Twin index - Revision history

BrianMcMahon: Added German and Spanish translations (U. Mueller)

2017-11-20T14:11:59Z

Added German and Spanish translations (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-17T13:52:53Z

Style edits to align with printed edition

BrianMcMahon at 11:48, 8 February 2012

2012-02-08T11:48:28Z

MassimoNespolo: /* Definition */

2007-05-29T09:00:19Z

‎Definition

MassimoNespolo at 17:34, 15 April 2007

2007-04-15T17:34:35Z

MassimoNespolo at 17:11, 15 April 2007

2007-04-15T17:11:06Z

MassimoNespolo: /* Definition */

2007-04-09T09:48:39Z

‎Definition

MassimoNespolo: /* Definition */

2007-04-09T09:42:49Z

‎Definition

MassimoNespolo at 09:41, 15 May 2006

2006-05-15T09:41:21Z

AndreAuthier at 16:41, 26 April 2006

2006-04-26T16:41:18Z

← Older revision		Revision as of 14:11, 20 November 2017
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−	<~~Font~~ color="blue"> Indice de macle </~~Font~~> (''Fr''). <~~Font~~ color="black"> Indice di geminazione </~~Font~~> (''It''). <~~Font~~ color="purple"> 双晶指数 </~~Font~~>(''Ja'').	+	<font color="blue">Indice de macle</font> (''Fr''). <font color="red">Zwillingsindex</font> (''Ge''). <font color="black">Indice di geminazione</font> (''It''). <font color="purple">双晶指数</font> (''Ja''). <font color="green">Índice de macla</font> (''Sp'').
		+

	== Definition ==		== Definition ==

@@ Line 1: / Line 1: @@
-<Font color="blue"> Indice de macle </Font> (''Fr''). <Font color="black"> Indice di geminazione </Font> (''It''), <Font color="purple"> 双晶指数 </Font>(''Ja'')
+<Font color="blue"> Indice de macle </Font> (''Fr''). <Font color="black"> Indice di geminazione </Font> (''It''). <Font color="purple"> 双晶指数 </Font>(''Ja'').
 == Definition ==
-A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)|twinning]]). The reciprocal ''n'' of the fraction 1/''n'' of (quasi)restored nodes is called ''twin index''
+A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)|twinning]]). The reciprocal ''n'' of the fraction 1/''n'' of (quasi)-restored nodes is called the '''twin index'''.
-Let (''hkl'') be the twin plane and [''uvw''] the lattice direction (quasi)-normal to it. alternatively, let [''uvw''] be the twin axis and (''hkl'') the lattice plane (quasi)-normal to it. For ''twofold operations'' (180º rotations or reflections) the twin index is:
+Let (''hkl'') be the twin plane and [''uvw''] the lattice direction (quasi)-normal to it. Alternatively, let [''uvw''] be the twin axis and (''hkl'') the lattice plane (quasi)-normal to it. For ''twofold operations'' (180º rotations or reflections) the twin index is:
 <div align="center">
-''n'' = ''X''/f, ''X'' = |''uh''+''vk''+''wl''|
+''n'' = ''X''/''f'', ''X'' = |''uh''+''vk''+''wl''|
 </div>
-where f depends on the [[direct lattice|lattice type]] and on the parities of ''X'', ''h'', ''k'', ''l'', ''u'', ''v'' and ''w'', as in the following table
+where ''f'' depends on the [[direct lattice|lattice type]] and on the parities of ''X'', ''h'', ''k'', ''l'', ''u'', ''v'' and ''w'', as in the following table.
 <table border cellspacing=0 cellpadding=5 align=center>
 <tr>
-<th>Lattice type</th><th>condition on ''hkl''</th><th>condition on ''uvw''</th><th>condition on ''X''</th><th>''n''</th>
+<th>Lattice type</th><th>Condition on ''hkl''</th><th>Condition on ''uvw''</th><th>Condition on ''X''</th><th>''n''</th>
 </tr>
 <tr>
@@ Line 88: / Line 88: @@
-When the twin operation is a rotation of higher degree about [''uvw''], in general the rotational symmetry of the two-dimensional mesh in the (''hkl'') plane does no longer coincide with that of the twin operation. The degree of restoration of lattice nodes must now take into account the two-dimensional coincidence index &Xi; for a plane of the family (''hkl''), which defines a super mesh in the [[twin lattice]]. Moreover, such a super mesh may exist in &xi; planes out of ''N'', depending on where is located the intersection of the [''uvw''] twin axis with the plane. The twin index ''n'' is finally given by:
+When the twin operation is a rotation of higher degree about [''uvw''], in general the rotational symmetry of the two-dimensional mesh in the (''hkl'') plane no longer coincides with that of the twin operation. The degree of restoration of lattice nodes must now take into account the two-dimensional coincidence index &Xi; for a plane of the family (''hkl''), which defines a super mesh in the [[twin lattice]]. Moreover, such a super mesh may exist in &xi; planes out of ''N'', depending on where is located the intersection of the [''uvw''] twin axis with the plane. The twin index ''n'' is finally given by
 <div align="center">
-''n'' = ''N''&Xi;/&xi;
+''n'' = ''N''&Xi;/&xi;.
 </div>
 == References ==
-*Chapter 3.1.9 in ''International Tables for X-Ray Crystallography'' (1959)
+*Chapter 3.1.9 of ''International Tables for X-ray Crystallography'' (1959)
 ==History==
-*Friedel, G. (1904). Étude sur les groupements cristallins. Extrait du Bullettin de la Société de l'Industrie minérale, Quatrième série, Tomes III e IV. Saint-Étienne, Société de l'imprimerie Thèolier J. Thomas et C., 485 pp.
+*Friedel, G. (1904). ''Étude sur les groupements cristallins. Extrait du Bullettin de la Société de l'Industrie minérale, Quatrième série'', Tomes III et IV. Saint-Étienne, Société de l'imprimerie Thèolier J. Thomas et C., 485 pp.
-*Friedel, G. (1926). Leçons de Cristallographie. Berger-Levrault, Nancy, Paris, Strasbourg, XIX+602 pp.
+*Friedel, G. (1926). ''Leçons de Cristallographie.'' Berger-Levrault, Nancy, Paris, Strasbourg, XIX+602 pp.
 == See also ==
-Chapter 1.3 of ''International Tables of Crystallography, Volume C''<br>
+*Chapter 1.3 of ''International Tables for Crystallography, Volume C''
-Chapter 3.3 of ''International Tables of Crystallography, Volume D''<br>
+*Chapter 3.3 of ''International Tables for Crystallography, Volume D''
 [[Category:Twinning]]

@@ Line 1: / Line 1: @@
 <Font color="blue"> Indice de macle </Font> (''Fr''). <Font color="black"> Indice di geminazione </Font> (''It''), <Font color="purple"> 双晶指数 </Font>(''Ja'')
 == Definition ==
@@ Line 14: / Line 13: @@
 where f depends on the [[direct lattice|lattice type]] and on the parities of ''X'', ''h'', ''k'', ''l'', ''u'', ''v'' and ''w'', as in the following table
-<center>
+<table border cellspacing=0 cellpadding=5 align=center>
 <tr>
 <th>Lattice type</th><th>condition on ''hkl''</th><th>condition on ''uvw''</th><th>condition on ''X''</th><th>''n''</th>
 <tr>
 <td rowspan="2" align="center">''P''</td><td rowspan="2">none</td><td rowspan="2">none</td><td>X odd</td><td>''n'' = ''X''</td>
@@ Line 35: / Line 34: @@
 <tr><td>''X''/2 even</td><td>''n'' = ''X''/4</td>
 </tr>
 <tr>
@@ Line 76: / Line 74: @@
 <td ''Italic text''rowspan="5" align="center">''F''</td><td>none</td><td>''u''+''v''+''w'' odd</td><td>none</td><td>''n'' = ''X''</td>
 </tr>
 <td rowspan="2">''h'', ''k'', ''l'' not all odd</td><td rowspan="2">u+v+w even</td><td>''X'' odd</td><td>''n'' = ''X''</td>
 </tr>
 <tr><td>''X'' even</td><td>''n'' = ''X''/2</td>
 </tr>
 <td rowspan="2">''h'', ''k'', ''l'' all odd</td><td rowspan="2">u+v+w even</td><td>''X''/2 odd</td><td>''n'' = ''X''/2</td>
 </tr>
 <tr><td>''X''/2 even</td><td>''n'' = ''X''/4</td>
 </table>
-</center>
 When the twin operation is a rotation of higher degree about [''uvw''], in general the rotational symmetry of the two-dimensional mesh in the (''hkl'') plane does no longer coincide with that of the twin operation. The degree of restoration of lattice nodes must now take into account the two-dimensional coincidence index &Xi; for a plane of the family (''hkl''), which defines a super mesh in the [[twin lattice]]. Moreover, such a super mesh may exist in &xi; planes out of ''N'', depending on where is located the intersection of the [''uvw''] twin axis with the plane. The twin index ''n'' is finally given by:

@@ Line 6: / Line 6: @@
 A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)|twinning]]). The reciprocal ''n'' of the fraction 1/''n'' of (quasi)restored nodes is called ''twin index''
-Let (''hkl'') be the twin plane and [''uvw''] the lattice direction (quasi)-normal to it. alternatively, let [''uvw''] be the twin axis and (''hkl'') the lattice plane (quasi)-normal to it. For ''binary operations'' (180º rotations or reflections) the twin index is:
+Let (''hkl'') be the twin plane and [''uvw''] the lattice direction (quasi)-normal to it. alternatively, let [''uvw''] be the twin axis and (''hkl'') the lattice plane (quasi)-normal to it. For ''twofold operations'' (180º rotations or reflections) the twin index is:
 <div align="center">

@@ Line 1: / Line 1: @@
-<Font color="blue"> Indice de macle </Font> (''Fr''). <Font color="black"> Indice di geminazione </Font> (''It''), <Font color="purple"> 晶双指数 </Font>(''Ja'')
+<Font color="blue"> Indice de macle </Font> (''Fr''). <Font color="black"> Indice di geminazione </Font> (''It''), <Font color="purple"> 双晶指数 </Font>(''Ja'')
 == Definition ==
-A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]|twinning). The reciprocal ''n'' of the fraction 1/''n'' of (quasi)restored nodes is called ''twin index''
+A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)|twinning]]). The reciprocal ''n'' of the fraction 1/''n'' of (quasi)restored nodes is called ''twin index''
 Let (''hkl'') be the twin plane and [''uvw''] the lattice direction (quasi)-normal to it. alternatively, let [''uvw''] be the twin axis and (''hkl'') the lattice plane (quasi)-normal to it. For ''binary operations'' (180º rotations or reflections) the twin index is:

← Older revision		Revision as of 17:11, 15 April 2007
Line 1:		Line 1:
−	<Font color="blue"> Indice de macle </Font> (''Fr''). <Font color="black"> Indice di geminazione </Font> (''It'')	+	<Font color="blue"> Indice de macle </Font> (''Fr''). <Font color="black"> Indice di geminazione </Font> (''It''), <Font color="purple"> 晶双指数 </Font>(''Ja'')

← Older revision		Revision as of 09:41, 15 May 2006
Line 101:		Line 101:
	Chapter 3.3 of ''International Tables of Crystallography, Volume D''<br>		Chapter 3.3 of ''International Tables of Crystallography, Volume D''<br>

−	[[Category:~~Fundamental crystallography~~]]	+	[[Category:Twinning]]