Determination of Mobility and Charge Carriers Concentration from Ionic Conductivity in Sodium Germanate Glasses above and below Tg

Abstract

The ionic conductivity and viscous flow data of xNa2O·(1−x)GeO2, 0.05<x<0.296, have been collected in a large temperature range, below and above their glass transition temperatures (Tg). A microscopic model is proposed, assuming that the ionic displacement would result from the migration of interstitial positively charged cationic pairs whose concentration is an activated function of temperature. Below Tg, their migration is also an activated mechanism, but a “free volume” would prevail above this temperature. This discontinuity in the migration mechanism justifies a Dienes-Macedo-Litovitz (DML) relationship to be representative of conductivity data above Tg and an Arrhenius law below. According to this model, the enthalpy deduced by the fit of high temperature data using a DML equation would correspond to the charge carrier formation, whose migration enthalpy, below Tg, could be deduced by the difference between the activation energy measured in the Arrhenius domain and the charge carrier formation enthalpy. To reduce the number of adjustable parameters numerical values were physically justified. We also applied a complete test for conductivity below Tg, using the so-called weak electrolyte model, splitting activation enthalpy EσA into formation and migration enthalpies and also explaining the variation of pre-exponential term of conductivity with composition.