Difference between revisions of "Lattice system"
From Online Dictionary of Crystallography
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| − | <font color="blue">Système réticulaire </font>(''Fr''). | + | <font color="blue">Système réticulaire</font> (''Fr''). <font color="red">Gittersystem</font> (''Ge''). <font color="black">Sistema reticolare</font> (''It''). <font color="purple">格子系</font> (''Ja''). |
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== Definition == | == Definition == | ||
| − | A '''lattice system''' of space groups contains complete [[Bravais | + | A '''lattice system''' of space groups contains complete [[Bravais class]]es. All those Bravais classes which intersect exactly the same set of [[geometric crystal class]]es belong to the same lattice system. |
== Alternative definition == | == Alternative definition == | ||
| − | A '''lattice system''' of space groups contains complete [[Bravais | + | A '''lattice system''' of space groups contains complete [[Bravais class]]es. All those Bravais classes belong to the same lattice system for which the [[Bravais arithmetic class]]es belong to the same (holohedral) [[geometric crystal class]]. |
== Lattice systems in two and three dimensions == | == Lattice systems in two and three dimensions == | ||
| − | In | + | In two-dimensional space there exist four lattice systems: |
* monoclinic | * monoclinic | ||
* orthorhombic | * orthorhombic | ||
| Line 16: | Line 15: | ||
* hexagonal | * hexagonal | ||
| − | In | + | In three-dimensional space there exist seven lattice systems: |
* triclinic | * triclinic | ||
* monoclinic | * monoclinic | ||
| Line 26: | Line 25: | ||
Note that the adjective ''trigonal'' refers to a [[crystal system]], not to a lattice system. Rhombohedral crystals belong to the trigonal [[crystal system]], but trigonal crystals may belong to the rhombohedral or to the hexagonal lattice system. | Note that the adjective ''trigonal'' refers to a [[crystal system]], not to a lattice system. Rhombohedral crystals belong to the trigonal [[crystal system]], but trigonal crystals may belong to the rhombohedral or to the hexagonal lattice system. | ||
| + | |||
| + | == Note == | ||
| + | In previous editions of ''Volume A'' of ''International Tables of Crystallography'' (before 2002), the lattice systems were called ''Bravais systems''. | ||
== See also == | == See also == | ||
| − | + | *[[Bravais class]] | |
| + | *Chapter 1.3.4.4.2 of ''International Tables for Crystallography, Volume A'', 6th edition | ||
[[category: Fundamental crystallography]] | [[category: Fundamental crystallography]] | ||
Latest revision as of 17:23, 30 May 2019
Système réticulaire (Fr). Gittersystem (Ge). Sistema reticolare (It). 格子系 (Ja).
Contents
Definition
A lattice system of space groups contains complete Bravais classes. All those Bravais classes which intersect exactly the same set of geometric crystal classes belong to the same lattice system.
Alternative definition
A lattice system of space groups contains complete Bravais classes. All those Bravais classes belong to the same lattice system for which the Bravais arithmetic classes belong to the same (holohedral) geometric crystal class.
Lattice systems in two and three dimensions
In two-dimensional space there exist four lattice systems:
- monoclinic
- orthorhombic
- tetragonal
- hexagonal
In three-dimensional space there exist seven lattice systems:
- triclinic
- monoclinic
- orthorhombic
- tetragonal
- rhombohedral
- hexagonal
- cubic
Note that the adjective trigonal refers to a crystal system, not to a lattice system. Rhombohedral crystals belong to the trigonal crystal system, but trigonal crystals may belong to the rhombohedral or to the hexagonal lattice system.
Note
In previous editions of Volume A of International Tables of Crystallography (before 2002), the lattice systems were called Bravais systems.
See also
- Bravais class
- Chapter 1.3.4.4.2 of International Tables for Crystallography, Volume A, 6th edition