# Twin law

(Difference between revisions)
 Revision as of 09:43, 26 April 2006 (view source)← Older edit Latest revision as of 14:15, 20 November 2017 (view source) (Added German and Spanish translations (U. Mueller)) (12 intermediate revisions not shown) Line 1: Line 1: - Loi de macle (''Fr''). Legge di geminazione (''It'') + Loi de macle (''Fr''). Zwillingsgesetz (''Ge''). Legge di geminazione (''It''). 双晶則 (''Ja''). Ley de macla (''Sp''). - = Twin law = + The '''twin law''' is the set of [[twin operation]]s mapping two individuals of a [[twin]]. It is obtained by [[coset]] decomposition of the point group of the [[twin lattice]] with respect to the intersection group of the point groups of the individuals in their respective orientations. Each operation in the same coset is a possible twin operation that, from the lattice viewpoint, is equivalent to any other operation in the same coset. Any of these can be taken as '''coset representative''' and indicated by the symbol of the twin element: $\bar 1$, [''uvw''] and (''hkl'') for the centre (''[[inversion twin]]''), direction of the rotation axis  (''[[rotation twin]]'') and [[Miller indices]] of the mirror plane (''[[reflection twin]]''), in that order. Except when one refers to a specific plane or direction, the symbols {''hkl''} or <''uvw''> have to be be used to indicate all the planes or directions which belong to the same [[coset]] and are therefore equivalent under the point group of the individual. - The ''twin law'' expresses the operation that generate a ''[[twin]]''. It is indicated by the symbol of the twinning element of symmetry: $\bar 1$, [uvw] and (''hkl'') for the centre of symmetry (''[[inversion twin]]''), direction of the rotation axis  (''[[rotation twin]]'') and [[Miller indices]] of the mirror plane (''[[reflection twin]]''), in the order. Usually, instead of the single (''hkl'') plane, the symbol {''hkl''} is used to indicate all the planes equivalent for symmetry. + In the case of [[TLQS twinning]] the equivalence of the operations in a coset is only approximate. - Chapter 3.3 of ''International Tables of Crystallography, Volume D''
+ ==See also== + *Chapter 3.3 of ''International Tables for Crystallography, Volume D'' - [[Category:Fundamental crystallography]] + [[Category:Twinning]]

## Latest revision as of 14:15, 20 November 2017

Loi de macle (Fr). Zwillingsgesetz (Ge). Legge di geminazione (It). 双晶則 (Ja). Ley de macla (Sp).

The twin law is the set of twin operations mapping two individuals of a twin. It is obtained by coset decomposition of the point group of the twin lattice with respect to the intersection group of the point groups of the individuals in their respective orientations. Each operation in the same coset is a possible twin operation that, from the lattice viewpoint, is equivalent to any other operation in the same coset. Any of these can be taken as coset representative and indicated by the symbol of the twin element: $\bar 1$, [uvw] and (hkl) for the centre (inversion twin), direction of the rotation axis (rotation twin) and Miller indices of the mirror plane (reflection twin), in that order. Except when one refers to a specific plane or direction, the symbols {hkl} or <uvw> have to be be used to indicate all the planes or directions which belong to the same coset and are therefore equivalent under the point group of the individual.

In the case of TLQS twinning the equivalence of the operations in a coset is only approximate.