Solid State Communications, Vol. 29, pp.507—510 Pergamon Press Ltd. 1979. Printed in Great Britain. ARE THE PREFACTOR ANOMALIES IN SUPERIONIC CONDUCTORS DUE TO l-D EFFECTS? J. B. Boyce, J. C. Mikkelsen, Jr., and B. A. Huberman Xerox Palo Alto Research Center Palo Alto, California 94304 (Received 12 December 1978 by A. A. Maradudin) We have examined both the ionic conductivity and the NMR line narrowing in two channel—structured superionic conductors in the light of Richards’ one—dimensional theory. For Li 2Ti3O7 the ionic conductivity is not suf- ficiently anisotropic to explain the observed small NMR prefactor in terms of l-D effects. For ~—LiA1SiO4 the NMR line narrowing in the crossover region does not yield the predicted large change in the activation energy given by the l—D theory. A recent communication by Richards’ pro— structure which consists of Ti06 octahedra which poses an alternative explanation to that offered share edges in such a way that there are channels by two of us 2 in order to explain the anomalously parallel to the c—axis. These channels are one low prefactors for ionic hopping rates extracted octahedron (a—axis) by two octahedra (b—axis) in from the nuclear magnetic resonance (NMR) data cross section. So one might expect this material for some superionic conductors. In our work, we to be a highly anisotropic Li ion conductor. We had observed that a conventional analysis of the find that the ionic conductivity is anisotropic NMR data on Li 2Ti3O7 yielded a prefactor, V~, but that the anisotropy should not be sufficient for the Li hopping rate of 4 x io~sec 1. This to yield l—D effects. The details of the mea— is five orders of magnitude smaller than typical surements will be reported elsewhere.4 In this optical phonon frequencies. L12Ti3O7 is not an study, the conductivity was determined to be isolated case in this regard since the low pre— ionic, the electronic component being negligible. factors appear in many other superionic conduc— The conductivities in the a—, b—, and c—direc- tors with rigid oxide skeleton structures through tions have approximately the same activation which the mobile ions move.2 We then proposed an energy, U~ 0.45 eV, but they differ somewhat in explanation in terms of a breakdown of absolute magnitude according to rate theory. Alternatively, Richards suggested that the channel structures of some of these su— o perionic conductors imply low dimensional behav- —.~ 7 and — 4 . (1) ior of the long— or short—range transport pro— Gb cesses, thereby leading to nuclear spin relaxa- tion processes different from those obtained This anisotropy, although significant, is con- within BPP theory. siderably smaller than the l0~ anisotropy ob- Since it is important to sort out the phy— tamed in the ionic conductivity of LiAlSiO 4. 3 sical mechanism for the observed anomalies, we These results on Li 2Ti3O7 hold over the tempera— have analyzed the behavior of both Li2Ti3O7 and ture range 20°C< T < 500°Cwhich encompasses 8-LiAlSiO4 in the context of Richards’ ideas, the region of our earlier NMR motional narrowing Both materials have channel structures, Li2Ti3O7 study. the ramsdellite structure and 8—LiAlSiO4 the ~ The NMR linewidth, t5w, is given in the con— eucryptite structure. The main conclusions of ventional BPP theory by 5 our study are the following: (1) The ionic con- ductivity of Li 2Ti3O7 is not anisotropic enough (A2~’/2 , 2~ > 2 in the temperature range over which the previous ‘ / > V 2 NMR studies were undertaken to be considered one— -, A 2 / 2 2 dimensional. As a result, a l—D model should not ( u > V (Au > << v be applicable. (2) In ~—LiAlSiO4, which is a l—D 2 ionic conductor (anisotropy ~ l0~),~ the applica— where (Au ) is the rigid lattice second moment and tion of the 1—ID expressions to our NMR linewidth V is the effective correlation frequency. V is data shows that it is not in either limiting re— usually identified with the ionic diffusion rate, gion treated by Richards but rather is in the hID. If, however, the System 1S one—dimensional, transition region for which no line—narrowing one has, for Aur3D < theory is available. A prediction of the l-D 1 theory, namely, a changing activation energy in 1 /T \/2 the transition region, is, however, not observed. - — (.P_) , 6uT~ < 1 , (3) First, in order to test the hypothesis of TD \T3D/ one-dimensional Li motion in Li2Ti3O7, we have measured the ionic conductivity in single crys— where 13D is the characteristic time for three— tals both parallel and perpendicular to the chan- dimensional effects to become significant. In a nel axis. Li 2Ti3O7 has the ramsdellite (8—Mn02) truly l—D system, rD << 13D and Eq. (3) yields 507