# Primitive cell

### From Online Dictionary of Crystallography

##### Revision as of 12:44, 18 December 2017 by MassimoNespolo (talk | contribs) (expression of the triple scalar product)

Maille primitive ou simple (*Fr*). Primitive Zelle (*Ge*). Cella primitiva (*It*). 単純単位胞、基本単位胞 (*Ja*). Celda primitiva (*Sp*).

## Definition

A primitive cell is a unit cell built on the basis vectors of a primitive basis of the direct lattice, namely a crystallographic basis of the vector lattice **L** such that every lattice vector **t** of **L** may be obtained as an integral linear combination of the basis vectors, **a**, **b**, **c**.

It contains only one lattice point and its volume is equal to the triple scalar product: [math] \mathbf{a}\cdot(\mathbf{b}\times \mathbf{c}) [/math].

*Non-primitive* bases are used conventionally to describe centred lattices. In that case, 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.

## See also

- Conventional cell
- Crystallographic basis
- Direct lattice
- Unit cell
- Chapter 1.3.2.4 of
*International Tables for Crystallography, Volume A*, 6th edition