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<Font color="blue"> Classes de Laue </Font> (''Fr''). <Font color="red"> Laue Klassen</Font> (''Ge'').<Font color="green"> Clases de Laue </Font> (''Sp'').<Font color="black"> Classi di Laue </Font>(''It'')
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<font color="blue">Classe de Laue</font> (''Fr''). <font color="red">Laue-Klasse</font> (''Ge''). <font color="black">Classi di Laue</font>(''It''). <font color="purple">ラウエ結晶類</font>(''Ja''). <font color="green">Clase de Laue</font> (''Sp'').
  
  
 
== Definition ==
 
== Definition ==
  
The Laue classes correspond to the eleven centrosymmetric crystallographic point groups. When absorption is negligible and [[Friedel's law]] applies, it is impossible to distinguish by diffraction between a centrosymmetric point group and one of its non-centrosymmetric subgroups.
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The Laue classes are eleven [[geometric crystal class]]es containing centrosymmetric crystallographic types of point groups and their subgroups. When absorption is negligible and [[Friedel's law]] applies, it is impossible to distinguish by diffraction between a centrosymmetric point group and one of its non-centrosymmetric subgroups; only point groups belonging to different Laue classes can then be distinguished.
  
  
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{| border cellspacing="0" cellpadding="5" align=center>
 
{| border cellspacing="0" cellpadding="5" align=center>
 
   
 
   
|Laue classes||Non-centrosymmetric groups<br> having the same Laue class
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|'''Laue classes'''||'''Non-centrosymmetric groups<br> in the same Laue class'''
 
|-
 
|-
 
| <math>{\bar 1}</math>|| 1
 
| <math>{\bar 1}</math>|| 1
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|4/''m''|| 4, <math>{\bar 4}</math>
 
|4/''m''|| 4, <math>{\bar 4}</math>
 
|-
 
|-
|4/''mmm''|| 422, <math>{\bar 4}2m</math>, 42''m''
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|4/''mmm''|| 422, <math>{\bar 4}2m</math>, 4''mm''
 
|-
 
|-
 
|6/''m''|| 6, <math>{\bar 6}</math>
 
|6/''m''|| 6, <math>{\bar 6}</math>
 
|-
 
|-
|6/''mmm''|| 622, <math>{\bar 6}2m</math>, 62''m''
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|6/''mmm''|| 622, <math>{\bar 6}2m</math>, 6''mm''
 
|-
 
|-
 
|<math>m{\bar 3}</math>|| 23
 
|<math>m{\bar 3}</math>|| 23
 
|-
 
|-
|<math>m{\bar 3}m</math>|| 432, <math>{\bar 4}</math>32
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|<math>m{\bar 3}m</math>|| 432, <math>{\bar 4}</math>3''m''
 
|}
 
|}
 
</center>
 
</center>
  
 
== See also ==
 
== See also ==
 
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*Chapter 1.6 of ''International Tables for Crystallography, Volume A'', 6th edition
Section 3.1 of ''International Tables of Crystallography, Section A''<br>
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*Chapter 2.4 of ''International Tables for Crystallography, Volume D''
  
 
[[Category:Fundamental crystallography]]
 
[[Category:Fundamental crystallography]]

Latest revision as of 11:20, 7 October 2019

Classe de Laue (Fr). Laue-Klasse (Ge). Classi di Laue(It). ラウエ結晶類(Ja). Clase de Laue (Sp).


Definition

The Laue classes are eleven geometric crystal classes containing centrosymmetric crystallographic types of point groups and their subgroups. When absorption is negligible and Friedel's law applies, it is impossible to distinguish by diffraction between a centrosymmetric point group and one of its non-centrosymmetric subgroups; only point groups belonging to different Laue classes can then be distinguished.


Laue classes Non-centrosymmetric groups
in the same Laue class
[math]{\bar 1}[/math] 1
2/m 2, m
mmm 222, 2mm
[math]{\bar 3}[/math] 3
[math]{\bar 3}m[/math] 32, 3m
4/m 4, [math]{\bar 4}[/math]
4/mmm 422, [math]{\bar 4}2m[/math], 4mm
6/m 6, [math]{\bar 6}[/math]
6/mmm 622, [math]{\bar 6}2m[/math], 6mm
[math]m{\bar 3}[/math] 23
[math]m{\bar 3}m[/math] 432, [math]{\bar 4}[/math]3m

See also

  • Chapter 1.6 of International Tables for Crystallography, Volume A, 6th edition
  • Chapter 2.4 of International Tables for Crystallography, Volume D