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BELL SYSTEM TECHNICAL JOURNAL 



Class 22 (Ditrigonal 



bipyramidal) 

 Xs trigonal, Xz plane of d = 



symmetry 

 X2 plane of symmetry 



Class 23 (Hexagonal 



pyramidal) d = 



Xs Hexagonal 



d = 



Class 24 (Hexagonal 



trapezohedral) 

 Xs hexagonal, .ti binary 



Class 25 (Hexagonal bipyramidal) center of symmetry, d — 



Class 26 (Dihexagonal 

 pyramidal) 

 Xs hexagonal, X2 plane 



d = 



Class 27 (Dihexagonal bipyramidal) center of symmetry, d — 



Class 28 (Cubic tetrahedral- 



pentagonal-dedoca- d — 

 hedral) 

 xi , 0C2 , Xs binary 



Class 29 (Cubic pentagonal-icositetrahedral) d = 



Class 30 (Cubic, dyakisdodecahedral) center of symmetry, ^ = 



Class 31 (Cubic, hexakis- /O du ^ 



tetrahedral) d = lo du 



Xi , X2 , Xs quaternary \0 du/ 

 alternating 



Class 32 (Cubic, hexakis-octahedral) center of symmetr}-', d = 



11.22) 



11.23) 



11.24) 

 11.25) 

 11.26) 

 11.27) 

 11.28) 



11.29) 



11.30) 



11.31) 



11.32) 



Whenever a center of symmetry exists the piezo-electric property vanishes 

 since a center of symmetry requires d' = {—I)dl= —d= —d'. Also 

 J = for the pentagonal icositetrahedral class. 



Classes 6, 11, 12, 24, 28 and 31 polarize only by shear. 



Classes 1, 3, 4, 7, 10, 14, 16, 20, 23, 26 can be polarized by hydrostatic 

 pressure. As an example of this let us consider tourmaline (which is ditri- 

 gonal pyramidal). For hydrostatic pressure, Xi = X2 = Xs , Xi = X5 

 = Xe = 0, whence from the polarization stress matrices we find, Di = 0, 

 £>2 = 0, A = {2dsi + dis) X pressure. As J31 = 0.75 X 10"^ and ^33 = 5.8 

 X 10""^ for tourmaline, we get 7.3 abcoulomlos per cm per dyne per cm . 



