44 



BELL SYSTEM TECHNICAL JOURNAL 



It is to be noted that although there is a sort of reciprocity between the 

 first order piezo effect and the converse effect, in that the matrices for one 

 are the conjugates of the matrices of the other, there is no such reciprocity 

 in the second order effects: if a center of symmetry exists no polarization 

 can be brought about by stress either as a first order effect or as a second 

 order eflfect; if a center of symmetry exists an electric field can cause a 

 strain through the second order effect but not through the first order eflfect. 



Dielectric Constants at Constant Stress and at Constant Strain 



Let us consider a unit crystal cube, initially unstressed, unstrained and in 

 zero electric field. We write k^ and ^" for the dielectric constant matrices 

 at constant stress and constant strain, respectively, C^ as the elastic con- 

 stant matrix at constant electric field E, C° as the same for zero field. We 

 study a cycle consisting of a strain caused by application of an electric field 

 E at zero stress followed by a stress applied at constant E to reduce the 

 strain to zero and completed by conducting away the electric charges at 

 zero strain so that the body is left in its original state. The cycle is de- 

 scribed by the table: 



whence C = C : also 



k" - k' = irdCdc (13.14) 



SECTION 14 



Pyro-Electricity 



If the electric polarization brought about by heating some kinds of crystals 

 is simply a function of the uniform temperature change, that is if this 

 polarization can be produced by taking the whole body quickly from the 



