MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 



35 



As y = 



4690 -795 -2180 



-795 3205 1691 



-2180 1691 2815 X 10" 



60( 











So that 



<l>n = Sil (1 - .0080) 012 = S\l {\ - .0305) 



022 = ^22 (1 - .0050) 013 = S[l (1 - .0103) 



033 = ^33 (1 - .0076) 023 = 5^3 (1 - .0107) 



044 = ^44 

 055 = S^i 

 066 = S(,6 



At the temperature of maximum piezo activity the components of 

 for Rochelle are smaller by about 3^%. 



SECTION 11 



The Piezo-electric Effect 



. Some crystals develop an electric charge when subjected to mechanical 

 stresses. As far as the effect is linear it may be expressed by: 



Di = dnXi + diiXi 

 A = diiXi + • • • 

 Dz = dziXi + • • • 



dz(,X^ 



(11.1) 



or in matrix notation 



D = dX (11.2) 



where the 18 constants d^ are called piezo-electric constants, and D is the 

 electric induction. 



On rotating the axes by means of a transformation a, the vector D be- 

 comes D' where D' = aD. The stress transforms as X' = aX whence D = 

 dX becomes D' = ada~^X' or D' = d'X' where: 



d' = ada 



(11.3) 



