# Difference between revisions of "Derivative structure"

### From Online Dictionary of Crystallography

(Created page with "<font color="blue">Structure dérivative</font> (''Fr''). <font color="black">Struttura derivativa</font> (''It''). A '''derivative structure''' is a crystal structure S’...") |
(category) |
||

(One intermediate revision by the same user not shown) | |||

Line 14: | Line 14: | ||

== See also == | == See also == | ||

− | [[Substructure]] | + | *[[Substructure]] |

− | [[Superstructure]] | + | *[[Superstructure]] |

+ | |||

+ | |||

+ | [[Category:Crystal chemistry]] | ||

+ | [[Category:Fundamental crystallography]] |

## Latest revision as of 09:24, 17 February 2019

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.