Difference between revisions of "Laue class"
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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''). |
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== Definition == | == Definition == | ||
| − | The Laue classes | + | 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 | + | |'''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>, | + | |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>, | + | |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> | + | |<math>m{\bar 3}m</math>|| 432, <math>{\bar 4}</math>3''m'' |
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</center> | </center> | ||
== See also == | == See also == | ||
| − | + | *Chapter 1.6 of ''International Tables for Crystallography, Volume A'', 6th edition | |
| − | + | *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