MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 



53 



of the 32 crystal classes only those of the trigonal and hexagonal systems 

 fail to have a" = a,-. These 12 classes must be examined individually but 

 the other classes may have their z matrices copied from the corresponding 

 dc matrices. 



Applying s' — azOc for a rotation of 120° about .V3 we tind for class 16 



The remaining 11 classes may be derived from class 16 by operations for 

 which either a = ac or a center of symmetry exists. Consequently, we 

 may form our z matrices from the </,'s in all cased if we leave out the 2's. 

 The electro-optic effect can be put in terms of the polarization instead of 

 the field by substituting in (17.3). 



E = Att {k-I) ^ P whence 



K' 



K-'° + riP 



(17.5) 



where 



Conversely 



r\ = 4:Trz(k — /)" 

 47r 



/) 



(17.6) 



The T] matrices transform exactly as did the 2's and hence may be formed 

 from the (//s but omitting the 2's. 



SECTION 18 



The Piezo-Optical Effect 



If the dielectric constants of a crystal are changed by the application of 

 stress, this may be represented by: 



K-' = (A'"Y + ttX 



(18.1) 



where the 36 constants im • • • Tree are stress-optical constants. 

 We may then form k^^ as 



(^11 + TTiiXi, kn + TTeiA'i, k -\- TTsiA'A 

 k\2 + T^fiiXi, ^22 + 7r2iXi, kiz -\- TTiiXi I . . . , 



^13 + TTbvA',, ^23 + 7r4iA'i, ^^3 -|- TTziX if 



(18.2) 



