Perovskite structure

A perovskite is a crystalline material of formula ABX₃ with a crystal structure similar to that of the mineral perovskite, this latter consisting of calcium titanium oxide (CaTiO₃). The mineral was first discovered in the Ural mountains of Russia by Gustav Rose in 1839 and named after Russian mineralogist L. A. Perovski (1792–1856). In addition to being one of the most abundant structural families, perovskites have wide-ranging properties and applications.

Structure

Perovskite structures are adopted by many compounds that have the chemical formula ABX₃. 'A' and 'B' are positively charged ions (i.e. cations), often of very different sizes, and X is a negatively charged ion (an anion, frequently oxide) that bonds to both cations. The 'A' atoms are generally larger than the 'B' atoms. The ideal cubic structure has the B cation in 6-fold coordination, surrounded by an octahedron of anions, and the A cation in 12-fold cuboctahedral coordination. Additional perovskite forms may exist where both/either the A and B sites have a configuration of A1_x-1A2_x and/or B1_y-1B2_y and the X may deviate from the ideal coordination configuration as ions within the A and B sites undergo changes in their oxidation states. 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. 38) and tetragonal (e.g. space group I4/mcm, no. 140, or P4mm, no. 99) structures are the most common non-cubic variants. Although the perovskite structure is named after CaTiO₃, this mineral has a non-cubic structure. SrTiO₃ and CaRbF₃ 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 X atoms (typically oxygen) 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 X at face-centered positions.

Four general categories of cation-pairing are possible: A⁺B²⁺X⁻₃, or 1:2 perovskites; A²⁺B⁴⁺X²⁻₃, or 2:4 perovskites; A³⁺B³⁺X²⁻₃, or 3:3 perovskites; and A⁺B⁵⁺X²⁻₃, 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 BO₆ 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 BaTiO₃ that distort in this fashion.

Complex perovskite structures contain two different B-site cations. This results in the possibility of ordered and disordered variants.

Defect perovskites

Rhenium trioxide is a simple example of a defect perovskite: the central atom found in classical perovskites is absent., 144px
Also common are the defect perovskites. Instead of the ideal ABO₃ stoichiometry, defect perovskites are missing some or all of the A, B, or O atoms. One example is rhenium trioxide. It is missing the A atoms. Uranium trihydride

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