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BELL SYSTEM TECHNICAL JOURNAL 



trie constant matrix \?, D = -— kE where, if Xz is the axis of transverse 

 isotropy: 



D = 



(20.1) 



Elasticity 



We must find the forms of S and C, (the elastic modulus and elastic con- 

 stant matrices) that are not changed by rotations about the axis of trans- 

 verse isotropy. We can simplify the work by starting with the crystal 

 class that has hexagonal symmetry only. On applying the transformation 

 S' = a,Sa = S for arbitrary rotations about Xz we find no further simplifi- 

 cation follows. Hence the S and C matrices can be copied from those for 

 the Hexagonal Pyramidal Class. 



The Piezo-Eledric Ejffect 



Again choosing Xz as the axis of transverse isotropy and starting with 

 hexagonal symmetry about X3 we find that in order to be invariant to all 

 rotations about Xz the matrix must simplify to: 



/O 0> 



J=[0 000 



\dzi dzi dzz 0; 



(20.2) 



A pitch solidified in an electric field would probably exhibit this kind of 

 piezo electric behaviour. It might also be expected to show an electro optic 

 efifect governed by a matrix like the conjugate of the above matrix. 



SECTION 21 

 Appendix • 



Transformations 



A counterclockwise rotation of the axes through an angle (j) about the .Ti 

 axis is represented by the matrices a and a as follows (where c is written for 

 cos </) and 5 for sin ^) : 



(21.1) 



