the spinel structure
/ spih-NEL /
The spinel structure, named after the gemstone spinel (magnesium aluminate, MgAl2O4), is the classic structure for oxides of formula AB2O4, where A and B are metal cations. Its trick is to close-pack the large oxygen ions and then distribute the two kinds of metal cation among the tetrahedral and octahedral holes left between them. It is the home structure of the technologically vital magnetic ferrites.
The oxygen ions form a face-centred-cubic (cubic close-packed) array, but the repeating unit is large: the conventional cubic cell contains 8 formula units, that is 8 A, 16 B, and 32 oxygen ions. Within that cell there are 64 tetrahedral holes and 32 octahedral holes; a normal spinel places the A cations in one eighth of the tetrahedral holes (8 filled) and the B cations in half of the octahedral holes (16 filled). An inverse spinel swaps things: the A cations move to octahedral sites while half of the B cations take the tetrahedral sites, as in magnetite (Fe3O4). Many real spinels lie somewhere between normal and inverse.
This normal-versus-inverse distribution is not academic bookkeeping, it controls magnetism. In ferrites the magnetic moments on tetrahedral and octahedral sublattices point in opposite directions, so shifting cations between the two changes the net magnetisation, which is why the inverse arrangement of magnetite makes it magnetic. Spinels also serve as tough refractories (MgAl2O4), and the same close-packed-oxygen plus cations-in-holes recipe underlies a whole family of functional oxides.
Magnetite (Fe3O4) is an inverse spinel: Fe3+ split between tetrahedral and octahedral sites, Fe2+ on octahedral sites, the imbalance leaving it ferrimagnetic.
Close-packed oxygen, metals shared between tet and oct holes: the ferrite family's home.
The spinel cell is large (8 formula units, 32 oxygens) and only one eighth of its tetrahedral holes and half its octahedral holes are filled, so careless hole-counting is a frequent error.