Polar point group

<h2 id="polar-crystallographic-point-group">Polar crystallographic point group</h2>
<p>Of the 32 <a href="/facts/Crystallographic_point_group/43NqYrf0">crystallographic point groups</a>, 10 are polar:<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>
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Polar crystallographic point groups<table><tbody><tr><th rowspan="2"><a href="/facts/Crystal_system/dMQLk1q4">Crystal system</a></th><th colspan="8">Polar point groups</th></tr><tr><td colspan="2"><a href="/facts/Sch%25C3%25B6nflies_notation/c4y0GtEt">   Schönflies   </a></td><td colspan="2"><a href="/facts/Hermann%25E2%2580%2593Mauguin_notation/NGHDFXKC">Hermann–Mauguin</a></td><td colspan="2"><a href="/facts/Orbifold_notation/HCbBoa2J">Orbifold</a></td><td colspan="2"><a href="/facts/Coxeter_notation/ArUw6goe">Coxeter</a></td></tr><tr><td><a href="/facts/Triclinic/Y6yEdqfN">Triclinic</a></td><td colspan="2">C1</td><td colspan="2">1</td><td>11</td><td></td><td colspan="2">[ ]+</td></tr><tr><td><a href="/facts/Monoclinic/5PCwXvzX">Monoclinic</a></td><td>C2</td><td>Cs</td><td>2</td><td>m</td><td>22</td><td>*</td><td>[2]+</td><td>[ ]</td></tr><tr><td><a href="/facts/Orthorhombic/3zo4F8P0">Orthorhombic</a></td><td colspan="2">C2v</td><td colspan="2">mm2</td><td></td><td>*22</td><td></td><td>[2]</td></tr><tr><td><a href="/facts/Trigonal/sSSok8wo">Trigonal</a></td><td>C3</td><td>C3v</td><td>3</td><td>3m</td><td>33</td><td>*33</td><td>[3]+</td><td>[3]</td></tr><tr><td><a href="/facts/Tetragonal/12Aop255">Tetragonal</a></td><td>C4</td><td>C4v</td><td>4</td><td>4mm</td><td>44</td><td>*44</td><td>[4]+</td><td>[4]</td></tr><tr><td><a href="/facts/Hexagonal/DPzuCzWE">Hexagonal</a></td><td>C6</td><td>C6v</td><td>6</td><td>6mm</td><td>66</td><td>*66</td><td>[6]+</td><td>[6]</td></tr><tr><td><a href="/facts/Cubic_crystal_system/92Co7BKM">Cubic</a></td><td colspan="8">(none)</td></tr></tbody></table>
<p>The <a href="/facts/Space_group/2XQx0J7M">space groups</a> associated with a polar point group do not have a discrete set of possible origin points that are unambiguously determined by symmetry elements.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>
</p><p>When materials having a polar point group crystal structure are heated or cooled, they may temporarily generate a voltage called <a href="/facts/Pyroelectricity/3H26PeCt">pyroelectricity</a>.
</p><p>Molecular crystals which have symmetry described by one of the polar space groups, such as <a href="/facts/Sucrose/7y1ke94L">sucrose</a>, may exhibit <a href="/facts/Triboluminescence/fwAkDFTp">triboluminescence</a>.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a>
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<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Jeremy Karl Cockcroft; Huub Driessen; David Moss; Ian Tickle (2006). "Polar Point Groups". University of London. Retrieved 2013-12-09. <a href="http://pd.chem.ucl.ac.uk/pdnn/symm2/polar1.htm" target="_blank">http://pd.chem.ucl.ac.uk/pdnn/symm2/polar1.htm</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Kasap, Safa O. (2006). Principles of electronic materials and devices. Boston: McGraw-Hill. ISBN 978-0-07-310464-5. <a href="978-0-07-310464-5" target="_blank">978-0-07-310464-5</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Jeremy Karl Cockcroft; Huub Driessen; David Moss; Ian Tickle (2006). "Polar Point Groups". University of London. Retrieved 2013-12-09. <a href="http://pd.chem.ucl.ac.uk/pdnn/symm2/polar1.htm" target="_blank">http://pd.chem.ucl.ac.uk/pdnn/symm2/polar1.htm</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Zink, Jeffery (1981). "Triboluminescence-Structure Relations in Polymorphs of Hexaphenylcarbodiphosphorane and Anthranilic Acid, Molecular Crystals, and Salts". J. Am. Chem. Soc. 103: 1074–1079. doi:10.1021/ja00395a014. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
</ol>

Polar point group open-in-new

Polar point group