First-principles calculation of defect energetics in cubic-BaTiO₃ and a comparison with SrTiO₃

The structural relaxation and formation energies of intrinsic vacancies in cubic-BaTiO₃ were studied by using a first-principles plane-wave-based pseudopotential calculation. The calculated defect formation energies and the atomic relaxations were compared with previously reported data for SrTiO₃ [Tanaka T, Matsunaga K, Ikuhara Y, Yamamoto T. Phys Rev B 2003;68:205213]. It was found that the formation energies of the partial Schottky species, V_Ti^{2 -} + V_O^{2 +} and V_Ba^{2 -} + V_O^{2 +}, are the lowest in the oxidized condition. In contrast, as the oxygen chemical potential decreased, namely the reduced condition, the O vacancy becomes dominant in cubic-BaTiO₃. Concerning the atomic relaxation, it was found that BaTiO₃ and SrTiO₃ show a difference in magnitude. It was also found that the overall vacancy formation energy in BaTiO₃ is higher than that in SrTiO₃.