Formation energies of possible neutral vacancies under different thermo-chemistry conditions were studied using an ab initio density functional theory and super-cell approach. Under O rich conditions, lead vacancies were ready to form due to its lowest formation energy. On the other hand, under O poor conditions, O vacancies become more dominant than Pb vacancies. The ab initio simulation showed that the vacancies of O bonded with Ti in the z-direction were more ready to form than those of O bonded with Ti in x and y directions, thus affecting the ferroelectricity of the crystal. The formation of Ti vacancies was found to be difficult under all the conditions. The results predicted by the model well agree with experimental results.

Ab Initio Study of Formations of Neutral Vacancies in Ferroelectric PbTiO3 at Different Oxygen Atmospheres. Z.Zhang, P.Wu, L.Lu, C.Shu: Journal of Alloys and Compounds, 2008, 449[1-2], 362-5