Spinel Structure

The spinel structure (sometimes called garnet structure) is named after the mineral spinel (MgAl2O4); the general composition is AB2O4. It is essentially cubic, with the O - ions forming a fcc lattice. The cations (usually metals) occupy 1/8 of the tetrahedral sites and 1/2 of the octahedral sites and there are 32 O-ions in the unit cell.

This sounds complicated, but it is not as bad as it could be; look at the drawing. We "simply" have two types of cubic building units inside a big fcc O-ion lattice, filling all 8 octants.

The spinel structure is very flexible with respect to the cations it can incorporate; there are over 100 known compounds. In particular, the A and B cations can mix! In other words, the composition with respect to one unit cell can be (A8) (B16)O32, or A8 (B8A8)O32 = A(AB)O4 in regular chemical spelling, or (A8/3B16/3) (A16/3B32/3)O32
and so on, with the atoms in the brackets occupying the respective site at random.

A few examples (in regular chemical symbols)
Magnetite; Fe3+( Fe2+ Fe3+)O4
Spinel; Mg2+( Al23+)O4
Chromite; Fe3+(Cr23+)O4
Jacobsite; Fe3+( Mn2+ Fe3+)O4

The spinel structure is also interesting because it may contain vacancies as regular part of the crystal. For example, if magnetite is slowly oxidized by lying around a couple of billion years, or when rocks cool, Fe2+ will turn into Fe3+ (oxidation, in chemical terms, means you take electrons away). If all Fe2+ is converted into Fe3+, charge balance requires a net formula of Fe21,67O32 per unit cell and this means that 2,33 sites must be vacant - we have what is called a defect spinel. In a way, the composition is now Fe21,67Vac2,33O3; having lots of vacancies as an integral part of the structure.

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