the diamond cubic structure

The diamond cubic structure is the arrangement of carbon atoms in diamond, and the same skeleton that silicon and germanium adopt. Its defining feature is that every atom bonds to exactly four neighbours pointing to the corners of a tetrahedron, a rigid, open, three-dimensional net held together entirely by strong directional covalent bonds. It is the archetype of tetrahedral covalent bonding.

Geometrically it is a face-centred-cubic lattice with a two-atom motif, one atom at (0, 0, 0) and one at (1/4, 1/4, 1/4). Equivalently it is two interpenetrating FCC lattices displaced by one quarter of the body diagonal. Counting gives 8 atoms per cubic cell, each with coordination number 4. Because fourfold coordination leaves so much room, the atomic packing factor is only 0.34, far below the 0.74 of close packing, so the diamond structure is remarkably open, a crystal held rigid by the geometry of its bonds rather than by dense stacking.

Silicon and germanium, the foundations of the entire electronics industry, are diamond cubic, as are grey tin and of course diamond itself. The strong, directional, corner-connected bonds explain why diamond is the hardest natural material and why these crystals are stiff and brittle rather than ductile. Colour the two sublattices with different elements and you get the closely related zinc-blende structure of the compound semiconductors.