= Primitive cubic lattice
= Simple cubic lattice
{synonym}
The primitive cubic lattice consists of all integer combinations of three perpendicular, equal-length primitive translations:
$$
\mathbf R=a(n_x,n_y,n_z),\qquad n_x,n_y,n_z\in\mathbb Z.
$$
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>.
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