# Difference between revisions of "Primitive cell"

### From Online Dictionary of Crystallography

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== Definition == | == 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'''. | + | 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 ('''a''', '''b''', '''c'''). | It contains only one lattice point and its volume is equal to the triple scalar product ('''a''', '''b''', '''c'''). |

## Revision as of 05:00, 5 May 2006

# Primitive cell

### Other languages

Maille primitive (*Fr*). Celda primitiva (*Sp*). Cella primitiva (*It*)

## 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 (**a**, **b**, **c**).

*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

crystallographic basis

direct lattice

Section 8.1 of *International Tables of Crystallography, Volume A*