Zero Temperature Coefficient Quartz Crystals for Very 

 High Temperatures 



By W. P. MASON 



{Manuscript Received Nov. 15, 1950) 



In order to determine the angles of cuts for low temperature coefficient crystals, 

 the elastic constants of quartz have been evaluated in the temperature range from 

 — 100°C to +200°C. This has been done by measuring a series of rotated Y-cut 

 crystals in the thickness shear mode and a series of rotated X-cuts in the longi- 

 tudinal length mode. From the measurements, low temperature coefficients AT, 

 BT, CT, and DT type crystals can be determined which have their temperature of 

 zero temperature coefficient at any prescribed temperature. Calculations are given 

 for the properties of crystals to operate at 200°C. The characteristics of an AT 

 type crystal have been investigated experimentally, and the measured results are 

 in reasonable agreement with the calculations. It is shown that there is a maxi- 

 mum temperature of 190°C for which an AT type crystal can have a zero temper- 

 ature coefficient. 



I. Introduction 



Most quartz crystals used to control the frequency of oscillators or time 

 measuring devices are used in places where the ambient temperature does 

 not exceed 60° to 70°C. The crystals are usually adjusted in angle so that 

 they have a zero temperature coefficient at a temperature of about 80°C 

 and they are temperature controlled at this temperature. However, a 

 class of uses occurs for which the ambient temperature may be considerably 

 higher and for these uses ordinary AT and BT crystals, for example, are 

 not satisfactory. This is evident from Figs. 1 and 2 which show the fre- 

 quency variations for these crystals over a temperature range from — 1(X)°C 

 to +200°C. For example, the flattest frequency temperature curve for the 

 AT cut occurs at an angle of +35°18' rotation about the X axis from the 

 Y cut. By going to +35°36' orientation about the X axis a minimum occurs 

 at 100°C. For the BT cut shown by Fig. 2 the angle of -49°16' orienta- 

 tion gives nearly a paraboHc shape centered at 20°C. By changing the orien- 

 tation to -47°22' the parabola centers at 75°C. 



Hence if one wishes to raise the temperature for which the zero tempera- 

 ture coefficient occurs he has to increase the rotation about X for the AT 

 cut and decrease it for the BT cut. The amount needed for either orienta- 

 tion can best be determined by evaluating the elastic constants as a func- 

 tion of orientation and temperature, and that is the main purpose of this 

 paper. The results are appHed to determining the best angles of orientation 

 for the AT, BT, CT, and DT type crystals to obtain zero temperature coeffi- 



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