LOW TEMPERATURE COEFFICIENT QUARTZ CRYSTALS 93 



bolas. This is what would be expected for in general we can write the 

 frequency as a function of temperature by the series 



/ = /o[l + a,(T - To) + OoCr - ToY + asCr - ToY +•••], (22) 



where To is any arbitrary temperature. Differentiating / with respect 

 to T we have 



^ = /o[ai + 2a.XT - To) + 3az{T - To)' +•••]• (23) 



For a zero coefficient crystal the change in frequency will pass through 

 zero at some temperature To- Hence cfi — 0, and the frequency will 

 then be 



/ = /o[l + a,iT - To)' + a^iT - To)' +•••]• (24) 



Since a2 will ordinarily be much larger than succeeding terms, a 

 parabolic curve will be obtained. If a^ is positive the frequency will 

 increase on either side of the zero coefficient temperature To and if 

 negative it will decrease. 



Recently a new crystal cut, labeled the GT, has been found for 

 which both ai and az are zero. As a result the parabolic variation with 

 temperature is eliminated and the frequency remains constant over a 

 much wider range of temperature. The variation obtained is plotted 

 on Fig. 14 by the curve labeled GT, and, as can be seen, the frequency 

 does not vary over a part in a million over a 100° C. change in tem- 

 perature. 



This crystal, which wall be described in a forthcoming paper, has 

 found considerable use in frequency standards, in very precise oscilla- 

 tors, and in filters subject to large temperature variations. It has 

 given a constancy of frequency considerably in excess of that obtained 

 by any other crystal. 



