Formation energies of different neutral vacancies (VPb, VTi, VO, VBa) in tetragonal PbTiO3 and tetragonal BaTiO3 were studied by performing first-principles pseudopotential calculations. Using thermodynamic laws, the constraints that yielded valid chemical potentials for atomic reservoirs in equilibrium with ferroelectric solids were also analytically determined, and it was determined how the energies of vacancy formation could be modified by varying reservoir conditions. The defect energetics in BaTiO3 were further contrasted with those in PbTiO3; thus revealing notable differences.

First-Principles Determination of Chemical Potentials and Vacancy Formation Energies in PbTiO3 and BaTiO3. Z.Alahmed, H.Fu: Physical Review B, 2007, 76[22], 224101 (8pp)