Symmorphic space groups - Revision history

MassimoNespolo: Grammar error corrected (Ru)

2025-02-20T14:50:16Z

Grammar error corrected (Ru)

BrianMcMahon: Tidied translations.

2017-11-20T09:20:38Z

Tidied translations.

BrianMcMahon: Style edits to align with printed edition

2017-05-22T13:12:12Z

Style edits to align with printed edition

BrianMcMahon: Style edits to align with printed edition

2017-05-17T12:00:27Z

Style edits to align with printed edition

MassimoNespolo: /* See also */ ITA 6th edition

2017-04-11T16:54:22Z

‎See also: ITA 6th edition

MassimoNespolo: /* Definition */ link

2016-11-24T13:45:22Z

‎Definition: link

MassimoNespolo: Spanish

2016-04-27T16:21:46Z

Spanish

MassimoNespolo: Ru

2016-04-27T13:34:30Z

MassimoNespolo: /* Subdivision */ typo (Pccm, not Pccn)

2016-04-06T09:25:01Z

‎Subdivision: typo (Pccm, not Pccn)

MassimoNespolo: /* Subdivision */ typo

2016-04-05T10:27:11Z

‎Subdivision: typo

← Older revision		Revision as of 14:50, 20 February 2025
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−	<font color="blue">Groupes d'espaces symorphiques</font> (''Fr''). <font color="red">Symmorphe Raumgruppen</font> (''Ge''). <font color="black">Gruppi spaziali simmorfici</font> (''It''). <font color="purple">共型空間群 </font>(''Ja''). <font color="brown">Симорфные ~~пространственных групп~~</font> (''Ru''). <font color="green">Grupos de espacio simórficos</font> (''Sp'').	+	<font color="blue">Groupes d'espaces symorphiques</font> (''Fr''). <font color="red">Symmorphe Raumgruppen</font> (''Ge''). <font color="black">Gruppi spaziali simmorfici</font> (''It''). <font color="purple">共型空間群 </font>(''Ja''). <font color="brown">Симорфные пространственные группы</font> (''Ru''). <font color="green">Grupos de espacio simórficos</font> (''Sp'').

← Older revision		Revision as of 09:20, 20 November 2017
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−	<~~Font~~ color="blue">Groupes d'espaces symorphiques</~~Font~~> (''Fr''). <~~Font~~ color="red">Symmorphe Raumgruppen</~~Font~~> (''Ge''). <~~Font~~ color="~~green~~">~~Grupos de espacio simórficos~~</~~Font~~> (''Sp''). <~~Font~~ color="~~black~~">~~Gruppi spaziali simmorfici~~</~~Font~~> (''It''). <~~Font~~ color="brown">Симорфные пространственных групп</~~Font~~> (''Ru''). <~~Font~~ color="~~Purple~~">~~共型空間群~~ </~~Font~~>(''Ja'').	+	<font color="blue">Groupes d'espaces symorphiques</font> (''Fr''). <font color="red">Symmorphe Raumgruppen</font> (''Ge''). <font color="black">Gruppi spaziali simmorfici</font> (''It''). <font color="purple">共型空間群 </font>(''Ja''). <font color="brown">Симорфные пространственных групп</font> (''Ru''). <font color="green">Grupos de espacio simórficos</font> (''Sp'').
		+

	== Definition ==		== Definition ==

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 ==Subdivision==
 Fedorov (see B.K. Vainshtein, ''Fundamentals of Crystals'') distinguished non-symmorphic space groups in two types:
-* ''hemisymmorphic'': non-[[Sohncke groups]] whose [[site symmetry|site-symmetry group]] of highest order is a a subgroup of index 2 of the point group and contains only operations of the first kind;
+* ''hemisymmorphic'': non-[[Sohncke groups]] whose [[site symmetry|site-symmetry group]] of highest order is a subgroup of index 2 of the point group and contains only operations of the first kind;
 * ''asymmorphic'': all the other groups.
-''Example''. ''Pmmm'' is a symmorphic type of space group whose site-symmetry group of highest order is of type ''mmm''. Among the other fifteen types of group in the same [[arithmetic crystal class]]. three (''Pnnn'' ''Pccm'' and ''Pban'') have a site-symmetry group of highest order of type 222, ''i''.''e''. a subgroup of order two of ''mmm'' that contains only operations of the first kind and are thus hemisymmophic according to Fedorov's definition. The other twelve are asymmorphic.
+''Example''. ''Pmmm'' is a symmorphic type of space group whose site-symmetry group of highest order is of type ''mmm''. Among the other fifteen types of group in the same [[arithmetic crystal class]]. three (''Pnnn''. ''Pccm'' and ''Pban'') have a site-symmetry group of highest order of type 222, ''i''.''e''. a subgroup of order two of ''mmm'' that contains only operations of the first kind and are thus hemisymmophic according to Fedorov's definition. The other twelve are asymmorphic.
 == See also ==

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-<Font color="blue">Groupes d'espaces symorphiques</Font> (''Fr''); <Font color="red">Symmorphe Raumgruppen</Font> (''Ge''); <Font color="green">Grupos de espacio simórficos</Font> (''Sp''); <Font color="black">Gruppi spaziali simmorfici</Font> (''It''); <Font color="brown">Симорфные пространственных групп</Font> (''Ru''); <Font color="Purple">共型空間群 </Font>(''Ja'').
+<Font color="blue">Groupes d'espaces symorphiques</Font> (''Fr''). <Font color="red">Symmorphe Raumgruppen</Font> (''Ge''). <Font color="green">Grupos de espacio simórficos</Font> (''Sp''). <Font color="black">Gruppi spaziali simmorfici</Font> (''It''). <Font color="brown">Симорфные пространственных групп</Font> (''Ru''). <Font color="Purple">共型空間群 </Font>(''Ja'').
 == Definition ==
-A [[space group]] is called '''symmorphic''' if, apart from the lattice translations, all generating symmetry operations leave one common point fixed. Permitted as generators are thus only the point-group operations: rotations, reflections, inversions and rotoinversions. The symmorphic space groups may be easily identified because their [[Hermann-Mauguin symbols|Hermann-Mauguin symbol]] does not contain a glide or screw operation. The combination of the Bravais lattices with symmetry elements with no translational components yields the 73 symmorphic space groups, ''e.g.'' ''P''2, ''Cm'', ''P''2/''m'', ''P''222, ''P''32, ''P''23. They are in one to one correspondence with the [[arithmetic crystal classes]].
+A [[space group]] is called '''symmorphic''' if, apart from the lattice translations, all generating symmetry operations leave one common point fixed. Permitted as generators are thus only the point-group operations: rotations, reflections, inversions and rotoinversions. The symmorphic space groups may be easily identified because their [[Hermann-Mauguin symbols|Hermann-Mauguin symbol]] does not contain a glide or screw operation. The combination of the Bravais lattices with symmetry elements with no translational components yields the 73 symmorphic space groups, ''e.g.'' ''P''2, ''Cm'', ''P''2/''m'', ''P''222, ''P''32, ''P''23. They are in one-to-one correspondence with the [[arithmetic crystal classes]].
 A characteristic feature of a symmorphic space group is the existence of a special position, the [[site symmetry|site-symmetry]] group of which is isomorphic to the point group to which the space group belongs. Symmorphic space groups have no [[zonal reflection conditions|zonal]] or [[serial reflection conditions]], but may have [[integral reflection conditions]] (''e.g.'' ''C''2, ''Fmmm'').
 ==Note==
-In  the literature sometimes it is found the wrong statement that a symmorphic space group does not contain glide planes or screw axes. This comes from a misunderstanding for the fact that, according to the [[priority rule]], glide planes and screw axes do not appear in the Hermann-Mauguin symbol of the space group, although they can be present in the group. For example, a space group of type ''Amm''2 contains ''c'' glides perpendicular to [010] and passing at ''x'',1/4,''z'' as well as two-fold screws parallel to [001] and passing at 0,1/4,''z''. This is not even limited to space groups with centred [[conventional cell]]s: for example, a space group of type ''P''422 contains two-fold screws parallel to the two-fold axes.
+In  the literature is sometimes found the wrong statement that a symmorphic space group does not contain glide planes or screw axes. This comes from a misunderstanding of the fact that, according to the [[priority rule]], glide planes and screw axes do not appear in the Hermann-Mauguin symbol of the space group, although they can be present in the group. For example, a space group of type ''Amm''2 contains ''c'' glides perpendicular to [010] and passing at ''x'',1/4,''z'' as well as two-fold screws parallel to [001] and passing at 0,1/4,''z''. This is not even limited to space groups with centred [[conventional cell]]s: for example, a space group of type ''P''422 contains two-fold screws parallel to the two-fold axes.
 ==Subdivision==
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 == See also ==
-*Section 1.3.3.3 of ''International Tables for Crystallography, Volume A'', 6<sup>th</sup> edition
+*Chapter 1.3.3.3 of ''International Tables for Crystallography, Volume A'', 6th edition
-*Section 1.4 of ''International Tables for Crystallography, Volume C''
+*Chapter1.4 of ''International Tables for Crystallography, Volume C''
 [[Category:Fundamental crystallography]]

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 == See also ==
-*Sections 2.2.5 and 8.1.6 of ''International Tables for Crystallography, Volume A''
+*Section 1.3.3.3 of ''International Tables for Crystallography, Volume A'', 6<sup>th</sup> edition
 *Section 1.4 of ''International Tables for Crystallography, Volume C''
 [[Category:Fundamental crystallography]]

← Older revision		Revision as of 16:21, 27 April 2016
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−	<Font color="blue">Groupes d'espaces symorphiques</Font> (''Fr''); <Font color="red">Symmorphe Raumgruppen</Font> (''Ge''); <Font color="black">Gruppi spaziali simmorfici</Font> (''It''); <Font color="brown">Симорфные пространственных групп</Font> (''Ru''); <Font color="Purple">共型空間群 </Font>(''Ja'').	+	<Font color="blue">Groupes d'espaces symorphiques</Font> (''Fr''); <Font color="red">Symmorphe Raumgruppen</Font> (''Ge''); <Font color="green">Grupos de espacio simórficos</Font> (''Sp''); <Font color="black">Gruppi spaziali simmorfici</Font> (''It''); <Font color="brown">Симорфные пространственных групп</Font> (''Ru''); <Font color="Purple">共型空間群 </Font>(''Ja'').

	== Definition ==		== Definition ==

← Older revision		Revision as of 13:34, 27 April 2016
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−	<Font color="blue">Groupes d'espaces symorphiques </Font>(''Fr''). <Font color="red"> Symmorphe Raumgruppen </Font> (''Ge''). <Font color="black"> Gruppi spaziali simmorfici </Font>(''It''). <Font color="Purple"> 共型空間群 </Font>(''Ja'').	+	<Font color="blue">Groupes d'espaces symorphiques</Font> (''Fr''); <Font color="red">Symmorphe Raumgruppen</Font> (''Ge''); <Font color="black">Gruppi spaziali simmorfici</Font> (''It''); <Font color="brown">Симорфные пространственных групп</Font> (''Ru''); <Font color="Purple">共型空間群 </Font>(''Ja'').

	== Definition ==		== Definition ==