Ideal perovskite

Figure 4.34 Brownmillerite structure (a) ideal perovskite structure (circles indicate oxygen atoms that need to be removed to convert octahedra to tetrahedra in brownmillerite) and (b) idealized brownmillerite structure consisting of sheets of octahedra and tetrahedra.

The largest number of ideal perovskites synthesized to date are oxides of general formula AB03. Some examples are ... 

X-ray and diffuse neutron scattering and diffraction studies of PMN have been interpreted in terms of the spherical layer model of Vakhrushev et al. [25,26]. The Pb atom is not situated at the (000) position as it should be for an ideal perovskite lattice, but is distributed over a sphere of radius R around this position. 

As a is already determined by a and p, a is not necessarily the optimum value for that particular bond. This is analogous to the situation in Na3Pt04 (Sect. 2.9.2) and in the ideal perovskite structure (Sect. 2.2). To relieve the overdetermination, the symmetry must be lowered and it is perhaps significant that lower symmetries have been reported for some pyrochlores (e.g. Cd2Nb207) . ... 

The simple or idealized perovskite structure is shown in Figure 1. 

Figure 2 Metal-oxygen sublattice present in ideal perovskite.

The discussion so far has been based upon the idealized perovskite structure. At this point we may consider the real crystal structures observed in these materials. 

Fig. 13.3. The phase diagram of Ao.33A o.67Mn03 (A = divalent cation, A = rare earth) as a function of temperature and the global instability index of the idealized perovskite structure. The points show the observed transition temperatures in various compounds. FMM = ferromagnetic metal, PMI = paramagnetic insulator, FMI = ferromagnetic insulator (from Rao et al. 1998).

In an ideal perovskite structure for an ABO3 compound, the larger, A, ions are surrounded by twelve oxygens and the smaller, B, ions by six oxygens. Eq. (31) shows the ionic radii relationship for a close-packed arrangement. 

ABOs compounds containing lanthanum are closer to the ideal perovskite than those containing smaller rare earth ions. Compounds of the smaller rare earth ions appear to have a distorted perovskite structure of lower symmetry. When, however, the relationship between the radii is very far from being ideal (eq. 31), strong distortion may result giving an entirely different structure. The Goldschmidt tolerance factor, t, for the perovskite structure is related to the ionic radii by... 

However, the monoclinic phase differs strongly in the distortions of oxygen MnO ] octahedra with respect to ideal perovskite structure. The observed monoclinic phase is much closer to the rhombohedral phase, which could be achieved by the R point BZ rotation of the MnOel octahedra around (1 1 1) direction. 

It means that monoclinic structure is the result of freezing of E% vibrational mode in rhombohedral structure T point (this mode corresponds exactly to the R12 mode of ideal perovskite). 

The transition from rhombohedral to monoclinic phase is, in fact, the freezing of T BZ point Eg vibrational mode of R3>c space group or R BZ point R12 ideal perovskite mode. This vibration is double degenerate and the relation between components in transition corresponds to (J> 7t/2. 

Fava et al. (16) prepared Balh03 from stoichiometric amounts of BaO and TTT02 and observed an ideal perovskite, whereas Nakamura (17) found that an excess of BaO is necessary and identified a distorted perovskite structure. It is also not obvious why BaO is not taken up in solid solution with Balh03 (15) BaU03 is... 

The behaviour of Re03 in a variety of aqueous, acidic solutions has been studied and the nature of the species formed discussed.668 A low-temperature neutron-diffraction study of cubic Ba2CoReOe has shown that the oxygen atoms are slightly displaced from the positions of an ideal perovskite towards the rhenium atoms, and... 

In body-centred cubic coordination, the eight ligands surrounding a transition metal ion lie at the vertices of a cube (cf. fig. 2.6a.). In one type of dodecahedral coordination site found in the ideal perovskite structure (cf. fig. 9.3), the 12 nearest-neighbour anions lie at the vertices of a cuboctahedron illustrated in fig. 2.6b. The relative energies of the eg and t2g orbital groups in these two cen-trosymmetric coordinations are identical to those of the e and t2 orbital groups... 

FIGURE 2.18 AB03 ideal perovskite structure, (a) The center of the cube is occupied by the A cation and (b) the B cation placed in the center of the cube. 

Subsequently, the results reported in Figure 5.25 and Table 5.1 can be explained if we include, besides the three oxygen, all the sites in the ideal perovskite structure as possible absorption sites for hydrogen (see Figure 2.19b). 

The ideal perovskite (AB03) structure which is a simple cubic structure with the space group Pm3m, provides the basis for the structures of a large variety of inorganic solids. The perovskits structure is conventionally described as consisting of a B03 array... 

Fig. 1—(a) Ideal perovskite structure (b) layer sequence in the perovskite structure parallel to (001) and (c) GdFeOj structure. 

For example, the family of perovskite minerals and high-temperature ceramic superconductors exhibits this descent of symmetry, from the cubic "ideal" perovskite structure (space group Pm3m, the real mineral perovskite is orthorhombic, space group Pnma, with a fourfold larger unit cell than the ideal cubic one) to orthorhombic structures for the highest-critical... 

K2NiF4-related structures, also called Ruddleston-Popper phases, are built of slabs of perovskite structure cut parallel to the (idealized) perovskite 100 planes united by way of lamellae of halite (NaCl) structure. The series formula for these compounds is where A is a large cation,... 

A third series of perovskite related intergrowths has a general formula A B 03 +2, where A is a large cation, and B a medium sized cation, typified by the (Na,Ca) Nb 03 +2 series. The oxides are intergrowths of slabs of perovskite stracture with the halite structure. They differ from the Ruddleston-Popper series in that the (idealized) perovskite slabs are sliced along 110 rather than 100. ... 

It is well-established that pure and iron-substituted MgSiOs, quenched to ambient pressure and temperature, exhibit a distortion to the so-called GdFeOs type structure in which the Mg and Fe ions are only eightfold coordinated, not twelvefold coordinated as in the ideal perovskite structure. However, their structures under the lower-mantle conditions still remain uncertain, though some experimental evidence suggesting transitions toward the ideal stmcture at elevated pressures and temperatures has beeu reported. 

Figure 7 The structure of ABO3 ideal perovskite. A-site B-site oxide ion...

Materials containing the elements Y, Ba, Cu, and O, that are superconductors (electrical resistance equals zero) at temperatures above that of liquid nitrogen, were recently discovered. The structures of these materials are based on the perovskite structure. Were they to have the ideal perovskite structure, the superconductors would have the structure shown in part (a) of the accompanying figure. 

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