Arithmetic crystal classes - Revision history

MassimoNespolo: redirect

2009-03-18T11:59:40Z

redirect

MassimoNespolo at 16:27, 23 February 2007

2007-02-23T16:27:53Z

MassimoNespolo: /* Definition */ Bold

2007-02-23T15:33:30Z

‎Definition: Bold

AndreAuthier at 05:11, 5 May 2006

2006-05-05T05:11:00Z

AndreAuthier at 04:47, 5 May 2006

2006-05-05T04:47:35Z

GiovanniFerraris at 15:18, 17 March 2006

2006-03-17T15:18:03Z

AndreAuthier at 08:29, 11 February 2006

2006-02-11T08:29:00Z

BrianMcMahon: /* Definition */

2006-01-31T09:17:28Z

‎Definition

AndreAuthier at 05:57, 31 January 2006

2006-01-31T05:57:22Z

AndreAuthier at 16:55, 30 January 2006

2006-01-30T16:55:58Z

← Older revision		Revision as of 11:59, 18 March 2009
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−	~~See~~ [[arithmetic crystal class]]	+	#redirect [[arithmetic crystal class]]

← Older revision		Revision as of 16:27, 23 February 2007
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−	<Font Color="blue"> Classes cristallines arithmétiques </Font> (''Fr.''). <Font Color="red"> Arithmetische Kristallklasse </Font>(''Ge''). <Font Color="green">Clases cristallinas aritméticas</Font>(''Sp''). <Font color="black"> Classi cristalline aritmetiche </Font>(''It'')	+	See [[arithmetic crystal class]]
−
−
−	~~== Definition ==~~
−
−	~~The '''arithmetic crystal classes''' are obtained in an elementary fashion by combining the~~ [[geometric crystal classes]] and the corrresponding types of Bravais lattices. For instance, in the monoclinic system, there are three geometric crystal classes, 2, ''m'' and 2/''m'', and two types of Bravais lattices, ''P'' and ''C''. There are therefore six monoclinic arithmetic crystal classes. Their symbols are obtained by juxtaposing the symbol of the geometric class and that of the Bravais lattice, in that order: 2''P'', 2''C'', ''mP'', ''mC'', 2/''mP'', 2/''mC'' (note that in the space group symbol the order is inversed: ''P''2, ''C''2, etc...). In some cases, the centring vectors of the Bravais lattice and some symmetry elements of the crystal class may or may not be parallel; for instance, in the geometric crystal class ''mm'' with the Bravais lattice ''C'', the centring vector and the two-fold axis may be perpendicular or coplanar, giving rise to two different arithmetic crystal classes, ''mm''2''C'' and 2''mmC'' (or ''mm''2''A'', since it is usual to orient the two-fold axis parallel to ''c''), respectively. There are 13 two-dimensional arithmetic crystal classes and 73 three-dimensional arithmetic ~~crystal classes that are listed in the attached [[Arithmetic~~ crystal class~~\| table]]. They do not contain glide or screw elements and are therefore in one to one correspondence with the [[symmorphic]] groups.~~
−
−	~~The group-theoretical definition of the arithmetic crystal classes is given in Section 8.2.3 of ''International Tables of Crystallography, Volume A''.~~
−
−	~~== See also ==~~
−
−	~~Section 8.2.3 of ''International Tables of Crystallography, Volume A''<br>~~
−	~~Sections 1.3.4 and 1.5.3 of ''International Tables of Crystallography, Volume B''<br>~~
−	~~Section 1.4 of ''International Tables of Crystallography, Volume C''<br>~~
−
−
−	~~[[Category:Fundamental crystallography~~]]

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 == Definition ==
-The arithmetic crystal classes are obtained in an elementary fashion by combining the [[geometric crystal classes]] and the corrresponding types of Bravais lattices. For instance, in the monoclinic system, there are three geometric crystal classes, 2, ''m'' and 2/''m'', and two types of Bravais lattices, ''P'' and ''C''. There are therefore six monoclinic arithmetic crystal classes. Their symbols are obtained by juxtaposing the symbol of the geometric class and that of the Bravais lattice, in that order: 2''P'', 2''C'', ''mP'', ''mC'', 2/''mP'', 2/''mC'' (note that in the space group symbol the order is inversed: ''P''2, ''C''2, etc...). In some cases, the centring vectors of the Bravais lattice and some symmetry elements of the crystal class may or may not be parallel; for instance, in the geometric crystal class ''mm'' with the Bravais lattice ''C'', the centring vector and the two-fold axis may be perpendicular or coplanar, giving rise to two different arithmetic crystal classes, ''mm''2''C'' and 2''mmC'' (or ''mm''2''A'', since it is usual to orient the two-fold axis parallel to ''c''), respectively. There are 13 two-dimensional arithmetic crystal classes and 73 three-dimensional arithmetic crystal classes that are listed in the attached [[Arithmetic crystal class| table]]. They do not contain glide or screw elements and are therefore in one to one correspondence with the [[symmorphic]] groups.
+The '''arithmetic crystal classes''' are obtained in an elementary fashion by combining the [[geometric crystal classes]] and the corrresponding types of Bravais lattices. For instance, in the monoclinic system, there are three geometric crystal classes, 2, ''m'' and 2/''m'', and two types of Bravais lattices, ''P'' and ''C''. There are therefore six monoclinic arithmetic crystal classes. Their symbols are obtained by juxtaposing the symbol of the geometric class and that of the Bravais lattice, in that order: 2''P'', 2''C'', ''mP'', ''mC'', 2/''mP'', 2/''mC'' (note that in the space group symbol the order is inversed: ''P''2, ''C''2, etc...). In some cases, the centring vectors of the Bravais lattice and some symmetry elements of the crystal class may or may not be parallel; for instance, in the geometric crystal class ''mm'' with the Bravais lattice ''C'', the centring vector and the two-fold axis may be perpendicular or coplanar, giving rise to two different arithmetic crystal classes, ''mm''2''C'' and 2''mmC'' (or ''mm''2''A'', since it is usual to orient the two-fold axis parallel to ''c''), respectively. There are 13 two-dimensional arithmetic crystal classes and 73 three-dimensional arithmetic crystal classes that are listed in the attached [[Arithmetic crystal class| table]]. They do not contain glide or screw elements and are therefore in one to one correspondence with the [[symmorphic]] groups.
 The group-theoretical definition of the arithmetic crystal classes is given in Section 8.2.3 of ''International Tables of Crystallography, Volume A''.

← Older revision		Revision as of 05:11, 5 May 2006
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−	<Font Color="blue"> Classes cristallines arithmétiques </Font> (''Fr.''). <Font Color="red"> Arithmetische ~~Kristallklassen~~ </Font>(''Ge''). <Font Color="green">Clases cristallinas aritméticas</Font>(''Sp''). <Font color="black"> Classi cristalline aritmetiche </Font>(''It'')	+	<Font Color="blue"> Classes cristallines arithmétiques </Font> (''Fr.''). <Font Color="red"> Arithmetische Kristallklasse </Font>(''Ge''). <Font Color="green">Clases cristallinas aritméticas</Font>(''Sp''). <Font color="black"> Classi cristalline aritmetiche </Font>(''It'')

← Older revision		Revision as of 04:47, 5 May 2006
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−	<Font Color="blue"> Classes cristallines arithmétiques </Font> (''Fr.''). <Font Color="red"> Arithmetische ~~Kristall Klassen~~ </Font>(''Ge''). <Font Color="green">Clases cristallinas aritméticas</Font>(''Sp''). <Font color="black"> Classi cristalline aritmetiche </Font>(''It'')	+	<Font Color="blue"> Classes cristallines arithmétiques </Font> (''Fr.''). <Font Color="red"> Arithmetische Kristallklassen </Font>(''Ge''). <Font Color="green">Clases cristallinas aritméticas</Font>(''Sp''). <Font color="black"> Classi cristalline aritmetiche </Font>(''It'')

← Older revision		Revision as of 15:18, 17 March 2006
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−	<Font Color="blue"> Classes cristallines arithmétiques </Font> (''Fr.''). <Font Color="red"> Arithmetische Kristall Klassen </Font>(''Ge''). <Font Color="green">Clases cristallinas aritméticas</Font>(''Sp'').	+	<Font Color="blue"> Classes cristallines arithmétiques </Font> (''Fr.''). <Font Color="red"> Arithmetische Kristall Klassen </Font>(''Ge''). <Font Color="green">Clases cristallinas aritméticas</Font>(''Sp''). <Font color="black"> Classi cristalline aritmetiche </Font>(''It'')
		+

	== Definition ==		== Definition ==

← Older revision		Revision as of 08:29, 11 February 2006
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−	~~(French: ''~~Classes cristallines arithmétiques''. ~~German:~~ ''Arithmetische Kristall Klassen ''~~. Spanish:~~ ''Clases cristallinas aritméticas'').	+	<Font Color="blue"> Classes cristallines arithmétiques </Font> (''Fr.''). <Font Color="red"> Arithmetische Kristall Klassen </Font>(''Ge''). <Font Color="green">Clases cristallinas aritméticas</Font>(''Sp'').

	== Definition ==		== Definition ==

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 (French: ''Classes cristallines arithmétiques''. German: ''Arithmetische Kristall Klassen ''. Spanish: ''Clases cristallinas aritméticas'').
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-=== See also ===
+== See also ==
 Section 8.2.3 of ''International Tables of Crystallography, Volume A''<br>