Nonlinear DC and Dispersive Conductivity of Ion Conducting Glasses and Glass Ceramics

Abstract

Frequency-dependent third-order conductivity spectra σ₃^´(ν) of various ion conducting glasses and glass ceramics were obtained by applying sinusoidal electric fields with high amplitudes and by analysing the resulting higher-harmonic currents. In the DC conductivity regime, the third-order conductivity σ_{3, dc} was found to be positive for all materials and at all temperatures. From the ratio of the third-order conductivity to the low-field conductivity, σ_{3, dc}/σ_{1, dc}, apparent jump distances were calculated. These apparent jump distances are much larger than jump distances between neighbouring sites in the glasses and decrease with increasing temperature. In (Li₂O)_1-x·(Na₂O)_x·Al₂O₃·(SiO₂)₄ glasses, the mixed alkali effect leads to a minimum in the apparent jump distance, while partial crystallisation of Li₂O·Al₂O₃·(SiO₂)₂ glasses leads to an increase of the apparent jump distance. In the dispersive regime, the third-order conductivity σ₃^´(ν) of all glasses and glass ceramics is negative and exhibits an approximate power-law dependence, however with a larger exponent than the dispersive low-field conductivity σ₁^´(ν). For a given material, the third-order conductivity spectra σ₃^´(ν) obey the time–temperature superposition principle and can be superimposed by using the Summerfield scaling. Remarkably, the shift between the σ₃^´(ν) master curves of different materials is much stronger than the shift between the σ₁^´(ν) master curves. In order to rationalize this effect, we calculate the nonlinear dispersive hopping conductivity in a double minimum potential approximation.