Conductivity of dispersed ionic conductors: A percolation model with two critical points

Abstract

The conductivity of ionic conductors containing a dispersed insulating second phase is investigated from the point of view of percolation theory. Using Monte Carlo simulations, we study a resistor model in two and three dimensions, which emphasizes the role of an enhanced interface conductivity. The existence of two critical concentrations $p_c^{\mathcal{’}}$ and $p_c^{2\mathrm{sprime}}$ of an insulating phase leads to a characteristic dependence of the overall conductivity on composition which is in remarkable agreement with experiment. Detailed calculations near the two thresholds $p_c^{\mathcal{’}}$ and $p_c^{2\mathrm{sprime}}$ yield critical properties in accord with random superconducting and random resistor networks. The question of a possible experimental verification of those critical properties is also discussed.