Divalent and mixed divalent/monovalent conduction in β″-alumina: A Monte Carlo study

A Monte Carlo method is developed for simulation of mixed ionic conductivity in β″-alumina-type materials. The conduction plane of these materials is represented by a lattice gas model in which monovalent and divalent cation carriers diffuse via a vacancy mechanism and interact through a nearest-neighbor coulombic repulsion. By comparing experimental data for pure Na⁺ and pure Ba²⁺ β″-aluminas with simulation results, it is possible to estimate the near-neighbor interaction energies ε_i and jump barriers U_i for both kinds of ions. On the basis of these estimations the total ionic conductivity of Na⁺Ba²⁺ β″-alumina is calculated as a function of temperature and concentration of carriers. As Ba²⁺ replaces Na⁺, the conductivity initially increases as more vacancies become available. For very high temperatures, this increase continues until exchange is complete; but at lower temperatures, the conductivity reaches a peak for some optimal ^{Ba2+ Na+} composition, and then drops off as the number of Ba²⁺, and hence the strength of ionic correlation, goes up. The presence of ordering in the fully exchanged (all Ba²⁺) case manifests itself in substantial curvature of the Arrhenius plots for conductivity. The activation energy for conductivity as a function of Ba²⁺ mole fraction (X_Ba²⁺) shows a pronounced rise near an X value of 2 3, in agreement with recent experimental observations.