# Primitive cell

(Difference between revisions)
 Revision as of 12:42, 18 December 2017 (view source)m (a bit smarter way of making the plural of a link ;-))← Older edit Latest revision as of 12:44, 18 December 2017 (view source) (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 ('''a''', '''b''', '''c'''). + It contains only one lattice point and its volume is equal to the triple scalar product: $\mathbf{a}\cdot(\mathbf{b}\times \mathbf{c})$. ''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: $\mathbf{a}\cdot(\mathbf{b}\times \mathbf{c})$.

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.