Difference between revisions of "Twinning"
From Online Dictionary of Crystallography
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In most twins the symmetry of a twin (''twin point group'') is that of the individual point group augmented by the symmetry of the twinning operation; however, a symmetry element that is oblique to the [[twin element]] is absent in the twin (e.g., ''spinel twins'': ''m''<math> \bar 3</math>''m'' crystal point group; {111} [[twin law]]; <math> \bar 3</math>/''m'' twin point group). | In most twins the symmetry of a twin (''twin point group'') is that of the individual point group augmented by the symmetry of the twinning operation; however, a symmetry element that is oblique to the [[twin element]] is absent in the twin (e.g., ''spinel twins'': ''m''<math> \bar 3</math>''m'' crystal point group; {111} [[twin law]]; <math> \bar 3</math>/''m'' twin point group). | ||
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= Classification of twins = | = Classification of twins = | ||
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The following categories of twins are described under the listed entries. | The following categories of twins are described under the listed entries. | ||
| − | + | *[[twinning by merohedry]] | |
| − | + | *[[twinning by pseudomerohedry]] | |
| − | + | *[[twinning by reticular merohedry]] | |
| − | + | *[[twinning by reticular pseudomerohedry]] | |
| − | + | *[[twinning by metric merohedry]] | |
| − | + | *[[twinning by reticular polyholohedry]] | |
| − | + | *hybrid twins | |
| − | + | *plesiotwins | |
| − | + | *allotwins | |
| − | + | *selective merohedry | |
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==Related articles== | ==Related articles== | ||
| + | *[[twinning (effects of)]] | ||
| + | *[[twin index]] | ||
| + | *[[twin lattice]] | ||
| + | *[[twin law]] | ||
| + | *[[twin obliquity]] | ||
| + | *[[corresponding twins]] | ||
| + | *[[twinning (endemic conditions of)]] | ||
| − | + | === Effects of twinning === | |
| − | + | *[[Twinning (effects of)]] | |
| − | + | *[[Twin (diffractions pattern of)]] | |
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| − | = Effects of twinning = | ||
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| − | [[Twinning (effects of)]] | ||
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| − | [[Twin (diffractions pattern of)]] | ||
= See also = | = See also = | ||
| − | + | *Chapter 1.3 of ''International Tables of Crystallography, Volume C'' | |
| − | Chapter 1.3 of ''International Tables of Crystallography, Volume C'' | + | *Chapter 3.3 of ''International Tables of Crystallography, Volume D'' |
| − | Chapter 3.3 of ''International Tables of Crystallography, Volume D'' | ||
[[Category:Twinning]] | [[Category:Twinning]] | ||
Revision as of 17:24, 15 April 2007
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Contents
[hide]Oriented association and twinning
Crystals (also called individuals) belonging to the same phase form an oriented association if they can be brought to the same crystallographic orientation by a translation, rotation or reflection. Individuals related by a translation form a parallel association; strictly speaking these individuals have the same orientation even without applying a translation. Individuals related by a reflection [either plane (reflection twin) or centre (inversion twin) of symmetry] or a rotation (rotation twin) form a twin.
symmetry of a twin - See Eigensymmetry
An element of symmetry crystallographically relating differently oriented crystals cannot belong to the individual. The element of symmetry that relates the individuals of a twin is called twin element of symmetry (or simply twin element) and the connected operation is a twin operation. The Mallard's law states that the twin element (i.e. the geometrical element relative to which the twining operation is defined) is restricted to a direct lattice element: lattice nodes (twin centres), lattice rows (twin axes) and lattice planes (twin planes).
In most twins the symmetry of a twin (twin point group) is that of the individual point group augmented by the symmetry of the twinning operation; however, a symmetry element that is oblique to the twin element is absent in the twin (e.g., spinel twins: m \bar 3m crystal point group; {111} twin law; \bar 3/m twin point group).
Classification of twins
Twins are classified following Friedel's reticular (i.e. lattice) theory of twinning (see: G. Friedel Lecons de Cristallographie, Nancy (1926) where reference to previous work of the author can be found; see also Friedel's law). This theory states that the presence, either in the lattice or a sublattice of a crystal, of (pseudo)symmetry elements is a necessary, even if not sufficient, condition for the formation of twins. In presence of the reticular necessary conditions, the formation of a twin finally still depends on the matching of the crystal structures at the contact surface between the individuals.
The following categories of twins are described under the listed entries.
- twinning by merohedry
- twinning by pseudomerohedry
- twinning by reticular merohedry
- twinning by reticular pseudomerohedry
- twinning by metric merohedry
- twinning by reticular polyholohedry
- hybrid twins
- plesiotwins
- allotwins
- selective merohedry
Related articles
- twinning (effects of)
- twin index
- twin lattice
- twin law
- twin obliquity
- corresponding twins
- twinning (endemic conditions of)
Effects of twinning
See also
- Chapter 1.3 of International Tables of Crystallography, Volume C
- Chapter 3.3 of International Tables of Crystallography, Volume D