These topics were investigated, and new insights were obtained, by considering isothermal frequency response data for 7 different materials having quite different conductivity spans and which involved various electrode polarization effects and temperatures. The data were fitted by using several models; including the Kohlrausch-related K0 and K1 ones derived from a stretched-exponential response in the temporal domain. The quasi-universal UN model, the K1 with its shape parameter, β1, fixed at 1/3, fitted most of the data very well, and its fits to these data were used to compare its predictions for hopping-rate with those derived from fits obtained using the conventional universal dynamic response Almond–West real-part-of-conductivity model. The K1-model theoretical hopping-rate, involving the mean waiting time for a hop and derived from a microscopic stochastic analysis, was found to be about twice as large as the empirical Almond–West rate for most of the materials considered. Its use in a generalized Nernst–Einstein equation led to a comparison of the estimates of the concentration of fully dissociated mobile charge carriers in superionic PbSnF4, with earlier estimates of Ahmad using an Almond–West hopping-rate value. Agreement with an independent structure-derived value was relatively poor. Fitting results obtained by using the K0 model, for Na2SO4 data sets for 2 different polycrystalline material phases, and involving severely limited conductivity variations, were much better than those obtained by using the K1 model. The estimated values of the K0 shape parameter, β0, were close to 1/3 for both phases. This strongly suggested that the charge motion was 1-dimensional for each phase; even though they involved different crystalline structures.

Slopes, Nearly Constant Loss, Universality and Hopping Rates for Dispersive Ionic Conduction. J.R.Macdonald, M.M.Ahmad: Journal of Physics - Condensed Matter, 2007, 19[4], 046215 (13pp)