Twinning - Revision history

BrianMcMahon: Tidied translations and added German (U. Mueller)

2017-11-20T14:24:17Z

Tidied translations and added German (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-22T13:44:14Z

Style edits to align with printed edition

BrianMcMahon: Style edits to align with printed edition

2017-05-17T14:59:26Z

Style edits to align with printed edition

MassimoNespolo: /* Oriented association and twinning */ extensive reformulation

2015-04-09T15:38:10Z

‎Oriented association and twinning: extensive reformulation

MassimoNespolo: /* Oriented association and twinning */ domains was not cited

2015-04-09T15:26:28Z

‎Oriented association and twinning: domains was not cited

MassimoNespolo: "ning" was not translated

2015-04-09T15:25:50Z

"ning" was not translated

MassimoNespolo: /* Related articles */ removing a link to a non-existing page

2015-04-09T15:25:02Z

‎Related articles: removing a link to a non-existing page

MassimoNespolo: /* Oriented association and twinning */ nowhere in the literature such a name!

2015-04-09T15:24:28Z

‎Oriented association and twinning: nowhere in the literature such a name!

MassimoNespolo: /* Classification of twins */ link

2008-06-15T09:19:12Z

‎Classification of twins: link

MassimoNespolo: /* Classification of twins */ lien

2008-06-15T09:11:58Z

‎Classification of twins: lien

← Older revision		Revision as of 14:24, 20 November 2017
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−	<~~Font~~ color="blue"> Maclage </~~Font~~>(''Fr''). <~~Font~~ color="red"> Zwillingsbildung </~~Font~~>(''Ge''). <~~Font~~ color="~~green~~"> ~~Maclado (formación de macla)~~ </~~Font~~> (''Sp''). <~~Font~~ color="~~brown~~"> ~~двойникование~~ </Font> (''Ru''). <~~Font~~ color="~~black~~"> ~~Geminazione~~ </~~Font~~>(''It''). <~~Font~~ color="~~purple~~"> ~~双晶化~~ </~~Font~~>(''Ja'').	+	<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 =

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 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 [[geometric element]] about which it is performed, associated with this operation, is called [[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'').
+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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-<Font color="blue"> Maclage </Font>(''Fr''). <Font color="red"> Zwillingsbildung </Font>(''Ge''). <Font color="green"> Maclado (formación de macla) </Font> (''Sp''). <Font color="brown"> двойникование </Font> (''Ru''). <Font color="black"> Geminazione </Font>(''It''). <Font color="purple"> 双晶化 </Font>(''Ja'')
+<Font color="blue"> Maclage </Font>(''Fr''). <Font color="red"> Zwillingsbildung </Font>(''Ge''). <Font color="green"> Maclado (formación de macla) </Font> (''Sp''). <Font color="brown"> двойникование </Font> (''Ru''). <Font color="black"> Geminazione </Font>(''It''). <Font color="purple"> 双晶化 </Font>(''Ja'').
 = Oriented association and twinning =
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 = 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.
+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.
+The following categories of twins are described under the listed entries:
-*[[twinning by merohedry]]
+*[[Twinning by merohedry]]
-*[[twinning by pseudomerohedry]]
+*[[Twinning by pseudomerohedry]]
-*[[twinning by reticular merohedry]]
+*[[Twinning by reticular merohedry]]
-*[[twinning by reticular pseudomerohedry]]
+*[[Twinning by reticular pseudomerohedry]]
-*[[twinning by metric merohedry]]
+*[[Twinning by metric merohedry]]
-*[[twinning by reticular polyholohedry]]
+*[[Twinning by reticular polyholohedry]]
-*[[hybrid twin]]s
+*[[Hybrid twin]]s
-*plesiotwins
+*[[Allotwin]]s
-*[[allotwin]]s
+*[[Selective merohedry]]
-==Related articles==
+== See also ==
-*[[twinning (effects of)]]
-*[[twin index]]
+*[[Twin index]]
-*[[twin lattice]]
+*[[Twin lattice]]
-*[[twin law]]
+*[[Twin law]]
-*[[twin obliquity]]
+*[[Twin obliquity]]
-*[[corresponding twins]]
+*[[Corresponding twins]]
-*[[twinning (endemic conditions of)]]
+*[[Twinning (endemic conditions of)]]
 *[[Twinning (effects of)]]
+*Chapter 1.3 of ''International Tables for Crystallography, Volume C''
-= See also =
+*Chapter 3.3 of ''International Tables for Crystallography, Volume D''
 [[Category:Twinning]]

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 = 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 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''.
+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]].
-'''symmetry of a twin''' - See ''[[Eigensymmetry]]''
+A [[mapping]] relating differently oriented crystals cannot be a symmetry operation of the individual: it is called a [[twin operation]] and [[geometric element]] about which it is performed, associated with this operation, is called [[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'').
-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'').
+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 =

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 = 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''.
+Crystals (also called individuals or components) or domains 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]]''

← Older revision		Revision as of 15:25, 9 April 2015
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−	<Font color="blue"> Maclage </Font>(''Fr''). <Font color="red"> Zwillingsbildung </Font>(''Ge''). <Font color="green"> Maclado (formación de macla) </Font> (''Sp''). <Font color="brown"> двойникование </Font> (''Ru''). <Font color="black"> Geminazione </Font>(''It''). <Font color="purple"> 双晶 </Font>(''Ja'')	+	<Font color="blue"> Maclage </Font>(''Fr''). <Font color="red"> Zwillingsbildung </Font>(''Ge''). <Font color="green"> Maclado (formación de macla) </Font> (''Sp''). <Font color="brown"> двойникование </Font> (''Ru''). <Font color="black"> Geminazione </Font>(''It''). <Font color="purple"> 双晶化 </Font>(''Ja'')

	= Oriented association and twinning =		= Oriented association and twinning =

@@ Line 7: / Line 7: @@
 '''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'').
+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).