1.17.7.11 Hexagonal perovskites
Hexagonal perovskites form when the tolerance factor is somewhat greater than unity. This is summarised schematically in the structure – field map, Fig. 1.42(f), in which A and B cation radii form the two axes. The crossover between different phase fields is not a rigid boundary, but is also a rich source of polymorphic structures, such as shown by BaTiO3 which exhibits both hexagonal and cubic perovskite polymorphs at temperatures above and below about 1450 °C, respectively.
The cubic perovskites considered so far may be regarded as layer structures in which cp AO3 layers are arranged in a ccp stacking sequence. Hexagonal perovskites also contain cp AO3 layers in which A is usually Ba, but the stacking sequence is either hcp or a more complex structure with a combination of ccp and hcp stacking. A useful and simple nomenclature to describe these mixed stacking sequences is to label a particular AO3 layer according to whether, in combination with the layers on either side, the local arrangement is hcp or ccp. Thus, if the layers on either side are in a similar position, the sequence is labelled h but if the layers to either side are in different positions, it is labelled c.
A major, and significant, difference between structures containing ccp and hcp anions concerns the relative positions of available tetrahedral and octahedral sites for occupancy by cations. In an hcp anion array, the octahedral cation sites form face‐sharing columns in one direction, as shown by NiAs, giving rise to short metal‐metal distances across the shared faces (and metallic bonding in NiAs). Face‐sharing of octahedral sites does not usually occur in ionic structures unless there is some kind of positive bonding interaction between the cations involved. In cubic perovskite, by contrast, the BO6 octahedra are well‐separated and share corners since only ¼ of the available octahedral sites that are suitable for cation occupancy have oxygen at all six corners (however, in a ccp structure such as rock salt in which all octahedral sites are occupied by cations, the octahedra share edges, Fig. 1.32).
Hexagonal perovskites form because their tolerance factor has a value greater than unity which means that, in a corresponding cubic perovskite, the B–O bonds would be somewhat elongated, as in Fig. 1.41(h). There is, therefore, a competitive energy balance between having either elongated B–O bonds or reduced B–B distances respectively, in the cubic and hexagonal perovskite structure types. The balance can be tipped in favour of one or other structure by either changes in temperature or doping, as observed with BaTiO3 in which either increased temperature or certain dopants lead to a transition from a cubic to a hexagonal structure.
The short metal‐metal distances in hexagonal perovskites appear to be facilitated by positive bonding interactions involving the d electrons of the transition metal B cations that act to counteract the effects of cation‐cation charge repulsion. The common occurrence of polytypism in the family of hexagonal perovskites, with mixed h,c stacking sequences of the AO3 layers, can be related to the formation of localised metal‐metal pair interactions. Strictly, the term polytypism refers to different stacking arrangements for the same composition (such as found with the many stacking sequences shown by silicon carbide) but here, it is convenient to use the term to allow compositional differences as well since there is a very large family of hexagonal perovskite compositions that are characterised mainly by different stacking sequences. Two other ways which illustrate reduced cation‐cation repulsions are observed in (i) structures that contain a low valence cation in some of the B sites, as in Ba4Nb3LiO12 and (ii) structures with some B site vacancies, as in Ba5Ta4O15.
The simplest hexagonal perovskite structure is that of BaNiO3 which is entirely hcp. It contains infinite chains of face‐sharing NiO6 octahedra running perpendicular to the BaO3 layers, with Ni in the 4+ valence state. An [001] projection of four unit cells is shown in Fig. 1.42(g). Two face‐sharing octahedra form the repeat unit along the c cell edge; the octahedra are highlighted at the right hand side in (g) and shown from a different perspective in (h) together with some of the Ba atoms that form the cp BaO3 layers. Other oxides that have a similar structure with h stacking of layers are BaMnO3, BaCoO3 and SrCoO3.
In most other hexagonal perovskites, the metal‐metal pair interactions do not extend as far as forming infinite columns of face‐sharing octahedra in a complete hcp anion array, as in BaNiO3. Thus, pairs of face‐sharing octahedra occur in BaRuO3 which are linked by corner‐sharing to adjacent pairs to give the ch sequence, as shown in (i); this may be written more completely as (ch)2 to indicate that two pairs form the repeat in the c unit cell direction and is alternately given the label 4H, referring to a 4‐layer repeat unit with overall hexagonal symmetry. In hexagonal BaTiO3, face‐sharing pairs are separated by single layers of a cubic structure, (j), to give the polytype (cch)2. In Ba8Ta4Ti3O12, (k), the stacking sequence is (cchc)2 and in Ba10Ta7.04Ti1.2O30 (l), the sequence is (cchcc)2. Many materials with more complex polytypic sequences have also been synthesised; overviews of these and other perovskite‐derivative structures, including those containing two types of cp layers which introduce an additional structural complexity, are given in the books by Tilley and Mitchell.
A recent development that has given fresh impetus to the study of hexagonal perovskite derivative phases is the discovery of a high level of oxide ion conductivity in Ba3MNbO8.5:M = Mo, W. The structure is a hybrid of two separate structures: first, a 9‐layer hexagonal perovskite, (hhc)3 of formula A3B2O9 that contains face‐sharing trimers of octahedra linked through their corners; second, a structurally related, but oxygen‐deficient palmierite structure in which (i) one of the AO3 layers has instead the stoichiometry AO2, (ii) the B cations are displaced from their octahedral sites to form layers of tetrahedra and (iii) the overall formula is A3B2O8. Given the wide range of hexagonal perovskites and their derivatives that are already known, many of which are similarly oxygen‐deficient, the discovery of other new oxide ion conducting materials in this family, as well as possible mixed conductors, may be anticipated.
1.17.8 Rhenium trioxide (ReO3), perovskite tungsten bronzes, tetragonal tungsten bronzes and tunnel structures
The structure of cubic ReO3 is closely related to the perovskite described above. It is the same as the ‘TiO3’ framework of perovskite, SrTiO3, but without the Sr atoms. Its unit cell is the same as that shown in Fig. 1.41(a) with Re at corners and O at edge centres. A few oxides and halides form the ReO3 structure, Table 1.20, together with an example of the anti‐ReO3 structure in Cu3N.
A wide variety of oxide and oxyfluoride structures, often with complex formulae, can be derived from the ReO3 structure by coupled rotation of groups of octahedra. To see this, we start with the ideal cubic ReO3 structure shown in Fig. 1.43(a). Each octahedron shares its six corners with other octahedra and in 2D, layers of corner‐sharing octahedra are obtained. In the cubic perovskite structure, large 12‐coordinate cavities are occupied by A cations, ideally without modification of the array of octahedra, (b).
The perovskite tungsten bronze structures are intermediate between ReO3 and perovskite. They occur in series such as Na x WO3 and have a 3D framework of WO6 octahedra, as in ReO3, but with some (0 < x < 1) of the large A sites occupied by Na. To accommodate a variation in stoichiometry, x, the oxidation state of tungsten is a mixture of, or intermediate between, V and VI. The formula of the bronzes may be written more completely as