MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 



71 



which transforms \ectors as .v' = 5x where 



8 = 



1 



-Ae 



ivi — K2 



-As _ 

 K\ — A3 A2 



/vi - A'2 



1 



-A4 



Ks 



(21.22) 



If A'l, A'2 and A'3 are not all different the preceding analysis falls down as 

 some terms become infinite; a finite transformation is needed in this case. 

 The dilSculty can generally be doged by applying a 45° rotation about one 

 of the axes. Sometimes the easiest solution is to rotate through an angle 

 (f) about a coordinate axis then solve for the value of (^ that will vanish 

 certain terms. As examples of these devices we give the following: 



Ki 

 K, 



A4 











rotated 45° about .vi becomes 



(21.23) 



Axl 



Ai 



Ai 



A4 

 A5 



D = electric induction 



E — electric field 



k = dielectric constant matrix (square) 



A = dielectric constant matrix (single column) 



a = transformation matrix for vectors 



a = transformation matrix for tensors (of stress tensor sort) 



A' = stress matrix (single column) 



e = strain matrix (square) 



e = strain matrix (single column) 



5 = elastic modulus matrix 



C = elastic constant matrix 



H = temperature change of elastic modulus matrix 



. (21.24) 



