QUARTZ CRYSTAL APPLICATIONS 223 



The value of Taft provides a check on the accuracy of measurement since 

 it has been measured in two ways. The agreement is within about 2 per 

 cent which shows the probable accuracy of the measurement. Combining 

 the coefficients of (A.69) with those given by equation (A. 74), the complete 

 temperature coefficients are given in Table VH together with previous 

 determinations ' ". The present determination differs from a previous 

 determination by the writer due to the use of the elastic constants found 

 here rather than Voigt's constants. 



The temperature coefficients of the cf; elastic constants are easily obtained 

 from the s^j constants by employing the relations of equation (A.8). These 

 result in the temperature coefficient values for the c constants given in 

 Table VHI. 



By using the elastic constant data, the temperature coefficient data, and 

 the equations of transformation for rotated axes it is possible to calculate 

 the frequency and temperature coefficient of any simple mode for any 

 orientation. Examples are given for a face shear mode and a thickness 

 shear mode in a previous paper "Low Temperature Coefficient Quartz 

 Crystals." This paper shows contour maps for low temperature coeffi- 

 cient crystals of these types. 



'^ The first determination of the temperature coefficients of the writer was given in a 

 paper "Electrical Wave Filters Employing Quartz Crystals As Elements," B. S. T. J., 

 July 1934, p. 446. A redetermination using better temperature coefficient data was given 

 in a paper "Low Temperature Coefficient Quartz Crystals," B. S. T. J., Jan. 1940. The 

 present determination uses the same temperature coefficient data but slightly different 

 elastic constants which results in slight changes in the temperature coefficients. 



'2 A partial determination of the coefficients was made by Koga, Rep. Rad. Research, 

 Japan 6, 1 (1934). Other complete determinations are R. Bechmann, Hoch: tech. U. Elek. 

 Akus. 44,145 (1934) and Atanasoff and Hart, Phys. Rev., Vol. 59, No. 1, Jan. 1, 1941, 

 pp. 85, 96. 



i^B.S. T. J., Vol. XIX, 74 (Jan. 1940). 



