First‐principles calculation of formation energy of neutral point defects in perovskite‐type BaTiO₃

Quantitative analysis of the formation energy of neutral point defects in perovskite‐type BaTiO 3 was carried out by first‐principles calculation. A 40‐atom supercell was employed and relaxation of atoms within the second‐nearest‐neighbor shell of the vacancy was taken into account. The formation energy was calculated as a function of the atomic chemical potential of the constituent atoms. The theoretical formation energy of the O vacancy in BaTiO 3 shows negative values in the case of the reduction limit of BaTiO 3 , which is in good agreement with experimental results showing an abundance of O vacancies when annealed in reducing atmosphere and n ‐type electrical conduction. On the other hand, the formation energies of the Ba vacancy and Ti vacancy in BaTiO 3 even under the oxidizing condition are as large as 2.21 and 5.65 eV, respectively. This also well corresponds to the experimental fact that the Ba and Ti vacancies are not formed alone in BaTiO 3 .