94 BELL S YSTEM TECH NIC A L JOURNA L 



£x = £i = ^^ ) dS, + 





)>b/D,<r O06/D,o OOi/s.a OOi / S.a 



+ f) ,,, + fl) ,. 



Oh/a.a OCT /S.D 



£. = £, = ^A ''51 + ^sl) ''5, + ^') ''•Ss + lf) i& 



OOi/Cff U02/ D,a OOZ/ D,a OOi/D.a 



+ ^^) ,5. + f) .6^, + f) .a, + f) .a, 



OOf,/ D,a OO^/D.a OOl/s.a OO2 / S,a 



dds/s.a OCT /a,D 



,e=|f) .5. + 11) .5, + 11) .53 + 11) </5, 



OOl/D.a OOi/D.a OOs/D.a OO4/ D.a 



J D,a 00%/ D,a OOl/s.o O02/S,a 



) d5z+f) da. 



:/S,a Off/s.D 





883/8,0 



The subscripts under the partial derivatives indicate the quantities kept 

 constant. A subscript D indicates that the electric induction is held 

 constant, a subscript a indicates that the entropy is held constant, while a 

 subscript 5 indicates that the strains are held constant. 



Examining the first equation, we see that the partial derivatives of the 

 stress Ti by the strains are the elastic constants c,-, which determine the 

 ratios between the stress Ti and the appropriate strain with all other strains 

 equal to zero. To indicate the conditions for the partial derivatives, the 

 superscripts D and a are given to the elastic constants and they are written 

 c^j'. The partial derivatives of the stresses by 5 = D/^t are the piezo- 

 electric constants //,/ which measure the increases in stress necessary to 

 hold the crystal free from strain in the presence of a displacement. Since 

 if the crystal tends to expand on the application of a displacement, the 

 stress to keep it from exi)anding has to be a compression or negative stress, 

 the negative sign is given to the /{"a constants. As the only meaning of 

 the // constants is obtained by measuring the ratio of the stress to 5 = D/iir 

 at constant strains, no superscript S is added. However there is a difference 

 I.etween isothermal and adiabatic piezoelectric constants in general, so 



