Difference between revisions of "Twinning"
From Online Dictionary of Crystallography
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'''symmetry of a twin''' - See ''[[Eigensymmetry]]'' | '''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 | + | 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]]'' 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''<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). | ||
Revision as of 15:24, 9 April 2015
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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 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[math] \bar 3[/math]m crystal point group; {111} twin law; [math] \bar 3[/math]/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