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Perovskite structures are adopted by many [[compound]]s that have the chemical formula ABX<sub>3</sub>. The idealized form is a cubic structure ([[space group]] Pm{{overline|3}}m, 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) structures are the most common non-cubic variants. Although the perovskite structure is named after [[Calcium titanate|CaTiO<sub>3</sub>]], this mineral has a non-cubic structure. [[Strontium titanate|SrTiO<sub>3</sub>]] and CaRbF<sub>3</sub> 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.<ref>{{Cite book|doi=10.1002/9780470022184.hmm411|chapter=Crystallography and Chemistry of Perovskites|title=Handbook of Magnetism and Advanced Magnetic Materials|year=2007|last1=Johnsson|first1=Mats|last2=Lemmens|first2=Peter|arxiv=cond-mat/0506606|isbn=978-0470022177|s2cid=96807089}}</ref>
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
Four general categories of cation-pairing are possible: A<sup>+</sup>B<sup>2+</sup>X<sup>−</sup><sub>3</sub>, or 1:2 perovskites;<ref>{{Cite journal|last1=Becker|first1=Markus|last2=Klüner|first2=Thorsten|last3=Wark|first3=Michael|date=2017-03-14|title=Formation of hybrid ABX3 perovskite compounds for solar cell application: first-principles calculations of effective ionic radii and determination of tolerance factors|url=https://pubs.rsc.org/en/content/articlelanding/2017/dt/c6dt04796c|journal=Dalton Transactions|language=en|volume=46|issue=11|pages=3500–3509|doi=10.1039/C6DT04796C|pmid=28239731|issn=1477-9234}}</ref> A<sup>2+</sup>B<sup>4+</sup>X<sup>2−</sup><sub>3</sub>, or 2:4 perovskites; A<sup>3+</sup>B<sup>3+</sup>X<sup>2−</sup><sub>3</sub>, or 3:3 perovskites; and A<sup>+</sup>B<sup>5+</sup>X<sup>2−</sup><sub>3</sub>, or 1:5 perovskites.
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