  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.
