https://dictionary.iucr.org/index.php?title=Polar_lattice&feed=atom&action=history
Polar lattice - Revision history
2024-03-29T10:29:27Z
Revision history for this page on the wiki
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https://dictionary.iucr.org/index.php?title=Polar_lattice&diff=4069&oldid=prev
BrianMcMahon: Style edits to align with printed edition
2017-05-16T13:14:41Z
<p>Style edits to align with printed edition</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 13:14, 16 May 2017</td>
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<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><font color="blue">Réseau polaire</font> (''Fr'')<del class="diffchange diffchange-inline">, </del><font color="black">Reticolo polare</font> (''It'').</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><font color="blue">Réseau polaire</font> (''Fr'')<ins class="diffchange diffchange-inline">. </ins><font color="black">Reticolo polare</font> (''It'').</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>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 <del class="diffchange diffchange-inline">" </del>mémoire<del class="diffchange diffchange-inline">" </del>presented to the ''Académie de Sciences de Paris'' on 11 December 1848.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>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 <ins class="diffchange diffchange-inline">'</ins>mémoire<ins class="diffchange diffchange-inline">' </ins>presented to the ''Académie de Sciences de Paris'' on 11 December 1848.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>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 <del class="diffchange diffchange-inline">Ångstroms</del>, instead of <del class="diffchange diffchange-inline">Ångstroms</del><sup><del class="diffchange diffchange-inline">-</del>1</sup>, like the reciprocal lattice.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>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 <ins class="diffchange diffchange-inline">ångströms</ins>, instead of <ins class="diffchange diffchange-inline">ångström</ins><sup><ins class="diffchange diffchange-inline">&minus;</ins>1</sup>, like the reciprocal lattice.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*The unit cell of the polar lattice has the same volume as that of the direct lattice.  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*The unit cell of the polar lattice has the same volume as that of the direct lattice.  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*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 <del class="diffchange diffchange-inline">Kroneker</del>'s tensor and the indices i and j point to the basis vectors.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*The scalar product of the basis vectors of the direct and polar lattice is V<sup>2/3</sup>&delta;<sub><ins class="diffchange diffchange-inline">''</ins>ij<ins class="diffchange diffchange-inline">''</ins></sub>, where &delta; is <ins class="diffchange diffchange-inline">Kronecker</ins>'s tensor and the indices <ins class="diffchange diffchange-inline">''</ins>i<ins class="diffchange diffchange-inline">'' </ins>and <ins class="diffchange diffchange-inline">''</ins>j<ins class="diffchange diffchange-inline">'' </ins>point to the basis vectors.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The polar lattice was introduced to facilitate the morphological study of crystals.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The polar lattice was introduced to facilitate the morphological study of crystals.</div></td></tr>
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BrianMcMahon
https://dictionary.iucr.org/index.php?title=Polar_lattice&diff=3471&oldid=prev
MassimoNespolo: cat
2015-02-25T03:17:14Z
<p>cat</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 03:17, 25 February 2015</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*[[Reciprocal lattice]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*[[Reciprocal lattice]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:History of crystallography]]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Morphological crystallography]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Morphological crystallography]]</div></td></tr>
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MassimoNespolo
https://dictionary.iucr.org/index.php?title=Polar_lattice&diff=3402&oldid=prev
MassimoNespolo: change cateogry
2014-08-24T19:39:16Z
<p>change cateogry</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 19:39, 24 August 2014</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*[[Reciprocal lattice]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*[[Reciprocal lattice]]</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Category:<del class="diffchange diffchange-inline">Fundamental </del>crystallography]]</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Category:<ins class="diffchange diffchange-inline">Morphological </ins>crystallography]]</div></td></tr>
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MassimoNespolo
https://dictionary.iucr.org/index.php?title=Polar_lattice&diff=2460&oldid=prev
MassimoNespolo at 10:25, 9 April 2007
2007-04-09T10:25:24Z
<p></p>
<p><b>New page</b></p><div><font color="blue">Réseau polaire</font> (''Fr''), <font color="black">Reticolo polare</font> (''It'').<br />
<br />
<br />
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.<br />
<br />
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.<br />
*The unit cell of the polar lattice has the same volume as that of the direct lattice. <br />
*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.<br />
The polar lattice was introduced to facilitate the morphological study of crystals.<br />
<br />
==See also==<br />
*[[Direct lattice]]<br />
*[[Reciprocal lattice]]<br />
<br />
[[Category:Fundamental crystallography]]</div>
MassimoNespolo