Spinel
Stoichiometry = AM2X4
Space Group = Fd3m (227)
a = 5.8 - 8.7

Atomic Positions
        A    8a      0, 0, 0
        M    16d    5/8, 5/8, 5/8
        X    32e    x, x, x         x ~ 0.385

Coordination Numbers/Geometry
        A     4       Tetrahedral coordination
        M     6       Octahedral coordination
        X     4       Distorted tetrahedral coordination

Representative Compounds*
        Oxides (104) - (i.e. Li0.5Al2.5O4, Ag2MoO4, CdRh2O4, FeV2O4, Co2GeO4, Zn2.33Nb0.67O4)
        Selenides (3) - (i.e. CdCr2Se4)
        Sulfides (32) - (i.e.Ag0.5Al2.5S4, CaIn2S4, CuTi2S4, ZnCr2S4)
        Tellurides (1) - (i.e. CuCr2Te4)

*The numbers in parentheses are the number of compounds of each type found in "Structure and Properties of Inorganic Solids" by Francis Galasso, Pergammon Press (1970).



Description
The spinel structure is a rather complex arrangement based upon a cubic close packed anion array, with 1/2 of the octahedral holes filled and 1/8 of the tetrahedral holes filled. It is one of the most prevalent structure types for ternary oxides and sulfides. A polyhedral based view of the structure reveals chains of edge-sharing octahedra, together with tetrahedra that are isolated from each other.

Spinels can be classified as either normal or inverse, depending upon the cation distribution. Normal spinels are contain A cations on the tetrahedral sites andM cations on the octahedral sites, as depicted in the description above. In contrast, the tetrahedral sites in an inverse spinel are occupied by the M cations and the octahedral sites by a 50:50 mixture of A and M cations.

Points of Interest
One of the most intensively studied spinel compounds is magnetite, Fe3O4. Magnetite is an inverse spinel, due to the fact that the tetrahedral sites are occupied by Fe3+, while the octahedral sites are occupied by 50:50 mixture of Fe2+ and Fe3+. It becomes ferrimagnetic below 850 K and undergoes the so called Verwey transition near 123 K. The Verwey transition corresponds to a charge-ordering transition where the Fe2+ and Fe3+ ions on the octahedral site adopt an ordered arrangement below the transition temperature. The resulting ordered superstructure is quite complex and the full details of this structure are still not fully understood.