Ab initio hybrid DFT calculations of BaTiO3, PbTiO3, SrZrO3 and PbZrO3 (111) surfaces

Abstract The results of ab initio calculations for polar BaTiO 3 , PbTiO 3 , SrZrO 3 and PbZrO 3 (111) surfaces using the CRYSTAL code are presented. By means of the hybrid B3LYP approach, the surface relaxation has been calculated for two possible B (B = Ti or Zr) or AO 3 (A = Ba, Pb or Sr) BaTiO 3 , PbTiO 3 , SrZrO 3 and PbZrO 3 (111) surface terminations. According to performed B3LYP calculations, all atoms of the first surface layer, for both terminations, relax inwards. The only exception is a small outward relaxation of the PbO 3 -terminated PbTiO 3 (111) surface upper layer Pb atom. B3LYP calculated surface energies for BaO 3 , PbO 3 , SrO 3 and PbO 3 -terminated BaTiO 3 , PbTiO 3 , SrZrO 3 and PbZrO 3 (111) surfaces are considerably larger than the surface energies for Ti (Zr)-terminated (111) surfaces. Performed B3LYP calculations indicate a considerable increase of Ti O (Zr O) chemical bond covalency near the BaTiO 3 , PbTiO 3 , SrZrO 3 and PbZrO 3 (111) surface relative to the BaTiO 3 , PbTiO 3 , SrZrO 3 and PbZrO 3 bulk. Calculated band gaps at the Γ -point near the PbTiO 3 , SrZrO 3 and PbZrO 3 (111) surfaces are reduced, but near BaTiO 3 (111) surfaces increased, with respect to the BaTiO 3 , PbTiO 3 , SrZrO 3 and PbZrO 3 bulk band gap at the Γ -point values.