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="black">Operazione di geminazione</Font> (''It''); <Font color="purple">双晶操作</Font> (''Ja''). |
Revision as of 11:16, 26 February 2007
Opération de maclage (Fr); Operazione di geminazione (It); 双晶操作 (Ja).
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 twin point group.
See also
Chapter 3.3 of International Tables of Crystallography, Volume D