Ionic transport in super ionic conductors: a theoretical model

• Published in: Journal of solid state chemistry Vol. 4; no. 2; pp. 294 - 310
• Main Authors: Rice, M.J., Roth, W.L.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.1972
• ISSN: 0022-4596; 1095-726X
• DOI: 10.1016/0022-4596(72)90121-1

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 ϵ 0 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 v m and energy ϵ m = 1 2 M v m 2 . 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 τ m . 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 K I , 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”, l 0 = v 0 τ 0, of the free-ion like state excited at the gap entry ϵ 0. The characteristic life-time τ 0 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.