Partial symmetry - Revision history

BrianMcMahon: Tidied translations and corrected German (U. Mueller)

2017-11-17T09:39:31Z

Tidied translations and corrected German (U. Mueller)

MassimoNespolo: languages

2017-10-12T08:30:10Z

languages

BrianMcMahon: Style edits to align with printed edition

2017-05-16T12:18:34Z

Style edits to align with printed edition

MassimoNespolo at 17:34, 28 December 2008

2008-12-28T17:34:24Z

New page

Symétrie partielle (Fr); Simmetria parziale (It)

The symmetry operations of a [[space group]] are [[Euclidean mapping|isometries]] operating on the whole [[crystal pattern]] and are also called '''total operations''' or '''global operations'''. More generally, the crystal space can be divided in ''N'' components S1 to S''N'', and a coincidence operation φ(S''i'')→S''j'' can act on just the ''i''-th component S''i'' to bring it to coincide with the ''j''-th component S''j''. Such an operation is not one of the operations of the space group of the crystal because it is not a coincidence operation of the whole crystal space; it is not even defined, in general, for any component ''k'' different from ''i''. It is called a '''partial operation''': from the mathematical viewpoint, partial operations are [[Groupoid|space-groupoid operations]].

When ''i'' = ''j'', ''i''.''e''. when the operation is φ(S''i'')→S''i'' and brings a component to coincide with itself, the partial operation is of special type and is called '''[[local symmetry|local]]'''. A local operation is in fact a symmetry operation, which is defined only on a part of the crystal space: local operations may constitute a [[subperiodic group]].

[[Category: Fundamental crystallography]]

← Older revision		Revision as of 09:39, 17 November 2017
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−	<font color="blue">Symétrie partielle</font> (~~<i>~~Fr~~</i>~~); <font color="red">~~Partielle symmetrie~~</font> (~~<i>~~Ge~~</i>~~); <font color="black">Simmetria parziale</font> (~~<i>~~It~~</i>~~); <font color="purple">部分対称</font> (~~<i>~~Ja~~</i>~~); <font color="green">Simetría parcial</font> (~~<i>~~Sp~~</i>~~).	+	<font color="blue">Symétrie partielle</font> (''Fr''). <font color="red">Teilsymmetrie</font> (''Ge''). <font color="black">Simmetria parziale</font> (''It''). <font color="purple">部分対称</font> (''Ja''). <font color="green">Simetría parcial</font> (''Sp'').

← Older revision		Revision as of 08:30, 12 October 2017
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−	<font color="blue">Symétrie partielle</font> (<i>Fr</i>). <font color="black">Simmetria parziale</font> (<i>It</i>).	+	<font color="blue">Symétrie partielle</font> (<i>Fr</i>); <font color="red">Partielle symmetrie</font> (<i>Ge</i>); <font color="black">Simmetria parziale</font> (<i>It</i>); <font color="purple">部分対称</font> (<i>Ja</i>); <font color="green">Simetría parcial</font> (<i>Sp</i>).

@@ Line 1: / Line 1: @@
-<font color="blue">Symétrie partielle</font> (<i>Fr</i>); <font color="black">Simmetria parziale</font> (<i>It</i>)
+<font color="blue">Symétrie partielle</font> (<i>Fr</i>). <font color="black">Simmetria parziale</font> (<i>It</i>).
-The symmetry operations of a [[space group]] are [[Euclidean mapping|isometries]] operating on the whole [[crystal pattern]] and are also called '''total operations''' or '''global operations'''. More generally, the crystal space can be divided in ''N'' components S<sub>1</sub> to S<sub>''N''</sub>, and a coincidence operation &phi;(S<sub>''i''</sub>)&rarr;S<sub>''j''</sub> can act on just the ''i''-th component S<sub>''i''</sub> to bring it to coincide with the ''j''-th component S<sub>''j''</sub>. Such an operation is not one of the operations of the space group of the crystal because it is not a coincidence operation of the whole crystal space; it is not even defined, in general, for any component ''k'' different from ''i''. It is called a '''partial operation''': from the mathematical viewpoint, partial operations are [[Groupoid|space-groupoid operations]].
+The symmetry operations of a [[space group]] are [[Euclidean mapping|isometries]] operating on the whole [[crystal pattern]] and are also called '''total operations''' or '''global operations'''. More generally, the crystal space can be divided in ''N'' components S<sub>1</sub> to S<sub>''N''</sub>, and a coincidence operation &phi;(S<sub>''i''</sub>)&rarr;S<sub>''j''</sub> can act on just the ''i''th component S<sub>''i''</sub> to bring it to coincide with the ''j''th component S<sub>''j''</sub>. Such an operation is not one of the operations of the space group of the crystal because it is not a coincidence operation of the whole crystal space; it is not even defined, in general, for any component ''k'' different from ''i''. It is called a '''partial operation''': from the mathematical viewpoint, partial operations are [[Groupoid|space-groupoid operations]].
-When ''i'' = ''j'', ''i''.''e''. when the operation is &phi;(S<sub>''i''</sub>)&rarr;S<sub>''i''</sub> and brings a component to coincide with itself, the partial operation is of special type and is called '''[[local symmetry|local]]'''. A local operation is in fact a symmetry operation, which is defined only on a part of the crystal space: local operations may constitute a [[subperiodic group]].
+When ''i'' = ''j'', ''i.e.'' when the operation is &phi;(S<sub>''i''</sub>)&rarr;S<sub>''i''</sub> and brings a component to coincide with itself, the partial operation is of special type and is called '''[[local symmetry|local]]'''. A local operation is in fact a symmetry operation, which is defined only on a part of the crystal space: local operations may constitute a [[subperiodic group]].
 [[Category: Fundamental crystallography]]