Derivative structure

From Online Dictionary of Crystallography

Structure dérivative (Fr). Struttura derivativa (It).

A derivative structure is a crystal structure S’ obtained from another crystal structure (called a basic structure) S under the following conditions:

  • the space group G’ of S is a subgroup of the space group G of S;
  • the translation lattice is preserved, i.e. the translation subgroup T(G’) of S’ is the same as the translation subgroup T(G) of S;
  • as a consequence, the point group of P’ of S’ is a subgroup of the point group P of S (i.e. S’ belong to a lower-symmetric geometric crystal class with respect to S);
  • at least one of the Wyckoff positions of S is split into two or more independent Wyckoff positions of S’ and the corresponding crystallographic orbits are occupied by chemically different atoms.
A structure S composed by a single crystallographic orbit
A structure S' obtained from S by reducing its point symmetry while preserving its translation lattice. Atomic positions represented by a different colour are not equivalent in S' and are occupied by chemically different atoms. S is called a basic structure, S' a derivative structure of S


The definition of derivative structure was introduced by Martin J. Buerger: Journal of Chemical Physics 15 (1947) 1-16.

See also