Ab initio study of formations of neutral vacancies in ferroelectric PbTiO3 at different oxygen atmospheres

Formation energies of possible neutral vacancies under different thermo-chemistry conditions were studied using an ab initio DFT and supercell approach. Under oxygen rich conditions, lead vacancies are ready to form due to its lowest formation energy. On the other hand, under oxygen poor conditions, oxygen vacancies become more dominant than lead vacancies. Our ab initio simulation shows the vacancies of oxygen bonded with Ti in z direction are readier to form than those of oxygen bonded with Ti in x and y directions, thus affecting the ferroelectricity of the crystal. The formation of titanium vacancies is found to be difficult under all the conditions. The results predicted by the model well agree with experimental results.