# Derivative structure

### From Online Dictionary of Crystallography

##### Revision as of 08:46, 17 February 2019 by MassimoNespolo (talk | contribs)

Revision as of 08:46, 17 February 2019 by MassimoNespolo (talk | contribs)

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.

## Notes

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