# Difference between revisions of "Primitive basis"

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− | < | + | <font color="blue">Base primitive</font> (''Fr''). <font color="red">Primitive Basis</font> (''Ge''). <font color="black">Base primitiva</font> (''It''). <font color="purple">単純基底</font> (''Ja''). <font color="green">Base primitiva</font> (''Sp''). |

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

A primitive basis is 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 basis is 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'''. | ||

+ | |||

+ | In mathematics, a primitive basis is often called a ''lattice basis'', whereas in crystallography the latter has a more general meaning and corresponds to a [[crystallographic basis]]. | ||

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+ | == See also == | ||

+ | |||

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

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

+ | *[[Primitive cell]] | ||

+ | *[[Reduced cell]] | ||

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

+ | |||

+ | [[Category:Fundamental crystallography]] |

## Latest revision as of 15:52, 18 December 2017

Base primitive (*Fr*). Primitive Basis (*Ge*). Base primitiva (*It*). 単純基底 (*Ja*). Base primitiva (*Sp*).

## Definition

A primitive basis is 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**.

In mathematics, a primitive basis is often called a *lattice basis*, whereas in crystallography the latter has a more general meaning and corresponds to a crystallographic basis.

## See also

- Crystallographic basis
- Direct lattice
- Primitive cell
- Reduced cell
- Chapter 1.3.2.4 of
*International Tables for Crystallography, Volume A*, 6th edition