Crystallographic orbit - Revision history

BrianMcMahon: Tidied translations and added German and Spanish (U. Mueller)

2017-11-09T17:35:15Z

Tidied translations and added German and Spanish (U. Mueller)

2017-05-13T11:21:45Z

2017-05-13T11:17:08Z

2007-04-09T09:15:20Z

‎Types of crystallographic orbits: typo

2007-04-09T09:14:08Z

‎Crystallographic orbits and Wyckoff sets: typo

2007-04-09T09:13:33Z

‎Crystallographic orbits and Wyckoff positions

2007-04-09T09:10:22Z

‎Definition: typo

2007-04-09T09:08:55Z

typo

2007-04-06T13:46:01Z

‎Crystallographic orbits and point configurations

2007-04-06T13:32:41Z

← Older revision		Revision as of 17:35, 9 November 2017
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−	<~~Font~~ Color="blue"> Orbite cristallographique</~~Font~~> (''Fr''). <~~Font Color~~="red"> ~~Punktklage~~ </~~Font~~>(''Ge''). <~~Font~~ color="black"> Orbita cristallografica </~~Font~~>(''It''). <font color="purple">結晶軌道</font> (''Ja'').	+	<font Color="blue">Orbite cristallographique</font> (''Fr''). <font color="red">Kristallographisches Orbit</font> (''Ge''). <font color="black">Orbita cristallografica</font>(''It''). <font color="purple">結晶軌道</font> (''Ja''). <font color="green">Órbita cristalográfica</font> (''Sp'').

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 == Definition ==
 From any point of the three-dimensional Euclidean space the symmetry operations of a given space group ''G'' generate an infinite set of points, called a '''crystallographic orbit'''. The space group ''G'' is called the '''generating space group''' of the orbit.
-Two crystallographic orbits are said configuration-equivalent if and only if their sets of points are identical.
+Two crystallographic orbits are said to be configuration-equivalent if and only if their sets of points are identical.
 == Crystallographic orbits and site-symmetry groups ==

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-<Font Color="blue"> Orbite cristallographique</Font> (''Fr''). <Font Color="red"> Punktklage </Font>(''Ge''). <Font color="black"> Orbita cristallografica </Font>(''It''), <font color="purple">結晶軌道</font> (''Ja'').
+<Font Color="blue"> Orbite cristallographique</Font> (''Fr''). <Font Color="red"> Punktklage </Font>(''Ge''). <Font color="black"> Orbita cristallografica </Font>(''It''). <font color="purple">結晶軌道</font> (''Ja'').
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 == See also ==
-* Chapter 8.3.2 of ''International Tables of Crystallography, Section A''
+* Chapter 1.4.4.1 of ''International Tables for Crystallography, Volume A'', 6th edition
 [[Category:Fundamental crystallography]]

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 == Types of crystallographic orbits ==
-The generating space group of any crystallographic orbit may be compared with the inherent symmetry of its [[point configuration]]. If both groups coincinde, the orbit is called a ''characteristic crystallographic orbit'', otherwise it is called a ''non-characteristic crystallographic orbit''.
+The generating space group of any crystallographic orbit may be compared with the inherent symmetry of its [[point configuration]]. If both groups coincide, the orbit is called a ''characteristic crystallographic orbit'', otherwise it is called a ''non-characteristic crystallographic orbit''.
 If the inherent symmetry group contains ''translations'' additional to those of the generating space group, the orbit is called an ''extraordinary crystallographic orbit''.

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 == Crystallographic orbits and Wyckoff sets ==
-Two crystallographic orbits of a space gorup ''G'' belong to the same [[Wyckoff set]] if and only if
+Two crystallographic orbits of a space group ''G'' belong to the same [[Wyckoff set]] if and only if
 the [[Site symmetry|site-symmetry groups]] of any two points from the first and the second orbit are conjugate subgroups of the affine [[normalizer]] of ''G''.

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 == Crystallographic orbits and Wyckoff positions ==
-Two crystallographic orbits of a space gorup ''G'' belong to the same [[Wyckoff position]] if and only if the [[Site symmetry|site-symmetry groups]] of any two points from the first and the second orbit are conjugate subgroups of ''G''.
+Two crystallographic orbits of a space group ''G'' belong to the same [[Wyckoff position]] if and only if the [[Site symmetry|site-symmetry groups]] of any two points from the first and the second orbit are conjugate subgroups of ''G''.
 == Crystallographic orbits and Wyckoff sets ==

← Older revision		Revision as of 09:08, 9 April 2007
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−	In mathematics, an ''orbit'' is a general group-theoretical term describing any set of objects that are mapped onto each other by the action of a group. In crystallography, the concept of orbit is used to indicate a [[point configuration]] in association with its ~~generatig~~ group.	+	In mathematics, an ''orbit'' is a general group-theoretical term describing any set of objects that are mapped onto each other by the action of a group. In crystallography, the concept of orbit is used to indicate a [[point configuration]] in association with its generating group.

	== Definition ==		== Definition ==

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 A set of points has an [[eigensymmetry|inherent symmetry]], which corresponds to the group which has generated the set. However, this set of points may occur not only in its generating space group, but also in other space groups of different type. A set of points taken with its [[eigensymmetry|inherent symmetry]] but detached from its generating group is called a ''[[point configuration]]''.
-The relation between crystallographic orbits and point configurations in [[point space]] has a close analogy in [[vector space]] in the relation between the [[face form]] joined to the [[point group]] that has generated the form and the [[face form]] detached from its generating [[point group]].
+The relation between crystallographic orbits and point configurations in [[point space]] has a close analogy in [[vector space]] in the relation between the [[Form|face form]] joined to the [[point group]] that has generated the form and the [[Form|face form]] detached from its generating [[point group]].
 == Types of crystallographic orbits ==

← Older revision		Revision as of 13:32, 6 April 2007
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−	<Font Color="blue"> Orbite cristallographique</Font> (''Fr''). <Font Color="red"> Punktklage </Font>(''Ge''). <Font color="black"> Orbita cristallografica </Font>(''It'').	+	<Font Color="blue"> Orbite cristallographique</Font> (''Fr''). <Font Color="red"> Punktklage </Font>(''Ge''). <Font color="black"> Orbita cristallografica </Font>(''It''), <font color="purple">結晶軌道</font> (''Ja'').