Unit cell

A unit cell is a volume whose translations along three lattice directions reproduce a crystal lattice. Its shape and dimensions describe the lattice, while its contents specify the crystal structure.

Crystal lattice: An infinite periodic arrangement of points that describes the translational structure of a crystal. The unit cell is a finite region whose translations generate this periodic arrangement.
Primitive unit cell: A unit cell containing exactly one lattice point, counting fractional contributions from boundaries. It is the smallest-volume cell that reproduces the lattice by translation.
X-ray crystallography: A method that determines atomic structures by analyzing X-ray diffraction from crystals. Diffraction patterns reveal unit-cell dimensions and the arrangement of its contents.
Primitive cell: A smallest-volume region that tiles a periodic structure under translations. This broader geometric term is often used for the crystallographic primitive unit cell.
Lattice parameters: The three edge lengths and three interaxial angles that specify a unit cell's geometry. These six measurements distinguish unit-cell shapes and define lattice dimensions.
Conventional unit cell: A unit cell chosen to display a lattice's symmetry clearly, even when it contains multiple lattice points. Its symmetry-friendly shape can be larger than the primitive cell.
Bragg's law: The relation connecting X-ray wavelength, diffraction angle, and spacing between crystal planes. Plane spacings derived from diffraction are measured relative to unit-cell geometry.
Molecular unit cell: A repeating crystallographic cell whose contents are described using whole molecules or molecular fragments. Molecular crystals require distinguishing the cell boundary from the molecule's shape.
Basis (crystallography): An atom or group of atoms associated with each point of a crystal lattice. Combining a lattice with its basis produces the crystal structure.
Lattice translation: A displacement that maps every point of a periodic lattice onto an equivalent point. Repeating the unit cell requires translations by lattice vectors.

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