The perovskite structures are adopted by many compounds with the stoichiometries ABO3. Examples of perovskite are BaTiO3, SrTiO3, PbTiO3, etc. In its ideal form, the perovskite structure is cubic with each A cation surrounded by 12 X anions and each B cation surrounded by 6 X anions. In fact, the perovskite structure may also be described as a close-packed array of A cations and O2- anions (arranged such that each A cation is surrounded by 12 O2- anions from the original close-packed layers; with B cations in all the octahedral holes that are formed from six of the O2- ions, giving Bn/4[AO3]n/4, which is equivalent to ABO3.
In oxides, X=O and the sum of the charges on the A and B ions must be +6. That sum can be achieved in several ways (A2+B4+ and A3+B3+ among them), including the possibility of mixed oxides of formula A(B0.5B′0.5)O3, as in La(Ni0.5Ir0.5)O3. The A-type cation in perovskites is therefore usually a large ion (of radius greater than 110 pm) of lower charge, such as Ba2+ or La3+, and the B cation is a small ion (of radius less than 100 pm, typically 60–70 pm) of higher charge, such as Ti4+, Nb5+, or Fe3+.
The mineral perovskite, CaTiO3, is the structural prototype of many ABX3 solids, particularly oxides. In fact, this is a very important structure type that is exhibited by a large number of other compounds.
By examining the structure, it is easy to see that a Ti4+ ion resides in the center of a cube, each corner of which is the location of a Ca2+ ion. The oxide ions are located at the center of the six faces of the cube. It is easy to see that the only bonds to the Ti4+ are those from its nearest neighbors, the six O2- ions. Therefore, each Ti–O bond must have a bond character of 4/6 because six such bonds total the +4 valence of Ti.
Consider now the bonds to each O2- ion in the perovskite structure. First, there are two bonds to Ti4+ ions that have a character of 4/6 each, which gives a total of 4/3. However, there are four Ca2+ ions on the corners of the face of the cube where an oxide ion resides. These four bonds must add up to a valence of 2/3 so that the total valence of 2 for oxygen is satisfied. If each Ca–O bond amounts to a bond character of 1/6, four such bonds would give the required 2/3 bond to complete the valence of oxygen. From this, it follows that each Ca2+ must be surrounded by 12 oxide ions so that 12(1/6) = 2, the valence of calcium.
Materials adopting the perovskite structure often show interesting and useful electrical properties, such as piezoelectricity, ferroelectricity, and high-temperature superconductivity.