The first-principle calculation of structures and defect energies in tetragonal PbTiO3

The first-principle calculation had been adopted to investigate various neutral vacancies and vacancy pairs under seven thermodynamic conditions in bulk PbTiO3. The electronic structures, atomic relaxations, and formation energies of vacancies were obtained. Depending on the thermodynamic condition, the main and stable defects are different. It was found that VO is the main defect under the reducing condition, whereas VPb becomes dominating under the oxidizing condition. The Pb–O vacancy pair forms more easily than the isolated vacancies under certain thermodynamic condition. Due to the introducing of vacancies, the acceptorlike levels and donorlike levels appear in the cases of the cation and anion vacancies, respectively.