Lattice system

From Online Dictionary of Crystallography

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== Definition ==
== Definition ==
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A '''lattice system''' of space groups contains complete [[Bravais flock]]s. All those Bravais flocks which intersect exactly the same set of [[geometric crystal class]]es belong to the same lattice system.
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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 ==
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A '''lattice system''' of space groups contains complete [[Bravais flock]]s. All those Bravais flocks belong to the same lattice system for which the [[Bravais class]]es belong to the same (holohedral) [[geometric crystal class]].
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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 ==

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