Unit cell

Maille (Fr). Elementarzelle (Ge). Cella unitaria (It). 単位胞（単位格子） (Ja). элементарная ячейка (Ru). Celda unidad (Sp).

Definition

The unit cell is the parallelepiped built on the vectors, a, b, c, of a crystallographic basis of the direct lattice. Its volume is given by the scalar triple product, V = (a, b, c) and corresponds to the square root of the determinant of the metric tensor.

If the basis is primitive, the unit cell is called the primitive cell. It contains only one lattice point. If the basis is non-primitive, the unit cell is a multiple cell and it contains more than one lattice point. The multiplicity of the cell is given by the ratio of its volume to the volume of a primitive cell.

Ambiguity in other languages

The terms maille élémentaire (French) and cella elementare (Italian), often adopted for the English unit cell, are sometimes incorrectly used in the meaning of conventional cell, whereas by definition they correspond to a primitive ('elementary') cell. It should be noticed that the term maille élémentaire is absent from the classical French textbooks on geometrical crystallography: Bravais used parallélogramme générateur or maille parallélogramme (E²) and parallélopipède générateur or noyau ('E'³), while Mallard used just maille and Friedel maille simple.

See also

• Asymmetric unit
• Conventional cell
• Direct lattice
• Primitive cell
• Chapter 1.3.2.3 of International Tables for Crystallography, Volume A, 6th edition