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BELL SYSTEM TECHNICAL JOURNAL 



Two other cuts not previously described are shown also by Fig. 1 .9. They 

 are the MT low coefficient longitudinally vibrating crystal and the iVT low 

 coefficient flexurally vibrating crystal. Both of these are related to the 

 +5° X cut crystal of Fig. 1.9. As shown by Fig. 1.19 a long thin 5° Z cut 

 crystal is the best length direction for an X cut crystal to obtain a low- 

 temperature coefficient. Figure 1.19 plots the temperature coefficients for 

 long thin oriented X cut crystals, and this data is used in the appendix to 

 derive the temperature coefficients of the six elastic constants. However, 

 as the width of the crystal is increased the temperature coefficient becomes 

 highly negative as shown by Fig. 1.20. 



02 0.3 04 



RATIO OF WIDTH TO LENGTH 



Fig. 1.20 — Temperature coefficient of a +5° X cut crystal (<p = 0°; = 90°; ^ ■ 

 as a function of the ratio of width to length. Ratio of thickness to length = 0.05. 



85°) 



This change of coefficient occurs due to the fact that as the crystal width 

 is increased, the face shear mode of motion becomes more strongly excited 

 and contributes to the elastic constant. Then since the temperature coeffi- 

 cient of the shear elastic constant is highly negative for this orientation 

 the temperature coefficient of the +5° X cut crystal becomes more highly 

 negative as the width is increased. 



The MT longitudinally vibrating crystal employs a rotation of the plane 

 of the crystal cut about the Y' or length axis. The effect of this rotation is 

 to change the temperature coefficient of the shear mode from highly nega- 

 tive to nearly zero. The result is that the temperature coefficient becomes 



