First-principles calculations of the atomic and electronic structure of SrZrO3 and PbZrO3 (001) and (011) surfaces

We present the results of calculations of surface relaxations, rumplings, energetics, optical band gaps, and charge distribution for the SrZrO3 and PbZrO3 (001) and (011) surfaces using the ab initio code CRYSTAL and a hybrid description of exchange and correlation. We consider both SrO(PbO) and ZrO2 terminations of the (001) surface and Sr(Pb), ZrO, and O terminations of the polar SrZrO3 and PbZrO3 (011) surfaces. On the (001) surfaces, we find that all upper and third layer atoms relax inward, while outward relaxations of all atoms in the second layer are found with the sole exception of the SrO-terminated SrZrO3 (001) surface second layer O atom. Between all (001) and (011) surfaces the largest relaxations, more than 15% of the bulk lattice constant, are for the Sr- and Pb-terminated SrZrO3 and PbZrO3 (011) surface upper layer Sr and Pb atoms. Our calculated surface rumpling for the SrO- and PbO-terminated SrZrO3 and PbZrO3 (001) surfaces (6.77 and 3.32% of a0) are by a factor of ten larger than the surface rumpling for the ZrO2-terminated (001) surfaces (-0.72 and 0.38% of a0, respectively). In contrast to the surface rumpling, the (001) surface energies are comparable and in the energy range from 0.93 eV/cell for the ZrO2-terminated PbZrO3 surface to 1.24 eV/cell for the ZrO2-terminated SrZrO3 surface. In contrast to the (001) surface, different terminations of the SrZrO3 and PbZrO3 (011) surfaces lead to very different surface energies ranging from 1.74 eV/cell for the Pb-terminated PbZrO3 (011) surface to 3.61 eV/cell for the ZrO-terminated SrZrO3 (011) surface. All our calculated (011) surface energies are considerably larger than the (001) surface energies. Our calculated optical band gap for the SrZrO3 bulk, 5.31 eV, is in fair agreement with the experimental value of 5.6 eV. All our calculated optical band gaps for the SrZrO3 and PbZrO3 (001) and (011) surfaces are reduced with respect to the bulk. We predict a considerable increase in the Zr-O chemical bond covalency near the SrZrO3 and PbZrO3 (011) surfaces as compared both to the bulk and to the (001) surface.