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Difference between revisions of "Bravais arithmetic class"

From Online Dictionary of Crystallography

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An [[arithmetic crystal class]] with matrix group of lattices is called a ''Bravais arithmetic crystal class'', or '''Bravais class''' for short.
 
An [[arithmetic crystal class]] with matrix group of lattices is called a ''Bravais arithmetic crystal class'', or '''Bravais class''' for short.
  
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 appropriateprimitive basis.
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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.
  
 
There exist 5 Bravais classes in two dimensions:
 
There exist 5 Bravais classes in two dimensions:

Revision as of 08:41, 25 May 2007

Classe de Bravais (Fr). Bravais klass (Ge). Classe di Bravais (It). ブラベークラス(Ja)

Definition

An arithmetic crystal class with matrix group of lattices is called a Bravais arithmetic crystal class, or Bravais class for short.

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.

There exist 5 Bravais classes in two dimensions:

  • 2p
  • 2mmp
  • 2mmc
  • 4mmp
  • 6mmh

There exist 14 Bravais 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

Section 8.2.5 in of International Tables of Crystallography, Volume A