Journal of the Less-Common Metals, 172-174 (1991) 509-521 509

NMR studies of localized interstitial hydrogen motion in the h.c.p. metals SC, Y and Lu”

Richard Barnes Ames Laboratory, VSDOE, and Department of Physics, Iowa State Vniuersity, Ames, IA 50011 (U.S.A.)

Abstract

The hexagonal close packed (h.c.p.) solid solution (a) phases of the SC-H, Y-H and Lu-H systems have been investigated by nuclear magnetic resonance (NMR) methods over the temperature range lo-300 K in which hydrogen pairs are known to form. At low temperatures (lo-120 K), localized motion of hydrogen between closely spaced (about 1.35 A) tetrahedral (T) interstitial sites gives rise to a peak in the proton spin--lattice relaxation rate R, in cc-ScH, and a-LuH,. This peak may be interpreted in terms of classical over-barrier hopping or tunnelling through the barrier between the close sites. The temperature and resonance frequency dependence of the R, peak in a-ScH, exhibit characteristics typically found in amorphous and disordered sys- tems, and which have been interpreted in terms of two-level systems (TLS). This leads to the suggestion that pair formation results effectively in a “proton glass”.

At a resonance frequency of 24 MHz, the proton R, maximum at about 40 K in g-ScHo.n corresponds to a hydrogen hopping frequency of v = 1.5 x 10’ s-l. This value is approximately two orders of magnitude slower than the minimum rate (about 1.6 x lOlo s-‘) found at about 100 K in recent quasielastic neutron scattering (QENS) measurements on single-crystal a-ScH,,,,. A hopping rate of the latter magnitude would not be detected by NMR measurements, so that the NMR and QENS measure- ments see different fast localized hydrogen motions. An interpretation based on recent theoretical work is presented.

1. Introduction

Nuclear magnetic resonance (NMR) provides several important experi- mental approaches to the study of hydrogen motion in metallic solids. In the work reported here, the primary approach has been to measure the temperature and resonance frequency dependence of the proton spin- lattice relaxation (SLR) rate, R, . In appropriate temperature intervals, R, furnishes information on the temperature dependence of the mean dwell time for both localized (i.e. short range) and long range (i.e. diffusive) hydrogen motion.

Investigations of the solid solution (CC) phases of the non-magnetic rare earth hydrogen systems, SC-H, Y-H and Lu-H, using these NMR methods [l-4] have provided information on both localized and long range hydrogen

*Invited paper presented at the International Symposium on Metal-Hydrogen Systems, Banff, Alberta, Canada, September 2-7, 1990.

0022-5088/91/$3.50 (1” Elsevier Sequoia/Printed in The Netherlands

510

Fig. 1. (a) Hexagonal close packed metal lattice (solid circles) showing the location of the tetrahedral interstitial sites (solid triangles). Sites A and B (and also C and D) form a close pair separated by about 0.25~. (b) Cross-section in the cb plane of the h.c.p. lattice showing the location of both tetrahedral (solid triangles) and octahedral (open circles) sites. As in (a), sites A and B form a close pair.

motion and on electronic structure changes that accompany the pairing phenomenon [5]. This brief account focuses on NMR evidence for localized motion, identification of the short range jump path, and on the glass-like features of the proton SLR at low temperatures.

As shown in Figs. l(a) and (b), the tetrahedral (T) sites occupied by hydrogen in these systems occur in close pairs (A and B; C and D) along the c axis. Neutron diffraction has shown in all three systems [5-71 that hydro- gen tends to order in pairs of T sites oriented along the c axis and separated by an intervening metal atom (B and C in Figs. l(a) and (b)). The concentra- tion of such pairs increases with decreasing temperature.

2. Experiment

The solid solution (u) phase samples were prepared from the highest purity Ames Laboratory (Materials Preparation Center) metals available, having total rare earth impurity contents typically less than 10 parts per million (ppm) and an iron content of about 15 ppm determined by mass spectrographic analysis. Measurements of the proton R, were made at reso- nance frequencies of 24, 40, 62 or 65, and 90 MHz (0.564, 0.939, 1.53 and 2.11 T respectively). Sample preparation and NMR instrumentation and techniques have been described in detail elsewhere [3,8].

Magnetization recovery signals were exponential at all temperatures, resonance frequencies and hydrogen concentrations, showing that the proton system remains always in the fast spin-diffusion regime.

2.1. NMR background Only a sketch of those features of spin relaxation theory relevant to the

present work is given here. Other important aspects of theory significant for

511

a-ScHo. 27

at 40 MHz

0 I

0 100 200 300 400 500 600 700

TEMPERATURE (k)

Fig. 2. Temperature dependence of the measured proton R, over the full range 6-625 K for x = 0.27 at 40 MHz. The solid line shows the electronic contribution, R,, = C,T, with c,. = 8.73 x 10~:~ s ’ K-’ (from ref. 2).

understanding NMR of hydrogen in metals have been discussed in recent comprehensive reviews [ 9, lo].

The measured proton SLR rate R, in metal-hydrogen systems results from the sum of contributions resulting from the dynamic interaction of the proton spin with fluctuating magnetic fields arising from conduction elec- trons (R,,), hydrogen motion (diffusion) (R,,), paramagnetic impurities (R,,) and (in some cases) cross-relaxation to the spins of the metal nuclei (R,,,):

R, = R,,. + R,, + R,, + R,c, (1)

In the work reported here, the paramagnetic impurity contribution R,, is negligible. In addition, the cross-relaxation contribution Rlc, only appears in the case of R, measurements on x-LuH, (see below) [4]. We therefore restrict the discussion to R,, + R,,,.

Figure 2 furnishes an example of the behaviour of the proton R, over the full temperature range 6-625 K in cc-ScH,,,,. The underlying rate R,, due to the conduction electrons follows Korringa law behaviour [ll], R,, = C,T, as shown by the straight line in the figure. The constant C, is proportional to the square of the product of the d-band contribution to the electronic density of states, Nd(EF), and the hyperfine field H& arising from core polarization by the d electrons of filled states derived from hydrogen 1s orbitals, i.e.

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C, cc [H&Nd(EF)]2. The strong peak in R, centred at T N 525 K reflects the R,, contribution from long range hydrogen motion (diffusion), and the weak peak at TN 50 K results from R,, from localized hydrogen motion.

The relaxation rate R,, may be described by a sum of terms, each of the general form

R,, = @w2)Fb,, wM, %> (2) where (Am’) is that part of the nuclear spin interaction with its electromag- netic environment that fluctuates in time due to the motion, and

F(c+, , wM, 7,) is a spectral density function that describes the dependence of the fluctuations in Aw on the resonance frequencies wn and oM of protons and (non-resonant) metal nuclei respectively and on the correlation time t, for the fluctuations, In all the relevant simple theories, this function is a sum of Debye terms, each of the form r,/(l + o”z~), where o = ou and/or wu + oM, depending on details of the system. This means that (a) R,, peaks when

%,r, = 1, (b) R,, K T’, when why, $1 (high temperatures), and (c) R,, cc oh2~;1 when WIT, B 1 (low temperatures). Furthermore, if the motion is governed by a single activated process, so that z, = z0 exp(E,/k,T), where E, is the activation energy, k, Boltzmann’s constant and T the temperature, then in a plot of In R,, against T-‘, the high and low temperature side slopes are just f E,/k, respectively.

2.2. Experimental results

2.2.1. cr-ScH, Because of the low hydrogen concentration, the dipolar field at the

proton sites is dominated by that of the metal nuclei. Thus, the strong 45Sc nuclear moment (about 5.1 times the proton moment) makes the SC-H system the best for studying localized hydrogen motion. Figure 3 shows proton R, measurements in a-ScH,,, at two resonance frequencies at temperatures up to about 300 K. A peak appears superimposed on the underlying conduction electron rate R,, shown by the straight lines representing the constancy of the Korringa product C,. A second feature, independent of OH, appears in the range 150-200 K. This reflects a change in C,, indicating that an electronic structure change accompanies the pairing. A similar change in C, is seen in a-YH, and a-LuH, [2,4].

The relaxation rate due to localized motion, RIL, is obtained by sub- tracting the electronic rate R,, from the measured rate R,, i.e. R,, = R, - R,,. In doing this, the low temperature value of C, = 8.55 x lo-” s-’ K-’ has been used to extend R,, into the region under the peak in R,,. Figure 4 shows the resulting dependence of RIL on reciprocal temperature for a-ScH,,,, at three resonance frequencies. The solid curves in the figure are the result of a least-squares fit of theory to the data (see below). These data display qualita- tively the expected dependence on the proton resonance frequency on at low and high temperatures: (i) on the high temperature side of the maximum rate R,, is independent of wn, whereas it is dependent on wn on the low

.A

L

a-ScHO. 27

A at 24 MHz + at 62 MHz +'//+

t/' /

0 40 80 120 160 200 240 280 320

TEMPERATURE (K)

Fig. 3. Temperature dependence of the proton R, in r-ScH,,,, measured at 24 and 62 MHz. The

upper two solid lines represent the electronic contribution, R,,. = C,. 7’, for temperatures above

and below about 170 K. Inset: temperature dependence of proton R, in r-YH,, ,x at 24 MHz.

temperature side; (ii) the maximum rate, R,,., max, increases with decreasing (Ron ; (iii) the temperature T max at the maximum rate increases with increasing frequency. However, these dependences disagree quantitatively with those expected for classical diffusion, in contrast to the case [l] of the high temperature peak in Fig. 2. Thus, on the low temperature side of the peak, R, ,, 81 OJ ;‘-2 rather than tu,“, and the maximum rate R,,,, max K to;2i’3 rather than tr)n-‘. Also, as seen in Fig. 4, when graphed in the form log R,,, against Tm’ the low temperature side slope of the R,,, peak is not constant and is much weaker than the high temperature side slope. Such behaviour is closely similar to that found in disordered and amorphous materials and indicates that the motion responsible for the peak is not characterized by a unique energy barrier, but rather by a distribution of barriers [12].

2.2.2. CI- YH, Because of the small nuclear moment of the yttrium nucleus, “Y (about

0.01 times that of 45Sc), the strength of the fluctuating dipolar field seen by the moving proton is negligible. Consequently, in contrast to 8~-ScH,, the localized motion rate R,,, is extremely small and only a faint suggestion of a low temperature peak is observed, as shown in the inset of Fig. 3.

514

TEMPERATURE (K) 25

r 1 I

l 24 MHZ I

l 40 MHZ

l 90 MHZ

1. I I I I I -I 20 40 60 80 100

RECIPROCAL TEMPERATURE (10”’ K-‘)

Fig. 4. Dependence of R,,, on reciprocal temperature in cc-ScH,,, at 24.40 and 90 MHz. The solid curves are the least-squares fit of eqn. (9) to data using a Gaussian distribution of activation

energies (from ref. 2).

Results similar to those for ol-ScH, have been obtained [4] for a-LuH,,, (the lY5Lu moment is about 0.5 times that of **SC), as shown in Fig. 5. A peak due to localized motion appears at about 80 K, and a change in the electronic contribution occurs at about 170 K. However, the low temperature peak does not show the expected inverse dependence on resonance frequency, rather the reverse is true. Moreover, the electronic contribution appears to be dependent on frequency. This behaviour reflects cross-relaxation of the proton spins to those of the metal nuclei, ‘75Lu. The measured rate R, is a function of the cross-relaxation rate Rlcr as well as of R,, and RI,, and although R,, has been determined from measurements made at a high resonance frequency (400 MHz) [4], it has not been possible to separate quantitatively Rlcr and RIL at low temperatures. Nonetheless, these measure- ments show that localized motion in a-LuH, is qualit~tive1~ similar to that in CC-ScH,.

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PROTON SPIN-LATTICE RELAXATION RATE in a-LuHg.15

0 80 160 240

TEMPERATURE (K)

Fig. 5. Temperature dependence of the proton R, in a-I,uH,, ,i measured at 24 and 40 MHz

3. Discussion

3.1. Interpretation of the low temperature SLR peak Several approaches may be invoked to account for the observed features

of the low temperature SLR within the above theoretical framework. The localized motion may be treated in (i) classical terms, i.e. over-barrier hopping, utilizing a distribution of activation energies, G(E,); (ii) in non- classical terms with a distribution of barrier heights in a tunnelling descrip- tion of the motion; or (iii) in terms of two-level systems (TLS).

3.1.1. Distribution of classical activation energies For the a-ScH, results, which reflect the fact that the localized and long

range motions occur on timescales differing by approximately two orders of magnitude, R,, may be written as the sum R,, = R,,, + Rid, in which the rates R,,, and R,, result from the localized and long range motions respec- tively. It is also necessary to take into account a possible asymmetry, A = EA - E,, in the depths of the potential wells between which the localized motion occurs. This asymmetry reduces the relaxation strength due to local- ized motion; the reduction factor is given by ( 1/4)sech2(A/2h, 2’) [2]. The final results for R,,, and R,, are then [2]

R,,. = 72HM2 (rIgid C,

2% 4c sech”( A/2kBT) F(O),, oM, T,,)

1 (3)

516

and

R Id

=I Y h MZ (rigid

2%

1 - $$- sech’( AfZks 2’) F(w, , oM) T& 1 >

with

(4)

providing the explicit form of the spectral density functions (T = td or zL, as appropriate). In these expressions, yH and yM are the nuclear gyromagnetic ratios of the proton and metal nuclei respectively, zL and zd are the mean dwell times for localized and long range hopping respectively, and C, and C, are lattice sums. In eqns. (3) and (4) the rigid-lattice second moment MZ Irigid (proportional to the square of the local dipolar field with the hydrogens frozen in position) has also been introduced. This quantity is given essen- tially by the metal nuclear dipolar contribution [9],

Mz /rjaid = (4/15)y~fi2S(S + 1)C,C-6 (6)

where S is the metal nucleus spin, A is Planck’s constant and c is the c axis lattice parameter. Correspondingly, C, is the lattice sum for that part of the second moment affected by the localized motion, i.e. resulting from a proton’s five nearest-neighbour 45Sc nuclei.

At high temperatures the characteristic time tL of the localized motion is too short for C, to contribute to Rid. Then, exp( -t/zL) = 0, and also seeh2( A/Zk, 7’) = 1, so that the effective second moment at high temperatures is, from eqn. (4) [Z],

MZ [fast = M2 [rigid {l - (Cz/4Ci)) = 9.728M~ Irigid (7)

independent of the asymmetry A between the well depths. The calculated value of M2 Irigid is 12.2 0e2, so the calculated M21fasL is 8.9 0e2. Experimen- tally [ 11, at high temperatures M2 Ifast = 8.8 0e2, in excellent agreement with this expectation. This demonstrates unambiguously that the localized motion occurs between sites A and 3 (or C and D) in Fig. 1.

The localized hopping rate at low temperatures is given by

rr, -’ = z&z{1 + exp( -A/k,T)lexp( -H/k,T) (6)

where H is the barrier height (activation energy) for the motion. Because of the apparent lack of correlation between the locations of hydrogen pairs situated on adjacent lines parallel to the c direction [6], we expect H and therefore zL to be characterized by distributions. The calculation of R,, follows from eqns. (3) and (5), but with the spectral density of eqn. (5) “distributed” by introducing a distribution function g(z) which is folded with eqn. (5) in evaluating R,i,. A simple approach is to attribute the distribution of zL values to a distribution of activation energies, g(H), taken to be

517

Gaussian for simplicity and for ease of visualization of the result. That is, g(H) = N exp{ -(H - H,)2/2a2j. We have then

Rx = R,,,WMW dH s (9)

where R,,(H) given by eqn. (3) with TV from eqn. (8) and with zoI, taken to be independent of H. In this way the temperature and resonance frequency dependence of R,, are accounted for with a single set of parameters. The solid curves in Fig. 4 show the result of this fitting procedure to R,I, data for a-ScH,,,, at three frequencies. The resulting parameter values are: H,, = 52 meV, 0 = 30 meV, to,, = 2.1 x lo-l4 s; similar values were obtained for

r-ScH,.,, ]21. Experimentally, the R,,, peak is much weaker in comparison to the high

temperature R,, peak than expected solely on the basis of the dipolar field averaged away by the localized motion, i.e. R,,,, max/R,d,max z 0.015 rather than 0.37. This reduction results in part from the width CJ of the distribution of barriers g(H) responsible for the distribution of hopping times g(t). Numerical simulations show that CJ reduces Rlr,,,,, by a factor of 0.2. The remaining reduction factor of 0.075 must be ascribed to the combined effects of well-depth asymmetry A and the fraction of hydrogen in motion. If the potential wells between which the localized motion occurs are of equal depth, then A = 0 and the factor 0.075 represents solely the fraction of hydrogen in motion at low temperatures. Neutron scattering measurements [6] show that 93% of the hydrogens in a-YH,,,, are paired at 120 K, and may be near or at the limit of the extent of pairing. Thus, 7% would remain unpaired, in excellent agreement with this estimate. However, if all the paired hydrogens participate in the motion the reduction in strength of R,,, results from the effect of A via the factor (C,/4C,)sechZ(A/2h,,T). This leads to an estimate of A z 22 meV, taking T = T,,, = 60 K for the x = 0.27 sample. The situation is surely more complex, since it is probable that a distribution of A values occurs for the same reasons we expect a distribution in H. Attempting to accommodate all these possibilities in the fitting process does not lead to unambiguous results.

3.1.2. Distribution of tunnelling barriers

The interpretation of the SLR rate R,,, given above and in ref. 2 relies on classical over-the-barrier hops by hydrogen atoms. An alternative ap- proach involving hydrogen tunnelling through the potential barrier has been advanced by Svare et al. [13]. Consistent quantitative results were obtained using a simple model for proton SLR driven by local magnetic field fluctua- tions associated with both phonon- and electron-assisted tunnelling transi- tions of the unpaired hydrogens. A sinusoidal barrier V,,/kR = 3200 K between the potential wells was chosen for the fit, with an estimated tunnel splitting AET, 2 0.37 K. A broad distribution of asymmetries between the potentials in the two wells was required to fit the experimental data [13]. The resulting fit

518

is significantly better on the low temperature side of the R,, peak than on the high temperature side.

3.1.3. Two-level systems and “proton glass” features As already noted, several features of the R,, behaviour closely resemble

that in amorphous and disordered systems. Nuclear SLR in inorganic glasses at low temperatures (i.e. below about 100 K) has been attributed to a spin-flip process caused by the excitation of disorder modes commonly described as two-level systems (TLS). Several specific mechanisms that yield the observed temperature dependence of R, in such glasses have been proposed [14,15]. These models also employ a tunnelling description of the motion, including an average over well-depth asymmetries and a continuous distribution of barrier heights up to a maximum energy E,,,. Experimentally, the temperature and frequency dependence of the low temperature rate has the form [15,16]

R, cc TIT1~pfi (10)

Thus, the slope of In R, against In T is 1 + SI. Theory suggests that 0 < c( d 1. The low temperature ou dependence of RIL in the x = 0.27 sample is

seen in Fig. 6, which shows that in this case p = 1.20, and the temperature dependence of R,, in the same sample at four resonance frequencies is given by T1.‘O, as seen in Fig. 7. The results of these determinations are summarized in Table 1, where the closely similar parameter values for “F relaxation in two alkali fluoride/alkali oxide glasses are also listed [15]. In addition, a value of a = 1.0 f 0.05 has been reported for lgF SLR in B,O,-CaF, glass and

a

a-SCHO .27

H

0.1 I I IllIll 10 20 50 100

RESONANCE FREQUENCY (MHz)

Fig. 6. Dependence of R,,, on wH at 2’ = 30 K for the x = 0.27 sample, showing that R,,, cc COG’ ‘. Also shown is the dependence of the maximum rate R,,>,,,, on u+, for the x =O.ll sample, showing that R,,, mHX cc w,T,~” (from ref. 2).

+ at 24 MHz m at 40 ” A at 62 ” l at 90 ”

TEMPERATURE (K)

Fig. 7. Temperature dependence of R,t, on the low temperature side of the relaxation peak for x = 0.27 at four resonance frequencies. The straight lines are least-squares fits to the data, showing that R, ,, ‘-K T’ s” in this case.

TABI,E 1

Values of the parameters I and /j characterizing the temperature and resonance frequency dependence of the localized motion contribution to proton SLR (see text for details)

r-ScH,

0.051 0.11 0.27

Glasses

Li- F--O Na F-O B,O,, CaF,

; 0.0 * 0.05 0.40 1 .oo * f 0.05 0.05 0.80 1.20 + * 0.05 0.05 0.34 1.18 0.25 1 .03 1 .oo

interpreted in terms of TLS [ 161. Comparison with ‘“F relaxation is important because “F is also a spin-l/2 nucleus relaxed by magnetic dipolar field fluctuations. The relaxation of other nuclear spins (e.g. 7Li, “B etc.) in inorganic glasses is also well described by this TLS model [16]; however, these are all quadrupolar nuclei, whose SLR is dominated by fluctuations in electric quadrupole couplings.

3.2. Comparison with neutron scattering results The most recent quasielastic neutron scattering (QENS) measurements

on hydrogen in single-crystal scandium have revealed the existence of an

520

even faster localized motion [17]. The minimum hopping rate of about 7 x lOlo ss’ inferred for this new motion at T E 100 K is again roughly 100 times faster than that seen in the low temperature NMR experiments. Hydrogen motion at such a rate would require that R,, measurements be made at a resonance frequency in the range 103P104 MHz in order to yield a discernible maximum in R, against T. Such measurements are on the edge of what is presently feasible, so that it is unlikely that this new motion will be detected by NMR in the near future. In any event, it appears that the QENS and NMR measurements “see” different localized motions. In addition to the large difference in hopping rates, the rate detected by QENS passes through a minimum at about 100 K, whereas that detected by NMR decreases contin- uously with decreasing temperature.

Cluster calculations by Jena and co-workers may furnish a rationaliza- tion of these observations [18]. Their calculations show that two potential minima occur at each T site, separated by about 0.2 A. If the frequency of fast, localized motion between such closely spaced sites were comparable to the proton resonance frequency, it would reduce the proton second moment, and therefore the strength of the high temperature Rid peak, by about 1%. Such an effect would not be detected. It seems probable that the motion between these extremely close sites occurs at a very high rate, and that it is the motion found in the QENS experiments. Whether or not this picture is correct in detail, three separate hydrogen motions, with jump rates differing in each case by roughly two orders of magnitude, evidently occur in these systems, i.e. (1) very fast localized motion detected by the QENS experiments; (2) fast localized motion detected by NMR; and (3) long range diffusive hopping found in both NMR and neutron experiments.

3.3. Other systems It is worth noting that very similar SLR behaviour due to localized

hydrogen motion has been observed in another entirely different system. Skripov et al. [19] have reported such effects for both proton and 51V SLR in the crystalline intermetallic hydride TaV,H, at temperatures in the range lo-100 K.

4. Conclusions

The NMR measurements demonstrate unambiguously that localized motion of hydrogen occurs at hopping rates of the order of 10’s_’ at temperatures in the range lo-100 K in both scandium and lutetium. More- over, the high temperature Rid measurements, which reflect long range diffusive hoping, serve to identify the sites between which the localized hopping occurs.

The absence of long range structural order and the marked similarity of the low temperature proton SLR in these systems to that in conventional glasses leads to the suggestion that these are “proton (or hydrogen) glasses”.

521

Moreover, tney 111ay constitute explicit examples of two-level system (TLS) behaviour, in that the states between which the system oscillates are clearly identified, which is virtually never the case in the usual glass systems. Hence, further study of the properties of x-ScH, etc. may also contribute to improved understanding of some of the fundamental concepts in the physics of disor- dered materials.

Acknowledgements

The author is indebted to many colleagues and co-workers for their valuable contributions of measurements and discussions of this problem, especially J-W. Han, L. R. Lichty, E. F. W. Seymour and D. R. Torgeson. Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under Contract No W-7405-Eng-82. This work was supported by the Director for Energy Research, Office of Basic Energy Sciences.

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