# Primitive cell

### From Online Dictionary of Crystallography

m (a bit smarter way of making the plural of a link ;-)) |
(expression of the triple scalar product) |
||

Line 5: | Line 5: | ||

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'''. | 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 | + | 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 lattice|centred lattice]]s. 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. | ''Non-primitive'' bases are used conventionally to describe [[centred lattice|centred lattice]]s. 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. |

## Latest revision as of 12:44, 18 December 2017

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: .

*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