LOW TEMPERATURE COEFFICIENT QUARTZ CRYSTALS 



83 



vibrations. This figure shows clearly that the strongest flexures en- 

 tering are controlled by the length of the X axis rather than the Z' axis. 

 As shown by equations (6), (7) and (8) the AT and BT cut crystals 

 have odd harmonic vibrations which are controlled by the same 

 elastic constants as the fundamental vibrations. Since they are 

 controlled by the same elastic constants, the harmonic vibrations have 

 the same temperature coefficients as the fundamental mode and hence 

 will have nearly zero coefftcients. This property has been made use 

 of in oscillators in controlling high-frequency vibrations with crystals 

 whose thicknesses can be obtained commercially. 



CT and DT Low- Frequency Zero Temperature Coefficient Crystals 

 Another set of zero temperature coefificient crystals which are 

 particularly useful for low frequencies has recently been described by 

 Hight and Willard." They are related to the AT and BT cuts dis- 

 cussed above in that they use the same shearing motion to produce 

 the low coefificient. This relation is illustrated by Fig. 6 which shows 



NODAL 



plane' 



electrical axis 



Fig. 6 — Relation between the A T and DT cuts. 



'1 "Presented before the Institute of Radio Engineers, March 3, 1937. PubHshed 

 in I. R. E. Proc. May, 1937, p. 549. Similar crystals are also discussed in U. S. 

 Patents 2,111,383 and 2,111,384 issued to S. A. Bokovoy. 



