Solid State Chemistry and its Applications. Anthony R. West

variations have been found. It is difficult to give clear guidelines as to which distorted or tilted structure may form for a particular composition because other factors may also be involved, including possible oxygen non‐stoichiometry and distortions of cation‐oxygen octahedra containing either Jahn‐Teller active cations or lone pair p‐block cations

      As well as the rock salt arrangement of B site cations, other ordered arrangements occur, especially in materials in which the B:B′ ratio is different from 1:1. Ideal 1:2 double perovskites typified by Ba₃SrTa₂O₉ have layered BB′ arrangements that are ordered along [111]_p. The AO₃ layers are separated by alternating layers of, in this case, Sr and Ta cations in octahedral sites. The ordering causes the structure to show a small rhombohedral distortion from the cubic symmetry of the parent perovskite. This ordered structure has a nine‐layer repeat consisting of six BaO₃ layers, two Ta layers and one Sr layer. Other members of the 1:2 family also show partial disorder of the BB′ sites and/or various tilted arrangements. A particularly important example is PbMg_1/3Nb_2/3O₃, referred to as PMN, in which the BB′ cations are neither fully ordered nor disordered but instead, form nanoscale ordered domains within a disordered lattice, resulting in a very high and temperature‐independent permittivity, leading to applications of PMN as a relaxor ferroelectric.

      The above examples concern B site order; A site order also occurs, as in NaLaMgWO₆, CaMnTi₂O₆ (Mn²⁺ on A sites) and notably, in the oxygen‐deficient superconducting phase YBa₂Cu₃O₇, Fig., in which the Cu coordination number is reduced from 6 to a mixture of 5 and 4. A strongly tilted arrangement with 1:3 A site order is shown by CaCu₃Ti₄O₁₂, Section 1.17.7.4, which has aroused recent interest as a supposed ‘giant dielectric’; however, the greatly reduced tolerance factor associated with Ca and Cu as A‐site cations causes extensive tilting, leading to square planar coordination for Cu.

       1.17.7.8 Hybrid organic–inorganic halide perovskites

      So far, we have considered A sites to be occupied, fully or partially, by large cations such as K⁺, Ba²⁺ and La³⁺. In a family of hybrid organic–inorganic perovskites, the A sites are large enough to contain ammonium, NH₄ ⁺ and small organic derivative cations such as methylammonium, MA (CH₃NH₃)⁺, tetramethylammonium, TMA [(CH₃)₄N]⁺ and formamidinium, FA (NH₂=CHNH)⁺. The inorganic BX₃ framework of corner‐sharing octahedra typically consists of the divalent cations of Ge, Sn or Pb with the larger halogens Cl, Br and I. These hybrid perovskites display a range of structural variants, including (i) tilted structures based on the BX₃ octahedra and (ii) ordered arrangements, based on the non‐spherical A cations, which may undergo phase transitions to disordered cubic structures with increasing temperature. In recent years, there has been great interest in these hybrid perovskites for high efficiency, solar cell applications.

      A very extensive family of hybrid layered or intergrowth perovskites has been reported which contain large organic cations that cannot fit within the A‐site cages. Instead the structures consist of BX₃ layers in various orientations: [100], [110] or [111], separated by layers of organic cations. The inorganic BX₃ component may be either a single layer or a multilayer block, similar to those found in the [100] orientation in the Ruddlesden–Popper family of perovskite‐rock salt intergrowth structures, Section 1.17.14. The polar, NH₃ ⁺ end of the organic component is bonded ionically to the anions of the inorganic layer and usually, the organic component consists of double layers in a head‐to‐head arrangement for bonding to the inorganic layers to either side. Given the many possible compositions for the organic component, which usually consists of chains of different lengths and with various side groups attached, there is great scope for generating novel hybrid layered perovskites. This provides one way to modify the properties that are associated primarily with the inorganic component of the structure.

       1.17.7.9 Anti‐perovskites

      The anti‐perovskites have the inverse of the expected cation–anion distribution. In these: X sites contain large atoms such as alkaline earth and rare earth elements; the octahedral B sites contain anions or small atomic species; a range of metallic elements or larger halogens occupy the A sites. However, it is difficult to give a description of a typical anti‐perovskite material. Some are best regarded as interstitial alloys, such as Fe₃NPt in which N occupies octahedral sites within the cubic close packed Fe₃Pt lattice. Others have metallic elements on the A sites and have properties and bonding that are intermediate between ionic and metallic, such as BiNCa₃, SnNNd₃ and MgCNi₃. Another group is a range of oxy‐compounds such as Na₃OCl, K₃OBr, Ag₃IS, Ca₃NAs and Cs₃OAu. Most have undistorted cubic structures analogous to SrTiO₃, but distorted structures also occur.

       1.17.7.10 Mixed anion perovskites: oxynitrides and oxyfluorides

      The oxide O²⁻, nitride N³⁻ and fluoride, F⁻ ions are of similar size and can readily substitute for each other in crystal structures, other although the number of mixed anion systems that have been studied and reported in the literature are far fewer than those of mixed cation‐based materials. The reasons for this are that first, oxynitrides do not usually have the same thermal stability as corresponding oxides since metal‐oxygen bonds are usually stronger than metal‐nitrogen bonds. Controlling the N stoichiometry presents difficulties during synthesis if N₂ gas is lost in an ‘open’ reaction. Second, the synthesis of oxyfluorides requires stringent safety precautions if F₂ gas is involved.

      A range of oxynitride perovskites are known with a 2:1 ratio of O:N and an overall cation charge of 7+. These include II/V cation charge combinations in ATaO₂N: A=Ca, Sr, Eu and III/IV combinations in ATiO₂N: A=Ce, Pr, Nd. Oxynitride perovskites with a 1:2 ratio of O:N form, such as LaTaON₂ and EuWON_2. Given the similar sizes but different valencies of O²⁻ and N³⁻, there is also much scope for the preparation of non‐stoichiometric oxynitrides that have variable O:N ratios together with different cation combinations, including mixed valence cations, to maintain charge balance.

      O and N are either disordered or ordered, fully or partially, in these perovskites and similar tilted or distorted structures occur to those found in oxide perovskites. For instance, LaZrO₂N, Ca(Ta,Nb)O₂N and NdTiO₂N adopt the GdFeO₃ structure with tilt system a ⁺ b ⁻ b ⁻ , whereas LaTiO₂N adopts the a ⁻ b ⁻ c ⁻ tilt system. In ordered 2:1 oxynitrides such as Sr(Nb,Ta)O₂N, the [(Nb,Ta)O₄N₂] octahedra show strong preference for a cis arrangement of the two N positions. Each N forms a linear B‐N‐B segment in the linkage of corner‐sharing octahedra; additional bonding interactions involving the transition metal d orbitals are believed to be responsible for the commonly observed cis configurations.

      Oxide perovskites exhibit a very wide range of electrical, magnetic and optical properties and these may be modified by substitution of N for O in oxynitrides. The property modifications are associated with the lower electronegativity of N than O which leads to (i) more covalent metal‐nitrogen bonds compared with the more ionic metal‐oxygen bonds and (ii) a consequent reduction in the band gap of oxynitrides and nitrides. The band gap is frequently in the visible part of the electromagnetic spectrum and can be fine‐tuned by adjusting the O:N ratio, leading to a range of brightly coloured materials with applications as non‐toxic pigments and in visible light, photocatalytic water‐splitting processes.

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