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
These materials have interesting colours and electrical properties. At low x, they are pale green/yellow in colour and semiconducting. As x rises and electrons begin to occupy the 5d band of tungsten, they become brightly coloured and metallic, hence the name ‘bronze’.
Table 1.20 Some compounds with the ReO3 structure
| Compound | a/Å | Compound | a/Å |
|---|---|---|---|
| ReO3 | 3.734 | NbF3 | 3.903 |
| UO3 | 4.156 | TaF3 | 3.9012 |
| MoF3 | 3.8985 | Cu3N | 3.807 |
Figure 1.43 The structure of (a) ReO3, (b) tungsten bronze NaxWO3, (c, d) bronze and tunnel structures derived from ReO3 by rotation of blocks of four octahedra and (e, f) the tetragonal tungsten bronze structure.
Adapted from B. G. Hyde and M. O'Keeffe, Acta Cryst. Sect. A 29, 243 (1973).
(g) The TTB structure of Ba2LaTi2Nb3O15.
Adapted from G. C. Miles et al., J. Mater. Chem. 15, 798 (2005).
(h, i) Tunnel structure of Mo5O14.
A variety of monovalent cations enter the tungsten bronze structure; similar series also occur with MoO3 in the molybdenum bronzes. Many other highly conducting bronzes based on oxides MO2 or MO3 form in which M is a transition metal, such as Ti, V, Nb, Ta, Mo, W, Re, Ru or Pt, that is capable of existing in mixed oxidation states.
Thus far, we have not modified the arrangement of octahedra. Different arrays of octahedra are, however, obtained by rotation of columns of four octahedra by 90° and reconnecting them with the parent structure as shown in Fig. 1.43(c) and (d). This has major consequences for the size and coordination number of the A cation sites. Some, A, retain their coordination number of 12 and in projection may be perceived as ‘square tunnels’; a second set of sites, A′, has a coordination number which is increased to 15 and in projection may be regarded as “pentagonal tunnels’. A third set, C, has coordination number reduced to nine and is referred to as ‘triangular tunnels’. We now have the building blocks for the tetragonal tungsten bronze, TTB, structure. This contains an important family of ferroelectric materials although, since they are insulating, it is rather a misnomer to call them bronzes.
Table 1.21 Some compounds with the tetragonal tungsten bronze, TTB, structure. Unit cell: tetragonal a 12.4, c 3.9 Å
| A2 | A′ | B4B′ | O15 |
|---|---|---|---|
| Ba2 | REa | Ti2, Nb3 | O15 |
| Sr2 | Na or K | Nb5 | O15 |
| Ba2 | Na | Nb5 | O15 |
| Ba2 or Sr2 | Ba or Sr | Ti, Nb4 | O15 |
| Sr2.5 | Nb5 | O15 | |
| K0.4–0.6 | W |
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