MODES OF M 01 ION IX QUARTZ CRYSTALS 



69 



6.41 Extensional to Shear and Extensional to Flexure Coupling 



The coupling between the extensional and shear motion can best be illus- 

 trated by taking the case of an X cut plate the length of which hes along the 

 Y axis and the width along the Z axis. This is shown in Fig. 6.8 together 

 with two other cases, one in which the plate is rotated about the X axis by 

 — 18° and the other a similar rotation but +18°. Also in Fig. 6.8 is shown 

 an enlarged view of the change in the elastic constants and frequency con- 

 stants as a function of the rotation of the plate about the electric or X axis. 

 For the case of an X cut plate the strains resulting from an applied exten- 



+18 -18 



ROTATION ABOUT X-AXIS IN DEGREES 



Fig. 6.8 — ]\Iotion in an X cut plate for different orientation about the X 

 crystallographic axis, 



sional stress along the length according to equation A.8 would be 



Xi = Sl2 Yy 



Vy = 522 Y„ 



Zz. = 523 Yy 

 yz = Suly 



where .v^ is an extensional strain along the thickness 

 y/' " " " " " length 



2, " " " " " " width 



yz " a shear strain in the length-width plane 



6.11 



