MANUFACTURING DEVIATIONS IN CRYSTAL UNITS 



263 



For that reason, any deviation in the orientation of the plates from nominal 

 will affect the electrical characteristics cf the crystal units. Tn addition, 

 these characteristics are affected by imperfections in the plates due to 

 deviations in linear dimensions, to the presence cf flaws, or to the condition 

 of the surface of the plates. The effects cf these deviations differ for various 

 cuts of crystal plates, for plates of various shapes and for the various modes 

 of vibration. In the following paragraphs, each type of deviation will be 

 considered in turn and data will be presented to show its effect on the charac- 

 teristics of crystal units using the various t>'pes of plates. 



14.21 Deviations in the Angle of Orientation 



Accurate information is available on the effect of deviation in angle of 

 orientation on the characteristics of X-cut plates vibrating in the exten- 





-0=0 



C = 



4 -rr t 



FARADS 



^ 2^J?^ 



L. = tt:? * 9x10" HENRIES 



8 d 



c = 



e dig our jg 



CYCLES PER 

 SECOND 



9«I0" 



Fig. 14.3. — Equivalent electrical circuit of piezoelectric crystal. 



sional mode. The relation between the electrical characteristics of this 

 type of vibration and the properties of the quartz are shown in Fig. 14.3. 

 This information, with minor changes, is reproduced from a preceding 

 pubUcation.^ In Fig. 14.3: IjW and / are the length, width and thickness 

 respectively of the plate; K is the dielectric constant; p is the density; 

 (/12 is the piezo-electric constant; and ^22 is the modulus of comphance 

 (inverse of Young's modulus). All these individual quantities are ex- 

 pressed in electrostatic units. The quantities which depend on the orien- 

 tation of the plates are the piezo-electric constant and the modulus of com- 

 pliance. The symbols for these quantities usually are primed when they 

 are used for a generalized orientation. When unprimed, the symbols desig- 

 nate quantities measured along the principal axes. For X-cut plates, devia- 

 tions of the plane of the major surface from the YZ plane have relatively 



1 "Electrical Wave Filters Employing Crystals with Normal and Divided Electrodes", 

 W. P. Mason and R. A. Sykes, B. S. T. J., April 1940, page 222. 



