Difference between revisions of "Bravais arithmetic class"
From Online Dictionary of Crystallography
(Modified to comply with the new terminology in the 6th edition of ITA.) |
(Modified to comply with the new terminology in the 6th edition of ITA.) |
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An [[arithmetic crystal class]] with matrix group of lattices is called a ''Bravais arithmetic crystal class''. | An [[arithmetic crystal class]] with matrix group of lattices is called a ''Bravais arithmetic crystal class''. | ||
| − | Each lattice is associated with a Bravais class, and each matrix group of a Bravais class represents the point group of a lattice referred to an appropriate primitive basis. | + | Each lattice is associated with a Bravais arithmetic class, and each matrix group of a Bravais arithmetic class represents the point group of a lattice referred to an appropriate primitive basis. |
| − | There exist 5 Bravais classes in two dimensions: | + | There exist 5 Bravais arithmetic classes in two dimensions: |
* 2''p'' | * 2''p'' | ||
* 2''mmp'' | * 2''mmp'' | ||
| Line 13: | Line 13: | ||
* 6''mmh'' | * 6''mmh'' | ||
| − | There exist 14 Bravais classes in three dimensions: | + | There exist 14 Bravais arithmetic classes in three dimensions: |
* <math>{\bar 1}</math>''P'' | * <math>{\bar 1}</math>''P'' | ||
* 2/''mP'' | * 2/''mP'' | ||
| Line 30: | Line 30: | ||
== See also == | == See also == | ||
| − | *[[Bravais | + | *[[Bravais class]] |
*Chapter 1.3.4.3 of ''International Tables for Crystallography, Volume A'', 6th edition | *Chapter 1.3.4.3 of ''International Tables for Crystallography, Volume A'', 6th edition | ||
[[category: Fundamental crystallography]] | [[category: Fundamental crystallography]] | ||
Revision as of 15:40, 30 May 2019
Classe de Bravais (Fr). Bravais-Klasse (Ge). Classe di Bravais (It). ブラベー類 (Ja). Clase de Bravais (Sp).
Definition
An arithmetic crystal class with matrix group of lattices is called a Bravais arithmetic crystal class.
Each lattice is associated with a Bravais arithmetic class, and each matrix group of a Bravais arithmetic class represents the point group of a lattice referred to an appropriate primitive basis.
There exist 5 Bravais arithmetic classes in two dimensions:
- 2p
- 2mmp
- 2mmc
- 4mmp
- 6mmh
There exist 14 Bravais arithmetic classes in three dimensions:
- [math]{\bar 1}[/math]P
- 2/mP
- 2/mS
- mmmP
- mmmS
- mmmI
- mmmF
- 4/mmmP
- 4/mmmI
- [math]{\bar 3}[/math]mR
- 6/mmmP
- m[math]{\bar 3}[/math]mP
- m[math]{\bar 3}[/math]mI
- m[math]{\bar 3}[/math]mF
See also
- Bravais class
- Chapter 1.3.4.3 of International Tables for Crystallography, Volume A, 6th edition