Density functional simulation of the BaZrO 3 (011) surface structure Eugene Heifets,* Justin Ho, and Boris Merinov † California Institute of Technology, MS 139-74, Pasadena, California 91125, USA Received 30 September 2006; revised manuscript received 6 December 2006; published 25 April 2007 The atomic structure and charge redistribution of different terminations of BaZrO 3 011 surfaces have been studied using density functional simulations. We found that the O-terminated 011 flat surface had the smallest cleavage energy among 011 surfaces, but this value was still twice as large as for the formation of a pair of complimentary 001 surfaces. The density functional calculations allowed us to estimate the excess surface Gibb’s free energy and to compare stability of different 011 surfaces as a function of chemical environment. In addition, we compared stability of BaZrO 3 011 surfaces with respect to BaZrO 3 001 surfaces. Within boundaries, where BaZrO 3 does not decompose, only the Ba- and O-terminated 011 surfaces appeared to be stable. However, if 001 surfaces are also taken into consideration, the BaO-terminated 001 surface is the only stable surface among all considered 001 and 011 surfaces. DOI: 10.1103/PhysRevB.75.155431 PACS numbers: 68.35.Bs, 68.35.Md, 68.47.Gh, 73.43.Cd I. INTRODUCTION Doped barium zirconate BaZrO 3  is presently considered a very promising proton conducting material, which can be applied in a variety of electrochemical devices, including fuel cells, sensors, electrolysis cells, and hydrogen pumps. 1 BaZrO 3 is also used as a substrate for growing high- temperature perovskite superconductors. 2 In all mentioned applications BaZrO 3 shares surface contacts with other ma- terials. Detailed information on BaZrO 3 surface structures would therefore be very helpful for understanding the struc- ture and behavior of its interfaces with other materials. To our knowledge, no experimental investigations of BaZrO 3 surfaces have been reported yet. Recently, the first computational study of the BaZrO 3 001 surface structure 3 has been performed using density functionals defined in the local density approximation, 4 in the Perdew-Burke- Ernzerhof PBE version 5 of the generalized gradient ap- proximation, and within the full potential linearized aug- mented plane wave method. We performed a similar study 6 with a basis set from localized Gaussian type orbitals while employing a PBE functional. Our study also included a ther- modynamic analysis of the relative stability of 001 surfaces with different terminations. Among similar materials the most-studied surfaces are those of SrTiO 3 . Both crystals, BaZrO 3 and SrTiO 3 , have the same cubic perovskite struc- ture at ambient and elevated temperatures. Formal ionic charges are identical in these crystals. We expect that surface properties of both crystals are similar as well. The SrTiO 3 100 surface relaxation and rumpling have been studied ex- perimentally by means of several powerful techniques: Low energy electron diffraction LEED, 7 reflective high energy electron diffraction, 8,9 and metastable impact electron spectroscopy. 10 Theoretically, the SrTiO 3 001 surface has been studied by atomistic methods 11–16 and by various first- principle methods. 17–27 There are two types of 011 crystal planes in perovskites like BaZrO 3 . One crystal plane contains two oxygen ions in each unit cell, and the other contains single Ba 2+ , Zr 4+ , and O 2- ions per unit cell. Both of these planes are charged with density of ±4e per unit cell e is the absolute value of the electron charge. If 011 surfaces were prepared by cleaving a BaZrO 3 crystal between these planes, the resulting surfaces would be charged. Such surfaces are commonly defined as polar. They are unstable because excess charge density causes spurious electric fields. Stabilization of polar surfaces is possible with a reduction of the charge density at the sur- faces. In the case of crystals built from two equidistant non- equivalent charged crystal planes, like in BaZrO 3 , the charge density must be reduced by half with respect to its bulk value. 28 Investigations of 011 perovskite surfaces are less com- mon than 001 surfaces. At present only the data for SrTiO 3 011 crystal surfaces are available. The SrTiO 3 110 polar perovskite surface has been studied experimentally using LEED, 29 which showed a number of surface reconstructions at high temperatures. Atomic force microscopy measure- ments also support the existence of surface modifications resulting from applied extensive thermal treatment. 30,31 How- ever, there are no experimental data on the relaxations of the SrTiO 3 110 surfaces at low temperatures. A few semiempir- ical quantum mechanical calculations 32,33 have been pub- lished for this type of perovskite surfaces. Recently, the atomic relaxations for the polar 110 surfaces of SrTiO 3 and BaTiO 3 have been studied by atomistic simulations employ- ing the shell model. 34 The local-density approximation method with plane waves was used in the first ab initio study of these surfaces. 35 Another ab initio study of these SrTiO 3 surfaces applied the Hartree-Fock method and localized basis sets built from Gaussian-type atomic orbitals. 36 All theoreti- cal investigations mentioned above examined SrTiO 3 011 surfaces obtained by simply cleaving the crystals between 011 planes or by cleaving and incorporating additional electrostatic stabilization through removal of some surface ions. Calculations of the total energy allow comparison be- tween different surface configurations with constant chemi- cal composition. However, the composition of perovskite surfaces is subject to variations. Therefore, stabilities of these surfaces can be compared only by means of corre- sponding thermodynamical potentials. An appropriate model must include exchange of atoms between the surfaces and external reservoirs. This picture corresponds to a standard PHYSICAL REVIEW B 75, 155431 2007 1098-0121/2007/7515/15543115 ©2007 The American Physical Society 155431-1