First-principles calculations of BaZrO₃(001) and (011) surfaces

In an extension of our previous studies of BaTiO₃, SrTiO₃, and PbTiO₃(001), as well as BaTiO₃ and SrTiO₃(011) surfaces [1–6], I present and discuss the results of calculations of BaZrO₃(001) surface relaxation and rumpling with two different terminations (BaO and ZrO₂), and BaZrO₃(011) polar surface relaxation with three terminations (Ba-, ZrO- and O-terminated, A-type). These are based on hybrid Hartree–Fock and density-functional theory exchange functionals, using Becke’s three-parameter method, combined with the nonlocal correlation functionals by Perdew and Wang [7]. According to the results of my calculations, all upper layer atoms for ZrO₂- and BaO-terminated BaZrO₃(001) surfaces relax inwards. The surface rumpling for the BaO-terminated BaZrO₃(001) surface is much larger than for the ZrO₂-terminated BaZrO₃(001) surface. Both BaO-terminated (1.30 eV) and ZrO₂-terminated (1.31 eV) surfaces are stable and energetically equally favourable. Unlike the BaZrO₃(001) surface, different terminations of the (011) surface lead to great differences in the surface energies. The A-type O-terminated surface has the lowest energy (2.32 eV). The Ba-terminated BaZrO₃(011) surface has a much higher surface energy of 2.90 eV, while the BaZrO₃ ZrO-terminated (011) surface has the highest energy (3.09 eV). I predict a considerable increase of the Zr–O chemical bond covalency near the (011) surface, as compared to both the bulk and the (001) surface.