. Narang & J.M. Pope, J. Phys. F: MetalPhys. 10, 2073 (1980). H. Frauenfelder & R.M. Steffen in Alpha-, Betaand Gamma-ray Spectroscopy, K. Sieg Bahn ed., North-Holland Publ. Co., Amsterdam (1965) p. 997. A. Abragam & R.V. Pound, Phys. Rev. 92, 943 (1953). A. Baudry, P. Boyer & A.L. de Oliveira, J. Phys. Chem. Solids, 43, 871 (1982). O. de O. Damasceno, Thesis, Belo Horizonte (1975). R. Heidinger, P. Peretto & S. Choulet, Solid State Commun. 47,283 (1983). R.L. Rasera, G.K. Shenoy, B.D. Dunlap & D.G. Westlake, J. Phys. Chem. Solids 40, 75 (1979). S.S. Sidhu, Leroy Heaton & D.D. Zauberis, Acta Cryst. 9, 607 (1956).
13. 14. 15. 16. 17. 18. 19.
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L. Espagno, B. Azou & P. Bastien, Compt. Rend. 250, 4352 (1960). M. Blume in Hyperfine Structure and Nuclear Radiations, E. Matthias and D.A. Shirley eds., North-Holland, Amsterdam (1968) p. 911. H. Winkler & E. Gerdau, Z. Physik, 262, 363 (1973). A. Baudry & P. Boyer (Unpublished). A. Magerl, J.J. Rush, J.M. Rowe, D. Richter & H. Wipf, Phys. Rev. B,27,927 (1983).
T. Matsumoto,J. Phys. Soc. Japan, 42,1583(1977). V.M. do Nascimento, J. Pedro Donoso, H. Panepucci, A.L. de Oliveira & O. de O. Damasceno, Communication at the 36th meeting of the Sociadade Brasileira Para o Progresso da Ciencia, Sgo Paulo (1984).