the corundum structure

The corundum structure is the home of alpha-alumina (Al2O3), one of the most important engineering ceramics of all, and of the gemstones sapphire and ruby, which are alumina coloured by traces of other metals. Its formula is M2O3, two trivalent cations for every three oxygens, and the challenge the structure has to solve is how to keep charge balance when the cation carries a 3+ charge.

The oxygens form a hexagonal close-packed array, and the aluminium ions fill the octahedral holes, but here is the twist: they can fill only two-thirds of them. If aluminium filled every octahedral hole the formula would be AlO, far too much positive charge; filling exactly two-thirds gives Al2O3 and perfect neutrality. The one-third of octahedral sites left empty are arranged in an orderly, repeating pattern, giving the crystal its rhombohedral symmetry, with aluminium in coordination 6 and oxygen in coordination 4.

Alpha-alumina is the hardest and most widely used oxide ceramic: cutting tools, wear-resistant parts, spark-plug insulators, electronic substrates, transparent armour and, doped with chromium, the ruby of the first lasers. The same structure is shared by chromium oxide (Cr2O3), hematite (Fe2O3), and others. Honest caveat: only the alpha form of Al2O3 is corundum; the transition aluminas such as gamma-alumina have quite different, spinel-related structures and convert irreversibly to alpha on heating.