Hexagonal perovskite-related layers

Perovskite-related Oxides.—The perovskite-related oxides have been studied extensively in recent years because of the large variety of device applications for which these materials are suited. The interaction between structure, properties, and stoicheiometry is significant at all levels, but here we will discuss only the narrow areas where intergrowth is a dominant structural feature. We will not, therefore, consider solid solutions typified by the Pb(Zr Tii )03 ferroelectrics, and neither will we discuss the structurally complex but stoicheiometric phases related to hexagonal BaTiOj, which includes BaNiOj, which has a simple two-layer repeat in the c-direc-tion, the nine layer BaRuOj, the twelve layer Ba4Re2CoOj2, and the twenty-four layer Sr5Re20ig phase. The crystal chemistry of these phases is treated in detail by Muller and Roy. The materials we shall discuss are the two series of phases A B 0 +2 and A + B 02n+, and the bismuth titanates. Some of the anion deficient perovskites, ABO -x, will be considered in Section 5. 

It is often convenient when describing the stractures of more complex perovskite-related phases (Chapters 2 and 3) to display the stmeture as linked ideal TiOg octahedra. The conventional view of the ideal perovskite stmeture (Figure 1.4a) is often shown tilted to make the (111) layers almost or exaedy horizontal (Figure 1.4b and c). More often the alkaline earth atoms are omitted and just the octahedral framework is shown (Figure 1.4d and e). Other projections, such as down [111], show the octahedra projected as hexagonal outlines or down [110] as diamond outlines (Figure 1.4f and g). 

As in all the perovskites — they might be defined that way — the A-and F-ions in the CsMnFs-structure form common close-packed layers AFs, in which the A-ion (Cs) displays a C. N. of 12 (Cs—F =3.12... 3.22 A in CsMnFs). The sequence ABC of three layers, characteristic of cubic perovskites, has been changed, however, to a hexagonal sequence of six layers ABC—ACB. This explains the relation found between the lattice constants ( hex = V2 eub Chex = 2 ]/3 acuu) from which follows Chex/ hex = ]/2 /3 = 2.45 or a value nearby. 

The structure of BaNiCh is closely related to perovskite (CaTiC>3, 3 2Pi/4 3/4O1/4), but the packing sequence is hep rather than ccp as for perovskite. The hexagonal cell contains two molecules, CB , C63me, a0 = 5.580 and c0 = 4.832 A. As shown in Figure 5.40, each Ni atom is at the center of an octahedron formed by six O atoms. With P layers at B and C positions all Ni atoms in O layers are at A positions, sharing three O atoms with another Ni atom. The Ba atom is at the center of a trigonal prism formed by six Ni atoms. The packing sequence of this structure is shown below ... 

Certain cations comparable in size with form c.p. layers AO3 which can be stacked in various c.p. sequences. Smaller cations can then occupy the octahedral holes between groups of six 0 ions to form structures of the type A B 03 . Some of these structures have been described in Chapter 4, and it was noted in Chapter 5 that these structures may alternatively be described in terms of the way in which the BOg octahedra are linked together. Only vertices and/or faces are shared, and the extent of face-sharing is indicated in Table 13.5. We shall deal in detail only with the simplest of the c.p. ABO3 structures, the perovskite structure. The structure of hexagonal BaTi03 is compared with perovskite in Fig. 13.1, and in Fig. 13.2 we show sections through the 5-, 9-, and 12- layer structures to illustrate the relations between the BOg octahedra. 

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