fluorite and antifluorite structures

The structures so far have all been 1:1 — one cation per anion. But many important compounds are 1:2 or 2:1, like the mineral fluorite, calcium fluoride (CaF2), with two fluorides for every calcium. The fluorite structure is the canonical way nature packs such compounds, and its mirror image, the antifluorite structure, handles the reverse ratio.

In fluorite, the calcium ions form a cubic close-packed (face-centred cubic) array, and the fluoride ions fill all of the tetrahedral holes — and recall there are twice as many tetrahedral holes as there are spheres, which is exactly the 1:2 ratio you need. Each calcium ends up surrounded by eight fluorides at the corners of a cube (coordination 8), while each fluoride is surrounded by only four calciums in a tetrahedron (coordination 4). So fluorite is 8:4 coordinate, with Z = 4 (four CaF2 per cell). The antifluorite structure simply swaps the roles: the anions take the close-packed positions and the smaller cations fill all the tetrahedral holes, so the coordination becomes 4:8. This is the structure of the alkali-metal oxides and sulfides such as Na2O and Li2S, where the small metal cations are the ones tucked into the holes.

Fluorite is adopted by compounds where a large, doubly-or-more charged cation pairs with smaller singly charged anions: CaF2, SrF2, BaF2, the dioxides UO2, ThO2, CeO2, and ZrO2 in a stabilized form. The structure has a famous practical twist: because the fluoride sublattice has lots of room, fluorite-type oxides like stabilized zirconia conduct ions remarkably well when oxide-ion vacancies are introduced, which is why they serve as the solid electrolyte in oxygen sensors and fuel cells. So a 200-year-old mineral name labels a structure at the heart of modern energy technology.