84 



BELL SYSTEM TECHNICAL JOURNAL 



the approximate orientations of the AT cut and the DT cut. In the 

 A T plate the Xy strain is produced by a shear mode of vibration as 

 shown by the arrows which represent instantaneous displacements. 

 In the DT plate the xj strain is produced by a shear mode of vibration 

 as shown again by the arrows. Two diagonally opposite corners 

 move radially outward while the other two move radially inward. 

 The relatively low frequency of the DT plate results from the relatively 

 large frequency-determining dimensions x and y' . The temperature 

 coefficient of frequency of these plates may be made zero, for the 

 proper angles of cut, since it goes from a large positive value at one 

 orientation to a large negative value for an orientation 90 degrees from 

 the first. Actually the angle of cut of the DT plate is not exactly 

 90 degrees from the AT. This is due to the fact that the frequency 



en 



H (r 

 z u 



^- 

 zi 



O -I 



^ d 



>- 5 



O 



z ^ 



UJ -J 



So 



CL O 

 Li_ —I 



-90 -75 -60 -45 -30 -15 15 30 45 60 75 90 



ORIENTATION ANGLE IN DEGREES (S) 



Fig. 7 — Frequency constant for low-frequency shear crystal 

 plotted against angle of cut. 



for a square plate involves the 566' constant rather than the Cee' constant 



which controls the frequency of a thin plate. Similarly we find that 



there is a crystal almost 90° from the BT which has a zero coefficient 



and this has been designated the CT. 



Figure 6 shows that the electrode faces of the DT crystal are placed 



on the z'x plane and hence the shear mode generated would ordinarily 



be called the zj mode even though it is similar to the x/ shear mode 



in the AT crystal at right angles to it. The measured frequency 



constant of such a Series of square plates is shown on Fig. 7. In the 



absence of a complete theoretical solution ^^ taking account of all the 



elastic couplings for a square plate vibrating in shear, an empirical 



^ An approximate solution neglecting coupling was given in a former paper 

 "Electrical Wave Filters Employing Quartz Crystals as Elements," page 446. This 

 solution is not complete enough, however, to allow calculations of temperature 

 coefficients with very great accuracy. 



