Brillouin zone - Revision history

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

2017-11-09T16:53:08Z

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

BrianMcMahon: moved Brillouin zones to Brillouin zone: Adopting singular for all pages

2017-11-09T16:50:36Z

moved Brillouin zones to Brillouin zone: Adopting singular for all pages

BrianMcMahon at 09:49, 13 May 2017

2017-05-13T09:49:21Z

BrianMcMahon: Edits to align with printed edition

2017-05-13T09:48:58Z

Edits to align with printed edition

MassimoNespolo: /* Definition */ double parentehses removed

2015-03-17T13:06:22Z

‎Definition: double parentehses removed

BrianMcMahon at 17:08, 3 February 2012

2012-02-03T17:08:44Z

TedJanssen: /* Definition */

2011-07-27T11:46:47Z

‎Definition

TedJanssen: /* Definition */

2011-07-27T10:49:50Z

‎Definition

TedJanssen: /* Definition */

2011-07-27T10:00:45Z

‎Definition

TedJanssen: /* Definition */

2011-07-27T09:30:14Z

‎Definition

← Older revision		Revision as of 16:53, 9 November 2017
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−	<~~Font~~ color=blue>~~Zones~~ de Brillouin </Font>(''Fr''). <~~Font~~ color=red>Brillouin ~~Zonen~~ </Font>(''Ge''). <~~Font~~ color=~~green~~> ~~Zonas de~~ Brillouin </~~Font~~>(''Sp''). <~~Font~~ color=~~"black"~~>~~Zone di Brillouin~~ </~~Font~~>(''It''). <~~Font~~ color=~~purple~~> ~~ブリュアンゾーン~~ </~~Font~~>(''Ja'').	+	<font color=blue>Zone de Brillouin</Font> (''Fr''). <font color=red>Brillouin-Zone</Font> (''Ge''). <font color="black">Zona di Brillouin</font> (''It''). <font color=purple>ブリュアンゾーン</font> (''Ja''). <font color=green>Zona de Brillouin</font> (''Sp'').

	== Definition ==		== Definition ==

@@ Line 18: / Line 18: @@
 *[[Domain of influence]]
 *Sayre, D. (1952). ''Acta Cryst.'' '''5''', 60-65. ''The squaring method: a new method for phase determination.''
-*Chapter 2.2 of ''International Tables of Crystallography, Volume D''<br>
+*Chapter 2.2 of ''International Tables for Crystallography, Volume D''<br>
 [[Category:Fundamental crystallography]]<br>

@@ Line 1: / Line 1: @@
-<Font color=blue> Zones de Brillouin </Font>(''Fr''). <Font color=red>  Brillouin Zonen </Font>(''Ge''). <Font color=green> Zonas de Brillouin </Font>(''Sp'').<Font color="black"> Zone di Brillouin </Font>(''It''). <Font color=purple> ブリュアンゾーン </Font>(''Ja'')
+<Font color=blue>Zones de Brillouin </Font>(''Fr''). <Font color=red>Brillouin Zonen </Font>(''Ge''). <Font color=green> Zonas de Brillouin </Font>(''Sp''). <Font color="black">Zone di Brillouin </Font>(''It''). <Font color=purple> ブリュアンゾーン </Font>(''Ja'').
 == Definition ==
-A ''Brillouin Zone'' is a particular choice of the unit cell of the reciprocal lattice. It is defined as the [[Wigner-Seitz cell]] (also called ''Dirichlet'' or ''Voronoi Domain'') of the reciprocal lattice. It is constructed as the set of points enclosed by the ''Bragg planes'', the planes perpendicular to a connection line from the origin to each lattice point and passing through the midpoint (See figure). Alternatively, it is defined as the set of points closer to the origin than to any other reciprocal lattice point. The whole reciprocal space may be covered without overlap
+A ''Brillouin zone'' is a particular choice of the unit cell of the reciprocal lattice. It is defined as the [[Wigner-Seitz cell]] (also called ''Dirichlet'' or ''Voronoi domain of influence'') of the reciprocal lattice. It is constructed as the set of points enclosed by the ''Bragg planes'', the planes perpendicular to a connection line from the origin to each lattice point and passing through the midpoint (see figure). Alternatively, it is defined as the set of points closer to the origin than to any other reciprocal lattice point. The whole reciprocal space may be covered without overlap with copies of such a Brillouin zone.
-For high-symmetry lattices one introduces sometimes the notion of ''n-th Brillouin Zone''. This is the set of points one reaches with a straight line from the origin and passing through ''n''-1 Bragg Planes. In this terminology, the Brillouin Zone defined above is the first Brillouin Zone. The ''n''-th Brillouin Zone is a shell around lower Brillouin Zones and
+For high-symmetry lattices one introduces sometimes the notion of ''n-th Brillouin Zone''. This is the set of points one reaches with a straight line from the origin and passing through ''n''-1 Bragg planes. In this terminology, the Brillouin zone defined above is the first Brillouin zone. The ''n''-th Brillouin zone is a shell around lower Brillouin zones and its shape becomes for higher values of ''n'' rapidly rather complicated (see figure).
 [[Image:BraggPl.gif|frame|Bragg plane perpendicular to and going through the midpoint of the line connecting the origin and ''K''. Particles in the crystal potential are elastically  scattered from wave vector ''k'' to wave vector ''k'''=''k''-''K''. The tips are in the Bragg plane.]]
-[[Image:NBZ2.001.gif|frame|Up to the 3rd BZ for a 2D square lattice; red lines are Bragg planes]]
+[[Image:NBZ2.001.gif|frame|Up to the 3rd Brillouin zone for a two-dimensional square lattice; red lines are Bragg planes.]]
 == See also ==
-Section 2.2 of ''International Tables of Crystallography, Volume D''<br>
+*[[Domain of influence]]
 [[Category:Fundamental crystallography]]<br>

@@ Line 3: / Line 3: @@
 == Definition ==
-A ''Brillouin Zone'' is a particular choice of the unit cell of the reciprocal lattice. It is defined as the [[[[Wigner-Seitz cell]]]] (also called ''Dirichlet'' or ''Voronoi Domain'') of the reciprocal lattice. It is constructed as the set of points enclosed by the ''Bragg planes'', the planes perpendicular to a connection line from the origin to each lattice point and passing through the midpoint (See figure). Alternatively, it is defined as the set of points closer to the origin than to any other reciprocal lattice point. The whole reciprocal space may be covered without overlap
+A ''Brillouin Zone'' is a particular choice of the unit cell of the reciprocal lattice. It is defined as the [[Wigner-Seitz cell]] (also called ''Dirichlet'' or ''Voronoi Domain'') of the reciprocal lattice. It is constructed as the set of points enclosed by the ''Bragg planes'', the planes perpendicular to a connection line from the origin to each lattice point and passing through the midpoint (See figure). Alternatively, it is defined as the set of points closer to the origin than to any other reciprocal lattice point. The whole reciprocal space may be covered without overlap
 with copies of such a Brillouin Zone.

@@ Line 1: / Line 1: @@
 <Font color=blue> Zones de Brillouin </Font>(''Fr''). <Font color=red>  Brillouin Zonen </Font>(''Ge''). <Font color=green> Zonas de Brillouin </Font>(''Sp'').<Font color="black"> Zone di Brillouin </Font>(''It''). <Font color=purple> ブリュアンゾーン </Font>(''Ja'')
 == Definition ==
 A ''Brillouin Zone'' is a particular choice of the unit cell of the reciprocal lattice. It is defined as the [[[[Wigner-Seitz cell]]]] (also called ''Dirichlet'' or ''Voronoi Domain'') of the reciprocal lattice. It is constructed as the set of points enclosed by the ''Bragg planes'', the planes perpendicular to a connection line from the origin to each lattice point and passing through the midpoint (See figure). Alternatively, it is defined as the set of points closer to the origin than to any other reciprocal lattice point. The whole reciprocal space may be covered without overlap
@@ Line 27: / Line 25: @@
 Section 2.2 of ''International Tables of Crystallography, Volume D''<br>
 [[Category:Fundamental crystallography]]<br>

← Older revision	Revision as of 16:50, 9 November 2017
(No difference)

@@ Line 5: / Line 5: @@
-A ''Brillouin Zone'' is a particular choice of the unit cell of the reciprocal lattice. It is defined as the [[[[Wigner-Seitz cell]]]] (also called ''Dirichlet'' or ''Voronoi Domain'') of the reciprocal lattice. It is constructed as the set of points enclosed by the ''Bragg planes'', the planes perpendicular to a connection line from the origin to each lattice point and passing through the midpoint. Alternatively, it is defined as the set of points closer to the origin than to any other reciprocal lattice point. The whole reciprocal space may be covered without overlap
+A ''Brillouin Zone'' is a particular choice of the unit cell of the reciprocal lattice. It is defined as the [[[[Wigner-Seitz cell]]]] (also called ''Dirichlet'' or ''Voronoi Domain'') of the reciprocal lattice. It is constructed as the set of points enclosed by the ''Bragg planes'', the planes perpendicular to a connection line from the origin to each lattice point and passing through the midpoint (See figure). Alternatively, it is defined as the set of points closer to the origin than to any other reciprocal lattice point. The whole reciprocal space may be covered without overlap
 with copies of such a Brillouin Zone.
 For high-symmetry lattices one introduces sometimes the notion of ''n-th Brillouin Zone''. This is the set of points one reaches with a straight line from the origin and passing through ''n''-1 Bragg Planes. In this terminology, the Brillouin Zone defined above is the first Brillouin Zone. The ''n''-th Brillouin Zone is a shell around lower Brillouin Zones and
-its shape becomes for higher values of ''n'' rapidly rather complicated.
+its shape becomes for higher values of ''n'' rapidly rather complicated (See figure).
 Vectors in the Brillouin Zone or on its boundary characterize states in a system with lattice periodicity, e.g. phonon or electron states. States are non-equivalent if
@@ Line 20: / Line 20: @@
-<center>
 [[Image:NBZ2.001.gif|frame|up to the 3rd BZ for a 2D square lattice; red lines are Bragg planes]]
 == See also ==

@@ Line 13: / Line 13: @@
 Vectors in the Brillouin Zone or on its boundary characterize states in a system with lattice periodicity, e.g. phonons or electrons. States are non-equivalent if
 they belong to different vectors in a unit cell of the reciprocal lattice. This is not necessarily the Brillouin Zone. Especially, for low-symmetry systems Brillouin Zones
-are sometimes difficult to visualize, and another choice of unit cell may be useful, e.g. the parallelepiped spanned b the basis vectors.
+are sometimes difficult to visualize, and another choice of unit cell may be useful, e.g. the parallelepiped spanned by the basis vectors.