Difference between revisions of "Twinning"
From Online Dictionary of Crystallography
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= Classification of twins = | = Classification of twins = | ||
| − | Twins are classified following Friedel ''reticular'' (i.e. lattice) ''theory of twinning'' | + | Twins are classified following Friedel ''reticular'' (i.e. lattice) ''theory of twinning''. 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 twing 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 merohedry]]''' | ||
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| − | + | '''[[twinning by reticular merohedry]]''' | |
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| − | + | '''[[twinning by reticular pseudomerohedry]]''' | |
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| + | * '''twinning by metric merohedry''' | ||
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* '''overlap of lattices''' | * '''overlap of lattices''' | ||
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Revision as of 15:28, 21 April 2006
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Contents
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 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 either by a reflection (mirror plane or centre of symmetry) or a rotation form a twin.
- symmetry of a twin
An element of symmetry crystallographically relating differently oriented crystals cannot belong to the individual. The element of symmetry that relates the indivduals of a twin is called twinning element of symmetry and the connected operation is a twinning operation of symmetry. The Mallard 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 twinning element of symmetry 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 reticular (i.e. lattice) theory of twinning. 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 twing 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 reticular merohedry
twinning by reticular pseudomerohedry
- twinning by metric merohedry
- overlap of lattices
By effect of a twinning operation, both the direct and reciprocal lattice of the individuals forming a twin are overlapped. Overlapping (restoration) of nodes belonging to different individuals can be: (i) exact and total (twinning by merohedry); (ii) exact but partial (i.e. only a fraction of the nodes of an individual lattice is restored; twinning by reticular merohedry); (iii) total but approximate (twinning by pseudomerohedry), approximate and partial (twinning by reticular pseudomerohedry).
- twin index
The reciprocal n of the fraction 1/n of (quasi)restored nodes is called twin index
- twin lattice
The lattice that is formed by the (quasi)restored nodes is the twin lattice. It corresponds to the crystal lattice in twins by (pseudo)merohedry and to a sublattice of the crystal (individual) in twins by reticular (pseudo)merohedry.
- twin obliquity
The twin obliquity is a measure of the distorsion of a (sub)lattice in twins by (reticular) pseudomerohedry.
- corresponding twins
Other categories of twins
Endemic conditions for twinning
See also
Chapter 1.3 of International Tables of Crystallography, Volume C
Chapter 3.3 of International Tables of Crystallography, Volume D