Difference between revisions of "Twin operation"
From Online Dictionary of Crystallography
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| − | <font color="blue">Opération de maclage</font> (''Fr''). < | + | <font color="blue">Opération de maclage</font> (''Fr''). <font color="red">Zwillingsoperation</font> (''Ge''). <font color="black">Operazione di geminazione</font> (''It''). <font color="purple">双晶操作</font> (''Ja''). <font color="green">Operación de macla</font> (''Sp''). |
Latest revision as of 14:21, 20 November 2017
Opération de maclage (Fr). Zwillingsoperation (Ge). Operazione di geminazione (It). 双晶操作 (Ja). Operación de macla (Sp).
The operation (action) of an element of symmetry that generates a twin.
Let Hi be the oriented point group of the i-th individual of a twin. The intersection group of the oriented vector point groups Hi of the individuals is indicated as H* = ∩iHi. The symmetry of a twin is identified in vector space by a point group K which is a supergroup of H*. The coset decomposition of K with respect to H* gives the possible twin laws, each coset representing a twin law, and each operation in a coset representing a twin operation; the operations in a coset are equivalent under the operations of H*.
Operations in H describe the vector point symmetry of the individuals, whereas those in the cosets obtained by decomposing K in terms of H* connect the different individuals. To underline their different nature, the twin operations are often associated with a 'colour' and K is a thus a chromatic vector point group, known as a twin point group.
See also
- Chapter 3.3 of International Tables for Crystallography, Volume D