We have analyzed the constant loss contribution to the ac conductivity in the frequency range 10 Hz–1 MHz and temperatures down to 8 K, for two Li ionic conductors, one crystalline ( ${\mathrm{Li}}_{0.18}{\mathrm{La}}_{0.61}{\mathrm{TiO}}_3$) and the other glassy ( $61{\mathrm{SiO}}_2̇35{\mathrm{Li}}_2\mathrm{O}̇3{\mathrm{Al}}_2{\mathrm{O}}_3̇{\mathrm{P}}_2{\mathrm{O}}_5$). As temperature is increased a crossover is observed from a nearly constant loss to a fractional power law frequency dependence of the ac conductivity. At any fixed frequency $\omega$, this crossover occurs at a temperature $T$ such that $\omega \approx {\nu }_0\exp \left({-E}_m/k_{B}T\right)$, where ${\nu }_0$ is the attempt frequency and $E_m$ is identified with the barrier for ${\mathrm{Li}}^{+}$ ions to leave their wells.

Lithium ionic conductivity of ${\mathrm{Li}}_{0.5}$ ${\mathrm{La}}_{0.5}$ ${\mathrm{TiO}}_3$ has been studied using nuclear magnetic resonance (NMR) and admittance spectroscopy (AS) techniques. Spin-lattice relaxation and electrical conductivity relaxation are well described in terms of stretched-exponential correlation functions in the time domain of the form φ(t)=exp(-(t/τ${)}^{\mathrm{\beta }}$), but showing different relaxation times scales (${\mathrm{\tau }}_0$=1.4×${10}^{\mathrm{-}11}$ s from NMR and ${\mathrm{\tau }}_0$=${10}^{\mathrm{-}14}$ s from AS), and activation energies (0.15 and 0.4 eV, respectively). Different β exponents, 1 from spin lattice relaxation and 0.4 from electric-field relaxation have been also deduced. A microscopic activation energy for lithium motion of 0.15 eV is deduced from both techniques. Discrepancies between both techniques are analyzed and discussed in terms of frequency-dependent correlation effects. © 1996 The American Physical Society.