Direct lattice - Revision history

BrianMcMahon: Tidied translations.

2017-11-10T13:42:09Z

Tidied translations.

BrianMcMahon at 08:08, 21 May 2017

2017-05-21T08:08:19Z

BrianMcMahon: Style edits to align with printed edition

2017-05-13T13:03:52Z

Style edits to align with printed edition

MassimoNespolo: /* See also */

2017-04-10T15:29:36Z

‎See also

MassimoNespolo: link

2008-03-03T14:01:05Z

link

MassimoNespolo: links

2007-04-12T08:43:13Z

links

MassimoNespolo: /* See also */

2007-04-09T10:27:06Z

‎See also

MassimoNespolo: link

2007-04-09T10:09:59Z

link

MassimoNespolo at 11:49, 27 February 2007

2007-02-27T11:49:09Z

AndreAuthier at 06:01, 18 March 2006

2006-03-18T06:01:39Z

← Older revision		Revision as of 13:42, 10 November 2017
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−	<~~Font~~ color="blue">Réseau direct </~~Font~~>(''Fr''). <~~Font~~ color="red">Direktes Gitter </~~Font~~>(''Ge''). <~~Font~~ color="~~green~~">~~Red directa~~ </~~Font~~>(''Sp''). <~~Font~~ color="~~black~~"> ~~Reticolo diretto~~ </Font>(''It''). <~~Font~~ color="~~purple~~"> ~~直格子~~ </~~Font~~>(''Ja'').	+	<font color="blue">Réseau direct</font> (''Fr''). <font color="red">Direktes Gitter</font> (''Ge''). <font color="black">Reticolo diretto</font> (''It''). <font color="purple">直格子</Font> (''Ja''). <font color="green">Red directa</font> (''Sp'').

	== Definition ==		== Definition ==

← Older revision		Revision as of 08:08, 21 May 2017
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	If the basis is primitive, the unit cell is called the ''[[primitive cell]]''. It contains only one lattice point. If the basis is non-primitive, the unit cell is a ''[[centred lattices\|multiple cell]]'' and it contains more than one lattice point. The multiplicity of the cell is given by the ratio of its volume to the volume of a primitive cell.		If the basis is primitive, the unit cell is called the ''[[primitive cell]]''. It contains only one lattice point. If the basis is non-primitive, the unit cell is a ''[[centred lattices\|multiple cell]]'' and it contains more than one lattice point. The multiplicity of the cell is given by the ratio of its volume to the volume of a primitive cell.
−
−	~~The generalization of the notion of point and vector lattices to ''n''-dimensional space is given in Chapter 8.1 of ''International Tables for Crystallography, Volume A'', fifth edition.~~

	== See also ==		== See also ==

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-<Font color="blue">Réseau direct </Font>(''Fr''). <Font color="red">Direktes Gitter </Font>(''Ge''). <Font color="green">Red directa </Font>(''Sp''). <Font color="black"> Reticolo diretto </Font>(''It''). <Font color="purple"> 直格子 </Font>(''Ja'')
+<Font color="blue">Réseau direct </Font>(''Fr''). <Font color="red">Direktes Gitter </Font>(''Ge''). <Font color="green">Red directa </Font>(''Sp''). <Font color="black"> Reticolo diretto </Font>(''It''). <Font color="purple"> 直格子 </Font>(''Ja'').
 == Definition ==
@@ Line 17: / Line 17: @@
 If the basis is primitive, the unit cell is called the ''[[primitive cell]]''. It contains only one lattice point. If the basis is non-primitive, the unit cell is a ''[[centred lattices|multiple cell]]'' and it contains more than one lattice point. The multiplicity of the cell is given by the ratio of its volume to the volume of a primitive cell.
-The generalization of the notion of point and vector lattices to ''n''-dimensional space is given in Section 8.1
+The generalization of the notion of point and vector lattices to ''n''-dimensional space is given in Chapter 8.1 of ''International Tables for Crystallography, Volume A'', fifth edition.
 == See also ==
 *[[Polar lattice]]
 *[[Reciprocal lattice]]
 [[Category:Fundamental crystallography]]

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 *[[Polar lattice]]
 *[[Reciprocal lattice]]
-*Section 8.1 of ''International Tables of Crystallography, Volume A''
 [[Category:Fundamental crystallography]]

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 '''t<sub>2</sub>''' and '''t<sub>3</sub>'''. One distinguishes two kinds of lattices, the ''vector lattices'' and the ''point lattices''.
-Any translation '''t''' = ''u<sup>i</sup>'' '''t<sub>i</sub>''' (''u<sup>i</sup>'' arbitrary integers) is also a translation of the pattern and the infinite set of all translation vectors of a crystal pattern is the '''vector lattice''' '''L''' of this crystal pattern.
+Any translation '''t''' = ''u<sup>i</sup>'' '''t<sub>i</sub>''' (''u<sup>i</sup>'' arbitrary integers) is also a translation of the pattern and the infinite set of all translation vectors of a crystal pattern is the '''vector lattice''' '''L''' of this [[crystal pattern]].
 Given an arbitrary point ''P'' in point space, the set of all the points ''P<sub>i</sub>'' deduced from one of them by a translation '''PP<sub>i</sub>''' = '''t<sub>i</sub>''' of the vector lattice '''L''' is called the '''point lattice'''.

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 A basis '''a''', '''b''', '''c''' of the vector space '''V<sup>n</sup>''' is a ''crystallographic basis'' of the vector lattice '''L''' if ''every'' integral linear combination '''t''' = ''u'' '''a''' + ''v'' '''b''' + ''w'' '''c''' is a lattice vector of '''L'''. It is called a ''primitive basis'' if ''every'' lattice vector '''t''' of '''L''' may be obtained
-as an integral linear combination  of the basis vectors, '''a''', '''b''', '''c'''. Referred to any crystallographic basis the coefficients of each lattice vector are either integral or rational, while in the case of a primitive basis they are integral. ''Non-primitive'' bases are used conventionally to describe ''centred lattices''.
+as an integral linear combination  of the basis vectors, '''a''', '''b''', '''c'''. Referred to any crystallographic basis the coefficients of each lattice vector are either integral or rational, while in the case of a primitive basis they are integral. ''Non-primitive'' bases are used conventionally to describe ''[[centred lattices]]''.
 The parallelepiped built on the basis vectors is the ''unit cell''. Its volume is given by the triple scalar product, ''V'' = ('''a''', '''b''', '''c''').
-If the basis is primitive, the unit cell is called the ''primitive'' cell. It contains only one lattice point. If the basis is non-primitive, the unit cell is a multiple cell and it contains more than one lattice point. The multiplicity of the cell is given by the ratio of its volume to the volume of a primitive cell.
+If the basis is primitive, the unit cell is called the ''[[primitive cell]]''. It contains only one lattice point. If the basis is non-primitive, the unit cell is a ''[[centred lattices|multiple cell]]'' and it contains more than one lattice point. The multiplicity of the cell is given by the ratio of its volume to the volume of a primitive cell.
 The generalization of the notion of point and vector lattices to ''n''-dimensional space is given in Section 8.1

← Older revision		Revision as of 11:49, 27 February 2007
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−	<Font color="blue">Réseau direct </Font>(''Fr''). <Font color="red">Direktes Gitter </Font>(''Ge''). <Font color="green">Red directa </Font>(''Sp''). <Font color="black"> Reticolo diretto </Font>(''It'')	+	<Font color="blue">Réseau direct </Font>(''Fr''). <Font color="red">Direktes Gitter </Font>(''Ge''). <Font color="green">Red directa </Font>(''Sp''). <Font color="black"> Reticolo diretto </Font>(''It''). <Font color="purple"> 直格子 </Font>(''Ja'')

	== Definition ==		== Definition ==

← Older revision		Revision as of 06:01, 18 March 2006
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−	= ~~Direct lattice =~~	+	<Font color="blue">Réseau direct </Font>(''Fr''). <Font color="red">Direktes Gitter </Font>(''Ge''). <Font color="green">Red directa </Font>(''Sp''). <Font color="black"> Reticolo diretto </Font>(''It'')
−
−	~~=== Other languages ===~~
−
−	Réseau direct (''Fr''). Direktes Gitter (''Ge''). Red directa (''Sp'').<Font color="black"> Reticolo diretto </Font>(''It'')

	== Definition ==		== Definition ==