Effective medium theory for ionic conductivity in polycrystalline solid electrolytes

It is usually found that for the relatively poor ion conducting solids, the ionic conductivity for the pure polycrystalline sample is higher than that of the single crystal. The difference has been suggested to be due to the presence of dislocations, grain boundaries etc. in the polycrystal. In this paper we propose a theoretical model for the polycrystal including these defects. A quantitative estimate of the grain boundary contribution to conductivity is made using an effective medium theory and it is found to exhibit an Arrhenius behaviour. The results for calcium fluoride, thallium chloride and cuprous chloride show that the grain boundary conductivity is approximate to 10(5) times that of the single crystal. The ratio of activation energy for grain boundary conduction to that of the single crystal is found to be 0.5-0.6 which is consistent with results obtained from other sources.