Anthony R. West - Solid State Chemistry and its Applications

i.e. with A in tetrahedral sites and B in octahedral sites. Examples of normal spinels are MgAl 2O 4and MgTi 2O 4. 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

Usually the A and B cations in octahedral sites are disordered. Examples of inverse spinels are MgFe 2O 4and Mg 2TiO 4.

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.

The olivine structure, typified by the minerals forsterite, Mg 2SiO 4, and triphylite, LiFePO 4, 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 LiFePO 4. The crystal structure is shown in Fig. 1.45 and some olivines are listed in Table 1.23. Olivines occur mainly with oxides but also with sulphides, selenides and some fluorides. Various cation charge combinations occur, such that in oxides the three cations have a net charge 8+.

Olivines (mainly forsterite and fayalite) are believed to be the main mineralogical constituent of the Earth's upper mantle. At high pressures, many olivines transform to the spinel structure and spinels are probably the main constituent of the Earth's lower mantle. Volume changes associated with the olivine to spinel phase transformation may have had fundamental geological consequences during the evolution of the Earth, involving the formation of mountain ranges and under‐sea ridges. When spinel material from the lower mantle was pushed upwards to the Earth's surface, it transformed to olivine due to the reduction in pressure. The reverse transformation, olivine to spinel, with a volume contraction may be a contributing factor to earthquakes.

Figure 1.45 Olivine structure of LiFePO4.

Modified from J. J. Biendicho and A. R. West, Solid State Ionics203, 33 (2011).

Table 1.23 Some compounds with the olivine structure

Unit cell: orthorhombic; for LiFePO 4, a = 10.33, b = 6.01, c = 4.70 Å; Z = 4.

There is much current interest in LiFePO 4as the cathode material in rechargeable lithium batteries. On charging, Li deintercalates from the structure and a corresponding amount of Fe is oxidised from Fe 2+to Fe 3+, as follows:

Lithium ions occupy channels parallel to the y axis, Fig. 1.45, which allows them to leave and enter the structure readily during cell charge and discharge. This is an example of a solid state redox reaction with a cell potential of about 3.08 V. LiFePO 4, and associated LiMnPO 4, are of interest because the redox reaction and the process of lithium removal and insertion are reversible over many cycles, giving a high cell capacity, and the materials are cheap, non‐toxic and environmentally friendly.

These three closely related structure types can be regarded, ideally, as hcp oxide ions with cations occupying two‐thirds of the octahedral sites. Conceptually, they are related to the NiAs structure in which all the octahedral sites are occupied, and to the CdI 2structure in which only half the octahedral sites are occupied, Table 1.4. The crystal structures are shown in Fig. 1.46 and some compounds adopting these structures are listed in Table 1.24. Corundum contains only one cation, Al 3+, whereas ilmenite contains two cations that are ordered over the octahedral sites that are occupied by Al in corundum. In LiNbO 3, the same octahedral sites are occupied but the cation ordering arrangement is different.