Solid State Chemistry and its Applications. Anthony R. West

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 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 Ionics 203, 33 (2011).

       Table 1.23 Some compounds with the olivine structure

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General formula
Octahedral site	Tetrahedral site	hcp anion	Examples
II2	IV	O4	Mg2SiO4 (forsterite) Fe2SiO4 (fayalite) CaMgSiO4 (monticellite) γ‐Ca2SiO4 A2GeO4: A = Mg, Ca, Sr, Ba, Mn
III2	II	O4	Al2BeO4 (chrysoberyl) Cr2BeO4
II, III	III′	O4	MgAlBeO4
I, II	V	O4	LiFePO4 (triphylite) LiMnPO4 (lithiophylite)
I, III	IV	O4