Difference between revisions of "Twinning"
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| − | < | + | <font color="blue">Maclage</font> (''Fr''). <font color="red">Zwillingsbildung, Verzwillingung</font> (''Ge''). <font color="black">Geminazione</font> (''It''). <font color="purple">双晶化</Font> (''Ja''). <font color="brown">двойникование</font> (''Ru''). <font color="green">Maclado (formación de macla)</font> (''Sp''). |
= Oriented association and twinning = | = Oriented association and twinning = | ||
| − | Crystals (also called individuals) belonging to the same phase form an oriented association if they can be brought to | + | Crystals (also called ''individuals'' or ''components'') or domains belonging to the same phase form an oriented association if they can be brought to coincidence by a translation, rotation, inversion or reflection. Individuals related by a translation form a ''parallel association''; domains related by a translation form ''antiphase domains''. Individuals or domains related by a reflection, inversion or rotation form a twin called, respectively, [[reflection twin]], [[inversion twin]] or [[rotation twin]]. |
| − | ''' | + | A [[mapping]] relating differently oriented crystals cannot be a symmetry operation of the individual: it is called a [[twin operation]] and the [[geometric element]] about which it is performed, associated with this operation, is called a [[twin element]]. [[Mallard's law]] states that the twin element is restricted to a [[direct lattice]] element: it can thus coincide with a lattice node (''twin centre''), a lattice row (''twin axis'') or a lattice plane (''twin plane''). |
| − | + | The symmetry of a twin (''twin point group'') is obtained by extending the intersection [[point group]] of the individuals in their respective orientations by the twin operation. | |
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= Classification of twins = | = Classification of twins = | ||
| − | Twins are classified following Friedel's ''reticular'' (i.e. lattice) ''theory of twinning'' | + | Twins are classified following Friedel's ''reticular'' (''i.e.'' lattice) ''theory of twinning'' [see G. Friedel (1926). ''Leçons de Cristallographie'', Nancy, 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 the presence of the necessary reticular conditions, the formation of a twin finally still depends on the matching of the crystal structures at the contact surface between the individuals. |
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| − | + | The following categories of twins are described under the listed entries: | |
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| − | [[ | + | *[[Twinning by merohedry]] |
| + | *[[Twinning by pseudomerohedry]] | ||
| + | *[[Twinning by reticular merohedry]] | ||
| + | *[[Twinning by reticular pseudomerohedry]] | ||
| + | *[[Twinning by metric merohedry]] | ||
| + | *[[Twinning by reticular polyholohedry]] | ||
| + | *[[Hybrid twin]]s | ||
| + | *[[Allotwin]]s | ||
| + | *[[Selective merohedry]] | ||
| − | = See also = | + | == See also == |
| − | Chapter 1.3 of ''International Tables | + | *[[Twin index]] |
| − | Chapter 3.3 of ''International Tables | + | *[[Twin lattice]] |
| + | *[[Twin law]] | ||
| + | *[[Twin obliquity]] | ||
| + | *[[Corresponding twins]] | ||
| + | *[[Twinning (endemic conditions of)]] | ||
| + | *[[Twinning (effects of)]] | ||
| + | *Chapter 1.3 of ''International Tables for Crystallography, Volume C'' | ||
| + | *Chapter 3.3 of ''International Tables for Crystallography, Volume D'' | ||
[[Category:Twinning]] | [[Category:Twinning]] | ||
Latest revision as of 14:24, 20 November 2017
Maclage (Fr). Zwillingsbildung, Verzwillingung (Ge). Geminazione (It). 双晶化 (Ja). двойникование (Ru). Maclado (formación de macla) (Sp).
Oriented association and twinning
Crystals (also called individuals or components) or domains belonging to the same phase form an oriented association if they can be brought to coincidence by a translation, rotation, inversion or reflection. Individuals related by a translation form a parallel association; domains related by a translation form antiphase domains. Individuals or domains related by a reflection, inversion or rotation form a twin called, respectively, reflection twin, inversion twin or rotation twin.
A mapping relating differently oriented crystals cannot be a symmetry operation of the individual: it is called a twin operation and the geometric element about which it is performed, associated with this operation, is called a twin element. Mallard's law states that the twin element is restricted to a direct lattice element: it can thus coincide with a lattice node (twin centre), a lattice row (twin axis) or a lattice plane (twin plane).
The symmetry of a twin (twin point group) is obtained by extending the intersection point group of the individuals in their respective orientations by the twin operation.
Classification of twins
Twins are classified following Friedel's reticular (i.e. lattice) theory of twinning [see G. Friedel (1926). Leçons de Cristallographie, Nancy, 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 the presence of the necessary reticular 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
- Allotwins
- Selective merohedry
See also
- Twin index
- Twin lattice
- Twin law
- Twin obliquity
- Corresponding twins
- Twinning (endemic conditions of)
- Twinning (effects of)
- Chapter 1.3 of International Tables for Crystallography, Volume C
- Chapter 3.3 of International Tables for Crystallography, Volume D