Ab initio calculations of BaTiO3 and PbTiO3 (001) and (011) surface structures

We present and discuss the results of calculations of surface relaxations and rumplings for the (001) and (011) surfaces of BaTiO(3) and PbTiO(3) using a hybrid B3PW description of exchange and correlation. On the (001) surfaces, we consider both AO (A=Ba or Pb) and TiO(2) terminations. In the former case, the surface AO layer is found to relax inward for both materials, while outward relaxations of all atoms in the second layer are found at both kinds of (001) terminations and for both materials. The surface relaxation energies of BaO and TiO(2) terminations on BaTiO(3) (001) are found to be comparable, as are those of PbO and TiO(2) on PbTiO(3) (001), although in both cases the relaxation energy is slightly larger for the TiO(2) termination. As for the (011) surfaces, we consider three types of surfaces, terminating on a TiO layer, a Ba or Pb layer, or an O layer. Here, the relaxation energies are much larger for the TiO-terminated surface than for the Ba- or Pb-terminated surfaces. The relaxed surface energy for the O-terminated surface is about the same as the corresponding average of the TiO- and Pb-terminated surfaces on PbTiO(3), but much less than the average of the TiO- and Ba-terminated surfaces on BaTiO(3). We predict a considerable increase of the Ti-O chemical bond covalency near the BaTiO(3) and PbTiO(3) (011) surfaces as compared to both the bulk and the (001) surface.