QUARTZ CRYSTAL PLATES 



517 



gators ^ have been able to set up the three types of vibration (longi- 

 tudinal, flexural, and torsional) common to isotropic bars. Moreover, 

 the formulae for these vibrations in isotropic material can be used to 

 determine the frequency of the quartz rods to a good first approxi- 

 mation. 



Returning to the problem of the plate, if the experimentally de- 

 termined facts concerning plates of certain definite orientations are 

 examined, it will be seen that they suggest the treatment of the plate 

 as a special case of a bar. A resume of these facts will illustrate this 

 point and at the same time indicate the effect of orientation on the 

 character of the modes of vibration. 



720 728 736 744 



FREQUENCY KILOCYCLES 



Fig. 1 — Response frequencies of 32x47x2.760 mm. parallel cut crystal plate in 

 the region of the major high frequency. 



In general, a quartz crystal plate cut with any orientation with 

 respect to the crystal axes will respond to a large number of fre- 

 quencies. A plot of these frequencies showing their spacing and the 

 relative magnitudes of response ^ may be termed the frequency 

 spectrum of the plate. Fig. 1 shows part of the high-frequency 

 region of such a spectrum. In these frequency spectra there are 

 usually one or more frequencies at which the crystal will react with 

 sufficient voltage to drive a vacuum tube in the usual crystal oscillator 

 circuit. 



4 Cady, Proc. I.R.E. 10, p. 83, 1922. Harrison, Proc. I.R.E. 15, p. 1040, 1927 

 Giebe, ZS.f. Phys. 46, p. 607, 1928. 



^ The amplitude of response in this case is the maximum amplitude of current 

 through the crystal at constant voltage, which in turn is a measure of the equivalent 

 series resonant impedance of the crystal system. 



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