196 



BELL SYSTEM TECHNICAL JOURNAL 



Another important cut is the GT,'^^ which has a very constant frequency 

 over a wide temperature range. As shown by Fig. 1 .14, all zero temperature 

 coefficient crystals are zero coefficient at one temperature only and usually 

 vary in a square law curve about this temperature. The GT crystal repre- 

 sented an attempt to get a crystal in which the frequency remained constant 

 over a wide temperature range. As can be seen from the figure, when prop- 

 erly adjusted this aim is attained, for the frequency does not vary more than 

 one part in a million over a 100-degree Centigrade range of temperature. 

 This crystal makes use of the fact that a face shear vibration can be 

 resolved into two longitudinal vibrations coupled together. As shown by 



30 



20 



20 



40 



50 



<^ 



/ 



/y 



/ 



/ 



P 



y- 



•"Z 



"^^r^^ 



\ 



/doughnut 



^ 



V- 



^ 



LONG BAR, LENGTH 

 ■ ALONG X AXIS 

 ._^^TST HARMONIC 

 / ^2ND HARMONIC 



m 



T^V^ 



/ 



^^ 



■U- 



X"'-- 



y^j 



'^Z 



bt 



\ 



oX 



V 



-^r 



\ 



V 



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^t 



20 30 40 50 60 70 80 90 



TEMPERATURE IN DEGREES CENTIGRADE 



Fig. 



1.14 — Temperature frequency characteristics of a number of low temperature 



coefficient crystals 



Fig. 1.15, if we cut a crystal at an angle of 45 degrees from that of a shear 

 vibrating crystal, an expansion occurs along one axis and a contraction 

 along the other indicating that a face shear can be resolved into two longi- 

 tudinal modes that are coupled together. Now since it can be shown that 

 all pure longitudinal modes for blanks cut in all possible directions in a 

 quartz crystal will have zero or negative temperature coefficients," it follows 

 that if we have a shear vibrating crystal with a positive coefficient, that 



1^ "A New Quartz Crystal Plate, Designated the GT, Which Produces a Very Constant 

 Frequency Over A Wide Temperature Range," W. P. Mason, Proc. I. R. E., Vol., 28 pr. 

 220-223, May 1940 



1^ This can be proved as discussed in the appendix b)' combining the Voigt expressions 

 for the elastic relations in a crj'stal with the measured temperature coefficients of the six 

 elastic constants. 



