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 BaTiO3 and PbTiO3 using a hybrid B3PW description of exchange and correlation. On the 001 surfaces, we consider both AO A=Ba or Pb and TiO2 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 TiO2 terminations on BaTiO3 001 are found to be comparable, as are those of PbO and TiO2 on PbTiO3 001 , although in both cases the relaxation energy is slightly larger for the TiO2 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 Baor Pb-terminated surfaces. The relaxed surface energy for the O-terminated surface is about the same as the corresponding average of the TiOand Pb-terminated surfaces on PbTiO3, but much less than the average of the TiOand Ba-terminated surfaces on BaTiO3. We predict a considerable increase of the Ti-O chemical bond covalency near the BaTiO3 and PbTiO3 011 surfaces as compared to both the bulk and the 001 surface.