Bragg's law - Revision history

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

2017-11-09T16:40:55Z

Tidied translations and corrected German (U. Mueller)

MassimoNespolo: correction (there is an internal link about that!). Also, added Ru

2017-10-12T14:31:42Z

correction (there is an internal link about that!). Also, added Ru

MassimoNespolo: Lang (Ar)

2017-09-14T09:11:22Z

Lang (Ar)

BrianMcMahon at 15:23, 12 May 2017

2017-05-12T15:23:24Z

BrianMcMahon: Style edits to align with printed edition

2017-05-12T14:34:52Z

Style edits to align with printed edition

MassimoNespolo: Ja, link, better wording (time to avoid the bad "extinction" expression)

2015-03-20T04:35:57Z

Ja, link, better wording (time to avoid the bad "extinction" expression)

BrianMcMahon at 17:05, 3 February 2012

2012-02-03T17:05:35Z

BrianMcMahon at 08:40, 25 May 2007

2007-05-25T08:40:15Z

BrianMcMahon at 08:37, 25 May 2007

2007-05-25T08:37:54Z

AndreAuthier at 08:02, 17 April 2006

2006-04-17T08:02:40Z

← Older revision		Revision as of 16:40, 9 November 2017
Line 1:		Line 1:
−	<font color="orange">قانون برافي</font> (''Ar''); <~~Font~~ color="blue">Loi de Bragg</~~Font~~> (''Fr''); <~~Font~~ color="red">Bragg Gesetz</~~Font~~> (''Ge''); <~~Font~~ color="black"> Legge di Bragg</~~Font~~> (''It''); <~~Font~~ color="purple">ブラッグの法則 </~~Font~~>(''Ja''); <~~Font~~ color="brown">Условие Вульфа — Брэгга</~~Font~~> (''Ru''); <~~Font~~ color="green">Ley de Bragg</~~Font~~> (''Sp'').	+	<font color="orange">قانون برافي</font> (''Ar''). <font color="blue">Loi de Bragg</font> (''Fr''). <font color="red">Bragg-Gesetz</font> (''Ge''). <font color="black">Legge di Bragg</font> (''It''). <font color="purple">ブラッグの法則</font> (''Ja''). <font color="brown">Условие Вульфа — Брэгга</font> (''Ru''). <font color="green">Ley de Bragg</font> (''Sp'').

	== Definition ==		== Definition ==

@@ Line 1: / Line 1: @@
-<Font color="blue">Loi de Bragg</Font> (''Fr''). <Font color="red">Bragg Gesetz</Font> (''Ge''). <Font color="green">Ley de Bragg</Font> (''Sp''). <Font color="black"> Legge di Bragg</Font> (''It''). <Font color="purple">ブラッグの法則 </Font>(''Ja''); <font color="orange">قانون برافي</font> (''Ar'').
+<font color="orange">قانون برافي</font> (''Ar''); <Font color="blue">Loi de Bragg</Font> (''Fr''); <Font color="red">Bragg Gesetz</Font> (''Ge''); <Font color="black"> Legge di Bragg</Font> (''It''); <Font color="purple">ブラッグの法則 </Font>(''Ja''); <Font color="brown">Условие Вульфа — Брэгга</Font> (''Ru''); <Font color="green">Ley de Bragg</Font> (''Sp'').
 == Definition ==
@@ Line 10: / Line 10: @@
 </center>
-where ''d'' is the '''[[lattice]]''' spacing, &theta; the angle between the wave vector of the incident plane wave, '''k<sub>o</sub>''', and the lattice planes, &lambda; its wavelength and ''n'' is an integer, the order of the reflection. It is equivalent to the [[Reciprocal lattice#Diffraction condition in reciprocal space|diffraction condition in reciprocal space]] and to the [[Laue equations]].
+where ''d'' is the [[interplanar spacing]], &theta; the angle between the wave vector of the incident plane wave, '''k<sub>o</sub>''', and the lattice planes, &lambda; its wavelength and ''n'' is an integer, the order of the reflection. It is equivalent to the [[Reciprocal lattice#Diffraction condition in reciprocal space|diffraction condition in reciprocal space]] and to the [[Laue equations]].
 == Direct derivation of Bragg's law ==

← Older revision		Revision as of 09:11, 14 September 2017
Line 1:		Line 1:
−	<Font color="blue">Loi de Bragg</Font> (''Fr''). <Font color="red">Bragg Gesetz</Font> (''Ge''). <Font color="green">Ley de Bragg</Font> (''Sp''). <Font color="black"> Legge di Bragg</Font> (''It''). <Font color="purple">ブラッグの法則 </Font>(''Ja'').	+	<Font color="blue">Loi de Bragg</Font> (''Fr''). <Font color="red">Bragg Gesetz</Font> (''Ge''). <Font color="green">Ley de Bragg</Font> (''Sp''). <Font color="black"> Legge di Bragg</Font> (''It''). <Font color="purple">ブラッグの法則 </Font>(''Ja''); <font color="orange">قانون برافي</font> (''Ar'').

	== Definition ==		== Definition ==

@@ Line 80: / Line 80: @@
 == See also ==
-[[Laue equations]]
+*[[Laue equations]]
 [[Category:X-rays]]

@@ Line 1: / Line 1: @@
-<Font color="blue">Loi de Bragg</Font> (''Fr''). <Font color="red">Bragg Gesetz</Font> (''Ge''). <Font color="green">Ley de Bragg</Font> (''Sp''). <Font color="black"> Legge di Bragg</Font> (''It''). <Font color="purple">ブラッグの法則 </Font>(''Ja'')
+<Font color="blue">Loi de Bragg</Font> (''Fr''). <Font color="red">Bragg Gesetz</Font> (''Ge''). <Font color="green">Ley de Bragg</Font> (''Sp''). <Font color="black"> Legge di Bragg</Font> (''It''). <Font color="purple">ブラッグの法則 </Font>(''Ja'').
 == Definition ==
@@ Line 7: / Line 7: @@
 <center>
-''d'' sin &theta; = ''n'' &lambda;.
+''d'' sin &theta; = ''n'' &lambda;
 </center>
-where ''d'' is the '''[[lattice]]''' spacing, &theta; the angle between the wavevector of the incident plane wave, '''k<sub>o</sub>''', and the lattice planes, &lambda; its wave length and ''n'' is an integer, the order of the reflection. It is equivalent to the [[Reciprocal lattice#Diffraction condition in reciprocal space|diffraction condition in reciprocal space]] and to the [[Laue equations]].
+where ''d'' is the '''[[lattice]]''' spacing, &theta; the angle between the wave vector of the incident plane wave, '''k<sub>o</sub>''', and the lattice planes, &lambda; its wavelength and ''n'' is an integer, the order of the reflection. It is equivalent to the [[Reciprocal lattice#Diffraction condition in reciprocal space|diffraction condition in reciprocal space]] and to the [[Laue equations]].
 == Direct derivation of Bragg's law ==
@@ Line 20: / Line 20: @@
 * '''Reflection from the second plane'''
-Since the phase of the reflected waves is independent of the position of the point scatterer in the plane, the phase difference between the waves reflected by two successive lattice planes is obtained by choosing arbitrarily a scattering point, ''A'', on the first plane and a scattering point, ''b'' on the second plane such that ''AB'' is normal to the planes. If ''C'' and ''d'' are the projections of ''A'' on the incident and reflected wave vectors passing through ''B'', it is clear from figure 1 that the path difference between the waves reflected at ''A'' and ''B'', respectively, is:
+Since the phase of the reflected waves is independent of the position of the point scatterer in the plane, the phase difference between the waves reflected by two successive lattice planes is obtained by choosing arbitrarily a scattering point, ''A'', on the first plane and a scattering point, ''B'', on the second plane such that ''AB'' is normal to the planes. If ''C'' and ''D'' are the projections of ''A'' on the incident and reflected wave vectors passing through ''B'', it is clear from Figure 1 that the path difference between the waves reflected at ''A'' and ''B'', respectively, is:
 <center>
-''CB'' + ''BD'' = 2 ''d'' sin &theta;
+''CB'' + ''BD'' = 2''d'' sin &theta;
 </center>
-and that the two waves will be in phase if this path difference is equal to ''n'' &lambda; where ''n'' is an integer.
+and that the two waves will be in phase if this path difference is equal to ''n''&lambda; where ''n'' is an integer.
-* '''Reflection from the third, etc., planes'''
+* '''Reflection from the third, etc. planes'''
-If Bragg's relation is satisfied for the first two planes, the waves reflected with wave vector '''k<sub>h</sub>''' will be in phase fo all the planes of the family.
+If Bragg's relation is satisfied for the first two planes, the waves reflected with wave vector '''k<sub>h</sub>''' will be in phase for all the planes of the family.
 == Order of the reflection ==
@@ Line 40: / Line 40: @@
 </center>
-One may then say that a Bragg reflection of order ''n'' on a family of lattice planes or order ''n'' is equivalent to reflection of order 1 on a family of fictitious, or imaginary, planes of lattice spacing:
+One may then say that a Bragg reflection of order ''n'' on a family of lattice planes of order ''n'' is equivalent to reflection of order 1 on a family of fictitious, or imaginary, planes of lattice spacing
 <center>
-<math>d_{hkl}</math> = ''d''/''n''
+<math>d_{hkl}</math> = ''d''/''n''.
 </center>
-This fictitious family is associated to the reciprocal lattice vector '''OH''' where ''OH'' = ''n''/''d'' = 1/<math>d_{hkl}</math>. The indices of the reflection are: ''hkl''. For instance, the dashed blue lines in Figure 1 correspond to the fistitious planes associated to the second order, ''n'' = 2.
+This fictitious family is associated with the reciprocal lattice vector '''OH''' where ''OH'' = ''n''/''d'' = 1/<math>d_{hkl}</math>. The indices of the reflection are ''hkl''. For instance, the dashed horizontal lines in Figure 1 correspond to the fictitious planes associated with the second order, ''n'' = 2.
 == [[Reflection conditions]] ==
@@ Line 76: / Line 76: @@
 == History ==
-Bragg (1890-1971) presented his derivation of the reflection condition at a meeting of the Cambridge Philosophical Society on 11 November 1912. His paper was published in 1913 (Bragg W.L., 1913, ''The Diffraction of Short Electromagnetic Waves by a Crystal'', ''Proc. Cambridge Phil. Soc.'', '''17''', 43-57. For details, see P. P. Ewald, 1962, IUCr, [http://www.iucr.org/iucr-top/publ/50YearsOfXrayDiffraction/ 50 Years of X-ray Diffraction], Section 5, page 64.
+Bragg (1890-1971) presented his derivation of the reflection condition at a meeting of the Cambridge Philosophical Society on 11 November 1912. His paper was published in 1913 [Bragg, W. L. (1913), ''Proc. Cambridge Phil. Soc.'' '''17''', 43-57. ''The Diffraction of Short Electromagnetic Waves by a Crystal'']. For details, see P. P. Ewald (1962), [http://www.iucr.org/iucr-top/publ/50YearsOfXrayDiffraction/ ''50 Years of X-ray Diffraction''], Utrecht: IUCr/Oosthoek, Section 5, p. 64 and A. Authier (2013), ''The Early Days of X-ray Diffraction'', Oxford: IUCr/Oxford University Press, Section 6.11, p. 120.
 == See also ==
@@ Line 82: / Line 82: @@
 [[Laue equations]]
-[[Category:X-rays]]<br>
+[[Category:X-rays]]

@@ Line 1: / Line 1: @@
-<Font color="blue">Loi de Bragg </Font>(''Fr''). <Font color="red">Bragg Gesetz </Font>(''Ge''). <Font color="green">Ley de Bragg </Font>(''Sp'').<Font color="black"> Legge di Bragg </Font>(''It'')
+<Font color="blue">Loi de Bragg</Font> (''Fr''). <Font color="red">Bragg Gesetz</Font> (''Ge''). <Font color="green">Ley de Bragg</Font> (''Sp''). <Font color="black"> Legge di Bragg</Font> (''It''). <Font color="purple">ブラッグの法則 </Font>(''Ja'')
 == Definition ==
@@ Line 10: / Line 10: @@
 </center>
-where ''d'' is the '''lattice''' spacing, &theta; the angle between the wavevector of the incident plane wave, '''k<sub>o</sub>''', and the lattice planes, &lambda; its wave length and ''n'' is an integer, the order of the reflection. It is equivalent to the [[Reciprocal lattice#Diffraction condition in reciprocal space|diffraction condition in reciprocal space]] and to the [[Laue equations]].
+where ''d'' is the '''[[lattice]]''' spacing, &theta; the angle between the wavevector of the incident plane wave, '''k<sub>o</sub>''', and the lattice planes, &lambda; its wave length and ''n'' is an integer, the order of the reflection. It is equivalent to the [[Reciprocal lattice#Diffraction condition in reciprocal space|diffraction condition in reciprocal space]] and to the [[Laue equations]].
 == Direct derivation of Bragg's law ==
@@ Line 48: / Line 48: @@
 This fictitious family is associated to the reciprocal lattice vector '''OH''' where ''OH'' = ''n''/''d'' = 1/<math>d_{hkl}</math>. The indices of the reflection are: ''hkl''. For instance, the dashed blue lines in Figure 1 correspond to the fistitious planes associated to the second order, ''n'' = 2.
-== [[Extinctions]], or [[systematic absences]] ==
+== [[Reflection conditions]] ==
 [[Image:BraggLaw-2.gif|left]]
@@ Line 66: / Line 66: @@
 for a screw axis ''q<sub>p</sub>''.
-The reflections of odd order for a glide plane and of order different from (''q''/''p'')''n'' for a screw axis are then absent. One speaks of extinctions or systematic absences related to the presence of glide or screw components.
+The reflections of odd order for a glide plane and of order different from (''q''/''p'')''n'' for a screw axis are then absent. One speaks of [[systematic absences]] related to the presence of glide or screw components.
-As an example, Figure 2 shows the case of a 2<sub>1</sub> screw axis: the reflecting planes are the blue planes and the green planes deduced from the latter by the action of the screw axis. Reflections of odd order will be sytematically absent.
+As an example, Figure 2 shows the case of a 2<sub>1</sub> screw axis: the reflecting planes are the blue planes and the green planes deduced from the latter by the action of the screw axis. Reflections of odd order will be systematically absent.
 == Influence of deformation ==

← Older revision		Revision as of 17:05, 3 February 2012
Line 82:		Line 82:
	[[Laue equations]]		[[Laue equations]]

−
−	~~----~~
	[[Category:X-rays]]<br>		[[Category:X-rays]]<br>