Kristallcentrumregel

The Kristallcentrumregel, often translated as the crystal center rule, is a principle in solid-state physics and crystallography that describes a fundamental property of the symmetry of crystal structures. Specifically, it pertains to the positioning of the crystallographic center of symmetry within a unit cell.

The rule states that if a crystal structure possesses a center of symmetry, this center must lie at a special position, which is typically a lattice point or a Wyckoff position with full site symmetry. This means that the symmetry element of inversion (a center of symmetry) is not arbitrarily located within the unit cell but is intrinsically linked to the crystallographic framework.

This principle has important implications for determining crystal structures and understanding their physical properties. For instance, the presence or absence of a center of symmetry dictates whether a material can exhibit certain phenomena like piezoelectricity. If a material is piezoelectric, it cannot possess a center of symmetry.

The Kristallcentrumregel is a consequence of the mathematical description of space groups, which classify all possible crystal symmetries. Within the framework of space groups, positions are classified by Wyckoff letters, and the site symmetry of these positions is well-defined. The rule ensures consistency between the overall symmetry of the crystal and the symmetry of the positions occupied by atoms.