Polar point group
In geometry, a polar point group is a point group in which there is more than one point that every symmetry operation leaves unmoved. The unmoved points will constitute a line, a plane, or all of space.
A straight line joining two unmoved points defines a unique axis of rotation, called a polar direction, unless the symmetry operations do not allow any rotation at all, such as mirror symmetry, in which case the polar direction must be parallel to any mirror planes.
A point group with more than one axis of rotation or with a mirror plane perpendicular to an axis of rotation cannot be polar.
Polar crystallographic point group
Of the 32 crystallographic point groups, 10 are polar:
|Crystal system||Polar point groups|
The space groups associated with a polar point group do not have a discrete set of possible origin points that are unambiguously determined by symmetry elements.
When materials having a polar point group crystal structure are heated or cooled, they may temporarily generate a voltage called pyroelectricity.
Molecular crystals that occupy polar space groups may exhibit triboluminescence. A common example of this is sucrose, demonstrated by smashing a wintergreen lifesaver in a darkened room.
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- Kasap, Safa O. (2006). Principles of electronic materials and devices. Boston: McGraw-Hill. ISBN 9780073104645.
- 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.