Ewald sphere - Revision history

ShigeruOhba at 13:08, 26 March 2019

2019-03-26T13:08:05Z

BrianMcMahon: Tidied translations.

2017-11-29T16:22:07Z

Tidied translations.

BrianMcMahon: Tidied translations.

2017-11-13T09:48:18Z

Tidied translations.

BrianMcMahon at 14:04, 13 May 2017

2017-05-13T14:04:23Z

BrianMcMahon at 14:04, 13 May 2017

2017-05-13T14:04:00Z

BrianMcMahon: Style edits to align with printed edition

2017-05-13T14:03:35Z

Style edits to align with printed edition

MassimoNespolo: link

2016-07-20T13:51:39Z

link

BrianMcMahon at 13:04, 6 February 2012

2012-02-06T13:04:52Z

GiovanniFerraris at 15:32, 17 March 2006

2006-03-17T15:32:25Z

AndreAuthier at 08:08, 24 February 2006

2006-02-24T08:08:42Z

← Older revision		Revision as of 13:08, 26 March 2019
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−	<font color="blue">Sphère d'Ewald</font> (''Fr''). <font color="red">Ewaldkugel, Ausbreitungskugel</font> (''Ge''). <font color="black">Sfera di Ewald</font> (''It''). <font color="green">Esfera de Ewald</font> (''Sp'').	+	<font color="blue">Sphère d'Ewald</font> (''Fr''). <font color="red">Ewaldkugel, Ausbreitungskugel</font> (''Ge''). <font color="black">Sfera di Ewald</font> (''It''). <font color="purple">エヴァルト球</font> (''Ja''). <font color="green">Esfera de Ewald</font> (''Sp'').

	== Definition ==		== Definition ==

← Older revision		Revision as of 16:22, 29 November 2017
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−	<font color="blue">Sphère d'Ewald</font> (''Fr''). <font color="red">Ewaldkugel, Ausbreitungskugel</font> (''Ge''). <font color="black">Sfera di Ewald </font>(''It''). <font color="green">Esfera de Ewald</font> (''Sp'').	+	<font color="blue">Sphère d'Ewald</font> (''Fr''). <font color="red">Ewaldkugel, Ausbreitungskugel</font> (''Ge''). <font color="black">Sfera di Ewald</font> (''It''). <font color="green">Esfera de Ewald</font> (''Sp'').

	== Definition ==		== Definition ==

← Older revision		Revision as of 09:48, 13 November 2017
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−	<~~Font~~ color="blue">Sphère d'Ewald </~~Font~~>(''Fr''). <~~Font~~ color="red">Ewaldkugel, Ausbreitungskugel </~~Font~~>(''Ge''). <~~Font~~ color="~~green~~">~~Esfera de~~ Ewald </~~Font~~>(''Sp'').<~~Font~~ color="~~black~~"> ~~Sfera di~~ Ewald </~~Font~~>(''It'').	+	<font color="blue">Sphère d'Ewald</font> (''Fr''). <font color="red">Ewaldkugel, Ausbreitungskugel</font> (''Ge''). <font color="black">Sfera di Ewald </font>(''It''). <font color="green">Esfera de Ewald</font> (''Sp'').

	== Definition ==		== Definition ==

@@ Line 24: / Line 24: @@
 == See also ==
-*Chapter 2.2 of ''International Tables for Crystallography, Volume C''.
+*Chapter 2.2 of ''International Tables for Crystallography, Volume C''
 [[Category:X-rays]]<br>

@@ Line 24: / Line 24: @@
 == See also ==
-*Chapter 2.2 of ''International Tables of Crystallography, Volume C''.
+*Chapter 2.2 of ''International Tables for Crystallography, Volume C''.
 [[Category:X-rays]]<br>

@@ Line 1: / Line 1: @@
-<Font color="blue">Sphère d'Ewald </Font>(''F''). <Font color="red">Ewaldkugel, Ausbreitungskugel </Font>(''Ge''). <Font color="green">Esfera de Ewald </Font>(''Sp'').<Font color="black"> Sfera di Ewald </Font>(''It'')
+<Font color="blue">Sphère d'Ewald </Font>(''Fr''). <Font color="red">Ewaldkugel, Ausbreitungskugel </Font>(''Ge''). <Font color="green">Esfera de Ewald </Font>(''Sp'').<Font color="black"> Sfera di Ewald </Font>(''It'').
 == Definition ==
@@ Line 5: / Line 5: @@
 [[Image:Ewald-1.gif|right]]
-The Ewald sphere, or sphere of reflection, is a sphere of radius 1/&#955; passing through the origin ''O'' of the reciprocal lattice. The incident direction is along a radius of the sphere, '''IO''' (Figure 1). A reflected direction, of unit vector '''s'''<sub>'''h'''</sub>, will satisfy the diffraction condition if the diffraction vector
+The Ewald sphere, or sphere of reflection, is a sphere of radius 1/&#955; passing through the origin ''O'' of the reciprocal lattice. The incident direction is along a radius of the sphere, '''IO''' (Fig. 1). A reflected direction, of unit vector '''s'''<sub>'''h'''</sub>, will satisfy the diffraction condition if the diffraction vector
-'''OH''' = '''IH''' – '''IO''' = '''s<sub>h</sub>'''/&#955; – '''s<sub>o</sub>'''/&#955; ('''s<sub>o</sub>''' unit vector in the direction '''IO''') is a reciprocal lattice vector, namely if ''H'' is a node of the reciprocal lattice (see [[reciprocal lattice|Diffraction condition in reciprocal space]]) . If other reciprocal lattice nodes, such as ''G'', lie also on the sphere, there will be reflected beams along '''IG''', etc.  This construction is known as the Ewald construction. When the wavelength is large, there are seldom more than two nodes, ''O'' and ''H'', of the reciprocal lattice simultaneously on the Ewald sphere. When there are three or more, one speaks of multiple diffraction, multiple scattering  or ''n''-beam diffraction. This situation becomes increasingly frequent as the wavelength decreases and is practically routine for very short wavelengths such as those of &#947;-rays and electrons. The curvature of Ewald sphere then becomes negligible and it can often be approximated by a plane. Many reflections must then be taken into account at the same time.
+'''OH''' = '''IH''' – '''IO''' = '''s<sub>h</sub>'''/&#955; – '''s<sub>o</sub>'''/&#955; ('''s<sub>o</sub>''' unit vector in the direction '''IO''') is a reciprocal lattice vector, namely if ''H'' is a node of the reciprocal lattice (see [[reciprocal lattice|Diffraction condition in reciprocal space]]). If other reciprocal lattice nodes, such as ''G'', lie also on the sphere, there will be reflected beams along '''IG''', etc.  This construction is known as the Ewald construction. When the wavelength is large, there are seldom more than two nodes, ''O'' and ''H'', of the reciprocal lattice simultaneously on the Ewald sphere. When there are three or more, one speaks of multiple diffraction, multiple scattering  or ''n''-beam diffraction. This situation becomes increasingly frequent as the wavelength decreases and is practically routine for very short wavelengths such as those of &#947;-rays and electrons. The curvature of the Ewald sphere then becomes negligible and it can often be approximated by a plane. Many reflections must then be taken into account at the same time.
 [[Image:Ewald-2.gif|left]]
-When the wavelength changes, the radius of the Ewald sphere changes and Figure 2 illustrates the case of the reciprocal (110) lattice plane of a silicon crystal and two Ewald spheres corresponding to AgK&#945; (&#955;<sub>1</sub> = 0.709 Å) and CuK&#945; (&#955;<sub>2</sub> = 1.54 Å) radiation, respectively. If the incident beam is a white beam, with a wavelength range &#955;<sub>min</sub> &#8804; &#955; &#8804; &#955;<sub>max</sub>, there will be a nest of Ewald spheres of radii 1/&#955;<sub>max</sub> &#8804; 1/&#955; &#8804; 1/&#955;<sub>min</sub>.
+When the wavelength changes, the radius of the Ewald sphere changes. Fig. 2 illustrates the case of the reciprocal (110) lattice plane of a silicon crystal and two Ewald spheres corresponding to Ag K&#945; (&#955;<sub>1</sub> = 0.709 Å) and Cu K&#945; (&#955;<sub>2</sub> = 1.54 Å) radiation, respectively. If the incident beam is a white beam, with a wavelength range &#955;<sub>min</sub> &#8804; &#955; &#8804; &#955;<sub>max</sub>, there will be a nest of Ewald spheres of radii 1/&#955;<sub>max</sub> &#8804; 1/&#955; &#8804; 1/&#955;<sub>min</sub>.
 == Limiting sphere ==
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 [[Image:Ewald-3.gif|right]]
-In order to explore the reciprocal space, one rotates the Ewald sphere around the origin, ''O'' (in practice one rotates the crystal); as the reciprocal lattice nodes  pass through the Ewald sphere, the corresponding reflections are successively excited. It is clear then that the only reflections that can be observed are those for which ''OH'' &#8804; 2/&#955; (diameter of the Ewald sphere) and for which the reciprocal nodes lie within a sphere of centre ''O'' and radius 2/&#955;. This sphere is called the limiting sphere (in yellow in Figure 3). Conversely, if the wavelength of the incident radiation is larger than the largest [[interplanar spacing]] ''d''<sub>max</sub> of the crystal, there is no reciprocal lattice node within the limiting sphere: no Bragg reflection can take place for &#955; > ''d''<sub>max</sub>.
+In order to explore the reciprocal space, one rotates the Ewald sphere around the origin, ''O'' (in practice one rotates the crystal); as the reciprocal lattice nodes  pass through the Ewald sphere, the corresponding reflections are successively excited. It is clear then that the only reflections that can be observed are those for which ''OH'' &#8804; 2/&#955; (diameter of the Ewald sphere) and for which the reciprocal nodes lie within a sphere of centre ''O'' and radius 2/&#955;. This sphere is called the limiting sphere (in yellow in Fig. 3). Conversely, if the wavelength of the incident radiation is larger than the largest [[interplanar spacing]] ''d''<sub>max</sub> of the crystal, there is no reciprocal lattice node within the limiting sphere: no Bragg reflection can take place for &#955; > ''d''<sub>max</sub>.
 == History ==
-The Ewald sphere was introduced by Ewald in 1913 under the name ''Ausbreitungskugel'' or sphere of reflection (Ewald P.P., 1913, ''Physik. Z.'', '''14''', 465-472. ''Zur Theorie der Interferenzen der Röntgentstrahlen in Kristallen.'' An English translation is given in D. W. J. Cruickshank, H. J. Juretschke and N. Kato, 1992, ''P. P. Ewald and his dynamical theory of X-ray diffraction.'' Oxford University Press, I.U.Cr and O.U.P. Book series, Oxford, 114-123). See also P. P. Ewald, 1962, IUCr, [http://www.iucr.org/iucr-top/publ/50YearsOfXrayDiffraction/ 50 Years of X-ray Diffraction], Section 15.3, page 250.
+The Ewald sphere was introduced by Ewald in 1913 under the name ''Ausbreitungskugel'' or sphere of reflection. [Ewald, P.P. (1913). ''Physik. Z.'' '''14''', 465-472. ''Zur Theorie der Interferenzen der Röntgentstrahlen in Kristallen.'' An English translation is given in D. W. J. Cruickshank, H. J. Juretschke and N. Kato, 1992, ''P. P. Ewald and his dynamical theory of X-ray diffraction.'' Oxford University Press, IUCr/OUP Book series, Oxford, 114-123). See also P. P. Ewald (1962). IUCr, [http://www.iucr.org/iucr-top/publ/50YearsOfXrayDiffraction/ 50 Years of X-ray Diffraction], Utrecht:IUCr/Oosthoek, Section 15.3, page 250.]
 == See also ==
-Section 2.2 of ''International Tables of Crystallography, Volume C''.
+*Chapter 2.2 of ''International Tables of Crystallography, Volume C''.
 [[Category:X-rays]]<br>

← Older revision		Revision as of 15:32, 17 March 2006
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−	<Font color="blue">Sphère d'Ewald </Font>(''F''). <Font color="red">Ewaldkugel, Ausbreitungskugel </Font>(''Ge''). <Font color="green">Esfera de Ewald </Font>(''Sp'').	+	<Font color="blue">Sphère d'Ewald </Font>(''F''). <Font color="red">Ewaldkugel, Ausbreitungskugel </Font>(''Ge''). <Font color="green">Esfera de Ewald </Font>(''Sp'').<Font color="black"> Sfera di Ewald </Font>(''It'')
		+

	== Definition ==		== Definition ==

← Older revision		Revision as of 08:08, 24 February 2006
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−	= ~~Ewald Sphere =~~	+	<Font color="blue">Sphère d'Ewald </Font>(''F''). <Font color="red">Ewaldkugel, Ausbreitungskugel </Font>(''Ge''). <Font color="green">Esfera de Ewald </Font>(''Sp'').
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−	~~=== Other languages ===~~
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−	Sphère d'Ewald (''F''). Ewaldkugel, Ausbreitungskugel (''Ge''). Esfera de Ewald (''Sp'').

	== Definition ==		== Definition ==