text: Perovskite structures are adopted by many oxides that have the chemical formula ABO. The idealized form is a cubic structure (space group Pmm, no. 221) which is rarely encountered. The orthorhombic (e.g. space group Pnma, no. 62, or Amm2, no. 68) and tetragonal (e.g. space group I4/mcm, no. 140, or P4mm, no. 99) phases are the most common non-cubic variants. Although the perovskite structure is named after CaTiO, this mineral forms a non-idealized form. SrTiO and CaRbF are examples of cubic perovskites. Barium titanate is an example of a perovskite which can take on the rhombohedral (space group R3m, no. 160), orthorhombic, tetragonal and cubic forms depending on temperature.
  In the idealized cubic unit cell of such a compound, the type A atom sits at cube corner position (0, 0, 0), the type B atom sits at the body-center position (1/2, 1/2, 1/2) and oxygen atoms sit at face centered positions (1/2, 1/2, 0), (1/2, 0, 1/2) and (0, 1/2, 1/2). The diagram to the right shows edges for an equivalent unit cell with A in the cube corner position, B at the body center, and O at face-centered positions.
  Four general categories of cation-pairing are possible: ABX, or 1:2 perovskites; ABX, or 2:4 perovskites; ABX, or 3:3 perovskites; and ABX, or 1:5 perovskites.
  The relative ion size requirements for stability of the cubic structure are quite stringent, so slight buckling and distortion can produce several lower-symmetry distorted versions, in which the coordination numbers of A cations, B cations or both are reduced. Tilting of the BO octahedra reduces the coordination of an undersized A cation from 12 to as low as 8. Conversely, off-centering of an undersized B cation within its octahedron allows it to attain a stable bonding pattern. The resulting electric dipole is responsible for the property of ferroelectricity and shown by perovskites such as BaTiO that distort in this fashion.
  Complex perovskite structures contain two different B-site cations. This results in the possibility of ordered and disordered variants.