Perovskite ABX3 Structures

Figure 3.18. The cubic ABX3 perovskite structure. The B cations (dark gray circles) are at the vertices of the octahedra (the midpositions of the ceii edges) and the A cation (light gray circle) is located in the center of the cube. Anions are at the corners of the cube.

Fortunately much of this diversity can be understood or rationalised in terms of an ideal cubic perovskite structure. In this chapter the ideal ABX3 perovskite structure is described together with some of the structural variations that occur which have significance for chemical and physical properties and which make precise structure determination a difficult task. 

Fig. 17a-c. The ideal cubic-perovskite structure for ABX3 and ordered A2BB Xs... 

FIGURE 1.44 The perovskite structure of compounds ABX3, such as CaTiOa- See colour insert following page 196. Ca, green sphere Ti, silver spheres 0, red spheres. 

The basic perovskite structure ABX3 forms the prototype for a wide range of other structures related to it by combinations of topological distortions, substitution of the A, B and X ions, and intergrowth with other structure types. These compounds exhibit a range of magnetic, electrical, optical, and catalytic properties of potential application in solid state physics, chemistry, and materials science. 

Structures for some common ternary compounds, (a) The perovskite structure for which the general formula is ABX3. The Ti is surrounded octahedrally by six oxide ions each O is surrounded by two Ti ions and four Ca ions. Each Ca is surrounded by 12 O ions, (b) The structure of compounds that have the formula AB2X2. 

FIG. 13.3. (a) The perovskite structure for compounds ABO3 (or ABX3). Large open circles represent 0 (or F) ions, the shaded circle A, and the small circles B ions, (b) The crystal structure of ReOs. 

When the A ion in an ABX3 compound is too small to form the perovskite structure, say when its radius is less than about i-o A, the alternative ilmenite arrangement sometimes occurs. This structure is closely related to that of corundum and haematite ( 8.46) and may be described as an hexagonal close-packed array of X ions (usually oxygen ions) with A and B ions each occupying one-third of the octahedrally co-ordinated interstices. Thus both A and B ions are now 6-co-ordinated by anion neighbours. 

Fig. 2. ABX3 ideal perovskite structure (a), cation A, or (b), cation B, at the center of the unit cell. (Reprinted by permission from Ref. 15.)...

In the last years, the research on catalysts has paid much attention to systems with perovskitic structure, of general formula ABX3, where A and B are usually cations of rare-earth and transition metals, respectively, and X is a non-metallic element (usually oxygen). The crystalline structure is characterised by a cubic cell in which A cations have a larger ionic radius and are co-ordinated with twelve X anions, while cations B, with a lower ionic radius, are co-ordinated with six anions. 

The perovskite family is one of the most important representative among a large variety of inorganic compoimds. The majority of chemical elements from the periodic table can form ABX3 compounds with the perovskite structure (Goodenough and Longo, 1970 Goodenough, 1971 Fesenko, 1972 Reller, 1993 Woodward,... 

SVM applied to mathematical modeling for the relative stability of perovskite structure and the hexagonal ABX3 structures involving face-shared octahedra ... 

It can be found that most of the systems without 1 1 compound formation have the radius ratio (Rj/Rx) 0.414. This fact can be explained by Pauling s first rule about the structure of complex ionic crystalline compounds (Rb/Rx) 0.414 means the BXg octahedron unstable, while BXe octahedron is one of the basic parts of perovskite structure. Therefore compounds ABX3 with (Ri/Rx) 0.414 can not form stable perovskite-type lattice, even if the value of tolerance factor t is in the favorable range for perovskite formation. 

Perovskite structure for ABX3 compounds. The quadravalent A cation is located in the center (darker sphere), octahedrally coordinated by the six divalent anions on the faces. The divalent cations sit on the comers, octahedrally coordinated by the six anions on the faces. 

The perovskite structure is a close-packed lattice with the general formula ABX3. Almost all the known rare earth perovskites are oxides with the rare earth ion occupying the A sites and the present discussion will hence be restricted to ABO3 type compounds. Since most of the rare earth ions are stable only in the trivalent state the valence relationship is A B " 03. It is much easier to obtain the compounds in polycrystalline than in single crystal form however in some instances crystals have been prepared for special applications. 

Notwithstanding, it was foxmd that the cubic perovskite structure, or slightly distorted variants of it, was still retained in ABX3 compounds even where this relation is not exaetly obeyed. As a measure of the deviation form ideality Goldschmidt [21], introduced a tolerance factor t, deirned as,... 

The perovskite structure, which is adopted by a large number of mixed-metal oxides [7], has ABX3 stoichiometry, where A and B are cations and X is an anion. The ideal perovskite structure, shown in Fig. 1, has the A-site cation occupying a 12-coordinate site within a framework of comer-connected [BXg/2] octahedra. The tolerance factor is a geometrical relationship based on a hard sphere model of the atom that gives a measure of the fit of the A-site cation to the octahedral framework. Mathematically the tolerance factor ( ) is given by the following expression, t = (1/V5) [( a + rx)/ rv, + x)]. where Ta, r, and rx are the radii of the A, B, and X ions, respectively. When f = 1 the A-site cation is a... 

Fig. 1 Crystal structure of a cubic ABX3 perovskite. Orange spheres represent the A cation, blue spheres B cations, and red spheres X anions...

The observed and predicted global instability index versus tolerance factor for untilted cubic ABX3 perovskites is shown in Fig. 4. As expected the G is smallest for compounds with a tolerance factor near 1. For unstrained structures the normal maximum value of G is 0.2 v.u., but here we see a number of compounds where G > 0.2. This can be explained in part by realizing that when t is significantly different than 1 the compounds can be classified as strained. The largest G observed (G = 0.47) is for KTa03 t = 1.08) which has shown on multiple occasions to be a cubic perovskite [13, 30, 31]. These studies used samples prepared with several synthetic techniques and both polycrystalline powders and single crystals have been examined, which support the accuracy of the crystal structure. 

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