# Difference between revisions of "Primitive cell"

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− | = | + | <font color="blue">Maille primitive ou simple</font> (''Fr''). <font color="red">Primitive Zelle</font> (''Ge''). <font color="black">Cella primitiva</font> (''It''). <font color="purple">単純単位胞、基本単位胞</font> (''Ja''). <font color="green">Celda primitiva</font> (''Sp''). |

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− | Maille primitive (''Fr''). | ||

== Definition == | == Definition == | ||

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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>. |

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− | [[unit 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. |

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+ | == See also == | ||

+ | *[[Conventional cell]] | ||

+ | *[[Crystallographic basis]] | ||

+ | *[[Direct lattice]] | ||

+ | *[[Unit cell]] | ||

+ | *Chapter 1.3.2.4 of ''International Tables for Crystallography, Volume A'', 6th edition | ||

[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] |

## 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: [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