# Twin law

(Difference between revisions)
 Revision as of 12:42, 17 March 2009 (view source) (→Twin law: Not necessarily true for twins with inclined axes)← Older edit Latest revision as of 14:15, 20 November 2017 (view source) (Added German and Spanish translations (U. Mueller)) (4 intermediate revisions not shown) Line 1: Line 1: - Loi de macle (''Fr''). Legge di geminazione (''It''). 双晶則(''Ja'') + 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''' 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 point group of the individual. Each operation in the same coset is a possible twin operation that, from the lattice viepoint, 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 the 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. - + - In case of [[TLQS twinning]] the equivalence of the operations in a coset is only approximate. + ==See also== ==See also== - Chapter 3.3 of ''International Tables of Crystallography, Volume D''
+ *Chapter 3.3 of ''International Tables for Crystallography, Volume D'' [[Category:Twinning]] [[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.