Primitive cell

From Online Dictionary of Crystallography

(Difference between revisions)
Jump to: navigation, search
(Other languages)
Line 7: Line 7:
== 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

Contents

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

unit cell

Section 8.1 of International Tables of Crystallography, Volume A