Ab initiocalculations ofBaTiO3andPbTiO

Abstract

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 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 PbTiO3, but much less than the average of the TiO and Ba-terminated surfaces on BaTiO3. We predict a considerable increase of the Ti-O chemical bond covalency near the BaTiO3 and PbTiO3 (011) surface as compared to both the bulk and the (001) surface.

Ab initiocalculations of the atomic and electronic structure ofCaTiO3(001) and (011) surfaces

“…According to our calculations, they move inwards by 0.42% of a 0 . Our calculated inward relaxation of the first-layer oxygen atoms on the CaO-terminated CaTiO 3 (001) surface is in line with previous ab initio studies dealing with BaTiO 3 , PbTiO 3 , and BaZrO 3 (001) surfaces, 32,42,61,62 but contrasts with the outward relaxation of first-layer oxygen atoms on the SrO-terminated SrTiO 3 (001) surface. 7,20,21 According to the results of our current calculations, outward relaxations are found for all atoms in the second layer for both CaO and TiO 2 terminations of the CaTiO 3 (001) surface.…”

“…This behavior contrasts with the atomic relaxation pattern of the TiO 2 -terminated BaTiO 3 (001) surface, where the upper-layer Ti relaxation is generally larger than the second-layer Ba relaxation. 32 where the second-layer anion (Pb or Ba) relaxations were larger than the upper-layer (Ti or Zr) ones. In order to compare the calculated surface structures with experimental results, the surface rumpling s (the relative oxygen displacement relative to the metal atom in the surface layer) and the changes in interlayer distances ∆d 12 and ∆d 23 (where 1, 2 and 3 label the nearsurface layers) are presented in Table III.…”

“…Moreover, we recently performed ab initio B3PW calculations for the technologically important BaTiO 3 and PbTiO 3 (011) surfaces. 32 Our calculated surface energies showed that the TiO 2 -terminated (001) surface is slightly more stable than the BaO-or PbO-terminated (001) surface for both materials, and that O-terminated BaTiO 3 and TiO-terminated PbTiO 3 (011) surfaces have surface energies close to that of the (001) surface.…”

“…7,32 As in the work of Zhang et al, 6 we do not explicitly include octahedral rotations in the surface calculations, even though such rotations are likely to be more important for CaTiO 3 than for many other perovskites; we discuss and justify this approximation at the end of Sec. II.…”

“…With the sole exception of the calculation on CaTiO 3 by Zhang et al, 6 all of the first-principles and shell-model studies of ABO 3 perovskite surface energies 7,12,16,23,30,32,42 have found that the lowestenergy (001) surface is lower in energy than any of the (011) terminations. Zhang et al, 6 on the contrary, reported a surface energy of 0.837 eV for their "A-type" O-terminated (011) surface of CaTiO 3 , to be compared with 1.021 eV for the TiO 2 -terminated (001) surface.…”