Incommensurate composite crystal - Revision history

BrianMcMahon at 17:15, 14 November 2017

2017-11-14T17:15:51Z

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

2017-11-14T17:13:45Z

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

MassimoNespolo: lang

2015-07-25T05:30:22Z

lang

BrianMcMahon at 14:03, 6 February 2012

2012-02-06T14:03:02Z

BrianMcMahon at 15:20, 30 June 2010

2010-06-30T15:20:26Z

TedJanssen at 06:20, 19 May 2009

2009-05-19T06:20:41Z

TedJanssen at 18:20, 18 May 2009

2009-05-18T18:20:52Z

TedJanssen at 15:47, 18 May 2009

2009-05-18T15:47:38Z

TedJanssen at 13:52, 18 May 2009

2009-05-18T13:52:45Z

New page

[[Incommensurate Composite Crystal]]

Cristal composite (Fr.)

'''Definition'''

An ''incommensurate composite crystal'' is a compound with two or more (''N'') subsystems that are
themselves modulated structures, with basis structures that are mutually incommensurate.
Each subsystem (numbered by ν) has a reciprocal lattice for its basic structure with three basis vectors
'''a'''i*ν. There is a basis of the module of diffraction spots that has at most
3''N'' basis vectors '''A'''j* such that

<math>{\bf a}_i^{*\nu}~=~\sum_{j=1}^n Z_{ij}^{\nu} {\bf A}_j^* ~~~(i=1,2,3),</math>

where Zijν are integer coefficients.
If ''n'' is larger than the dimension of space (three), the composite crystal is an aperiodic crystal.

'''Applications'''

Examples are intergrowth crystals and adsorbed monolayers. To the former belongs
Hg3-δAsF6 with two systems of Hg chains inside the host lattice formed
by AsF6 octahedra. Another example is nonadecane in the channels of a urea
host crystal.

← Older revision		Revision as of 17:15, 14 November 2017
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−	<font color="blue">Cristal composite incommensurable</font> (''Fr''). <font color="red">Inkommensurabler Kompositkristall</font> (''Ge''). <font color="black">Cristallo composito incommensurabile</font> (''It''). <font color="purple">非整合複合結晶</font> (''Ja''). <font color="green">Estructura inconmensurable compuesta</font> (''Sp'').	+	<font color="blue">Cristal composite incommensurable</font> (''Fr''). <font color="red">Inkommensurabler Kompositkristall</font> (''Ge''). <font color="black">Cristallo composito incommensurabile</font> (''It''). <font color="purple">非整合複合結晶</font> (''Ja''). <font color="green">Estructura inconmensurable compuesta crystal</font> (''Sp'').

← Older revision		Revision as of 17:13, 14 November 2017
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−	<~~Font~~ color="blue">Cristal composite incommensurable</font> (''Fr''). <~~Font~~ color="black">Cristallo composito incommensurabile</font> (''It'').　<~~Font~~ color="purple">非整合複合結晶</font> (''Ja'').	+	<font color="blue">Cristal composite incommensurable</font> (''Fr''). <font color="red">Inkommensurabler Kompositkristall</font> (''Ge''). <font color="black">Cristallo composito incommensurabile</font> (''It''). <font color="purple">非整合複合結晶</font> (''Ja''). <font color="green">Estructura inconmensurable compuesta</font> (''Sp'').

← Older revision		Revision as of 05:30, 25 July 2015
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−	<Font color="blue">Cristal composite</font> (Fr.)	+	<Font color="blue">Cristal composite incommensurable</font> (''Fr''). <Font color="black">Cristallo composito incommensurabile</font> (''It'').　<Font color="purple">非整合複合結晶</font> (''Ja'').
		+

	An ''incommensurate composite crystal'' is a compound with two or more (''N'') subsystems that are		An ''incommensurate composite crystal'' is a compound with two or more (''N'') subsystems that are

@@ Line 1: / Line 1: @@
 <Font color="blue">Cristal composite</font> (Fr.)
 An ''incommensurate composite crystal'' is a compound with two or more (''N'') subsystems that are
 themselves modulated structures, with basis structures that are mutually incommensurate.
-Each subsystem (numbered by &nu;) has a reciprocal lattice for its  basic structure with three basis vectors
+Each subsystem (numbered by &nu;) has a reciprocal lattice for its basic structure with three basis vectors
 <math>a_i^{*\nu}</math>. There is a basis of the [[vector module]] of diffraction spots that has at most
 ''N'' basis vectors  <math>A_j^*</math> such that
@@ Line 25: / Line 19: @@
 by AsF<sub>6</sub> octahedra. Another example is nonadecane in the channels of a urea
 host crystal.

@@ Line 5: / Line 5: @@
 <Font color="blue">Cristal composite</font> (Fr.)
- '''Definition'''
+== Definition ==
 An ''incommensurate composite crystal'' is a compound with two or more (''N'') subsystems that are
@@ Line 19: / Line 19: @@
 ''n'' is the rank of the vector module.
- '''Applications'''
+== Applications ==
 Examples are intergrowth crystals and adsorbed monolayers. To the former belongs

@@ Line 10: / Line 10: @@
 themselves modulated structures, with basis structures that are mutually incommensurate.
 Each subsystem (numbered by &nu;) has a reciprocal lattice for its  basic structure with three basis vectors
-'''a'''<sub>i</sub><sup>*&nu;</sup>. There is a basis of the module of diffraction spots that has at most
+<math>a_i^{*\nu}</math>. There is a basis of the [[vector module]] of diffraction spots that has at most
-''N'' basis vectors  '''A'''<sub>j</sub><sup>*</sup> such that
+''N'' basis vectors  <math>A_j^*</math> such that
 <math> a_i^{*\nu}~=~\sum_{j=1}^n Z_{ij}^{\nu}  A_j^* ~~~(i=1,2,3),</math>
-where Z<sub>ij</sub><sup>&nu;</sup> are integer coefficients.
+where <math>Z_{ij}^{\nu}</math> are integer coefficients.
 If ''n'' is larger than the dimension of space (three), the composite crystal is an aperiodic crystal.
   '''Applications'''

← Older revision		Revision as of 15:47, 18 May 2009
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−	Cristal composite (Fr.)	+
		+	<Font color="blue">Cristal composite</font> (Fr.)

	'''Definition'''		'''Definition'''