Communication: Dimensionality of the ionic conduction pathways in glass and the mixed-alkali effect.

A revised empirical relationship between the power law exponent of ac conductivity dispersion and the dimensionality of the ionic conduction pathway is established on the basis of electrical impedance spectroscopic (EIS) measurements on crystalline ionic conductors. These results imply that the "universal" ac conductivity dispersion observed in glassy solids is associated with ionic transport along fractal pathways. EIS measurements on single-alkali glasses indicate that the dimensionality of this pathway D is ∼2.5, while in mixed-alkali glasses, D is lower and goes through a minimum value of ∼2.2 when the concentrations of the two alkalis become equal. D and σ display similar variation with alkali composition, thus suggesting a topological origin of the mixed-alkali effect.