Stretched exponentials with T-dependent exponents from fixed distributionsof energy barriers for relaxation times in fast-ion conductors

The conductivity modulus in fast ion conductors (FIC) has often been fitted with stretched exponential relaxation functions of the form exp[-(t/tau(K) )(beta)], where the beta values are taken to be independent of temperature. This analysis corresponds to the assumption of an asymmetric distribution of relaxation times (DRT) that does not have the T dependence observed in t he conductivity modulus spectra found for many FIC glasses and expected fro m a fixed distribution of activation energies (DAE) against the ion hops. I n this paper, it is shown, rather, that a fixed DAE leads to the temperatur e dependence of beta proportional to T-0.5 for beta values near 0.6, and co nductivity modulus data for some Li+ glasses are presented where beta varie s nearly in this way. Similar behavior can be inferred from published data for many other FIC. It is also shown that the DRT calculated from the corre sponding stretched exponential relaxation function closely approximates the tail of the DRT calculated from the DAE and truncated at the conductivity percolation limit of 0.3.