Modulated crystal structure - Revision history

BrianMcMahon: Added German and Spanish translations (U. Mueller)

2017-11-16T12:58:53Z

Added German and Spanish translations (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-15T17:01:33Z

Style edits to align with printed edition

MassimoNespolo: removed double point, link decoration, italics, internal links added

2015-03-20T04:30:47Z

removed double point, link decoration, italics, internal links added

MassimoNespolo: /* See also */ moved below the figure and added a link

2015-03-17T13:28:10Z

‎See also: moved below the figure and added a link

BrianMcMahon at 17:05, 6 February 2012

2012-02-06T17:05:09Z

MassimoNespolo: titles level

2011-09-07T14:15:57Z

titles level

MassimoNespolo: it, ja

2011-09-07T14:14:52Z

it, ja

GervaisChapuis at 07:51, 4 September 2011

2011-09-04T07:51:20Z

TedJanssen at 15:49, 18 May 2009

2009-05-18T15:49:45Z

TedJanssen at 14:19, 18 May 2009

2009-05-18T14:19:23Z

New page

[[Modulated Crystal Structure]]

Structure modulée cristallographique (Fr.)

'''Definition'''

A ''modulated crystal structure'' is a density (or atom arrangement) that may be obtained from a density
(or atom arrangement) with space-group symmetry by a finite density change (or finite displacement
of each atom, respectively) that is (quasi)periodic. A function or a displacement field is periodic
if it is invariant under a lattice of translations. Then its Fourier transform consists of
δ-peaks on a reciprocal lattice that spans the space and is nowhere dense. A quasiperiodic
function has a Fourier transform consisting of δ-peaks on a vector module of finite rank. This means that the peaks may be indexed with integers using a finite number of basis vectors. If the modulation consists of deviations from the basic structure in the positions,
the modulation is ''displacive'' ([[displacive modulation]], see Figure.). When the probability distribution deviates from
that in the basic structure the modulation is occupational.

'''See also''': Displacive modulation.

[[Image:BO01F05.gif]]

Figure Caption: Model for a displacively modulated crystal structure. The basic structure
is two-dimensional rectangular, with lattice constants ''a'' and ''b'', the modulation
wave vector is in the ''b''-direction, the wavelength of the periodic modulation
is λ such that λ/''b'' is an irrational number.

← Older revision		Revision as of 12:58, 16 November 2017
Line 1:		Line 1:
−	<~~Font~~ color="blue">Structure cristalline modulée</font> (''Fr''). <~~Font~~ color="black">Struttura cristallina modulata </~~Font~~>(''It''). <~~Font~~ color="purple"> 変調構造 </~~Font~~>(''Ja'').	+	<font color="blue">Structure cristalline modulée</font> (''Fr''). <font color="red">Modulierte Kristallstruktur</font> (''Ge''). <font color="black">Struttura cristallina modulata</font> (''It''). <font color="purple">変調構造</font> (''Ja''). <font color="green">Estructura cristalina modulada</font> (''Sp'').

	== Definition ==		== Definition ==

@@ Line 1: / Line 1: @@
-<Font color="blue">Structure cristalline modul&eacute;e</font> (Fr.), <Font color="black"> Struttura cristallina modulata </Font>(''It''), <Font color="purple"> 変調構造 </Font>(''Ja'')
+<Font color="blue">Structure cristalline modul&eacute;e</font> (''Fr''). <Font color="black">Struttura cristallina modulata </Font>(''It''). <Font color="purple"> 変調構造 </Font>(''Ja'').
 == Definition ==
@@ Line 9: / Line 9: @@
 &delta;-peaks on a reciprocal lattice that spans the space and is nowhere dense. A quasiperiodic
 function has a Fourier transform consisting of &delta;-peaks on a vector module of finite rank. This means that the peaks may be indexed with integers using a finite number of basis vectors. If the modulation consists of deviations from the basic structure in the positions,
-the modulation is [[displacive modulation|''displacive'']] (see Figure). When the probability distribution deviates from
+the modulation is [[displacive modulation|''displacive'']] (see figure). When the probability distribution deviates from
 that in the basic structure the modulation is ''occupational''.
 [[Image:BO01F05.gif]]
-Figure Caption: Model for a displacively modulated crystal structure. The basic structure is two-dimensional rectangular, with lattice constants ''a'' and ''b'', the modulation wave vector is in the ''b''-direction, the wavelength of the periodic modulation is &lambda; such that &lambda;/''b'' is an irrational number.
+Model for a displacively modulated crystal structure. The basic structure is two-dimensional rectangular, with lattice constants ''a'' and ''b'', the modulation wave vector is in the ''b''-direction, the wavelength of the periodic modulation is &lambda; such that &lambda;/''b'' is an irrational number.
 == See also ==
-[[Displacive modulation]]<br>
+*[[Displacive modulation]]
-[[Modular crystal structure]]
+*[[Modular crystal structure]]
 [[Category:Fundamental crystallography]]

@@ Line 12: / Line 12: @@
 that in the basic structure the modulation is occupational.
-== See also ==
+[[Image:BO01F05.gif]]
-[[Image:BO01F05.gif]]
+Figure Caption: Model for a displacively modulated crystal structure. The basic structure is two-dimensional rectangular, with lattice constants ''a'' and ''b'', the modulation wave vector is in the ''b''-direction, the wavelength of the periodic modulation is &lambda; such that &lambda;/''b'' is an irrational number.
-Figure Caption: Model for a displacively modulated crystal structure. The basic structure is two-dimensional rectangular, with lattice constants ''a'' and ''b'', the modulation wave vector is in the ''b''-direction, the wavelength of the periodic modulation is &lambda; such that &lambda;/''b'' is an irrational number.]]
+== See also ==
 [[Category:Fundamental crystallography]]

@@ Line 1: / Line 1: @@
 <Font color="blue">Structure cristalline modul&eacute;e</font> (Fr.), <Font color="black"> Struttura cristallina modulata </Font>(''It''), <Font color="purple"> 変調構造 </Font>(''Ja'')
-==Definition==
+== Definition ==
 A  ''modulated crystal structure'' is a density (or atom arrangement) that may be obtained from a density
@@ Line 12: / Line 12: @@
 that in the basic structure the modulation is occupational.
-==See also==
+== See also ==
 [[Displacive modulation]]
 [[Image:BO01F05.gif]]
-Figure Caption: Model for a displacively modulated crystal structure. The basic structure
+Figure Caption: Model for a displacively modulated crystal structure. The basic structure is two-dimensional rectangular, with lattice constants ''a'' and ''b'', the modulation wave vector is in the ''b''-direction, the wavelength of the periodic modulation is &lambda; such that &lambda;/''b'' is an irrational number.]]
 is two-dimensional rectangular, with lattice constants ''a'' and ''b'', the modulation
-wave vector is in the ''b''-direction, the wavelength of the periodic modulation
+[[Category:Fundamental crystallography]]

← Older revision		Revision as of 14:14, 7 September 2011
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−	~~[[Modulated Crystal Structure]]~~	+	<Font color="blue">Structure cristalline modulée</font> (Fr.), <Font color="black"> Struttura cristallina modulata </Font>(''It''), <Font color="purple"> 変調構造 </Font>(''Ja'')
−
−
−
−	<Font color="blue">Structure cristalline modulée</font> (Fr.)

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

← Older revision		Revision as of 07:51, 4 September 2011
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−	<Font color="blue">Structure modulée ~~cristallographique~~</font> (Fr.)	+	<Font color="blue">Structure cristalline modulée</font> (Fr.)

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

← Older revision		Revision as of 15:49, 18 May 2009
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−	Structure modulée cristallographique (Fr.)	+
		+	<Font color="blue">Structure modulée cristallographique</font> (Fr.)

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