First-principles calculations for the H center in SrF2 crystals.

The ground state of H-center systems for the SrF(2) crystal is simulated with two different arrangements, which are oriented along either [100] or [111] axes. The calculations are based on hybrid Hartree-Fock and density functional theory exchange functionals by using Becke's three-parameter method combined with the nonlocal correlation functionals of Perdew and Wang. The energy difference between H centers with different orientations shows that the H center oriented in the [111] direction in alkaline earth fluorides is the most stable configuration. The geometric relaxations of the neighboring atoms surrounding the H centers are presented. The combination energy of an H center and the formation energy of the related F-H pair in both alkaline earth fluorides are discussed. We report also the electronic structure of the H center systems. The effective charges and spins of the substitutional and interstitial fluorine atoms show that the hole is located at the interstitial fluorine in the system with the [111] orientation of the H center. The band structures are illustrated. With the help of studying the total and partial density of states, the constituents of the defect bands are clarified.

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 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.

The electronic properties of an oxygen vacancy at ZrO(2)-terminated (001) surfaces of a cubic PbZrO(3): computer simulations from the first principles.

Combining B3PW hybrid exchange-correlation functional within the density functional theory (DFT) and a supercell model, we calculated from the first principles the electronic structure of both ideal PbZrO(3) (001) surface (with ZrO(2)- and PbO-terminations) and a neutral oxygen vacancy also called the F center. The atomic relaxation and electronic density redistributions are discussed. Thermodynamic analysis of pure surfaces indicates that ZrO(2) termination is energetically more favorable than PbO-termination. The O vacancy on the ZrO(2)-surface attracts approximately 0.3 e (0.7 e in the bulk PbZrO(3)), while the remaining electron density from the missing O(2-) ion is localized mostly on atoms nearest to a vacancy. The calculated defect formation energy is smaller than in the bulk which should lead to the vacancy segregation to the surface. Unlike Ti-based perovskites, the vacancy-induced (deep) energy level lies in PbZrO(3) in the middle of the band gap.