PIEZOELECTRIC CR YSTA LS IN TENSOR FORM 131 



tion occurs in the crystal. When spontaneous polarization occurs, the 

 dipoles of the crystal are Uned up in one direction in a given domain. For 

 Rochelle salt this direction is the ±X axis of the crystal. Now the electric 

 displacement Dz is equal to 



47r 47r 47r 



= f:^^ = f:f + P,„ + P,^ = ^o p,^ (165) 



where Px^ is the electronic and atomic polarization, and Px^ the dipole 

 polarization The electronic and atomic polarization is determined by the 

 field and hence can be combined with the field through the dielectric constant 

 eo , which is the temperature independent part of the dielectric constant. 

 When the crystal becomes spontaneously polarized, a field E^ will result, but 

 this soon is neutralized by the flow of electrons through the surface and 

 volume conductance of the crystal and in a short time Ez = 0. Hence for 

 any permanent changes occurring in the crystal we can set 



8x = — =PxD = dipole polarization (166) 



47r 



which we will write hereafter as Pi . 



In the absence of external stresses the direct effects of spontaneous polari- 

 zation are a spontaneous set of strains introduced by the product of the 

 spontaneous polarization by the piezoelectric constant, and another set 

 produced by the square of the polarization times the appropriate electro- 

 strictive components. For example, Rochelle salt has a spontaneous 

 polarization Pi along the Xi axis between the temperatures — 18°C to 

 + 24°C. The curve for the spontaneous polarization as a function of 

 temperature is shown by Fig. 6. The only piezoelectric constant causing 

 a spontaneous strain will be ^14/2 = gnz • Hence the spontaneous polariza- 

 tion causes a spontaneous shearing strain 



S, = guPz = 120 X 10"' X 760 = 9.1 X 10~* (167^ 



if we introduce the experimentally determined values. Since .5'4 is the 

 cosine of 90° plus the angle of distortion, this would indicate that the right 

 angled axes of a rhombic system would be distorted 3.1 minutes of arc. 

 This is the value that should hold for any domain. For a crystal with 

 several domains, the resulting distortion will be partly annulled by the 

 different signs of the polarization and should be smaller. Mueller measured 

 an angle of 3'45" at 0°C for one crystal. This question has also been 



* This has been measured by measuring the remanent polarization, when ail the domains 

 are lined up. See "The Dielectric Anomalies of Rochelle Salt," H. Mueller, Annals of 

 the N. Y. Acad. Science, Vol. XL, Art. 5, page 338, Dec. 31, 1940. 



^ "Properties of Rochelle Salt," H. Mueller, Phys. Rev., Vol. 57, No. 9, May 1, 1940. 



