Polar lattice - Revision history

BrianMcMahon: Style edits to align with printed edition

2017-05-16T13:14:41Z

Style edits to align with printed edition

MassimoNespolo: cat

2015-02-25T03:17:14Z

cat

MassimoNespolo: change cateogry

2014-08-24T19:39:16Z

change cateogry

MassimoNespolo at 10:25, 9 April 2007

2007-04-09T10:25:24Z

New page

Réseau polaire (''Fr''), Reticolo polare (''It'').

The '''polar lattice''' is a lattice dual of the [[direct lattice]], which is the ancestor of the [[reciprocal lattice]]. It was introduced by Auguste Bravais in a " mémoire" presented to the ''Académie de Sciences de Paris'' on 11 December 1848.

The construction of the polar lattice is essentially the same as that of the reciprocal lattice but the parameter along a row of the polar lattice is V2/3/''d''(''hkl'') instead of 1/''d''(''hkl''). The polar lattice has thus the same dimensions as the direct lattice, namely Ångstroms, instead of Ångstroms-1, like the reciprocal lattice.
*The unit cell of the polar lattice has the same volume as that of the direct lattice.
*The scalar product of the basis vectors of the direct and polar lattice is V2/3δij, where δ is Kroneker's tensor and the indices i and j point to the basis vectors.
The polar lattice was introduced to facilitate the morphological study of crystals.

==See also==
*[[Direct lattice]]
*[[Reciprocal lattice]]

[[Category:Fundamental crystallography]]

@@ Line 1: / Line 1: @@
-<font color="blue">Réseau polaire</font> (''Fr''), <font color="black">Reticolo polare</font> (''It'').
+<font color="blue">Réseau polaire</font> (''Fr''). <font color="black">Reticolo polare</font> (''It'').
-The '''polar lattice''' is a lattice dual of the [[direct lattice]], which is the ancestor of the [[reciprocal lattice]]. It was introduced by Auguste Bravais in a " mémoire" presented to the ''Académie de Sciences de Paris'' on 11 December 1848.
+The '''polar lattice''' is a lattice dual of the [[direct lattice]], which is the ancestor of the [[reciprocal lattice]]. It was introduced by Auguste Bravais in a 'mémoire' presented to the ''Académie de Sciences de Paris'' on 11 December 1848.
-The construction of the polar lattice is essentially the same as that of the reciprocal lattice but the parameter along a row of the polar lattice is V<sup>2/3</sup>/''d''(''hkl'') instead of 1/''d''(''hkl''). The polar lattice has thus the same dimensions as the direct lattice, namely Ångstroms, instead of Ångstroms<sup>-1</sup>, like the reciprocal lattice.
+The construction of the polar lattice is essentially the same as that of the reciprocal lattice but the parameter along a row of the polar lattice is V<sup>2/3</sup>/''d''(''hkl'') instead of 1/''d''(''hkl''). The polar lattice has thus the same dimensions as the direct lattice, namely ångströms, instead of ångström<sup>&minus;1</sup>, like the reciprocal lattice.
 *The unit cell of the polar lattice has the same volume as that of the direct lattice.
-*The scalar product of the basis vectors of the direct and polar lattice is V<sup>2/3</sup>&delta;<sub>ij</sub>, where &delta; is Kroneker's tensor and the indices i and j point to the basis vectors.
+*The scalar product of the basis vectors of the direct and polar lattice is V<sup>2/3</sup>&delta;<sub>''ij''</sub>, where &delta; is Kronecker's tensor and the indices ''i'' and ''j'' point to the basis vectors.
 The polar lattice was introduced to facilitate the morphological study of crystals.

← Older revision		Revision as of 03:17, 25 February 2015
Line 13:		Line 13:
	*[[Reciprocal lattice]]		*[[Reciprocal lattice]]

		+	[[Category:History of crystallography]]
	[[Category:Morphological crystallography]]		[[Category:Morphological crystallography]]

← Older revision		Revision as of 19:39, 24 August 2014
Line 13:		Line 13:
	*[[Reciprocal lattice]]		*[[Reciprocal lattice]]

−	[[Category:~~Fundamental~~ crystallography]]	+	[[Category:Morphological crystallography]]