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Article: Crystallographic point group

Crystallographic point group

Introduction to Crystallographic Point Groups

  • A crystallographic point group is a set of symmetry operations in crystallography.
  • These operations leave the structure of a crystal unchanged.
  • There are 32 crystallographic point groups.
  • These groups determine the directional variation of physical properties in a crystal.
  • The groups must maintain three-dimensional translational symmetry.

Notations for Crystallographic Point Groups

  • Crystallographers, mineralogists, and physicists use standard notations.
  • Schoenflies notation is one of the notations used.
  • Schoenflies notation uses letter symbols with subscripts.
  • The symbols represent different symmetry elements.
  • The symbols indicate rotation axes, mirror planes, and other elements.
  • Hermann-Mauguin notation is another notation used for crystallographic point groups.
  • It represents the 32 crystallographic point groups.
  • The notation uses symbols and numbers to represent different symmetry elements.
  • Subgroup relations can be determined using Hermann-Mauguin notation.
  • The notation helps in understanding the symmetry properties of crystals.

Schoenflies Notation

  • Schoenflies notation denotes point groups with letter symbols.
  • The symbols represent different types of symmetry elements.
  • The symbols indicate rotation axes, mirror planes, and other elements.
  • The letter 'C' represents cyclic rotation axes.
  • The letter 'D' represents dihedral rotation axes.

Hermann-Mauguin Notation

  • Hermann-Mauguin notation is another notation used for crystallographic point groups.
  • It represents the 32 crystallographic point groups.
  • The notation uses symbols and numbers to represent different symmetry elements.
  • Subgroup relations can be determined using Hermann-Mauguin notation.
  • The notation helps in understanding the symmetry properties of crystals.

Deriving Crystallographic Point Group

  • The crystallographic point group can be derived from the space group.
  • The Bravais lattice type is excluded in the derivation.
  • Symmetry elements with translational components are converted into elements without translation symmetry.
  • Axes of rotation, rotoinversion axes, and mirror planes remain unchanged.
  • The derived crystallographic point group represents the crystal class.

Crystallographic point group Data Sources

Reference URL
Glossary https://harryandcojewellery.com.au/blogs/glossary/crystallographic-point-group
Wikipedia http://en.wikipedia.org/wiki/Crystallographic_point_group
Wikidata https://www.wikidata.org/wiki/Q1066315
Knowledge Graph https://www.google.com/search?kgmid=/m/030w_c

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