Frequency-dependent proton spin relaxation in Zr2PdHx

Journal

of the Less-Common

Frequency-dependent in Zr, PdH, David B. Baker, E.-K. Department

of Physics,

R. C. Bowman, Aerojet

Electrosystems,

373

Metals, 172-I 74 (1991) 373-378

proton spin relaxation

Jeong, Mark S. Conradi and R. E. Norberg

Washington

University, St. Louis, MO 63130 (U.S.A.)

Jr. P.O. Box 296, Azusa,

CA 91702 ( U.S.A.)

Abstract The proton nuclear spin-lattice relaxation rates T;’ of amorphous Zr,PdH,,, and crystalline Zr,PdH,,, were examined from 4 to 400 K at several frequencies. The observed temperature dependence is nearly T;’ K T, but the relaxation rate depends on frequency, unlike the behavior of the expected Heitler-Teller-Korringa mechanism. Furthermore, the relaxation rates in the crystalline and amorphous samples are surprisingly similar. The frequency dependence can be explained by two models: proton cross-relaxation to metal nuclei and low frequency tunneling motions.

1. Introduction The Zr,PdH, system is available as an amorphous and a crystalline alloy, both being stable at room temperature [l, 21. Of particular interest is a comparison of hydrogen motion in the two phases [3]. As part of such a study of proton motion in these alloys, we are investigating the low temperature spin-lattice relaxation rate 2’;’ of the protons. Experimental results show an unexpected frequency (field) dependence of T;’ as presented in our data below. Since the proton resonance frequency co is related to the magnetic field H by o = 1/H, where 1’ is the nuclear magnetogyric ratio, the frequency and field dependences cannot be distinguished. For metal&hydrogen systems in general, T;’ can be expressed as the sum of contributions from conduction electrons (Heitler-Teller-Korringa mechanism) and from modulation of the nuclear dipole-dipole interactions by hydrogen motion [4,5]. In some samples, but not ours, paramagnetic impurities also contribute to the relaxation rate [5, 61. Consequently, at low temperatures where diffusion contributions should be absent, only the electronic motions will be appreciable and the proton relaxation rate is expected to exhibit Korringa behavior [7]. Specifically, T,-’ is predicted to be linear in the absolute temperature and independent of the resonance frequency. The predicted absence of a magnetic field dependence is due to the short mean free electron path in these disordered alloys. Further, the frequencies characteristic of the electronic motions are much greater than nuclear precession frequencies. Thus, the frequency (field) dependence that we present below

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cannot be explained by direct relaxation of the protons via the conduction electrons. Other metal-hydrogen systems such as NbH,.2,, Nb,,V,,,H,,,, and relaxation rates T;l at low temperaTaH*.,, also show frequency-dependent tures [8,9]. Following a presentation of the data, two models will be examined to explain the unexpected frequency dependence.

2. Experimental

details

The two Zr,PdH, samples used in the present nuclear magnetic resonance (NMR) experiments were prepared by reacting amorphous and crystalline Zr,Pd alloys with gaseous hydrogen, as described earlier [l-3]. The finely powdered samples were sealed in glass tubes. The T;’ data for both samples are reported for four resonance frequencies (5, 21.25, 34.5, and 53.14 MHz). In addition, 200 MHz data for the amorphous sample are included. A super-heterodyne pulsed NMR spectrometer and a water-cooled electromagnet with a “F NMR field regulator were used in our experiments. Z’, was determined with a saturate-wait-inspect pulse sequence. At 34.5 MHz, the invert-wait-inspect sequence was used and a different spectrometer was employed [3]. Either a conventional free induetion decay (FID) or a magic echo [lo-121 was used for inspection of the recovered magnetization. The magic echo sequence, tX-W?~--903ytserved to delay the spin signal away from the r.f. pulses and subsequent ringing. This was especially useful. at low resonance frequencies. Furthermore, at low frequencies we found it important to reduce the coil Q in order for the magic echo sequence to function properly. The Jeener-Broekaert pulse sequence was used to measure T,, [13]. Temperatures were controlled in a flowing gas helium dewar. A carbonin-glass thermometer and a thermocouple were used for temperature measurement.

3. Results The experimental results of our work are presented in Figs. 1 and 2 and may be summarized as follows. (1) The spin-lattice relaxation rates T;’ for Zr,PdH, show an obvious frequency dependence below 200 K, especially at low resonance frequencies. T;’ monotonically increases with decreasing frequency, at least over the range studied. (2) At high resonance frequencies (34.5200 MHz), T;’ is nearly independent of frequency below 200 K. This suggests that at these high frequencies the protons may relax directly via the conduction electrons. (3) In general, T;’ is proportional to approximateIy T0.8. Although the exact exponent differs from the various data (different samples and different

375

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Fig. 1. The proton spin-lattice relaxation frequency dependence is observed. Fig. 2. Proton 7’;’ for c-Zr,PdH,

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frequencies), the temperature dependence is weaker than linear, particularly for the amorphous sample. (4) The T,’ data for amorphous and crystalline Zr,PdH,X below 200 K are similar. If conduction electrons dominate the relaxation, this result is expected since the electronic structures of amorphous and crystalline counterparts are generally similar. However, the frequency dependence argues for a more complex relaxation mechanism. Thus, the similar rates in amorphous and crystalline samples are surprising. (5) The relaxation rate T;: (measured at 53.14 MHz) of the dipolar ordered state is considerably faster than T;’ in the same field. (6) The relaxation rate T;’ in the amorphous sample increases substantially at temperatures above 250 K. This signals the onset of hydrogen diffusion. Evidently, diffusion occurs at lower temperatures in the amorphous material than in the crystalline sample, as has been previously studied [3].

4. Discussion Proton cross-relaxation with quadrupolar metal nuclei has been proposed to explain frequency-dependent relaxation in metal hydrides [8,9]. Metal nuclei with spin I > l/2 are reasonable candidates for cross-relaxation since they possess nuclear quadrupole moments. In our experiment, both zirconium and palladium have abundant isotopes with spin I = 512. In this model, nuclear quadrupole moments interact with electric field gradients (EFG) created by some kind of disorder (proton site occupation, strain, etc.). As a result, the metal nuclear resonances are distributed over a wide range of frequencies, typically several megahertz. Protons may cross-relax on@ to those metal

376

Fig. 3. Proposed cross-relaxation mechanism with protons relaxing to the lattice through two sequential steps. First, the protons exchange spin energy with metal nuclei. Subsequently, the metal nuclei relax to the lattice via the conduction electrons. In addition (a parallel path), the protons may relax directly via the conduction electrons. Only a small fraction of the metal nuclei are expected to be on resonance with the protons and to participate in cross-relaxation.

nuclei which have resonance frequencies near the proton frequency (to within the dipolar linewidth, approximately 50 kHz). Subsequently, the metal nuclei relax to the lattice via conduction electrons (Fig. 3). The magnetogyric ratio y of the proton is much larger than those of the metal nuclei, while the metal quadrupole frequencies are typically only several megahertz. Thus, at sufficiently high fields no spectral overlap and consequently no cross-relaxation between protons and metal nuclei occurs. This is in accord with the measurements (see Section 3 paragraph (2)). The observation T;’ cc T” with x nearly 1.0 is reasonable within the cross-relaxation model. If the proton to metal spin-spin cross-path (see Fig. 3) is very rapid, then the metal nuclear relaxation rate to the lattice is rate limiting. In this case, one expects the measured proton relaxation rate to be some constant (a spin heat capacity ratio) times the direct (intrinsic) relaxation rate of the metal nuclei (presumably linear in T, from the Korringa mechanism). If the spin-spin cross-path is partly rate limiting, then one expects a temperature dependence slower than T”,‘. Thus, the observed approximate To.8 dependence is not surprising in this model. 7’;; is normally thought of as a zero-field relaxation rate [7,13,14]. However, as shown by Anderson and Hartmann [Xi], a multi-spin system is characterized by a single dipolar spin temperature (i.e. not separate dipolar spin temperatures for like and unlike spins). The lifetime of the dipole ordered state T,, is thus limited by the T, of each of the interacting nuclei. Hence, in this cross-relaxation model, !I’,,, is to be interpreted as the intrinsic T, of the metal nuclei to within a factor of order two [7]. In the cross-relaxation model, the intrinsic metal T;’ must be substantially faster than the measured proton T;‘. This results from the small spin heat capacity ratio (i.e. typically only one metal nucleus in around 500 is on

resonance with the protons, to within the proton linewidth). Therefore, relatively few metal nuclei relax many proton spins. According to this model, one expects Z’,, of the protons (essentially the intrinsic metal T,) to be much shorter than the proton T,, just as observed. A more conventional interpretation of the frequency dependence of T;’ is to invoke some low frequency tunneling motion 1161. That is, one assumes that some small fraction of the protons participate in motions, even at temperatures as low as 5 K. The power spectrum of these motions must increase strongly at low frequencies to explain the frequency dependence of the observed T;‘. In this model, 7’~; is to be interpreted [7] simply as the relaxation rate in zero field. Since T;’ increases as the frequency decreases, one expects in this model to find that the zero field relaxation rate T,-d 9 T;‘, in agreement with the data. A difficult feature to explain is the T;’ x To.’ temperature dependence. Further, if tunneling centers are responsible, one might expect the relaxation to be much more rapid in the amorphous than the crystalline samples. However, this is not observed. In a recent study of some ionically conducting glasses, low frequency motions were proposed to explain anomalous frequency-dependent relaxation [ 171.

5. Conclusions The proton spin-lattice relaxation rates T;’ for Zr,PdH, show an obvious frequency dependence at low temperatures. Direct proton relaxation via the conduction electrons cannot explain this unusual effect. Another mechanism(s), therefore, must be invoked. The two most likely explanations are proton cross-relaxation to the metal nuclei and low frequency tunneling motions. Other experiments reported at this conference [18] unambiguously identify cross-relaxation as the relaxation mechanism. These experiments use a.c. field modulation or sample rotation to modulate the proton or metal nuclear frequencies during the relaxation interval. It may seem that the origin of the frequency dependence observed here is of interest only as a resonance phenomenon. However, we caution that some previous interpretations of metal-hydride relaxation data may be incorrect, owing to the presence of cross-relaxation. This should be particularly likely at low frequencies and with metals having abundant quadrupolar nuclei.

Acknowledgments The samples were prepared by A. J. Maeland and W. L. Johnson, and the 200 MHz data were obtained by Dr. M. P. Volz; we appreciate their

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efforts. The work was supported in part by NSF Grants DMR 8841260 and DMR 87-02847 and by the Nishi Luthra Fund. We benefited from several conversations with P. A. Fedders, R. C. Barnes, and D. Torgeson.

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