Primitive cubic lattice

The primitive cubic lattice consists of all integer combinations of three perpendicular, equal-length primitive translations:Its conventional cubic unit cell is already primitive, with volume $a^3$ and one lattice point after shared-boundary counting. Each point has six nearest neighbors at distance $a$.

The reciprocal lattice is also simple cubic, with primitive vectors of length $2\pi /a$ in the usual diffraction convention. A primitive cubic Bravais lattice specifies translations rather than a chemical motif: placing several atoms at each lattice point changes the atomic basis of a crystal without automatically changing the translation lattice. This distinction is essential when interpreting crystal basis structure factors.