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

Abstract

The temperature and frequency dependence of electrical conductivity (${\ensuremath{\sigma}}_{\mathrm{dc}}$) 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 \ensuremath{\beta}\ensuremath{\equiv}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 ${\ensuremath{\sigma}}_{\mathrm{dc}}$, shows the best anticorrelation with n, as expected from the model.