First-principles calculations of the atomic and electronic structure of SrZrO₃and PbZrO₃(001) and (011) surfaces

Abstract

We present the results of calculations of surface relaxations, rumplings, energetics, optical band gaps, and charge distribution for the SrZrO(3) and PbZrO(3) (001) and (011) surfaces using the ab initio code CRYSTAL and a hybrid description of exchange and correlation. We consider both SrO(PbO) and ZrO(2) terminations of the (001) surface and Sr(Pb), ZrO, and O terminations of the polar SrZrO(3) and PbZrO(3) (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 SrZrO(3) (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 SrZrO(3) and PbZrO(3) (011) surface upper layer Sr and Pb atoms. Our calculated surface rumpling for the SrO- and PbO-terminated SrZrO(3) and PbZrO(3) (001) surfaces (6.77 and 3.32% of a(0)) are by a factor of ten larger than the surface rumpling for the ZrO(2)-terminated (001) surfaces (-0.72 and 0.38% of a(0), 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 ZrO(2)-terminated PbZrO(3) surface to 1.24 eV/cell for the ZrO(2)-terminated SrZrO(3) surface. In contrast to the (001) surface, different terminations of the SrZrO(3) and PbZrO(3) (011) surfaces lead to very different surface energies ranging from 1.74 eV/cell for the Pb-terminated PbZrO(3) (011) surface to 3.61 eV/cell for the ZrO-terminated SrZrO(3) (011) surface. All our calculated (011) surface energies are considerably larger than the (001) surface energies. Our calculated optical band gap for the SrZrO(3) bulk, 5.31 eV, is in fair agreement with the experimental value of 5.6 eV. All our calculated optical band gaps for the SrZrO(3) and PbZrO(3) (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 SrZrO(3) and PbZrO(3) (011) surfaces as compared both to the bulk and to the (001) surface.

Ab initio hybrid DFT calculations of BaTiO3, PbTiO3, SrZrO3 and PbZrO3 (111) surfaces

“…B3LYP calculated surface energies for BaO 3 , PbO 3 , SrO 3 and PbO 3 -terminated BaTiO 3 , PbTiO 3 , SrZrO 3 and PbZrO 3 (111) surfaces are considerably larger than the corresponding surface energies for Ti (Zr)-terminated BaTiO 3 , PbTiO 3 , SrZrO 3 and PbZrO 3 (111) surfaces. According to performed ab initio calculations, the BaTiO 3 , PbTiO 3 , SrZrO 3 and PbZrO 3 (111) surface energy, for both terminations, is always considerably larger than the earlier calculated respective (011) and (001) surface energy [6,11]. Performed B3LYP calculations indicate a considerable increase of Ti O (Zr O) chemical bond covalency near the BaTiO 3 , PbTiO 3 , SrZrO 3 and PbZrO 3 (111) surface (0.118e, 0.116e, 0.098e and 0.114e, respectively) relative to the BaTiO 3 , PbTiO 3 , SrZrO 3 and PbZrO 3 bulk (0.100e, 0.100e, 0.092e and 0.106e, respectively).…”

“…For the Zr atom, in SrZrO 3 and PbZrO 3 perovskites, the same BS as in Refs. [11,26,38] was used. With aim to perform (111) surface calculations for neutral supercells, 2 electrons have been added to Ba 2+ , Pb 2+ and Sr 2+ ions, 4 electrons to Ba 4+ and Zr 4+ ion, and 2 electrons were removed from the O 2− ion.…”

Under Pressure DFT Investigations on Optical and Electronic Properties of PbZrO3

“…5. It is well known that GGA functional un- derestimates in calculating the electronic band-gap, but the use of hybrid exchange-correlation functionals, such as B3LYP and B3PW, provides better results [45,46]. DOS plots represents the inside picture of electronelectron correlation effects in a unit cell.…”

Comparative ab initio calculations of SrTiO3/BaTiO3 and SrZrO3/PbZrO3 (0 0 1) heterostructures

“…The BaTiO 3 /SrTiO 3 and PbZrO 3 /SrZrO 3 (0 0 1) interfaces present an excellent possibility for developing novel materials with outstanding properties, as well as they are extremely important in studying the fundamental physics of ferroelectric materials. Despite the huge technological importance of SrTiO 3 (STO), BaTiO 3 (BTO), SrZrO 3 (SZO) and PbZrO 3 (PZO) perovskites, and numerous ab initio studies of their (0 0 1) surfaces, [1][2][3][4][5][6][7][8][9][10][11][12][13], it is hard to understand, why only a small amount of ab initio and experimental studies exist dealing with BTO/STO (0 0 1) interface [14][15][16][17][18][19]. There are no experimental studies available, and only single ab initio calculation [20] exist dealing with PZO/SZO (0 0 1) interface.…”