unitcell

A unit cell is the smallest repeating unit of a crystalline solid that, when translated by the lattice vectors, reproduces the entire crystal lattice. The cell is defined by three edge vectors a, b, c and the interaxial angles α, β, γ between them. The cell volume is V = |a · (b × c)|.

A primitive cell is the smallest possible unit that contains exactly one lattice point; a conventional cell is chosen to display the symmetry of the lattice and may contain more than one lattice point. Crystals are described as a Bravais lattice plus a basis: the lattice specifies the periodic array of lattice points, and the basis consists of the atoms associated with each lattice point.

There are 14 Bravais lattices in three dimensions, grouped into crystal systems such as cubic, tetragonal, orthorhombic, monoclinic, triclinic, and hexagonal (including rhombohedral representations). Conventional unit cells are defined for each lattice type; for example, simple cubic, body-centered cubic, and face-centered cubic cells illustrate how different lattice arrangements are accommodated within the same framework. Positions inside the cell are given by fractional coordinates (x, y, z) relative to a, b, c.

The unit cell serves as the reference frame for crystallographic data, including lattice parameters, symmetry, and composition, and is used to compute properties such as density and structure factors. In crystallography practice, the choice of unit cell is not unique; a larger conventional cell can be subdivided into smaller primitive cells as long as it tiles space.