Correlation between the activation enthalpy and Kohlrausch exponent for ionic conductivity in alkali aluminogermanate glasses

Abstract

The temperature and frequency dependence of electrical conductivity (${\sigma }_{\mathrm{dc}}$) and the electrical modulus of sodium, rubidium, and Na-Rb mixed alkali germanate and aluminogermanate glasses have been determined for varying alkali concentrations, and [Al]/[Ge] and [Na]/[Rb] ratios. In a few glasses the spin-lattice relaxation times $T_1$ for ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ have also been determined above room temperature. The frequency dependence of modulus is well fitted by the Kohlrausch (‘‘stretched exponential’’ decay) function with exponent β≡1-n (0<n<1) where n, according to the ‘‘coupling model,’’ is a measure of ion-ion correlations. The microscopic activation energy, determined either directly from the temperature dependence of $T_1$ or as the product of 1-n and the activation energy of ${\sigma }_{\mathrm{dc}}$, shows the best anticorrelation with n, as expected from the model.