spinel structure

Magnetite — the lodestone that first told humans which way is north — and many of the magnetic powders once used in recording tape share a single crystal architecture called the spinel structure, named after the gemstone spinel, MgAl2O4. It is the standard structure for a large family of mixed oxides of formula AB2O4, where A and B are metal cations (often in the +2 and +3 oxidation states), and it is the clearest everyday example of cations choosing between tetrahedral and octahedral holes.

The oxide ions form a cubic close-packed array. Recall that gives N octahedral and 2N tetrahedral holes; in spinel the cations fill one eighth of the tetrahedral holes and one half of the octahedral holes. In a normal spinel, the A2+ cations (such as Mg2+) occupy tetrahedral holes (coordination 4) and the B3+ cations (such as Al3+) occupy octahedral holes (coordination 6) — written A[B2]O4 with brackets marking the octahedral site. But there is a famous twist: in an inverse spinel the A2+ cations swap into octahedral holes, displacing half the B3+ ions into the tetrahedral holes, written B[AB]O4. Which arrangement wins is decided by the crystal field stabilization energies of the particular d-electron cations — a rare case where ligand-field ideas reach into bulk structure.

The normal-versus-inverse distinction is not an academic detail; it governs magnetism. Magnetite, Fe3O4 (which is Fe2+ Fe2(3+) O4), is an inverse spinel, and the way its iron ions are split between tetrahedral and octahedral sites makes their magnetic moments add up to a net ferrimagnetism — the reason it is magnetic at all. Spinel ferrites of the form MFe2O4 (M = Mn, Ni, Zn, Co) are tuned by this site preference for use in transformer cores, microwave devices and magnetic memory. So a gemstone's structure, read through where the cations sit, explains the magnet on your fridge.