Читать книгу Solid State Chemistry and its Applications - Anthony R. West - Страница 69

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	O3

^a RE = La, …, Dy, Bi.

The general formula of the ideal TTB structure is A₂A′B₄B′O₁₅ or A₂A′B₃B′₂O₁₅, depending on the oxidation states of A, A′, B, and B′. The structure is built of corner‐sharing BO₆ and B′O₆ octahedra; the B,B′:O ratio is 1:3, as in ReO₃, but the linkage of the octahedra is different from that in ReO₃. In the TTB structure, blocks of octahedra which form four‐membered rings are rotated by 90° relative to the parent ReO₃ structure to give a framework containing triangular, square and pentagonal columns, Fig. 1.43(e) and (f). In the c direction, the unit cell is only one octahedron thick. In principle, all the sites are available for cation occupancy. In practice, large cations such as K⁺ and Ba²⁺ occupy the pentagonal tunnels with a coordination number to the oxygen of 15, whereas somewhat smaller cations such as La³⁺ occupy square tunnels with coordination number 12; the triangular tunnels, C in the formula, remain either empty or occupied by smaller ions such as Li⁺.

A selection of compounds with the TTB structure is shown in Table 1.21. The structure is versatile since cations on the A and A′ sites can be either fully ordered, disordered or only partially occupied. In addition, there are two crystallographically distinct, octahedral B and B′ sites, which can be occupied by one species or a mixture. As with all crystal structures, it may be useful to view them in different ways and the TTB structure is shown from three different perspectives in Fig. 1.43(g).

The structure of Mo₅O₁₄ is based on the same principles but is rather different to the TTB structure, Fig. 1.43(h) and (i). Pentagonal columns are again present and these are occupied by rows of Mo and O atoms, as shown by open and closed circles in (i). Because of the extra oxygens in the columns, Mo occupies small sites whose coordination number is reduced greatly from 15 to 7. Other pentagonal columns, and triangular columns, remain empty. In addition, new hexagonal columns are created by the array of octahedra and these remain empty in Mo₅O₁₄. Many other complex structures are built using similar principles, for example, NaNb₆O₁₅F, Nb₁₆W₁₈O₉₄, Bi₆Nb₃₄O₉₄ and Ta₃O₇F.