the fluorite structure
/ FLOR-ite /
The fluorite structure, named after the mineral fluorite (calcium fluoride, CaF2), is the archetype for an AX2 ceramic, one cation for every two anions. The neatest way to picture it: put the cations on a face-centred-cubic grid, then place an anion in every one of the tetrahedral holes. Because an FCC array has eight tetrahedral holes and four cations, filling them all gives the 1:2 ratio automatically.
The coordination is lopsided, 8:4. Each large cation sits at the centre of a cube of eight anions (coordination 8), while each anion is surrounded by only four cations in a tetrahedron (coordination 4). There are four formula units in the cubic cell. Crucially, the octahedral holes of this structure are left completely empty, leaving roomy channels running through the crystal.
Those empty channels are what make fluorite-structured oxides so useful. Cubic zirconia (ZrO2), urania (UO2, nuclear fuel), thoria (ThO2) and ceria (CeO2) all take this structure, and their open lattice tolerates missing oxygen and interstitials, so doping them creates oxygen vacancies that hop freely, turning them into oxygen-ion conductors for fuel cells and sensors. Honest caveat: pure ZrO2 is only cubic fluorite at very high temperature; it must be stabilised with additives like yttria to hold that structure at room temperature.
Uranium dioxide nuclear fuel, UO2, is fluorite: a face-centred-cubic uranium array with oxygen filling every tetrahedral hole. The open, vacancy-tolerant lattice lets the fuel soak up fission products and extra oxygen (UO2+x) without falling apart.
FCC cations, anions in all tetrahedral holes; octahedral holes empty; 8:4.
The empty octahedral sites are not a flaw but the point: they are the highways for fast oxygen-ion conduction in doped zirconia and ceria, the basis of solid-oxide fuel cells.