Ionic transport in super ionic conductors: a theoretical model

Ionic solids exhibiting exceptionally high levels of ionic conductivity are found among the cation disordered ionic compounds of the silver halide-chalcogenide type, the various cation substituted beta aluminas, and certain defect-stabilized ceramic oxides. We present in this paper a theoretical model for ionic transport phenomena in such “super” ionic conductors. The model is based on the hypothesis that there exists in the ionic conductor an energy gap ϵ0 above which ions of mass M, belonging to the conducting species, can be thermally excited from localized ionic states to free-ion like states in which an ion propagates throughout the solid with a velocity vm and energy ϵm = 12Mvm2. On account of the interaction with the rest of the solid such an excited free-ion like state is supposed to have a finite life-time τm. On the basis of a postulated Boltzmann transport equation for the thermal occupations of the various free-ion like states, simple expressions are derived for the ionic conductivity σ, thermal conductivity KI, and thermoelectric power Q. The theoretical result for Q is well substantiated by available experimental data. The result for σ may be used to deduce empirical values for the characteristic “mean-free path”, l0 = v0τ0, of the free-ion like state excited at the gap entry ϵ0. The characteristic life-time τ0 could be deduced in principal from measurements of the frequency dependent ionic conductivity σ(ω) which, according to the model, should be of the Drude type.