The ionic-conductivity (σ) and electric-modulus ($M^{\mathrm{*}}$) data for melt-grown Na β-alumina in the ${10}^2$–${10}^7$-Hz frequency range have been previously interpreted with a formalism in which the decay of an observable, such as the time-dependent electric field in the sample, follows the (‘‘fractional-exponential’’) form exp[(-t/τ${)}^{1\mathrm{-}n}$], where 0<n<1. Ionic-conductivity data for frequencies between ${10}^8$ and ${10}^{11}$ Hz cannot be interpreted in terms of this formalism, but instead the ionic relaxation at high frequencies is consistent with a simple exponential (i.e., with n=0). These observations are in agreement with the predictions of a relaxation model in which the frequency ${\omega }_c$, which defines the crossover from fractional to simple exponential relaxation, is included as an explicit parameter.

• Received 28 April 1988

DOI:https://doi.org/10.1103/PhysRevB.38.10350