Friedel's law - Revision history

BrianMcMahon: Tidied translations.

2017-11-30T09:50:34Z

Tidied translations.

BrianMcMahon: Tidied translations and corrected German (U. Mueller)

2017-11-13T13:41:14Z

Tidied translations and corrected German (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-15T11:37:29Z

Style edits to align with printed edition

MassimoNespolo: /* See also */

2017-04-10T15:42:09Z

‎See also

MassimoNespolo: /* See also */ 6th edition of ITA

2017-04-10T15:41:56Z

‎See also: 6th edition of ITA

MassimoNespolo: Ja

2015-12-06T09:34:42Z

HowardFlack: /* Definition */

2013-10-11T15:21:52Z

‎Definition

HowardFlack: /* Definition */

2013-10-11T13:56:18Z

‎Definition

HowardFlack: /* Definition */

2013-10-11T13:53:53Z

‎Definition

GervaisChapuis: /* Definition */

2013-08-26T19:01:55Z

‎Definition

← Older revision		Revision as of 09:50, 30 November 2017
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−	<font color="blue">Loi de Friedel</Font> (''Fr''). <font color="red">Friedelsches Gesetz</font> (''Ge''). <font color="black">Legge di Friedel </font>(''It''). <font color="purple">フリーデル則</font>(''Ja''). <font color="green">Ley de Friedel</font> (''Sp'').	+	<font color="blue">Loi de Friedel</Font> (''Fr''). <font color="red">Friedelsches Gesetz</font> (''Ge''). <font color="black">Legge di Friedel</font>(''It''). <font color="purple">フリーデル則</font>(''Ja''). <font color="green">Ley de Friedel</font> (''Sp'').

← Older revision		Revision as of 13:41, 13 November 2017
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−	<~~Font~~ color="blue">Loi de Friedel</Font> (''Fr''). <~~Font~~ color="red"> ~~Friedelsche~~ Gesetz</~~Font~~> (''Ge''). <~~Font~~ color="~~green~~">~~Ley de~~ Friedel</~~Font~~> (''Sp''). <~~Font~~ color="~~black~~"> ~~Legge di Friedel~~ </~~Font~~>(''It''). <~~Font~~ color="~~purple~~">~~フリーデル則~~</~~Font~~>(''Ja'').	+	<font color="blue">Loi de Friedel</Font> (''Fr''). <font color="red">Friedelsches Gesetz</font> (''Ge''). <font color="black">Legge di Friedel </font>(''It''). <font color="purple">フリーデル則</font>(''Ja''). <font color="green">Ley de Friedel</font> (''Sp'').

@@ Line 1: / Line 1: @@
-<Font color="blue">Loi de Friedel</Font> (''Fr'').  <Font color="red"> Friedelsche Gesetz</Font> (''Ge''). <Font color="green">Ley de Friedel</Font> (''Sp''). <Font color="black"> Legge di Friedel </Font>(''It''). <Font color="purple">フリーデル則</Font>(''Ja'')
+<Font color="blue">Loi de Friedel</Font> (''Fr'').  <Font color="red"> Friedelsche Gesetz</Font> (''Ge''). <Font color="green">Ley de Friedel</Font> (''Sp''). <Font color="black"> Legge di Friedel </Font>(''It''). <Font color="purple">フリーデル則</Font>(''Ja'').
 == Definition ==
-Friedel's law, or rule, states that the intensities of the ''h'', ''k'', ''l'' and <math>{\bar h}, {\bar k}, {\bar l}</math> reflections are equal. This is true either if the crystal is centrosymmetric or if no [[Resonant_scattering|resonant scattering]] is present. It is in that case not possible to tell by diffraction whether an inversion center is present or not. The apparent symmetry of the crystal is then one of the eleven [[Laue classes]].
+Friedel's law, or rule, states that the intensities of the ''h'', ''k'', ''l'' and <math>{\bar h}, {\bar k}, {\bar l}</math> reflections are equal. This is true either if the crystal is centrosymmetric or if no [[Resonant_scattering|resonant scattering]] is present. It is in that case not possible to tell by diffraction whether an inversion centre is present or not. The apparent symmetry of the crystal is then one of the eleven [[Laue classes]].
-The reason for Friedel's rule is that the diffracted intensity is proportional to the square of the modulus of the structure factor, |''F<sub>h</sub>''|<sup>2</sup>, according to the  geometrical, or [[kinematical theory]] of diffraction. It depends similarly on the modulus of the structure factor according to the [[dynamical theory]] of diffraction. The structure factor is given by:
+The reason for Friedel's rule is that the diffracted intensity is proportional to the square of the modulus of the structure factor, |''F<sub>h</sub>''|<sup>2</sup>, according to the  geometrical, or [[kinematical theory]] of diffraction. It depends similarly on the modulus of the structure factor according to the [[dynamical theory]] of diffraction. The structure factor is given by
 <center>
-<math>F_h = \Sigma_j f_j {\rm exp - 2 \pi i} {\bold h} . {\bold r_j}</math>
+<math>F_h = \sum_j f_j {\exp(2 \pi i} \mathbf{h} . \mathbf{r_j})</math>
 </center>
-where ''f<sub>j</sub>'' is the atomic scattering factor of atom ''j'', '''h''' the reflection vector and <math>{\bold r_j}</math> the position vector of atom ''j''. There comes:
+where ''f<sub>j</sub>'' is the atomic scattering factor of atom ''j'', '''h''' the reflection vector and <math>{\bold r_j}</math> the position vector of atom ''j''. It follows that
 <center>
@@ Line 21: / Line 21: @@
 <center>
-<math>F_{\bar h} \ne F_h^*</math>
+<math>F_{\bar h} \ne F_h^*</math>.
 </center>
@@ Line 28: / Line 28: @@
 == History ==
-Friedel's law was stated by G. Friedel (1865-1933) in 1913 (Friedel G., 1913, ''Sur les symétries cristallines que peut révéler la diffraction des rayons X.'', ''C.R. Acad. Sci. Paris'', '''157''', 1533-1536.
+Friedel's law was stated by G. Friedel (1865-1933) in 1913 [Friedel, G. (1913). ''C.R. Acad. Sci. Paris'', '''157''', 1533-1536. ''Sur les symétries cristallines que peut révéler la diffraction des rayons X''].
 == See also ==
-*[[Absolute structure]]<br>
+*[[Absolute structure]]
-*Section 3.2.1.1 of ''International Tables of crystallography, Volume A'', 6<sup>th</sup> edition
+*Chapter 3.2.1.1 of ''International Tables for Crystallography, Volume A'', 6th edition
 [[Category:X-rays]]<br>

@@ Line 32: / Line 32: @@
 == See also ==
 *[[Absolute structure]]<br>
-*Section 3.2.1.1 of ''International Tables of crystallography, Volume A''<br>, 6<sup>th</sup> edition
+*Section 3.2.1.1 of ''International Tables of crystallography, Volume A'', 6<sup>th</sup> edition
 [[Category:X-rays]]<br>

@@ Line 31: / Line 31: @@
 == See also ==
+*[[Absolute structure]]<br>
-[[Absolute structure]]<br>
+*Section 3.2.1.1 of ''International Tables of crystallography, Volume A''<br>, 6<sup>th</sup> edition
 [[Category:X-rays]]<br>

← Older revision		Revision as of 09:34, 6 December 2015
Line 1:		Line 1:
−	<Font color="blue"> Loi de Friedel </Font>(''Fr''). <Font color="red"> Friedelsche Gesetz</Font> (''Ge''). <Font color="green"> Ley de Friedel </Font> (''Sp'').<Font color="black"> Legge di Friedel </Font>(''It'')	+	<Font color="blue">Loi de Friedel</Font> (''Fr''). <Font color="red"> Friedelsche Gesetz</Font> (''Ge''). <Font color="green">Ley de Friedel</Font> (''Sp''). <Font color="black"> Legge di Friedel </Font>(''It''). <Font color="purple">フリーデル則</Font>(''Ja'')

@@ Line 4: / Line 4: @@
 == Definition ==
-Friedel's law, or rule, states that the intensities of the ''h'', ''k'', ''l'' and <math>{\bar h}, {\bar k}, {\bar l}</math> reflections are equal. This is true either if the crystal is centrosymmetric or if no resonant scattering is present. It is in that case not possible to tell by diffraction whether an inversion center is present or not. The apparent symmetry of the crystal is then one of the eleven [[Laue classes]].
+Friedel's law, or rule, states that the intensities of the ''h'', ''k'', ''l'' and <math>{\bar h}, {\bar k}, {\bar l}</math> reflections are equal. This is true either if the crystal is centrosymmetric or if no [[Anomalous_dispersion|resonant scattering]] is present. It is in that case not possible to tell by diffraction whether an inversion center is present or not. The apparent symmetry of the crystal is then one of the eleven [[Laue classes]].
 The reason for Friedel's rule is that the diffracted intensity is proportional to the square of the modulus of the structure factor, |''F<sub>h</sub>''|<sup>2</sup>, according to the  geometrical, or [[kinematical theory]] of diffraction. It depends similarly on the modulus of the structure factor according to the [[dynamical theory]] of diffraction. The structure factor is given by:

@@ Line 18: / Line 18: @@
 </center>
-if the atomic scattering factor, ''f<sub>j</sub>'', is real. The intensities of the ''h'', ''k'', ''l'' and <math>{\bar h}, {\bar k}, {\bar l}</math> reflections are then equal. If the crystal is absorbing, however, due to [[anomalous dispersion]], the atomic scattering factor is complex and
+if the atomic scattering factor, ''f<sub>j</sub>'', is real. The intensities of the ''h'', ''k'', ''l'' and <math>{\bar h}, {\bar k}, {\bar l}</math> reflections are then equal. If the crystal is absorbing, however, due to [[Anomalous_dispersion|resonant scattering]], the atomic scattering factor is complex and
 <center>

@@ Line 24: / Line 24: @@
 </center>
-Friedel's law therefore does not hold for absorbing crystals. The reflections ''h'', ''k'', ''l'' and <math>{\bar h}, {\bar k}, {\bar l}</math> are called a [[Friedel pair]]. They are used in the resolution of the phase problem for the solution of crystal structures.
+The reflections ''h'', ''k'', ''l'' and <math>{\bar h}, {\bar k}, {\bar l}</math> are called a [[Friedel pair]]. They are used in the resolution of the phase problem for the solution of crystal structures and in the determination of absolute structure.
 == History ==