LOW TEMPERATURE COEFFICIENT QUARTZ CRYSTALS 75 



The first types of zero temperature coefficient crystals were the 

 so-called coupled types which obtained their low coefficient by virtue 

 of the interaction between two modes of motion. The first crystal of 

 this type was the "doughnut" crystal invented by W. A. Marri- 

 son/ which was used in the Bell System frequency standard. In this 

 crystal the principal vibration is a shear and this is coupled to a 

 flexure motion in the ring. The low coefficient is obtained from the 

 fact that the shear has a positive temperature coefficient, while the 

 flexure has a negative coefficient, and due to the coupling there is one 

 region for which the temperature coefficient goes through zero. The 

 next crystal of the coupled type was a Y cut crystal of specified 

 dimensions invented by R. A. Heising.^ In this crystal a high- 

 frequency shear with a positive temperature coefficient was coupled 

 to a harmonic of a low-frequency flexure, and a zero coefficient resulted 

 at one temperature due to the coupling. Outside of their use in a 

 frequency standard, such coupled types of crystals have not been 

 applied much for commercial purposes on account of the difficulty of 

 adjusting them, the difficulty of mounting them, and the prevalence 

 of spurious frequencies near the desired frequency. 



The next low-temperature coefficient crystals were crystals of the 

 long bar type. It has been known for a long time that the temperature 

 coefficient of an X cut crystal with its length lying along the Y or 

 mechanical axis was very low provided the width of the crystal lying 

 along the optic axis is very small compared to the length. This is 

 illustrated by Fig. 1 taken from a former paper ^ which shows that 

 for a crystal whose width is less than 0.15 of its length the temperature 

 coefficient is about 2 parts per million per degree centigrade. Further- 

 more, it was found by the writer in 1930 ^ that if the thickness of the 

 crystal laying along the X or electrical axis was increased the temper- 

 ature coefficient was decreased and in fact for certain ratios of axes 

 the coefficient approached zero. For a bar of square cross section the 

 zero coefficient occurs when the ratio of width to length is approxi- 

 mately 0.272. This apparently is also the method for obtaining a 

 low-temperature coefficient used in the Hilger resonator. The second 

 harmonic of this vibration has been used in the frequency standards 

 of the Physikalisch-Technische Reichsanstaldt.* In their standards 



"■"A High Precision Standard of Frequency," W. A. Marrison, Proc. I. R. E., 

 April 3, 1929. 



2 This crystal is described by F. R. Lack in "Observation on Modes of Vibration 

 and Temperature Coefficients of Quartz Crystal Plates," Proc. I. R. E., July 1929, 

 Vol. 17, pp. 1123-1141, and Patent No. 1,958,620 issued May 15, 1934. 



*" Electrical Wave Filters Employing Quartz Crystals as Elements," B. S. T. J., 

 July 1934, Pages 411 and 412. 



* A. Scheibe and V. Adelsberger, Ann. d. Phys. 18, 1, 1933. 



