Review of Systematic Tendencies in (001), (011) and (111) Surfaces Using B3PW as Well as B3LYP Computations of BaTiO 3 , CaTiO 3 , PbTiO 3 , SrTiO 3 , BaZrO 3 , CaZrO 3 , PbZrO 3 and SrZrO 3 Perovskites.

We performed B3PW and B3LYP computations for BaTiO (BTO), CaTiO (CTO), PbTiO (PTO), SrTiO (STO), BaZrO (BZO), CaZrO (CZO), PbZrO (PZO) and SrZrO (SZO) perovskite neutral (001) along with polar (011) as well as (111) surfaces. For the neutral AO- as well as BO-terminated (001) surfaces, in most cases, all upper-layer atoms relax inwards, although the second-layer atoms shift outwards. On the (001) BO-terminated surface, the second-layer metal atoms, as a rule, exhibit larger atomic relaxations than the second-layer O atoms. For most ABO perovskites, the (001) surface rumpling is bigger for the AO- than BO-terminated surfaces. In contrast, the surface energies, for both (001) terminations, are practically identical. Conversely, different (011) surface terminations exhibit quite different surface energies for the O-terminated, A-terminated and BO-terminated surfaces. Our computed ABO perovskite (111) surface energies are always significantly larger than the neutral (001) as well as polar (011) surface energies. Our computed ABO perovskite bulk B-O chemical bond covalency increases near their neutral (001) and especially polar (011) surfaces.