PIEZOELECTRIC CRYSTALS IN TENSOR FORM 



135 



The difference between the normal curves and the measured values in the 

 Curie region is shown plotted by the points of Fig. 8. The solid and dashed 

 curves represent curves proportional to the square of the spontaneous 

 polarization and with multiplying constants adjusted to give the best fits 

 for the measured points. These give values of Qim , Qizn , Qasn equal to 



Qnu = -86.5 X 10-^^'; Q^,u = +17.3 X 10~''; 



Q^^n=-2A.2xm-'' (172) ^^^^^ 



Another effect noted for Rochelle salt is that some of the elastic constants 

 suddenly change by small amounts at the Curie temperatures. This is a 

 consequence of the tensor Mfy^^,,, for if a spontaneous polarization P 



5 -15 



o -40 



-4 4 8 12 16 



TEMPERATURE IN DEGREES CENTIGRADE 



Fig. 8. — Spontaneous electrostrictive strain in Rochelle Salt along the 

 three crystallographic axes. 



occurs, a sudden change occurs in some of the elastic constants as can be seen 

 from the first of equations (164). The second equation of (164) shows 

 that this same tensor causes a nonlinear response in the piezoelectric con- 

 stant. Since a change in the elastic constant is much more easily deter- 

 mined than a nonlinear change in the piezoelectric constant, the first effect 

 is the only one definitely determined experimentally. Since all three crys- 

 tallographic axes are binary axes in Rochelle salt, it is easily shown that 

 the only terms that can exist for a fifth rank tensor are terms of the types 



Mxxm ; Mf2223 ; iWf2333 (173) 



with permutations and combinations of the indices. Hence when a spon- 

 taneous polarization l\ occurs, the elastic constants become 



s%kt - MtikdPx (174) 



