Laue class

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== Definition ==
== Definition ==
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The Laue classes correspond to the eleven centrosymmetric point groups. When absorption is negligible and [[Friedel's law]] applies, it impossible to distinguish by diffraction between a centrosymmetric point group and one of its non-centrosymmetric subgroups.
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The Laue classes correspond to the eleven centrosymmetric 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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{| border cellspacing="0" cellpadding="5" align=center>
{| border cellspacing="0" cellpadding="5" align=center>
   
   
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|Laue class||Non-centrosymmetric groups having the same Laue class
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|Laue classes||Non-centrosymmetric groups<br> having the same Laue class
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| <math>{\bar 1}</math>|| 1
| <math>{\bar 1}</math>|| 1
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|<math>m{\bar 3}m</math>|| 432, <math>{\bar 4}</math>32
|<math>m{\bar 3}m</math>|| 432, <math>{\bar 4}</math>32
|}
|}
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<table border cellspacing="0" cellpadding="5" align=center>
 
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<tr>
 
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<th> Laue class</th> <th> Non-centrosymmetric groups </th>
 
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</tr>
 
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<th> </th> <th> having the same Laue class</th>
 
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</tr>
 
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<tr>
 
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<td> <math>{\bar 1}</math></td> <td> 1</td>
 
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</tr>
 
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<tr>
 
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<td>2/''m''</td> <td> 2, ''m''</td>
 
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</tr>
 
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<tr>
 
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<td>''mmm''</td><td> 222, 2''mm''</td>
 
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</tr>
 
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<tr>
 
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<td><math>{\bar 3}</math></td><td> 3</td>
 
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</tr>
 
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<tr>
 
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<td><math>{\bar 3}m</math></td><td> 32, 3''m''</td>
 
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</tr>
 
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<tr>
 
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<td>4/''m''</td><td> 4, <math>{\bar 4}</math></td>
 
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</tr>
 
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<tr>
 
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<td> 4/''mmm''</td><td> 422, <math>{\bar 4}2m</math>, 42''m''</td>
 
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</tr>
 
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<tr>
 
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<td>6/''m''</td><td> 6, <math>{\bar 6}</math></td>
 
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</tr>
 
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<tr>
 
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<td>6/''mmm''</td><td> 622, <math>{\bar 6}2m</math>, 62''m''</td>
 
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</tr>
 
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<tr>
 
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<td><math>m{\bar 3}</math></td><td> 23</td>
 
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</tr>
 
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<tr>
 
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<td><math>m{\bar 3}m</math></td><td> 432, <math>{\bar 4}</math>32</td>
 
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</tr>
 
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</table>
 
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</center>
</center>

Revision as of 07:45, 26 March 2006

Classes de Laue (Fr). Laue Klassen (Ge). Clases de Laue (Sp).

Definition

The Laue classes correspond to the eleven centrosymmetric 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.


Laue classesNon-centrosymmetric groups
having the same Laue class
{\bar 1} 1
2/m 2, m
mmm 222, 2mm
{\bar 3} 3
{\bar 3}m 32, 3m
4/m 4, {\bar 4}
4/mmm 422, {\bar 4}2m, 42m
6/m 6, {\bar 6}
6/mmm 622, {\bar 6}2m, 62m
m{\bar 3} 23
m{\bar 3}m 432, {\bar 4}32

See also

Section 3.1 of International Tables of Crystallography, Section A