Surfaces cubic perovskites

The oxide Ba Inp adopts the brownmillerite structure at lower temperatures (Section 2.4). The structure begins to disorder at approximately 900°C and forms a cubic perovskite phase with a high concentration of oxygen vacancies somewhere above this temperature. Proton conduction in the solid is brought about by the incorporation of water molecules. Water vapour can react directly with the oxide at higher temperatures, following disproportionation at the oxide surface ... 

Two competing types of phenomena that arise at the ferroelectric interfaces can affect the properties of the superlattices. The strain field, generated by the mechanical mismatch between superlattice layers, influences the polarization orientation and generally increases the ferroelectric transition temperature Tc [32]. In contrast, the electric depolarization field, produced by interfacial surface charges is unfavorable to formation of the ferroelectric phase [33]. In fact, in cubic perovskite-like ferroelectrics the situation can be even more complex due to both 180° ferroelectric [27] and 90° ferroelastic [21, 32, 34] domain formation. 

In the next sections we describe the slab models of the surface and illustrate the choice of the slab by examples of metal oxides with sodium chloride, rutile and cubic perovskite structures. 

Table 11.3 gives the formal plane charges in the stack of different surfaces in the cubic perovskite ABO3 crystal with one formula unit in the primitive unit ceU. The bulk atoms distribution over atomic planes is shown on Fig. 11.4. 

Fig. 11.4. Stacking of atomic planes for cubic perovskite ABO3 surfaces...

All the surfaces in cubic perovskite structure are type-3 surfaces being stcicks of alternately charged planes. It is less obvious in the case of the (001) surface in AiiBiVQg as the repeat unit consists of neutral atomic planes (see below). It is also seen that the charge of the atomic plane depends both on the oxidation states of A and B atoms (the sum of oxidation states is in all cases 6) and MiUer indexes of the surface. 

For the cubic perovskite ABO3 (001) surface the nonstoichiometric slabs with AO or BO2 terminations can be introduced. Figure 11.4 shows a AO-terminated slab, consisting of 7 atomic planes - 4 AO planes and 3 BO2 planes. As is seen from Fig. 11.4, the slab termination is different for different surfaces. 

The symmetry of the 3D-slab model is given by one of the 3D space groups G (see Table 11.1) and may depend on the slab thickness, i.e. number of layers in the slab and its termination. As is seen from Fig. 11.1, for MgO crystal (001) surface slabs of an odd number of atomic planes have inversion symmetry (relative to the central atomic plane) but slabs of an even number of atomic planes have no inversion symmetry. For the cubic perovskite ABO3 (001) surface the stoichiometric slabs (AO-BO2-AO-BO2-) consist of an even number of atomic planes and have no inversion symmetry. But the nonstoichiometric AO- or B02-terminated slabs have inversion symmetry relative to the central AO or BO2 planes, respectively. 

The first attempt to compare 2D- and 3D-slab models within the same calculation scheme was made in [775] for HF LCAO studies of the surface properties of BaTiOs in the cubic perovskite structure. The authors of [775] concluded that results for periodic 3D-slabs are systematically affected by the interactions among repeated images, and possibly the fictitious field imposed by periodic boundary conditions. 

In the next section we consider the surface modeling in cubic perovskites. 

We discuss here in more detail the results of a hybrid HF-DFT LCAO comparative study of cubic SrZrO and SrTiOa (001) surface properties in the single-slab model [825). As known from [824], the consideration of systems with 7 8 atomic layers is sufficient to reproduce the essential surface properties of cubic perovskites. Three different slab models have been used in [825]. The first (I) and the second (II) ones consist of 7 crystalline planes (either SrO- or MO2-terminated, respectively) being symmetrical with respect to the central mirror plane but nonstoichiometric (see Fig. 11.4). The central layer is composed of MO2 (M = Ti, Zr) units in the model 1 and SrO units in the model 11. Both models 1 and 11 have been apphed for studying the surface properties of titanates by ab-initio calculations [832]. The asymmetric model 111 is stoichiometric and includes 4 SrO and 4 MO2 atomic planes. Accordingly, it is terminated by a SrO plane on one side and by a MO2 plane on the other side and there is no central atomic layer. The model 111 has been included in the simulation to investigate the influence of the stoichiometry-violation in the symmetrical models 1 and II on the calculated surface properties. For all slabs a 1 x 1 surface unit cell has been taken. For the 2D translations in slabs the experimental bulk lattice constants of SrZrOs (4.154 A) and SrTiOs (3.900 A) were used that does not differ significantly from DFT B3PW LCAO theoretical values (4.165 A and 3.910 A respectively). 

Dl, particle size calculated from the Sherrer equation Sjh, specific surface area calculated assuming cubic particles and a density of LaCo03 equal to 7.29 D2, equivalent cubic particle size calculated from BET surface area. P, perovskite C, cobalt oxide. 

Regarding the morphology, a polyhedron terminated by the (001) face is expected for cubic II-IV perovskites, i.e., AB03 perovskites in which A and B are divalent and tetravalent, respectively. In these perovskites, two nonpolar (001) surface terminations are possible (AO and BO2). On an A-O terminated surface, the cation A is octa-coordinated, whereas on the BO2 terminated surface the cation B is penta-coordinated. Ill—III perovskites, bulk structures with lower symmetry, are more stable (orthorombic or rhombohe-dral) than II-IV perovskites, and the nonpolar low-index faces are more complex and show a different coordinative environment for both A and B cations. 

Figure 1 presents the dependence of the catalytic activity and isobutane selectivity of samples precipitated at pH = 9 on the CaO concentration. This study made it possible to evaluate the role of the cubic solid solution in their catalytic properties. One can see an obvious maximum on the dependence of the activity on the alkaline earth metal concentration in the structure of Zrj.xCaxOz-x solid solution. Without calcium the catalytic activity is low. This agrees with the literature data that sulfation of a calcined monoclinic phase without any special treatment does not yield an active catalyst [9]. The maximum activity is observed for the samples with the CaO concentration of 5-10 mol.%. The material with the calcium concentration of 50 mol.% does not show any catalytic activity at all. This sample is mostly composed of perovskite crystalline phase CaZrOs. A comparison of the catalytic activity of the samples with their surface areas clearly indicates that the activity growth is mostly caused by the formation of the cubic phase rather than just by an increased surface area. 

Ultrafme pure BaTi03 powders were obtained by a modified oxalate precipitation method as described previously [13], The powders had a specific surface area of 57 m g and the particle size was nearly spherical from 20 to 30 nm. The main impurities contained in the powders were at the following levels 0.04 wt% Sr, 0.02 wt% Na, and 0.006 wt% K. The Ba/Ti atomic ratio was 1 0.003 for all the powders. The X-ray diffraction (XRD) patterns of nanocrystalline powders apparently correspond to a pseudo-cubic structure without peak splitting of lines such as (002) and (200). We also used Raman spectra to detect local symmetry of the nanocrystalline powder samples. It showed that the local symmetry in the nanopowder appears to be a cubic structure even at a very low temperature of 123 K. Therefore, XRD patterns and Raman spectra revealed that the BaTiOs powder exhibited the commonly reported pseudocubic perovskite structure. 

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