Nonlinear conductivity spectra of ionically conducting glasses and glass ceramics: Analysis of spectral shape and scaling properties

Abstract

We present higher order conductivity spectra ${\ensuremath{\sigma}}_{3}^{\ensuremath{'}}(\ensuremath{\nu})$ of different ion conducting glasses and glass ceramics, which were taken over broad frequency ranges and at different temperatures. The ${\ensuremath{\sigma}}_{3}^{\ensuremath{'}}(\ensuremath{\nu})$ spectra are characterized by a change in sign, namely from positive values in the dc regime to negative values in the dispersive regime. In the dispersive regime, ${\ensuremath{\sigma}}_{3}^{\ensuremath{'}}(\ensuremath{\nu})$ exhibits an approximate power-law-type frequency dependence, albeit with a significantly larger exponent than the low-field conductivity ${\ensuremath{\sigma}}_{1}^{\ensuremath{'}}(\ensuremath{\nu})$. The ${\ensuremath{\sigma}}_{3}^{\ensuremath{'}}(\ensuremath{\nu})$ isotherms of an individual glass or glass ceramic can be superimposed by using the Summerfield scaling. The resulting ${\ensuremath{\sigma}}_{3}^{\ensuremath{'}}(\ensuremath{\nu})$ master curves of different materials show strong shifts on the scaled frequency axis with respect to each other. This implies strong differences between the materials regarding the nonlinearity of the dispersive conductivity. In order to rationalize this effect, we calculate the nonlinear dispersive hopping conductivity in a double-well potential approximation.