Atomic modulation function - Revision history

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

2017-11-08T18:07:59Z

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

BrianMcMahon: Edits to align with printed edition

2017-05-12T12:30:55Z

Edits to align with printed edition

BrianMcMahon: Style edits to align with printed edition

2017-05-12T12:29:45Z

Style edits to align with printed edition

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2015-03-20T13:47:32Z

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2015-02-26T07:55:23Z

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BrianMcMahon at 16:00, 3 February 2012

2012-02-03T16:00:43Z

TedJanssen at 17:05, 18 May 2009

2009-05-18T17:05:30Z

TedJanssen at 15:45, 18 May 2009

2009-05-18T15:45:31Z

TedJanssen at 13:22, 18 May 2009

2009-05-18T13:22:29Z

New page

[[Atomic Modulation Function]]

Fonction de modulation atomique (Fr.)

'''Definition'''

A modulated structure is a structure that may be obtained from a crystalline system
with space group symmetry, and therefore with lattice periodicity, by a regular
displacement of atoms (displacive modulation) and/or change in the occupation
probability of a site in the basic structure. The deviation from the positions
in the basic structure are given by

<math>{\bf r}({\bf n},j)~=~{\bf n}+{\bf r}_j+{\bf u}_j({\bf n}+{\bf r}_j).</math>

The occupation probability to find an atom of species ''A'' at the position <math>{\bf n}+{\bf r}_j</math>
is <math>p_A({\bf n},j)</math>, where the sum over the species of the functions <math>p_A</math>
is one. Instead of a different species, one may have a vacancy. The functions
<math>{\bf u}({\bf n},j)</math> and <math>p_A({\bf n},j)</math> are the ''atomic modulation functions''.
For a crystal they should have Fourier modules of finite rank, ''i.e''. the
functions have Fourier transforms with delta peaks on wave vectors '''k''' of the form

<math>{\bf k}~=~\sum_{i=1}^n h_i {\bf a}_i^*,~~(h_i~~{\rm integers},~n~{\rm finite}.)</math>

Modulation functions may be continuous or discontinuous.

← Older revision		Revision as of 18:07, 8 November 2017
Line 1:		Line 1:
−	<~~Font~~ color="blue">Fonction de modulation atomique</font> (''Fr''). <~~Font~~ color="black">Funzione di modulazione atomica</font> (''It''). <~~Font~~ color="purple">原子変調関数</font> (''Ja'').	+	<font color="blue">Fonction de modulation atomique</font> (''Fr''). <font color="red">Atomare Modulationsfunktion</font> (''Ge''). <font color="black">Funzione di modulazione atomica</font> (''It''). <font color="purple">原子変調関数</font> (''Ja''). <font color="green">Función de modulación atómica</font> (''Sp'').

	== Definition ==		== Definition ==

← Older revision		Revision as of 12:30, 12 May 2017
Line 17:		Line 17:

	Modulation functions may be continuous or discontinuous.		Modulation functions may be continuous or discontinuous.
		+
		+	==See also==
		+	*[[Displacive modulation]]

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

@@ Line 5: / Line 5: @@
 A [[modulated crystal structure]] is a [[crystal pattern|structure]] that may be obtained from a crystalline system with [[space group]] symmetry, and therefore with [[lattice]] periodicity, by a regular displacement of atoms ([[displacive modulation]]) and/or change in the occupation probability of a site in the basic structure. The deviation from the positions in the basic structure are given by
-<math>r(n,j) = n~+~r_j+u_j((n+r_j).</math>
+<math>r(n,j) = n~+~r_j+u_j (n+r_j).</math>
 The occupation probability to find an atom of species ''A'' at the position <math>n+r_j</math>
-is <math>p_A(n,j)</math>, where the sum over the species of the functions <math>p_A</math>
+is <math>p_A(n, j)</math>, where the sum over the species of the functions <math>p_A</math>
 is one. Instead of a different species, one may have a vacancy. The functions
-<math>u(n,j)</math> and <math>p_A(n,j)</math> are the  ''atomic modulation functions''.
+<math>u(n, j)</math> and <math>p_A(n, j)</math> are the  ''atomic modulation functions''.
 For a crystal they should have Fourier modules of finite rank,  ''i.e''. the
 functions have Fourier transforms with delta peaks on wave vectors  '''k''' of the form
-<math>k~=~\sum_{i=1}^n h_i a_i^*,~~(h_i~~{\rm integers},~n~{\rm finite}.)</math>
+<math>k~=~\sum_{i=1}^n h_i a_i^*~~(h_i~~{\rm integers},~n~{\rm finite}).</math>
 Modulation functions may be continuous or discontinuous.
 [[Category: Fundamental crystallography]]

@@ Line 3: / Line 3: @@
 == Definition ==
-A [[modulated crystal structure]] is a [[crystal pattern|structure]] that may be obtained from a crystalline system with [[space group]] symmetry, and therefore with [[lattice]] periodicity, by a regular displacement of atoms (displacive modulation) and/or change in the occupation probability of a site in the basic structure. The deviation from the positions in the basic structure are given by
+A [[modulated crystal structure]] is a [[crystal pattern|structure]] that may be obtained from a crystalline system with [[space group]] symmetry, and therefore with [[lattice]] periodicity, by a regular displacement of atoms ([[displacive modulation]]) and/or change in the occupation probability of a site in the basic structure. The deviation from the positions in the basic structure are given by
 <math>r(n,j) = n~+~r_j+u_j((n+r_j).</math>

@@ Line 1: / Line 1: @@
-<Font color="blue">Fonction de modulation atomique</font> (Fr.)
+<Font color="blue">Fonction de modulation atomique</font> (''Fr''). <Font color="black">Funzione di modulazione atomica</font> (''It''). <Font color="purple">原子変調関数</font> (''Ja'').
 == Definition ==
-A modulated structure is a structure that may be obtained from a crystalline system
+A [[modulated crystal structure]] is a [[crystal pattern|structure]] that may be obtained from a crystalline system with [[space group]] symmetry, and therefore with [[lattice]] periodicity, by a regular displacement of atoms (displacive modulation) and/or change in the occupation probability of a site in the basic structure. The deviation from the positions in the basic structure are given by
 <math>r(n,j) = n~+~r_j+u_j((n+r_j).</math>

← Older revision		Revision as of 07:55, 26 February 2015
Line 21:		Line 21:

	Modulation functions may be continuous or discontinuous.		Modulation functions may be continuous or discontinuous.
		+
		+	[[Category: Fundamental crystallography]]

@@ Line 1: / Line 1: @@
 [[Atomic Modulation Function]]
 Fonction de modulation atomique (Fr.)
   '''Definition'''