View source for Derivative structure

<font color="blue">Structure dérivative</font> (''Fr''). <font color="black">Struttura derivativa</font> (''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 position]]s of S is split into two or more independent Wyckoff positions of S’ and the corresponding [[crystallographic orbit]]s are occupied by chemically different atoms.

[[Image:basic structure.png|right|thumb|A structure S composed by a single crystallographic orbit]]
[[Image:derivative structure.png|right|thumb|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]]
== Notes ==
The definition of derivative structure was introduced by Martin J. Buerger: ''Journal of Chemical Physics'' '''15''' (1947) 1-16.

== See also ==
*[[Substructure]]
*[[Superstructure]]


[[Category:Crystal chemistry]]
[[Category:Fundamental crystallography]]