QUARTZ CRYSTAL APPLICATIONS 



193 



formance of oscillators since the plates do not have as many secondary modes 

 of motion as do the -Y plates. They have, however, one drawback. The 

 frequency increases about 86 parts in a million for every degree Centigrade 

 increase in temperature. This requires regulating the temperature quite 

 closely. 



In order to improve on the performance of the I' cut crystal, investiga- 

 tions were made by Lack, Willard and Fair, Koga, Bechmann, Straubel 

 and others'' on how the properties of such crystals varied as the orientation 

 angle of cutting blanks from the natural crystal was varied. As shown by 

 Fig. 1.9, the crystals investigated all had one edge along the A' or electrical 

 axis with the normals making positive and negative angles with the Y axis. 

 All of these crystals will have a component of field along the Y axis, which 



z in 



I- LU 



§^2000 



Ss 



-90 -80 -70 -60 -50 -40 -30 -20 -10 



ROTATION ON X AXIS - -• 



IN DEGREES 



10 20 30 40 50 60 70 80 

 — • + ROTATION ABOUT X AXIS 

 IN DEGREES 



Fig. 1.11 — Frequency constant of oriented Y cut crystals 



will produce a shearing motion until the angles of cut approach 90 degrees 

 from the Y axis. The smaller the angle A^ the more strongly will the shear 

 mode be driven. However, advantageous elastic relationships can be ob- 

 tained by using oriented cuts. As shown by Fig. 1.11, Lack, Willard and 

 Fair found that the frequency constant of a rotated crystal expressed in kilo- 

 cycle millimeters varied with angle of cut and that there was a minimum fre- 

 quency at + 31 degrees and a maximum at —59 degrees. It was subse- 

 quently pointed'- out that these minimum and maximum points were signifi- 

 cant angles in the elastic behavior of the crystal for they were the angles for 



^' "Some Improvements in Quartz Crystal Circuit Elements," F. R. Lack, G. W. Wil- 

 lard, I. E. Fair— B. S. T. J., Vol. 13, pp. 453-463, July 1934; R. Bechmann— F/=' Techn. ii. 

 EL Ak. 44, 145 (1934); I. Koga— i?e/). of Rad. Res. i. Jap. 6, 1 (1934); J. Straubel, Z. tech. 

 Phvsik., 35, 179, 1934. 



12 See patent 2,173,589. 



