PYROELECTRICITY AND PIEZOELECTRICITY 157 



The deformation of an element of a body is completely 

 expressed in terms of six quantities * which we may denote 

 by ABC abc. If the intensities of electrification due to the 

 strains are E l E 2 E 3 in three directions at right angles, we may 

 suppose that each term in the strain contributes to the electrifica- 

 tion, and so we get 



A 2 B 



A 3 C 



with similar values for E 2 and E 3 , and for the most general case 



with different values for the coefficients A. Thus for this most 



general case a hemihedral crystal with 



inclined faces in the triclinic system 



we shall have eighteen independent 



coefficients of the type A. In all but 



this general case there are relations 



holding between the coefficients owing 



to the symmetry of the crystal about 



certain planes or directions, and their 



number may be greatly reduced. Thus 



we get definite values of the intensities 



of electrification in terms of the change 



of shape whether it is produced by 



heat or by stress. 



Riecke and Voigt f have tested the 

 theory for tourmaline and quartz. 

 Knowing the piezoelectricity produced 

 by given deformations, they were able 

 to determine the coefficients. Then, 

 measuring the dilatations in different 

 directions with rise of temperature, 

 they were able to determine the 

 charges which should be produced 

 merely by the change of shape on 

 heating. Voigt } found that in a 

 tourmaline crystal about four-fifths 

 of the pyroelectric charge could be accounted for by dilatation. 



Pockels found a fairly close agreement with Voigt's theory in 

 the case of sodium chlorate. 



Electric deformation of crystals : Lippmann's 

 theory. Soon after the discovery of piezoelectricity Lippmann \\ 

 pointed out that there should be a converse effect, viz. a change in 

 the dimensions of a piezoelectric crystal when it was subjected to 

 electric strain. We may present Lippmann's theory as follows : 



* Thomson and Tait, Natural Philosophy, vol. ii. p. 461. 



t Wied. Ann. 45, p. 523 (1892). 



Wied. Ann. 66, p. 1030 (189s). 



Winkelmann, Ifandbuch der Physik, 2nd. ed. iv. p. 783. 



Ann. >i<. ''/,/, ,/ <l, I'l,,js. (5), vol. xxiv. p. 145 (1881); Principe de hi Con* 



FIG. 105. 



