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

The temperature and frequency dependence of electrical conductivity (σdc) 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 T₁ for ²³Na 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 T₁ or as the product of 1-n and the activation energy of σdc, shows the best anticorrelation with n, as expected from the model.