PIEZOELECTRIC CR YSTA LS IN TENSOR FORM 81 



Second order effects are also considered. These eflfects (neglecting second 

 order temperature eflfects) are elastic constants whose values depend on 

 the applied stress and the electric displacement, the electrostrictive eflfect, 

 piezoelectric constants that depend on the applied stress, the piezo-optical 

 effect and the electro-optical effect. These second order equations can 

 also be used to discuss the changes that occur in ferroelectric type crystals 

 such as Rochelle SaU, for which between the temperature of — 18°C. and 

 -f24°C.,a spontaneous polarization occurs along one direction in the crystal. 

 This spontaneous polarization gives rise to a first order piezoelectric deforma- 

 tion and to second order electrostrictive effects. It produces changes in 

 the elastic constants, the piezoelectric constants and the dielectric constants. 

 Some measurements have been made for Rochelle Salt evaluating these 

 second order constants. 



Mueller in his theory of Rochelle Salt considers that the crystal changes 

 from an orthorhombic crystal to a monoclinic crystal when it becomes 

 spontaneously polarized. An alternate view developed here is that all of 

 the new constants created by the spontaneous polarization are the result of 

 second order eflfects in the orthorhombic crystal. As shown in section 7 

 these produce new constants proportional to the square of the spontaneous 

 polarization which are the ones existing in a monoclinic crystal. 0.i this 

 view "morphic" eflfects are second order eflfects produced by the spontaneous 

 polarization. 



1. Stress and Strain Relations in Aeolotropic Crystals 



I.I. Specification of Stress 



The stresses e.xerted on any elementary cube of material with its edges 

 along the three rectangular axes X, Y and Z can be specified by considering 

 the stresses on each face of the cube illustrated by Fig. 1. The total stress 

 acting on the face ABCD normal to the X axis can be represented by a 

 resultant force R, with its center of application at the center of the face, 

 plus a couple which takes account of the variation of the stress across the 

 face. The force R is directed outward, since a stress is considered posi- 

 tive if it exerts a tension. As the face is shrunk in size, the force R will be 

 proportional to the area of the face, while the couple will vary as the cube of 

 the dimension. Hence in the limit the couple can be neglected with respect 

 to the force R. The stress (force per unit area) due to R can be resolved 

 into three components along the three axes to which we give the designation 



Here the first letter designates the direction of the stress component and the 

 second letter x^ denotes the second face of the cube normal to the X axis. 

 Similarly for the first X face OEFG, the stress resultant can be resolved 



