Low-temperature nuclear spin relaxation in β-aluminas

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Solid State Communications, Printed in Great Britain.

Vol.46,No.6,

LOW-TEMPERATURE

pp.437-440,

NUCLEAR SPIN RELAXATION

S. G. Greenbaum* Naval Research Laboratory, Received:

1983.

0038-I098/83/180437-04503.00/0 Pergamon Press Ltd.

IN ~-ALUMINAS

and U. Strom Washington,

D.C. 20375

December 6, 1982, by M. Cardona

27A~ NMR T 1 measurements for Na-, K-, and Na K B-alumina in the temperature range ~5-180K are reported. Bo%h5 ~ and KB-alumina exhibit a nearly_~inear temperature dependence of the spin-lattice relaxation rate T. up to ~55K which is attributed to the presence of two-level system ~TLS) tunneling modes. A shallow T l m i n i m u m at ~30K is observed in Na 0 _K 0 _B-alumina. It is suggested that the origin of . . . . . b .b . . . thls mlnlmum is associated wlth the distrlbutlon of TLS parameters, and may be a low-temperature manifestation of the mixed-alkali effect commonly observed in glasses in the higher temperature ionic hopping regime.

1.

data were acquired within one week of sample preparation, and subsequent IR absorption spectra verified the absence of absorbed H20 in the crystals. The T. measurements were performed with a standard pulsed NMR spectrometer and He gas-flow system, utilizing a repetitionrate technique. The sample orientation was fixed at C[[H , and the spectrometer frequency was II.1M}{Z. o

Introduction

The low temperature properties of the B-aluminas (NaB-alumina , in particular) have recently received considerable attention due to their similarity to those of a glass. 1-s The reasons for this interest are twofold: first, the B-aluminas offer a favorable opportunity to study systematic variations in disorder parameters (i.e. by changing the mobile ion) with the hope of obtaining a better understanding of disordered systems in general; second, a more comprehensive view of the intimate relationship between structural disorder in the conduction planes and the superionic properties of B-aluminas could have far-reaching technological significance.

3.

The 27 A~ T_ t e m p e r a t u r e dependences for KB- , Na O ~K O ~ ~ - , a nd N a B - a l u m i n a a r e d i s played -i'ff VF~g. I. The "pure" B-aluminas exhibit qualitatively similar behavior, namely a nearly linear region between 4.5 and 50K followed by an abrupt decrease in T at higher 1 temperatures, corresponding to a transition from power law to exponential temperature dependence in the 50-60K region. The NaBalumina T 1 temperature dependence has previously been explained in terms of parallel relaxation processes: electric field gradient (efg) fluctuations associated with tunneling motion of Na ions due to the presence of two-level system (TLS) disorder modes; and thermally activated ion diffusion. 6 The ~ormer process is dominant at low temperatures (~55K), while the Arrhenius behavior (60-120K) yields an activation energy (EA ~ 0.05 eV) similar to that observed at higher temperatures up to the T 1 minimum, s'9

The two-level system (TLS) tunneling description of anomalous low temperature behavior in glasses has been applied successfully to heat capacity, 3's low frequency dielectric loss, 4 and microwave 1'2 measurements in Na B alumina. Additional evidence of glass-like behavior of NaB-alumina has been provided by recent NMR relaxation measurements which demonstrated a nearly linear dependence of the ZTA£ spin-lattic~ relaxation rate (I/T.) on temperature, for T ~ 55K. 6 We report 27~£ T. measurements for KB-alumlna , and N a o N K 0 5~-alumlna in the temperature range ~4-18DK], a~ well as new T 1 data for a dehydrated NaB-alumina sample. 2.

Results and Discussion

Experimental The KB-alumina T ] values differ from those of the NaB-alumina b y almost two orders of magnitude at a given temperature, a result which can be predicted qualitatively when substituting the larger K cation for Na ions. With increasing cation radius, the cation sublattice becomes more rigid, leading to a greatly reduced number of nearly equivalent cation sites. I Such increased local structural order has in fact been demonstrated by the observation of increasing correlation length in diffuse X-ray scattering for the cation sequence (Na, K, Rb)-B-alumina. I0 The associ-

The samples were cut from the same meltgrown single crystal obtained from Union Carbide, having the approximate composition 1.25 Na20 11A£203. The potassium and mixed-alkali samples were prepared by immersion in the appropriate molten alkali nitrate at 350C (KNO R for KB-alumina ; 16M°~ KNOo, 84M~ NaNO~ fo~ Na0.sK0. 5 B-alumina 7) for J24 hours. T~e NMR

National Research Council Postdoctoral ate

Associ-

437

LOW TEMPERATURE NUCLEAR SPIN RELAXATION

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B3orkstam et al. 11 interpreted their 27A£ T I measurements in Li 0 4- Na0 -- ~-alumina in the context of two separate d ~ f u s i o n processes, whereby 27A£ relaxation is driven by the "fast" ion at low temperatures and the "slow" ion at high temperatures. The above argument is clearly not applicable to the Na 5 K_ 5 ~-alumina behavior below NTOK since ~hermaYly activated ion diffusion is highly improbable in this temperature range. In fact, it is shown in Fig. 2 (a plot of 23Na T_ vs. T superimposed on the 27A£ data from Fig. ~) that the 23Na and 27A~ relaxation behaviors are qualitatively similar in the region of+interest (~4-70K). Thus it appears that the K ion has no direct effect on T 1 (27A~) at low temperatures.

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Vol. 46, No. 6

IN ~-ALUMINAS

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Plot of 27A~ T l vs. T for Na(squares), K(triangles) , and Nan _K~ _~-alumina at =II.I MHz. U.D U..b. o The straight lines are least-squares fits to the _~ata and describe the relation T.aT ~ with ~=I.18+0.03 and 0.87+0.07 Ifor Na- and K~-alumina, respectively.

ated reductions in number of tunneling modes and cation site availability (for hopping conduction) with increasing ion size is therefore consistent with the nearly parallel behaviors and difference in magnitudes of the Na- and K~-alumina T I curves. The lines drawn through the low temperature region of the Na- and K~-alumina data in Fig. 1 represent least s~ua res fits which define the relations T_~T ~, with ~=I.18+.03 for Na~-alumina and ~=0.187+-.07 for K~-alumina. The physical significance of this slight difference in slope (exponent) is not at present clear, but may again be related to differences in the density of TLS modes and/or their coupling to the lattice. it is clear from Fig. I that the mechanism responsible for 27A£ spin-lattice relaxation in the mixed alkali ~-alumina is qualitatively different from that in the pure Na or K~alumina. The 27A£ T passes through a shallow minimum centered rolughly at 30K instead of decreasing monotonically with some characteristic exponent ~ l . The T 1 behavior in the alloy is intermediate to those of the Na and K~aluminas only in the sense that the alloy T. values are bounded by the Na and K~-alumina1 T1's at the low and high ends, respectively.

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23Na T. vs. T data (diamonds for Na K I ~-alumina superimposed on 27Rj~5 % ~ a (circles) from Fig. I.

In attempting to understand the relaxation mechanism in the Na-K alloy, it is necessary to review some of the central concepts relevant to nuclear spin-lattice relaxation ~ amorphous solids. A relaxation rate (T.)-I~T ~ with I ~ < 2 is commonly observed for quadrupolar (I>l) nuclei in glasses below 10OK. Various models have been proposed 12 which seek to account for the rapid relaxation and weak temperature dependence. All contain some disagreements with experimental observation, but all are in qualitative agreement that TLS modes are a crucial component of the NMR relaxation process at low temperature. The phonon-mediated interaction between a relaxing TLS and a nuclear site modulates the electric field gradient at the nucleus resulting in an efficient nuclear spin relaxation mechanism (via the quadrupole interaction). The exact nature of the TLSnuclear coupling is the subject of considerable controversy, but a satisfactory expression relating T I to the TLS energy distribution function can be obtained: 12 T;I = constants*f:

cosh'2(2~)dE

,

(I)

where E is the TLS energy in the standard TLS formalism. I'12 Equation (I) yields a T-linear law for T: 1. Small departures of the tempera1 ture exponent from unity have been accounted for by other investigators 13 by assuming the existence of a weakly energy-dependent density of states.

Vol. 46, No. 6

LOW TEMPERATURE NUCLEAR SPIN RELAXATION

It is clear that some of the key assumptions employed in the derivation of eq. (I) must be re-examined in light of the mixed alkali ~-alumina T 1 data. It can be shown 14 that the nuclear spin-lattice relaxation rate associated with lattice fluctuations of characteristic lifetime I is proportional to ~(1+w212) -I, where w is the Larmor frequency. In this case, ~ is taken to be the TLS relaxation time. Szeftel and Allou112 argue that if T is identified with the TLS-lattiee relaxation time, then T. should be an increasing function of temperature, contrary to experimental observation. Their reasoning is based on the experimentally observed frequency i~dependence of T. which implies w2~2<
A possible explanation for the existence of the shallow T. minimum at 30K in the Na_ _ K^ _~-alumina (i~ the context of the S z e f ~ a~d DAlloul model) concerns the temperature at which TLS-lattiee relaxation processes become important to the extent that I is comparable in magnitude to I'. Since T' is temperature independent and ~ decreases with temperature, the point at which :NT' should correspond roughly to the T I minimum (30K in Na 0 ~K 0 ~ alumina). However, it is difficult to'lma~ine a mechanism whereby the TLS-lattiee relaxation rate can be enhanced by the required amount in the mixed alkali ~-alumina.

Alternative explanations for the T 1 minimum bring into question several of the important assumptions in the Szeftel and Alloul model, particularly the approximation w1<
IN ~-ALUMINAS

439

Regardless of the specific model employed in describing disorder phenomena, the Na- and K~-alumina T data are consistent with the presence of ~ S modes. However, the anomalous temperature dependence of T_ observed in 1 Na 0 .b _K 0 _~-alumina is not understood simply in terms o ~ e x i s t i n g descriptions of low-temperature phenomena in disordered systems. The well-known mixed-alkali effect, commonly occurring in glasses, has been observed in Na-K~aluminas and their isomorphic ~-gallates. 19'20 The mixed-alkali effect embodies a variety of phenomena concerning the non-additive behavior of certain properties when one alkali is sequentially substituted for another. The properties are principally those that can be directly related to alkali ion motion such as ionic conductivity and diffusivity, dielectric loss, internal friction and chemical durability. The effect appears to result from the lowering of the ionic mobility of each alkali ion by the addition of the other. Most theories of the mixed-alkali effect in glasses can be placed in either of two general categories. zl The first emphasizes the geometric aspects of the host substance and the fact that, if there is more than one kind of site, the two kinds of mobile ions will exhibit site preference. The second category emphasizes the importance of ion-ion interactions and predicts that there will be a minimum in conductivity when there is a maximum number of mixed ion pairs. The natures and specific manifestations of either (or both) of these situations at low temperatures, where ion conduction/diffusion processes associated with thermally activated hopping are "frozen out," have not received a great deal of attention. It stands to reason that the site preference and/or ion-ion interactions that dictate the physical properties associated with the mixed-alkali effect at high temperatures will affect the distribution of TLS parameters at low temperatures. In particular, it is suggested that the striking differences between pure and mixed alkali B-aluminas (with regard to T]) are attributable to substantially altered TLS distributions of parameters (i.e. E,I) in the alloy. In terms of the tunneling model, the nearly temperature-independent ae conductivity observed between N0.3 and 7K at 102-104 Hz for Na~-alumina is a direct consequence of the broad distribution of I. 4 Similarly, the broad plateau observed in N1 GHz acoustic loss measurements 18 up to nearly 100K is also attributed to the broad distribution of I. A single value or narrowly peaked distribution of I would lead to a r a p i ~ d e c r e a s e in conductivity with temperature T~IOK (at I0 GHz), contrary to observation. I A possible relationship between ae conductivity and nuclear spinlattice relaxation measurements is predicted by the fluctuation-dissipation theorem. 22 Thus ae conductivity data for mixed-alkali ~-aluminas may also exhibit unusual behavior in the temperature range dominated by tunneling motion. Unfortunately, however, low-temperature ae conductivity data for mixed-alkali B-alumina are currently unavailable, but it is believed that such measurements would shed additional light on the mixed-alkali effect.

440

LOW TEMPERATURE NUCLEAR SPIN RELAXATION IN E-ALUMINAS

In summary, 27A~ NMR T 1 measurements performed on Na- and KS-alumlna indicate a nearly linear temperature dependence of< the relaxation rate T. I at low temperatures (~55K) similar to that observed for quadrupolar nuclei in glasses. The difference in magnitudes between the Na- and K~-alumina T~s is understood in terms of the reduction in the number

Vol. 46, No. 6

o~ tunneling modes associated with the larger K ion. It is suggested that the shallow T] minimum at ~30K observed in Na_ .K 0 . ~-alumina is a consequence of an altere~'~is£~ibution of TLS parameters (compared to Na- or K~-alumina) which in turn may be associated with a lowtemperature manifestation of the mixed-alkali effect.

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6. 7. 8.

9. I0.

II.

U. Strom, M. von Schickfus, S. Hunklinger, Phys. Rev. B 25, 2405 (1982). S. R. Kurtz, H. J. Stapleton, Phys. Rev. Lett. 42, 1773 (1979). P. J. Anthony, A. C. Anderson, Phys. Rev. B 16, 3827 (1977). P. J. Anthony, A. C. Anderson, Phys. Rev. B 19, 5310 (1979). D. B. McWhan, C. M. Varma, F. L. S. Hsu, J. P. Remeika, Phys. Hey. B 15, 553 (1977). S. G. Greenbaum, U. Strom, M. Rubinstein, Phys. Rev. B 266, 5226 (1982). Y. Y. Yao, J. T. Kummer, J. Inorg. Nucl. Chem. 29, 2453 (1967). R. E. Walstedt, R. Dupree, J. P. Remeika, A. Rodriguez, Phys. Rev. B 15, 3442 (1977). M. Villa, J. L. Bjorkstam, Phys. Rev. B 22, 5033 (1980). D.B. McWhan, S.S. Allen, Jr., J.P. Remeika, P. D. Dernier, Phys. Rev. Lett. 35, 953 (1975); 36, 341 (E) (1976). J. L. Bjorkstam, S. Manzini, M. Villa, in Fast lon Transport in Solids, ed. Vashista, Mundy, Shenoy (Elsevier North Holland, Inc., 1979), pg. 293.

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J. Szeftel, H. Alloul, J. Noncryst. Sol. 29, 253 (1978); and references therein. T. L. Reinecke, K. L. Ngai, Phys. Rev. B 12, 3476 (1975). A. Abragam, The Principles of Nuclear M a$netism (Oxford Univ. Press, London, 1978). J. J~ckle, Z. Phys. 25__/7, 212 (1972). J. L. Black, B. I. Halperin, Phys. Rev. B 16, 2879 (1977). M. T. Loponen, R. C. Dynes, V. Narayanamurti, J. P. Garno, Phys. Rev. Lett. 45, 457 (1980). T. Doussineau, C. Frenois, R. G. Leisure, A. Levelut, J. Y. Prieur, J. de Physique 41, 1193 (1980). G. V. Chandrashekhar, L. M. Foster, Solid State Commun. 27, 269 (1978). L. M. Foster, M. P. Anderson, G. V. Chamdrashakhar, G. Burns, R. B. Bradford, J. Chem. Phys. 75, 2412 (1981). D. E. Day, J. Noncryst. Solids, 21, 343 (1976). K. L. Ngai, Comments Solid State Physics 2, 127 (1979); 2, 141 (1980).