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Difference between revisions of "Laue class"

From Online Dictionary of Crystallography

(Definition: better formulation to emphasize the difference between a class and a group)
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== 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
 
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| <math>{\bar 1}</math>|| 1
 
| <math>{\bar 1}</math>|| 1

Revision as of 14:26, 22 December 2016

Classes de Laue (Fr). Laue Klassen (Ge). Clases de Laue (Sp). Classi di Laue (It)


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], 42m
6/m 6, [math]{\bar 6}[/math]
6/mmm 622, [math]{\bar 6}2m[/math], 62m
[math]m{\bar 3}[/math] 23
[math]m{\bar 3}m[/math] 432, [math]{\bar 4}[/math]32

See also

Chapter 3.1 of International Tables of Crystallography, Section A
Chapter 2.4 of International Tables of Crystallography, Section D