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. The mineral was first discovered in the Ural mountains of Russia by Gustav Rose in 1839 and named after Russian mineralogist L. A. Perovski. 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, often of very different sizes, and X is a negatively charged ion 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, which is rarely encountered. The orthorhombic and tetragonal 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, 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, the type 'B' atom sits at the body-center position and X atoms sit at face centered positions, and. 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

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 is another example of a simple defect perovskite. Here, all B sites are vacant, H⁻ occupies the O sites, and the large U³⁺ ion occupies the A site.
Many high temperature superconductors, especially cuprate superconductor, adopt defect perovskite structures. The prime example is yttrium barium copper oxide, which has the formula YBa₂Cu₃O₇. In this material Y³⁺ and Ba²⁺, which are relatively large, occupy all A sites. Cu occupies all B sites. Two O atoms per formula unit are absent, hence the term defect. The compound YBa₂Cu₃O₇ is a superconductor. The average oxidation state of copper is Cu⁺ since Y3+ and Ba2+ have fixed oxidation states. When heated in the absence of O₂, the solid loses its superconducting properties, relaxes to the stoichiometry YBa₂Cu₃O_6.5, and all copper sites convert to Cu²⁺. The material thus is an oxygen carrier, shuttling between two defect perovskites:

Layered perovskites

Perovskites can be deposited as epitaxial thin films on top of other perovskites, using techniques such as pulsed laser deposition and molecular-beam epitaxy. These films can be a couple of nanometres thick or as small as a single unit cell.
Perovskites may be structured in layers, with the structure separated by thin sheets of intrusive material. Based on the chemical makeup of their intrusions, these layered phases can be defined as follows:

Aurivillius phase: the intruding layer is composed of a ²⁺ ion, occurring every n layers, leading to an overall chemical formula of -. Their oxide ion-conducting properties were first discovered in the 1970s by Takahashi et al., and they have been used for this purpose ever since.
Dion-Jacobson phase: the intruding layer is composed of an alkali metal every n layers, giving the overall formula as
Ruddlesden-Popper phase: the simplest of the phases, the intruding layer occurs between every one or multiple layers of the lattice. Ruddlesden−Popper phases have a similar relationship to perovskites in terms of atomic radii of elements with A typically being large with the B ion being much smaller typically a transition metal.
Double perovskites

Double perovskites are ordered derivatives of the perovskite structure with the general chemical formula A₂BB′O₆, in which two chemically distinct cations occupy the B site in an ordered manner. From a crystallographic viewpoint, double perovskites can be described as superstructures of the simple ABO₃ perovskite, where periodic B/B′ ordering leads to a doubling of the primitive perovskite unit cell while preserving the three-dimensional network of corner-sharing octahedra.
The most prevalent ordering motif in double perovskites is rock-salt ordering of the B-site cations, resulting in alternating BO₆ and B′O₆ octahedra along all three crystallographic directions. This ordered arrangement lowers the translational symmetry relative to simple perovskites and introduces additional degrees of freedom for structural distortions and symmetry reduction.

Symmetry

Ideal rock-salt ordered double perovskites commonly adopt the cubic space group Fm3̅m. However, deviations from ideal ionic size ratios and bonding preferences frequently induce octahedral tilting and distortions, analogous to those observed in simple perovskites. These distortions can be systematically classified using Glazer tilt notation, although B-site ordering imposes additional symmetry constraints compared to ABO₃ systems.
The coupling between B/B′ ordering and octahedral tilting leads to a rich variety of reduced-symmetry structures, with monoclinic and orthorhombic space groups being particularly common among oxide double perovskites. Such symmetry lowering reflects the combined effects of lattice strain accommodation and cooperative octahedral rotations.

Cation ordering, disorder, and defects

In practice, perfect long-range B-site ordering is rarely achieved. A characteristic defect in double perovskites is antisite disorder, in which B and B′ cations exchange crystallographic positions. Antisite disorder disrupts the periodic potential associated with ideal rock-salt ordering and can significantly modify structural coherence and physical properties.
The degree of cation ordering is governed by differences in formal charge, ionic radius, and bonding character between the B-site cations, as well as synthesis conditions such as temperature and oxygen partial pressure. Experimental studies, particularly on thin films and epitaxial systems, have shown that ordering can be sensitively tuned through strain and growth conditions, highlighting the close interplay between crystallography and processing.

Electronic and magnetic properties

B-site ordering in double perovskites has important consequences for electronic and magnetic structure by modifying orbital hybridization, bandwidth, and superexchange pathways. Ordered arrangements of transition-metal cations enable magnetic interactions that are symmetry-forbidden or strongly suppressed in chemically disordered perovskites, leading to a wide range of magnetic ground states.
First-principles calculations further indicate that the double perovskite framework provides a versatile platform for tuning electronic structure through compositional control and ordering, allowing systematic variation of band gaps and carrier characteristics. These trends underscore the central role of crystallographic order in governing structure–property relationships in double perovskites.

Antiperovskites

The lattice of an antiperovskites is the same as that of the perovskite structure, but the anion and cation positions are switched. The typical perovskite structure is represented by the general formula ABX₃, where A and B are cations and X is an anion. When the anion is the oxide ion, A and B cations can have charges 1 and 5, respectively, 2 and 4, respectively, or 3 and 3, respectively. In antiperovskite compounds, the general formula is reversed, so that the X sites are occupied by an electropositive ion, i.e., cation, while A and B sites are occupied by different types of anion. In the ideal cubic cell, the A anion is at the corners of the cube, the B anion at the octahedral center, and the X cation is at the faces of the cube. Thus the A anion has a coordination number of 12, while the B anion sits at the center of an octahedron with a coordination number of 6. Similar to the perovskite structure, most antiperovskite compounds are known to deviate from the ideal cubic structure, forming orthorhombic or tetragonal phases depending on temperature and pressure.
Whether a compound will form an antiperovskite structure depends not only on its chemical formula, but also the relative sizes of the ionic radii of the constituent atoms. This constraint is expressed in terms of the Goldschmidt tolerance factor, which is determined by the radii, r_a, r_b and r_x, of the A, B, and X ions.

Tolerance factor =

For the antiperovskite structure to be structurally stable, the tolerance factor must be between 0.71 and 1. If between 0.71 and 0.9, the crystal will be orthorhombic or tetragonal. If between 0.9 and 1, it will be cubic. By mixing the B anions with another element of the same valence but different size, the tolerance factor can be altered. Different combinations of elements result in different compounds with different regions of thermodynamic stability for a given crystal symmetry.