HermannMauguinnotationen

Hermann–Mauguin notation is a system used in crystallography and materials science to describe the symmetry of crystal structures and point groups. Developed independently by German physicist Friedrich Hermann and French crystallographer Charles-Victor Mauguin in the late 19th century, this notation provides a standardized way to classify the 32 crystallographic point groups, which represent the rotational symmetries of crystals.

The notation consists of a sequence of symbols that indicate the types and multiplicities of symmetry operations present in a crystal. Each symbol corresponds to a specific axis of symmetry, with letters representing the order of rotation:

- *C* (or *n*) denotes a rotation axis of order *n* (e.g., *C₂* for a twofold axis).

- *S* indicates a screw axis, combining rotation and translation.

- *M* represents a mirror plane.

- *G* denotes a glide plane.

- *I* signifies an inversion center.

For example, the notation *4/mmm* describes a crystal with a fourfold rotation axis, two mirror planes perpendicular to it, and three mirror planes intersecting the axis. This system is particularly useful for visualizing and comparing the symmetry properties of different crystal systems, including cubic, tetragonal, orthorhombic, hexagonal, trigonal, and monoclinic structures.

Hermann–Mauguin notation is widely adopted in crystallography due to its clarity and efficiency. It complements the international tables for crystallography, which provide detailed descriptions of space groups and their symmetry elements. The notation is also applicable in fields such as solid-state physics and materials engineering, where understanding crystal symmetry is essential for predicting material properties.