LOW TEMPERATURE COEFFICIENT QUARTZ CRYSTALS 77 



are more difficult to cut than the standard crystals and are more 

 subject to couplings to other modes of motion and hence most of them 

 are probably of more theoretical interest than of practical value. 



All of the zero coefficient crystals described above are zero coefficient 

 at a specified temperature only and for temperatures on either side of 

 the specified temperature the frequency usually increases or decreases 

 in a parabolic curve with temperature. This merely expresses the 

 fact that the frequency-temperature curve is not exactly linear, but 

 must be expressed more generally in a series of powers of the tempera- 

 ture. Then for all the crystals considered above, the first derivative 

 of the frequency by the temperature is zero at the specified temperature 

 To. The next term of importance is the square term and hence most 

 crystals have a frequency which varies as the square term of the 

 temperature about the zero coefficient temperature To- A crystal 

 cut, labelled the GT crystal, has recently been found for which both 

 the first and second derivatives of the frequency by the temperature 

 are zero. As a result this "GT" crystal has a very constant frequency' 

 over a very wide temperature range, and in fact does not vary by 

 more than one part in a million for a temperature range of 100° centi- 

 grade. For a temperature range of ± 15° C. it can be adjusted so 

 that it does not vary by more than one part in ten million. This 

 crystal has been applied to portable and fixed frequency standards 

 and has given a constancy of frequency considerably in excess of any 

 other piezo-electric crystal used under the same conditions. It has 

 also been applied in quartz crystal filters to give pass bands which do 

 not vary appreciably with temperature. 



II. Standard Zero Temperature Coefficient Crystals 

 AT and BT Zero Temperature Coefficient Crystals 

 Crystals which employ the characteristics of a single shear mode of 

 vibration to obtain a zero temperature coefficient are the AT and BT 

 cut crystals.^ These crystals vibrate in shear and their frequencies 

 are determined principally by the thickness of the quartz plate. 

 Their mode of vibration is similar to the ordinary Y cut, and they 

 obtain their zero coefficient from the fact that the temperature coeffi- 

 cient of the shear mode changes from positive to negative as the angle 

 of cut is rotated about the X axis by positive or negative angles from 

 the position of the Y cut crystal. Figure 2 shows the method of 

 cutting these plates from the natural crystal. Figure 3 shows the 

 temperature coefficient of these crystals plotted against the angle of 



* "Some Improvements in Quartz Crystal Circuit Elements," F. R. Lack, G. W. 

 Willard, and I. E. Fair, B. S. T. J., July 1934, pp. 453-463. 



