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