Formation energy profiles of oxygen vacancies at grain boundaries in perovskite-type electroceramics

Oxygen vacancy formation energies play a major role in the electric field assisted abnormal grain growth of technologically relevant polycrystalline perovskite phases. The underlying effect on the atomic scale is assumed to be a redistribution of cationic and anionic point defects between grain boundaries and the bulk interior regions of the grains due to different defect formation energies in the structurally different regions, accompanied by the formation of space charge zones. Using atomistic calculations based on classical interatomic potentials, we derive and discuss optimized structures of the symmetric tilt grain boundaries $\Sigma$5(210)[001] and $\Sigma$5(310)[001], and of the asymmetric tilt grain boundary (430)[001]||(100)[001] in the electroceramic perovskite materials SrTiO$_3$, BaTiO$_3$, and BaZrO$_3$. We present profiles of oxygen vacancy formation energies across those GBs and discuss their dependence on composition and grain boundary type.