440 



BELL SYSTEM TECHNICAL JOURNAL 



axis is the principal axis of motion, the mutual compliances of principal 

 interest are 523', determining the coupling between the Y' extensional 

 motion and the Z' extensional motion, and 524' determining the coupling 

 between the Y' extensional motion and the Y^' shear motion. It is 

 the shear motion which is most objectionable, because it is more highly- 

 coupled than the Z' extensional motion, because it is lower in frequency, 

 and because it is coupled to a flexural mode. Hence, if this motion 

 can be eliminated or made very small, a much better crystal for most 

 purposes is obtained. We note that if d is —18.5° or if = 41.5° the 

 shear coupling coefficient vanishes and hence a force in the Yy direction 

 produces no y^ shear or vice versa. Of these the —18.5° crystal is 

 driven more strongly by the piezo-electric effect and hence has a more 

 prominent resonance. 



390 



a. 330 



290 



230 



0.1 



0.2 



0.3 



0.4 



0.5 0.6 



0.7 



0.8 



0.9 



1.0 



• RATIO filO) 



Fig. 32 — Measured resonances of a = + 18.5° perpendicularly cut crystal. 



Accordingly the resonances of a = —18.5° cut crystal have been 

 measured in a similar way to the = 0° cut crystal shown in Fig. 25. 

 The result is shown on Fig. 31. As will be seen from the figure, the 



