BELL SYSTEM TECHNICAL JOURNAL 



Quartz is not the only type of crystal which is piezoelectric. In fact 

 there are hundreds of crystals that exhibit this property. Whether a 

 crystal is piezoelectric or not and the relation between the stresses and 

 charge displacements depend on the symmetry of the crystal. M'henever 

 there is a center of symmetry; that is, when the properties of the crystal 

 are the same in both directions along any line, no piezoelectric efifect can 

 occur. This is illustrated by the simple arrangement of atoms shown by 

 Fig. 1.7. It is obvious that no symmetrical application of forces can separate 

 the center of gravity of the charges and hence such a crystal will not be 



Fig. 1.7 — Crystal with a center of symmetry 



piezoelectric. Crystals can be classified into il possible classes on the basis 

 of the symmetry they exhibit; and of these 32 classes, 20 are piezoelectric 

 and 12 are not. As illustrated by the model for quartz, the response to 

 different types of force depends solely on the type of symmetry existing in 

 the crystal. 



1.4. Electrical Impedance and Low Dissipation in Crystals 



The first crystal used by Cady in controlling oscillators, was a crystal cut 

 with its major faces perpendicular to the X or electrical axis and with its 

 length along the Y or mechanical axis. Referring to Fig. 1 .5B, we see that a 

 stretch along the Y axis will produce a charge displacement along the E 



