alt="Schematic illustration of representative parts of the spinel structure."/>
Figure 1.44 Representative parts of the spinel structure. (a) One octant of the unit cell showing oxygens at corner and face centres, empty (□) and occupied (•) octahedral sites. (b) A second octant, underneath the one in (a), showing in addition the occupation of two tetrahedral sites, A. (c) One face of the cubic unit cell of the spinel structure. The dashed part coincides with the base of the subcell shown in (b). (d) Alternating arrangement of the two types of octant (a) and (b). (e) Cation positions in spinel. Numbers refer to fractional heights, as multiples of c/8. Octahedral cation sites O′ are also shown in (b) and (c). (f) Two perspectives of the spinel structure of MgAl2O4 showing a framework of AlO6 octahedra with MgO4 tetrahedra in channel sites.
A complicating factor in some spinel structures is that the cation distribution may vary. Two extreme types of behaviour may be distinguished. In normal spinels, the cations occupy sites given by the formula
i.e. with A in tetrahedral sites and B in octahedral sites. Examples of normal spinels are MgAl2O4 and MgTi2O4. In inverse spinels, half of the B ions occupy tetrahedral sites, leaving the remaining B ions and all the A ions in octahedral sites, i.e.
Table 1.22 Some compounds with the spinel structure
| Compound | Type | a/Å | Structure | Compound | Type | a/Å | Structure |
|---|---|---|---|---|---|---|---|
| MgAl2O4 | 2, 3 | 8.0800 | Normal | Mgln2O4 | 2, 3 | 8.81 | Inverse |
| CoAl2O4 | 2, 3 | 8.1068 | Normal | Mgln2S4 | 2, 3 | 10.708 | Inverse |
| CuCr2S4 | 2, 3 | 9.629 | Normal | Mg2TiO4 | 2, 4 | 8.44 | Inverse |
| CuCr2Se4 | 2, 3 | 10.357 | Normal | Zn2SnO4 | 2, 4 | 8.70 | Inverse |
| CuCr2Te4 | 2, 3 | 11.051 | Normal | Zn2TiO4 | 2, 4 | 8.467 | Inverse |
| MgTi2O4 | 2, 3 | 8.474 | Normal | LiAlTiO4 | 1, 3, 4 | 8.34 | Li in tet |
| Co2GeO4 | 2, 4 | 8.318 | Normal | LiMnTiO4 | 1, 3, 4 | 8.30 | Li in tet |
| Fe2GeO4 | 2, 4 | 8.411 | Normal | LiZnSbO4 | 1, 2, 5 | 8.55 | Li in tet |
| MgFe2O4 | 2, 3 | 8.389 | Inverse | LiCoSbO4 | 1, 2, 5 | 8.56 | Li in tet |
| NiFe2O4 | 2, 3 | 8.3532 | Inverse |
Usually the A and B cations in octahedral sites are disordered. Examples of inverse spinels are MgFe2O4 and Mg2TiO4.
In addition to normal and inverse spinels, a complete range of intermediate cation distributions is possible and, in some cases, the distribution changes with temperature. The cation distribution may be quantified using a parameter, γ, which is the fraction of A ions on the octahedral sites:
normal: [A]tet[B2]octO4 γ = 0
inverse: [B]tet[A, B]octO4 γ = 1
random: [B0.67A0.33]tet[A0.67B1.33]octO4 γ = 0.67.
The cation distribution in spinels and the degree of inversion, γ, have been studied in considerable detail. Several factors influence γ, including the site preferences of ions in terms of size, covalent bonding effects and crystal field stabilisation energies (see Chapter 2). The γ value in any particular spinel is given by the net effect of these various parameters taken together. Some compounds with the spinel structure are given in Table 1.22.
1.17.10 Olivine
The olivine structure, typified by the minerals forsterite, Mg2SiO4, and triphylite, LiFePO4, is the hcp analogue of the spinel structure. One‐eighth of the tetrahedral sites are occupied by Si or P and half of the octahedral sites by Mg or Li, Fe within an hcp oxide array. There are two crystallographically distinct octahedral sites in olivine, which are occupied in ordered fashion by Li and Fe in LiFePO4. The crystal structure
