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BELL SYSTEM TECHNICAL JOURNAL 



The relation between these major response frequencies and the 

 dimensions of the plate for the two principal orientations can be 

 outlined as follows: 



Curie or Perpendicular Cut 



When the crystal plate is so cut that its major surfaces are parallel 

 to the optic axis and perpendicular to an electric axis (the Curie or 

 perpendicular cut, see Fig. 2) there are two major response frequencies, 

 one high and one low.*^ The high frequency is a function of the 



OPTIC AXIS 



Fig. 2 — Orientation of a perpendicular or Curie cut plate with respect 

 to the crystal axes. 



thickness of the plate and to a good approximation is given by the 

 expression 



/ 



K 



t ' 



(1) 



where / is the thickness in millimeters and K = 2.860 X 10". If the 

 plate could be considered as a bar of length / then the frequency of a 

 simple longitudinal vibration would be given by the expression 





(2) 



where E^j/ is Young's modulus in the X- Y plane and d is the density. 

 If the numerical values ^ of E^cy and d are substituted in the above 



" For this discussion the low-frequency flexural vibration of the type described 

 by Harrison will not be considered. 



' For numerical values of the elastic constants and the density of quartz, see 

 Sossman, "The Properties of Silica," the American Chemical Society Monograph 

 Series. 



