Study of Σ3 BaZrO₃ (210)[001] tilt grain boundaries using density functional theory and a space charge layer model

Abstract

We studied Σ3 BaZrO₃ (210)[001] tilt grain boundaries using density functional theory and a space charge layer model. Formation enthalpies of BaZrO₃ and competing oxides were calculated using fitted elemental-phase reference energy (FERE) correction, and a stable region of BaZrO₃, as functions of Ba and O chemical potentials, was determined. Grain boundary energies were evaluated as functions of Ba and O chemical potentials within the determined stable region of BaZrO₃ from the FERE correction. Among the six tested grain boundaries, an energetically favorable nonstoichiometric grain boundary was determined. Based on the nonstoichiometric grain boundary, we calculated the electrostatic potential and concentrations of proton and oxygen vacancy using a space charge layer model.