https://dictionary.iucr.org/index.php?action=history&feed=atom&title=Family_structureFamily structure - Revision history2026-06-03T23:18:33ZRevision history for this page on the wikiMediaWiki 1.30.0https://dictionary.iucr.org/index.php?title=Family_structure&diff=3995&oldid=prevBrianMcMahon: Style edits to align with printed edition2017-05-15T11:00:49Z<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;">← Older revision</td>
<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 11:00, 15 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>By superposing two or more identical copies of the same [[polytypism|polytype]] translated by a superposition vector (''i<del class="diffchange diffchange-inline">''</del>.<del class="diffchange diffchange-inline">''</del>e''<del class="diffchange diffchange-inline">. </del>a vector corresponding to a submultiple of a translation period) a fictitious structure is obtained, which is termed a ''superposition structure''. Among the infinitely possible superposition structures, that structure having all the possible positions of each [[OD structure|OD layer]]<del class="diffchange diffchange-inline">s </del>is termed a '''family structure''': it exists only if the shifts between adjacent layers are rational, i.e. if they correspond to a submultiple of lattice translations.</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>By superposing two or more identical copies of the same [[polytypism|polytype]] translated by a superposition vector (''i.e'' a vector corresponding to a submultiple of a translation period) a fictitious structure is obtained, which is termed a ''superposition structure''. Among the infinitely possible superposition structures, that structure having all the possible positions of each [[OD structure|OD layer]] is termed a '''family structure''': it exists only if the shifts between adjacent layers are rational, <ins class="diffchange diffchange-inline">''</ins>i.e.<ins class="diffchange diffchange-inline">'' </ins>if they correspond to a submultiple of lattice translations.</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 family structure is common to all polytypes of the same family. From a group-theoretical viewpoint, building the family structure corresponds to transforming (<del class="diffchange diffchange-inline">“completing”</del>) all the local symmetry operations of a space groupoid into the global symmetry operations of a space<del class="diffchange diffchange-inline">-</del>group.</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 family structure is common to all polytypes of the same family. From a group-theoretical viewpoint, building the family structure corresponds to transforming (<ins class="diffchange diffchange-inline">'completing'</ins>) all the local symmetry operations of a space groupoid into the global symmetry operations of a space group.</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;"><div>==See also==</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>==See also==</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>Chapter 9.2 of ''International Tables <del class="diffchange diffchange-inline">of </del>Crystallography, Volume C''</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><ins class="diffchange diffchange-inline">*</ins>Chapter 9.2 of ''International Tables <ins class="diffchange diffchange-inline">for </ins>Crystallography, Volume C''</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;"><div>[[Category:Fundamental 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:Fundamental crystallography]]</div></td></tr>
</table>BrianMcMahonhttps://dictionary.iucr.org/index.php?title=Family_structure&diff=2799&oldid=prevMassimoNespolo at 09:27, 15 June 20082008-06-15T09:27:44Z<p></p>
<p><b>New page</b></p><div>By superposing two or more identical copies of the same [[polytypism|polytype]] translated by a superposition vector (''i''.''e''. a vector corresponding to a submultiple of a translation period) a fictitious structure is obtained, which is termed a ''superposition structure''. Among the infinitely possible superposition structures, that structure having all the possible positions of each [[OD structure|OD layer]]s is termed a '''family structure''': it exists only if the shifts between adjacent layers are rational, i.e. if they correspond to a submultiple of lattice translations.<br />
<br />
The family structure is common to all polytypes of the same family. From a group-theoretical viewpoint, building the family structure corresponds to transforming (“completing”) all the local symmetry operations of a space groupoid into the global symmetry operations of a space-group.<br />
<br />
==See also==<br />
Chapter 9.2 of ''International Tables of Crystallography, Volume C''<br />
<br />
[[Category:Fundamental crystallography]]</div>MassimoNespolo