Ab initio calculations of BaTiO_3 and PbTiO_3 (001) and (001) surface structures

摘要

We present and discuss the results of calculations of surface relaxations and rumplings for the (001) and (001) 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.