Bulk SrZrOs

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). 

In Table 11.21 the calculated bandgaps (BG) for slabs are compared. It is clearly seen that in all cases the BG for SrZrOs systems is wider. This agrees with the larger ionicity of SrZrOs in comparison with SrTiOs. One can notice that in the case of SrTiOs the BG for the model I is markedly greater than that for models II and III. The substantial reduction of BG for the TiOs surface relative to the bulk value is due to an extended shoulder in the valence-band electronic DOS (see below). The same picture has been found in DFT PW calculations [829], in spite of the fact that the LDA gaps are half of others (see Table 11.21). 

In all figures below the zero energy is taken at the Fermi level of the bulk crystal (SrZrOs or SrTiOs) and aU curves were shifted so that the centers of O Is bands... 

It is clearly seen in Fig. 11.22 that the new O-subbands appear in the slabs at the top of the bulk VB. The corresponding peaks for the oxygen on an SrO-terminated SrZrOs surface (in models I and III) are significantly higher than the peaks for oxygen on Zr02-terminated surfaces. Also, the charge of the O atom in the first layer in SrO-terminated slab of a SrZrOs crystal is noticeably lower than its bulk value (1.50 vs. 

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