Correlation between the Activation Energies for Ionic Conductivity for Short and Long Time Scales and the Kohlrausch Stretching Parameterβfor Ionically Conducting Solids and Melts

Abstract

The temperature dependence of the dc conductivity \ensuremath{\sigma} of most glass-forming and crystalline ionic conductors is Arrhenius with constant activation energy, ${E}_{\ensuremath{\sigma}}$, at sufficiently low temperatures or conductivity levels. However, \ensuremath{\sigma} becomes non-Arrhenius at high temperatures or conductivity levels. We have found that the product, $\ensuremath{\beta}{E}_{\ensuremath{\sigma}}$, of the Kohlrausch stretching exponent for the conductivity relaxation, $\ensuremath{\beta}$, and the dc conductivity activation energy in the Arrhenius regime is approximately the same as the high temperature apparent activation energy, ${E}_{a}$, of $\ensuremath{\sigma}$ at the temperature where \ensuremath{\sigma} reaches the high level of $1{\ensuremath{\Omega}}^{\ensuremath{-}1}{\mathrm{cm}}^{\ensuremath{-}1}$ and the conductivity relaxation time ${\ensuremath{\tau}}_{\ensuremath{\sigma}}$ is of the order of 1 psec.