The polarization of a nearest-neighbor Pb-O vacancy pair [(VPb-VO)nn] in PbTiO3 was calculated, using the modern theory of polarization, implemented in the density-functional-theory ultra-soft pseudopotential formalism. The dipole moment per divacancy, μ(VPb-VO)nn, was about 2.28ernn, where rnn was the vector from the VPb site to the VO site. This value was slightly larger than the value of 2ernn for a purely ionic model of PbTiO3. The dipole moment was about twice as large as typical polarizations per cell in Pb-based ferroelectrics, which indicated that VPb compensated by VO could be an important source of local polarization and electric fields in Pb-containing perovskites.

Dipole Moment of a Pb-O Vacancy Pair in PbTiO3. E.Cockayne, B.P.Burton: Physical Review B, 2004, 69[14], 144116 (5pp)