QUARTZ CRYSTAL PLATES 535 



is found that the magnitude of the negative coefficient for this region 

 approximates that to be expected for the transverse vibration alone. 

 In general, however, a frequency jump occurs just after the zero 

 temperature coefficient region is passed. 



This interchange of activity of these two periods as they inter- 

 change temperature coefficients can be studied in detail by examining 

 the changes in the spectrum of a crystal at different temperature 

 levels. Fig. 15 shows a series of spectra of a crystal taken for different 

 temperatures in the region of zero temperature coefficient, the dimen- 

 sions of the crystal being unchanged. These spectra illustrate the 

 rapid decrease in activity of the frequency co' after it passes through 

 zero temperature coefficient while at the same time co" increases and 

 assumes the place of major activity vacated by co'. 



The assumption that the coupling increases with the decrease in 

 the order of the harmonic finds confirmation in the experimentally 

 determined facts as computed from curves of the type shown by 

 Fig. 10. As the coupling increases the temperature range for which 

 there is no frequency change with temperature increases, that is the 

 region of zero temperature coefficient becomes extended. To illustrate 

 this, Fig. 16 shows two curves of frequency versus temperature, one 

 for the coupling of a fifth harmonic, the other for an eighth. 



It would, of course, be desirable to extend the zero temperature 

 coefficient range over the limits of temperature to be expected in 

 normal operation. This necessitates tight coupling of the two modes 

 which in turn demands a dimensional ratio in the neighborhood of 

 unity. The cross sectional area of such a plate in the direction of its 

 thickness and width approaches a square in shape which, for high- 

 frequency crystals, is of very small dimensions. 



Before concluding it should be noticed that since both modes of 

 the perpendicular cut crystals have a negative temperature coefficient, 

 it is to be expected that it would be impossible to obtain zero tempera- 

 ture coefficient crystals with this orientation. This seems to be true 

 as far as our experience with those crystals is concerned. 



