Aperiodic crystal - Revision history

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

2017-11-08T18:01:09Z

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

BrianMcMahon: Style edits to align with printed edition

2017-05-12T12:07:54Z

Style edits to align with printed edition

MassimoNespolo: wikification

2015-07-25T05:21:27Z

wikification

GervaisChapuis at 09:32, 23 July 2015

2015-07-23T09:32:26Z

GervaisChapuis at 09:27, 23 July 2015

2015-07-23T09:27:14Z

GervaisChapuis at 09:25, 23 July 2015

2015-07-23T09:25:21Z

GervaisChapuis at 09:15, 23 July 2015

2015-07-23T09:15:02Z

MassimoNespolo: Lang

2015-03-04T05:59:31Z

Lang

BrianMcMahon at 15:56, 3 February 2012

2012-02-03T15:56:07Z

BrianMcMahon at 11:52, 2 February 2012

2012-02-02T11:52:05Z

← Older revision		Revision as of 18:01, 8 November 2017
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−	<~~Font~~ color="blue">Cristal apériodique</font> (''Fr''). <~~Font~~ color="black">Cristallo aperiodico</font> (''It''). <~~Font~~ color="purple">非周期性結晶</font> (''Ja'').	+	<font color="blue">Cristal apériodique</font> (''Fr''). <font color="red">Aperiodischer Kristall</font> (''Ge''). <font color="black">Cristallo aperiodico</font> (''It''). <font color="purple">非周期性結晶</font> (''Ja''). <font color="green">Cristal aperiódico</font> (''Sp'').

	==Definition==		==Definition==

@@ Line 1: / Line 1: @@
-<Font color="blue">Cristal ap&eacute;riodique</font> (''Fr''). <Font color="black">Cristallo aperiodico</font> (''It''). <Font color="purple">非周期性結晶</font> (''Ja'')
+<Font color="blue">Cristal ap&eacute;riodique</font> (''Fr''). <Font color="black">Cristallo aperiodico</font> (''It''). <Font color="purple">非周期性結晶</font> (''Ja'').
 ==Definition==
-The definition of aperiodic crystal was included in the definition of crystal proposed by the IUCr Commission on Aperiodic structures (1): by ''crystal'' we mean any solid having an essentially discrete diffraction diagram and ''aperiodic crystal'' we mean any crystal in which three-dimensional lattice periodicity can be considered to be absent. As an extension, the latter term will also include those crystals in which three-dimensional periodicity is too weak to describe significant correlations in the atomic configuration, but which can be properly described by crystallographic methods developed for actual aperiodic crystals.
+The definition of aperiodic crystal was included in the definition of ''crystal'' proposed by the IUCr Commission on Aperiodic Structures (International Union of Crystallography, 1992): by ''crystal'' we mean any solid having an essentially discrete diffraction diagram and ''aperiodic crystal'' we mean any crystal in which three-dimensional lattice periodicity can be considered to be absent. As an extension, the latter term will also include those crystals in which three-dimensional periodicity is too weak to describe significant correlations in the atomic configuration, but which can be properly described by crystallographic methods developed for actual aperiodic crystals.
 For practical purposes, however, many scientists currently working in the field use a narrower definition of aperiodic crystal, namely
@@ Line 9: / Line 9: @@
 of the  ''direct lattice''. Periodicity here means ''lattice periodicity''. Any structure without this property is  ''aperiodic''. For example, an amorphous system is aperiodic. An  ''aperiodic crystal'' is a structure with sharp diffraction peaks, but without lattice periodicity. Therefore, amorphous systems are not aperiodic crystals. The positions of the sharp diffraction peaks of an aperiodic crystal belong to a ''vector module'' of finite rank. This means that the diffraction wave vectors are of the form
-<math>\textbf{k}=\sum_{i=1}^n h_i \textbf{a}_i^*, ( \textrm{integer}\ h_i).</math>
+<math>\textbf{k}=\sum_{i=1}^n h_i \textbf{a}_i^* ( \textrm{integer}\ h_i).</math>
-The basis vectors  <math>a_i^*</math> are supposed to be independent over the rational numbers, i.e. when a linear combination of them with rational coefficients is zero, all coefficients are zero. The minimum number of basis vectors is the  ''rank'' of the vector module. If the rank ''n'' is larger than the space dimension, the structure is not periodic, but aperiodic.
+The basis vectors  <math>\textbf{a}_i^*</math> are supposed to be independent over the rational numbers, ''i.e.'' when a linear combination of them with rational coefficients is zero, all coefficients are zero. The minimum number of basis vectors is the  ''rank'' of the vector module. If the rank ''n'' is larger than the space dimension, the structure is not periodic, but aperiodic.
 ==Applications==
@@ Line 22: / Line 22: @@
 * and [[incommensurate magnetic structure]]s
-== References ==
+== Reference==
 [[Category:Fundamental crystallography]]

@@ Line 17: / Line 17: @@
 There are four classes of aperiodic structures, but these classes have an overlap:
-* ''incommensurately modulated crystal phases'' (See incommensurate modulated crystal phases),
+* [[incommensurate modulated structure]]s
-* ''incommensurate composite structures'' (See incommensurate composites),
+* [[incommensurate composite crystal]]s
-* ''quasicrystals'' (see quasicrystals),
+* [[quasicrystal]]s
-* and  ''incommensurate magnetic structures'' (See incommensurate magnetic structures).
+* and [[incommensurate magnetic structure]]s
 == References ==

@@ Line 28: / Line 28: @@
 == References ==
-(1) ''Acta Cryst.'' (1992), '''A48''', 928, '''Terms of reference''' of the IUCr commission on aperiodic crystals.
+(1) [http://dx.doi.org/10.1107/S0108767392008328''Acta Cryst.'' (1992), '''A48''', 928, '''Terms of reference''' of the IUCr commission on aperiodic crystals.]
 [[Category:Fundamental crystallography]]

@@ Line 22: / Line 22: @@
 * and  ''incommensurate magnetic structures'' (See incommensurate magnetic structures).
-'''See also''': Incommensurately modulated crystal phases, incommensurate composite structures, quasicrystals, incommensurate magnetic structures.
+== See also ==
 == References ==

← Older revision		Revision as of 09:25, 23 July 2015
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	'''See also''': Incommensurately modulated crystal phases, incommensurate composite structures, quasicrystals, incommensurate magnetic structures.		'''See also''': Incommensurately modulated crystal phases, incommensurate composite structures, quasicrystals, incommensurate magnetic structures.
		+
		+	== References ==
		+
		+	(1) ''Acta Cryst.'' (1992), '''A48''', 928, '''Terms of reference''' of the IUCr commission on aperiodic crystals.
		+

	[[Category:Fundamental crystallography]]		[[Category:Fundamental crystallography]]

← Older revision		Revision as of 05:59, 4 March 2015
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−	<Font color="blue">Cristal apériodique</font> (''Fr.'')	+	<Font color="blue">Cristal apériodique</font> (''Fr''). <Font color="black">Cristallo aperiodico</font> (''It''). <Font color="purple">非周期性結晶</font> (''Ja'')

	==Definition==		==Definition==

← Older revision		Revision as of 15:56, 3 February 2012
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	'''See also''': Incommensurately modulated crystal phases, incommensurate composite structures, quasicrystals, incommensurate magnetic structures.		'''See also''': Incommensurately modulated crystal phases, incommensurate composite structures, quasicrystals, incommensurate magnetic structures.

−	~~----~~
	[[Category:Fundamental crystallography]]		[[Category:Fundamental crystallography]]