High-frequency dielectric loss of Naβ-alumina: Evidence for relaxation crossover

The ionic-conductivity ({σ}) and electric-modulus (M*) data for melt-grown Na {β}-alumina in the 10²--10⁷-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-n], where 0<n<1. Ionic-conductivity data for frequencies between 10⁸ and 10¹¹ 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 ωc, which defines the crossover from fractional to simple exponential relaxation, is included as an explicit parameter.