MODES OF MOTION IN QUARTZ CRYSTALS 91 



On the abscissae are shown certain discreet frequencies as well as frequency 

 ranges which have been found to result in crystal units having no serious 

 dips in activity over a wide range in temperature. These are for square 

 crystals in the 18 millimeter size range and have been obtained by Mr. G. M. 

 Thurston of the Bell Laboratories and Mr. F, W. Schramm of the Western 

 Electric Company. It will be noted that no so-called ok regions have been 

 found at the frequencies of the three principal coupled modes. 



While the use of the chart shown in Fig. 6.23 will often lead directly to 

 the proper .Y and Z' dimensions for a given oscillator it cannot be overem- 

 phasized that only the three principal interfering modes are shown and only 

 the odd orders for the shears and only the even orders for the flexure modes. 

 Since the even order shear modes are excited due to slight variations which 

 would produce wedge shaped air gaps or quartz blanks, it is advisable to 

 avoid these regions also. Complex combinations of the three principal 

 modes as shown in Figs. 6.2 and 6.4 are also driven. Therefore when it is 

 necessary to produce a crystal unit possessing the highest activity for a 

 given area of quartz plate over an extended temperature range it is necessary 

 to scan the supposed desirable regions shown in Fig. 6.23 by complete meas- 

 urements on finished units of a given size and varying frequency or of con- 

 stant frequency and varying size. As an illustration the region shown in 

 Fig. 6.23 between 10.025 and 10.080 megacycles was determined in this 

 manner with the use of crystal plates approximately 18 millimeters square. 

 The use of crystals with other than square dimensions could undoubtedly 

 have increased the range of this region but their use is undesirable from a 

 manufacturing standpoint. Assuming that the electrodes and crystal 

 holder permit a variation in size of the quartz plate from 17.20 millimeters 

 to 18.20 millimeters this approved region will immediately specify the 

 dimensions of crystals to cover the frequency range from 5508 to 5727 kilo- 

 cycles. This also assumes crystal blanks cut to precise orientations with 

 controlled contours and electrodes of uniform flatness and constant airgap. 

 WTiile the theory would indicate that the frequency range given above could 

 be expanded to considerably higher values by utilizing a smaller crystal 

 blank this has not been proven so far since most crystals produced by the 

 Western Electric Company require large area plates to meet high activity 

 requirements. 



As an illustration of the effect on the behavior of oscillators of changing 

 the X and Z' dimensions of ^T-cut quartz plates measurements have been 

 made of the activity, in a conventional tuned plate circuit with the crystal 

 connected between grid and cathode of quartz plates of constant thickness 

 and varying X and Z' dimensions. Fig. 6.24 shows the effect of changing 

 the X dimension of a quartz plate on its activity as an oscillator. By taking 

 the product of the frequency and dimension we can determine the dimen- 



