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must be parallel to a polar direction. In polar point groups of high symmetry, the polar direction can be a unique axis of rotation, but if the symmetry operations do not allow any rotation at all, such as mirror symmetry, there can be an infinite number of such axes: in that case the only
35:, leaves all points invariant, most polar point groups will move some, but not all points. To describe the points which are unmoved by the symmetry operations of the point group, we draw a straight line joining two unmoved points. This line is called a polar direction. The
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Zink, Jeffery (1981). "Triboluminescence-Structure
Relations in Polymorphs of Hexaphenylcarbodiphosphorane and Anthranilic Acid, Molecular Crystals, and Salts".
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associated with a polar point group do not have a discrete set of possible origin points that are unambiguously determined by symmetry elements.
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When materials having a polar point group crystal structure are heated or cooled, they may temporarily generate a voltage called
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A point group with more than one axis of rotation or with a mirror plane perpendicular to an axis of rotation cannot be polar.
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Molecular crystals which have symmetry described by one of the polar space groups, such as
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restriction on the polar direction is that it must be parallel to any mirror planes.
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leaves unmoved. The unmoved points will constitute a line, a plane, or all of space.
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Jeremy Karl
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24:in which there is more than one point that every
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361:Principles of electronic materials and devices
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75: Schönflies
59:Polar crystallographic point groups
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47:Polar crystallographic point group
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31:While the simplest point group, C
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53:crystallographic point groups
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363:. Boston: McGraw-Hill.
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341:. University of London
37:electric polarization
339:"Polar Point Groups"
398:10.1021/ja00395a014
69:Polar point groups
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26:symmetry operation
370:978-0-07-310464-5
315:triboluminescence
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18:polar point group
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386:J. Am. Chem. Soc
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343:. Retrieved
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297:space groups
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155:Orthorhombic
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22:point group
412:Categories
345:2013-12-09
321:References
215:Tetragonal
120:Monoclinic
51:Of the 32
250:Hexagonal
97:Triclinic
418:Symmetry
180:Trigonal
85:Orbifold
311:sucrose
289:(none)
90:Coxeter
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285:Cubic
20:is a
365:ISBN
295:The
394:doi
390:103
275:*66
269:6mm
240:*44
234:4mm
205:*33
170:*22
165:mm2
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262:6v
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227:4v
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192:3v
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260:C
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254:C
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219:C
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184:C
159:C
145:*
139:m
136:2
132:s
130:C
126:2
124:C
107:1
103:1
101:C
33:1
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