Ideal halide perovskites adopt a cubic ABX₃ lattice (space group Pm3̅m), but most undergo distortions (to tetragonal or orthorhombic symmetry) as a function of temperature, composition and ionic sizes. In the cubic form the B cation is octahedrally coordinated (6-fold) by X, and the A cation sits in a 12-fold cuboctahedral site formed by the vertices of eight adjacent BX₆ octahedra. (This can be quantified by the Goldschmidt tolerance factor t = (r_A + r_X) / √2(r_B + r_X), which must be ≈0.8–1 for a stable perovskite.)
For example, MAPbI₃ crystallizes in a tetragonal perovskite structure at room temperature, consisting of PbI₆ octahedra sharing corners, with MA⁺ cations occupying the interstitial spaces. Variants of the perovskite structure also exist: for instance, layered (2D) perovskites have alternating organic and inorganic sheets (formula A₂BX₄), and “double” perovskites (e.g. A₂BB′X₆) replace Pb²⁺ by a combination of a monovalent and trivalent cation to eliminate lead. However, the defining feature of halide perovskites is the 3D corner-sharing BX₆ framework with monovalent A ions in the cavities
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