Acceptance domain - Revision history

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

2017-11-08T17:44:09Z

Tidied translations and added German (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-12T11:08:28Z

Style edits to align with printed edition

MassimoNespolo: /* See also */ cat

2015-02-26T07:54:58Z

‎See also: cat

BrianMcMahon at 15:52, 3 February 2012

2012-02-03T15:52:13Z

BrianMcMahon at 15:23, 30 June 2010

2010-06-30T15:23:54Z

BrianMcMahon at 15:23, 30 June 2010

2010-06-30T15:23:34Z

TedJanssen at 15:44, 18 May 2009

2009-05-18T15:44:52Z

TedJanssen at 13:14, 18 May 2009

2009-05-18T13:14:16Z

TedJanssen at 13:13, 18 May 2009

2009-05-18T13:13:00Z

TedJanssen at 18:25, 17 May 2009

2009-05-17T18:25:12Z

New page

[[Acceptance domain]]

Synonyms: window, atomic domain

Domaine d'acceptation, fenetre (Fr.)

'''Definition'''

When an aperiodic crystalline point set is obtained by the intersection method, as the intersection of a periodic array of finite, disjoint components in superspace and the physical
space, then there is, for each point , a component in the higher-dimensional
unit cell. These components are called ''acceptance domains'', ''atomic surfaces'', ''atomic domains'', or ''windows'' in the literature. The positions of atoms in aperiodic crystals (or vertices in the case of a tiling)
are the intersection of the atomic surfaces with the physical space. This construction of the
points is called the ''intersection method''.

'''History'''

The term ''window'' comes from an alternative construction. One considers a 'tube'
in ''n''-dimensional superspace
that is the product of the ''m''-dimensional physical space ''V'' and a transversal finite (''n-m'')-dimensional object ''O'':
''V times O''. Then the points of the ''n''-dimensional lattice, corresponding
to the periodic embedding of the structure in ''V'', that lie inside the tube are projected
on ''V'' (See Fig. ). These are the points of the aperiodic structure in ''V''.
The construction is called the ''cut-and-project method''. The object ''O''
is the ''window'', or ''acceptance domain''. The latter expresses the fact that only
lattice points inside the tube are projected. The result is the same as attaching a copy
of ''O'' to each lattice point, and considering the intersection of this
periodic array with ''V''. Actually, the latter construction is more special, in the
sense that the atomic surfaces in this are by definition flat, whereas the intersection
method allows arbitrarily shaped ones.

[[Image:BO02F20.gif]]

Figure caption: The grey strip in superspace is the product of the (infinite) physical space (in this
case the horizontal line) and a vertical finite line interval, the acceptance domain. The centres
of the vertical lines form a lattice. When a lattice point falls inside the strip it is projected on the physical space. The projected points form an aperiodic crystal. These projected points are also the intersections of the array of vertical lines with the physical space.

'''See also''': atomic surface.

@@ Line 1: / Line 1: @@
 Synonyms: window, atomic domain, atomic surfaces
-<Font color="blue">Domaine d'acceptation, fen&ecirc;tre </font> (''Fr'').
+<font color="blue">Domaine d'acceptation, fen&ecirc;tre</font> (''Fr''). <font color="red">Atomare Oberfläche, Akzeptanz-Domäne</font> (''Ge'').
 == Definition ==

← Older revision		Revision as of 07:54, 26 February 2015
Line 35:		Line 35:
	== See also ==		== See also ==
	[[atomic surface]]		[[atomic surface]]
		+
		+
		+	[[Category: Fundamental crystallography]]

@@ Line 1: / Line 1: @@
 Synonyms: window, atomic domain
 <Font color="blue">Domaine d'acceptation, fen&ecirc;tre </font> (Fr.)
@@ Line 34: / Line 33: @@
 of the vertical lines form a lattice. When a  lattice point falls inside the strip it is projected on the physical space. The projected points form an aperiodic crystal. These projected points are also the intersections of the array of vertical lines with the physical space.
 == See also ==
 [[atomic surface]]

← Older revision		Revision as of 15:23, 30 June 2010
Line 1:		Line 1:
−	~~[[Acceptance domain]]~~
−
	Synonyms: window, atomic domain		Synonyms: window, atomic domain

@@ Line 6: / Line 6: @@
 <Font color="blue">Domaine d'acceptation, fen&ecirc;tre </font> (Fr.)
- '''Definition'''
+== Definition ==
 When an aperiodic crystalline point set is obtained by the intersection method, as the intersection of a periodic array of finite, disjoint components in superspace and the physical
@@ Line 14: / Line 14: @@
 points is called the  ''intersection method''.
- '''History'''
+== History ==
 The term  ''window'' comes from an alternative construction. One considers a 'tube'
@@ Line 37: / Line 37: @@
-'''See also''': atomic surface.
+== See also ==

@@ Line 1: / Line 1: @@
-Synonyms: window, atomic domain
+Synonyms: window, atomic domain, atomic surfaces
-<Font color="blue">Domaine d'acceptation, fen&ecirc;tre </font> (Fr.)
+<Font color="blue">Domaine d'acceptation, fen&ecirc;tre </font> (''Fr'').
 == Definition ==
 When an aperiodic crystalline point set is obtained by the intersection method, as the intersection of a periodic array of finite, disjoint components in superspace and the physical
-space, then  there is, for each point , a component in the higher-dimensional
+space, then  there is, for each point, a component in the higher-dimensional
 unit cell. These components are called  ''acceptance domains'',  ''atomic surfaces'',  ''atomic domains'', or ''windows'' in the literature. The positions of  atoms in aperiodic crystals (or vertices in the case of a tiling)
 are the intersection of the atomic surfaces with the physical space. This construction of the
@@ Line 18: / Line 18: @@
 <math>V\otimes O</math>. Then the points of the ''n''-dimensional lattice, corresponding
 to the periodic embedding of the structure in ''V'', that lie inside the tube are projected
-on ''V'' (See Fig. ). These are the points of the aperiodic structure in ''V''.
+on ''V'' (see figure). These are the points of the aperiodic structure in ''V''.
 The construction is called the  ''cut-and-project method''. The object ''O''
 is the  ''window'', or  ''acceptance domain''. The latter expresses the fact that only
@@ Line 29: / Line 29: @@
 [[Image:BO02F20.gif]]
-Figure caption: The grey strip in superspace is the product of the (infinite) physical space (in this
+The grey strip in superspace is the product of the (infinite) physical space (in this
 case the horizontal line) and a vertical finite line interval, the acceptance domain. The centres
 of the vertical lines form a lattice. When a  lattice point falls inside the strip it is projected on the physical space. The projected points form an aperiodic crystal. These projected points are also the intersections of the array of vertical lines with the physical space.
 == See also ==
-[[atomic surface]]
+*[[Atomic surface]]
 [[Category: Fundamental crystallography]]

@@ Line 3: / Line 3: @@
 Synonyms: window, atomic domain
-Domaine d'acceptation, fenetre (Fr.)
+Domaine d'acceptation, fen&ecirc;tre (Fr.)
   '''Definition'''