Centred lattice - Revision history

MassimoNespolo: /* See also */ link to Orthohexagonal

2018-02-02T16:46:07Z

‎See also: link to Orthohexagonal

BrianMcMahon: Tidied translations.

2017-11-09T17:04:36Z

Tidied translations.

BrianMcMahon: moved Centred lattices to Centred lattice: Adopting singular for all pages

2017-11-09T17:02:32Z

moved Centred lattices to Centred lattice: Adopting singular for all pages

BrianMcMahon at 10:32, 13 May 2017

2017-05-13T10:32:58Z

MassimoNespolo: /* See also */

2017-04-10T15:11:47Z

‎See also

MassimoNespolo: /* See also */ 6th edition of ITA

2017-04-10T15:09:04Z

‎See also: 6th edition of ITA

MassimoNespolo: /* Types of centred lattices */ typoè one space missing

2016-12-20T22:30:39Z

‎Types of centred lattices: typoè one space missing

MassimoNespolo: /* See also */ referenence

2016-12-20T12:20:36Z

‎See also: referenence

MassimoNespolo: link

2016-11-24T13:37:46Z

link

MassimoNespolo: /* See also */ Now directly in the table

2015-02-25T07:30:03Z

‎See also: Now directly in the table

@@ Line 77: / Line 77: @@
 == See also ==
+*[[Orthohexagonal]]
 *Chapter 1.3.2.4 of ''International Tables for Crystallography, Volume A'', 6th edition
 *Chapter 1.1 of ''International Tables for Crystallography, Volume C''

← Older revision		Revision as of 17:04, 9 November 2017
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−	<~~Font~~ color="blue">~~Réseaux centrés~~ </Font>(''Fr''). <~~Font~~ color="red">~~Zentrierte~~ Gitter</~~Font~~> (''Ge''). <~~Font~~ color="~~green~~">~~Redes centradas~~</~~Font~~> (''Sp''). <~~Font~~ color="~~black~~"> ~~Reticoli centrati~~ </Font>(''It''). <~~Font~~ color="~~purple~~"> ~~複合格子~~ </~~Font~~>(''Ja'').	+	<font color="blue">Réseau centré</Font> (''Fr''). <font color="red">Zentriertes Gitter</font> (''Ge''). <font color="black">Reticoli centrati</font> (''It''). <font color="purple">複合格子</Font> (''Ja''). <font color="green">Red centrada</font> (''Sp'').

	== Definition ==		== Definition ==

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-<Font color="blue">Réseaux centrés </Font>(''Fr''). <Font color="red">Zentrierte Gitter</Font> (''Ge''). <Font color="green">Redes centradas</Font> (''Sp''). <Font color="black"> Reticoli centrati </Font>(''It''). <Font color="purple"> 複合格子 </Font>(''Ja'')
+<Font color="blue">Réseaux centrés </Font>(''Fr''). <Font color="red">Zentrierte Gitter</Font> (''Ge''). <Font color="green">Redes centradas</Font> (''Sp''). <Font color="black"> Reticoli centrati </Font>(''It''). <Font color="purple"> 複合格子 </Font>(''Ja'').
 == Definition ==
-When the unit cell does not reflect the symmetry of the lattice, it is usual in crystallography to refer to a '[[conventional cell|conventional]]', non-primitive, crystallographic basis, '''a<sub>c</sub>''', '''b<sub>c</sub>''', '''c<sub>c</sub>''' instead of a [[primitive_cell| primitive basis]], '''a''', '''b''', '''c'''. This is done by adding lattice nodes at the center of the unit cell or at one or three faces. The vectors joining the origin of the unit cell to these additional nodes are called 'centring vectors'. In such a lattice '''a<sub>c</sub>''', '''b<sub>c</sub>''' and '''c<sub>c</sub>''' with all their integral linear combinations are lattice vectors again, but there exist other lattice vectors '''t''' &#8712; '''L''', '''t''' = ''t<sub>1</sub>'' '''a<sub>c</sub>''' + ''t<sub>2</sub>'' '''b<sub>c</sub>''' + ''t<sub>3</sub>'' '''c<sub>c</sub>'''; with at least two of the coefficients ''t<sub>1</sub>'', ''t<sub>2</sub>'', ''t<sub>3</sub>'' being fractional. The table below gives the various types of centring vectors and the corresponding types of centring. Each one is described by a letter, called the Bravais letter, which is to be found in the [[Hermann-Mauguin symbols|Hermann-Mauguin symbol]] of a space group.
+When the unit cell does not reflect the symmetry of the lattice, it is usual in crystallography to refer to a '[[conventional cell|conventional]]', non-primitive, crystallographic basis, '''a<sub>c</sub>''', '''b<sub>c</sub>''', '''c<sub>c</sub>''' instead of a [[primitive_cell| primitive basis]], '''a''', '''b''', '''c'''. This is done by adding lattice nodes at the center of the unit cell or at one or three faces. The vectors joining the origin of the unit cell to these additional nodes are called 'centring vectors'. In such a lattice, '''a<sub>c</sub>''', '''b<sub>c</sub>''' and '''c<sub>c</sub>''' with all their integral linear combinations are lattice vectors again, but there exist other lattice vectors '''t''' &#8712; '''L''', '''t''' = ''t<sub>1</sub>'' '''a<sub>c</sub>''' + ''t<sub>2</sub>'' '''b<sub>c</sub>''' + ''t<sub>3</sub>'' '''c<sub>c</sub>'''; with at least two of the coefficients ''t<sub>1</sub>'', ''t<sub>2</sub>'', ''t<sub>3</sub>'' being fractional. The table below gives the various types of centring vectors and the corresponding types of centring. Each one is described by a letter, called the Bravais letter, which is to be found in the [[Hermann-Mauguin symbols|Hermann-Mauguin symbol]] of a space group.
 The 'multiplicity', ''m'', of the centred cell is the number of lattice nodes per unit cell (see table).
-The [[unit_cell|volume of the unit cell]], ''V<sub>c</sub>'' = ('''a<sub>c</sub>''', '''b<sub>c</sub>''', '''c<sub>c</sub>''') is given in terms of the volume of the primitive cell, ''V'' = ('''a''', '''b''', '''c'''), by:
+The [[unit_cell|volume of the unit cell]], ''V<sub>c</sub>'' = ('''a<sub>c</sub>''', '''b<sub>c</sub>''', '''c<sub>c</sub>''') is given in terms of the volume of the primitive cell, ''V'' = ('''a''', '''b''', '''c'''), by
 <div align="center">
-''V<sub>c</sub>'' = ''m V''
+''V<sub>c</sub>'' = ''m V.''
 </div>
-==Centred cells vs. "centred lattices"==
+==Centred cells vs 'centred lattices'==
-A lattice being an infinite, symmetric and periodic collection of zero-dimensional nodes, rigorously speaking it is neither primitive nor centred. The expression "centred lattice" has to be considered as a shortcut for "lattice whose [[conventional cell]] is centred".
+A lattice being an infinite, symmetric and periodic collection of zero-dimensional nodes, rigorously speaking it is neither primitive nor centred. The expression 'centred lattice' has to be considered as a shortcut for 'lattice whose [[conventional cell]] is centred'.
 == Types of centred lattices ==
@@ Line 73: / Line 73: @@
 The letter ''S'' is also used to indicate a single pair of centred faces. This happens in the monoclinic and orthorhombic [[crystal family|crystal families]].
-*In the monoclinic crystal family, b-unique axis, the centred cells ''mA'', ''mC'', ''mI'' and ''mF'' are equivalent in the sense that a different choice of axes in the (010) plane interchanges these centrings. The letter ''mS'' is sometimes used to collectively indicate any of these cells. The cell ''mB'' is instead equivalent to the cell ''mP''.
+*In the monoclinic crystal family, ''b''-unique axis, the centred cells ''mA'', ''mC'', ''mI'' and ''mF'' are equivalent in the sense that a different choice of axes in the (010) plane interchanges these centrings. The symbol ''mS'' is sometimes used to collectively indicate any of these cells. The cell ''mB'' is instead equivalent to the cell ''mP''.
-*In the orthorhobic crystal family, the centred cells ''oA'', ''oB'' and ''oC'' are transformed one into the other when the axes are permuted. The symbol ''oS'' is sometimes used to collectively indicate these three equivalent cells.
+*In the orthorhombic crystal family, the centred cells ''oA'', ''oB'' and ''oC'' are transformed one into the other when the axes are permuted. The symbol ''oS'' is sometimes used to collectively indicate these three equivalent cells.
 == See also ==
-*Section 1.3.2.4 of ''International Tables of Crystallography, Volume A'', 6<sup>th</sup> edition
+*Chapter 1.3.2.4 of ''International Tables for Crystallography, Volume A'', 6th edition
-*Section 1.1 of ''International Tables of Crystallography, Volume C''
+*Chapter 1.1 of ''International Tables for Crystallography, Volume C''
-*[http://pubs.acs.org/doi/abs/10.1021/ed070p959 Discussion about centred lattices ''vs''. centred cells]
+*[http://pubs.acs.org/doi/abs/10.1021/ed070p959 Discussion about centred lattices ''vs'' centred cells]
 [[Category:Fundamental crystallography]]<br>

@@ Line 78: / Line 78: @@
 == See also ==
-*Sections 1.3.2.4 of ''International Tables of Crystallography, Volume A'', 6<sup>th</sup> edition
+*Section 1.3.2.4 of ''International Tables of Crystallography, Volume A'', 6<sup>th</sup> edition
 *Section 1.1 of ''International Tables of Crystallography, Volume C''
 *[http://pubs.acs.org/doi/abs/10.1021/ed070p959 Discussion about centred lattices ''vs''. centred cells]

@@ Line 78: / Line 78: @@
 == See also ==
-*Sections 1.2 and 9 of ''International Tables of Crystallography, Volume A''
+*Sections 1.3.2.4 of ''International Tables of Crystallography, Volume A'', 6<sup>th</sup> edition
 *Section 1.1 of ''International Tables of Crystallography, Volume C''
 *[http://pubs.acs.org/doi/abs/10.1021/ed070p959 Discussion about centred lattices ''vs''. centred cells]

← Older revision	Revision as of 17:02, 9 November 2017
(No difference)

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 |-
 |rowspan=2|  ''[[D centred cell|D]]''
-|rowspan=2| [[D centred cell|Rhombohedrallycentred]]
+|rowspan=2| [[D centred cell|Rhombohedrally centred]]
 |&#8531;'''a<sub>c</sub>'''+&#8531;'''b<sub>c</sub>'''+&#8531;'''c<sub>c</sub>'''
 |rowspan=2| <center>3</center>