ceramic crystal structures

A ceramic is usually a compound of a metal and a non-metal, like table salt (NaCl) or sapphire (Al2O3). Picture the atoms as charged balls of two different sizes: fat, low-charge cations (the metal, having given electrons away) and bigger anions (the non-metal, having taken them). The structure is the tidiest way to stack these two ball sizes so that plus sits next to minus, never plus-next-to-plus, and the whole pile stays electrically neutral.

Two rules set the packing. First, every cation surrounds itself with as many touching anions as it can, and that number, the coordination number, is fixed by the ratio of the two radii. A small cation only fits 4 anions around it (a tetrahedron); a medium one fits 6 (an octahedron); a big one fits 8 (a cube). For example, in rock salt NaCl each Na+ touches 6 Cl- and each Cl- touches 6 Na+, so it is called the 6-6 or AX structure. Second, the overall formula must balance charge: in Al2O3 three O(2-) balance two Al(3+), a so-called A_mX_p structure. CaF2 (fluorite) is AX2, with 8 F around each Ca.

These packings explain why ceramics behave as they do. The bonds are ionic and/or covalent, strong and directional, so ceramics are stiff, hard, and melt at very high temperature. But there is a price: to slide one plane of atoms over another you would have to push like charges together, which the crystal fiercely resists, so ceramics cannot deform plastically the way metals do. That is the deep reason they are brittle. Do not picture a ceramic as purely ionic; most, like alumina and silica, are a mix of ionic and covalent bonding.