First Principles Calculations of Vacancy Formation Energies in Σ13 Pyramidal Twin Grain Boundary of α-Al₂O₃

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Defect energetics in Σ13 pyramidal twin grain boundary (GB) of Al₂O₃ was investigated by a first principles projector-augmented wave method. It was found that the vacancy formation energy depends on the atomic site and the defect energetics at the GB is similar to that in the bulk Al₂O₃, namely the oxygen vacancy shows much higher formation energy than the aluminum vacancy and the Schottky defect is the most preferable species in a wide range of atmospheres. By analyzing the atomic structures of the GB in detail, it was found that the defect energetics at the GB is closely related to the structural distortions, such as strains and dangling-bonds in the vicinity of the GB.