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BELL SYSTEM TECHNICAL JOURNAL 



the length is cut along the X axis and the vibration is excited by 

 fields applied along the length of the bar. Since a rotation about the 

 optic or Z axis does not change the properties of the elastic constants 

 involved in this vibration, this bar should have a zero temperature 

 coefficient at about the same ratio of axes as that given above. The 

 zero angle of orientation is, however, not the most favorable angle of 

 orientation for the fundamental vibration of a long bar, for if the 

 length of the crystal lies at an angle of + 5° with respect to the F or 

 mechanical axis, the coefficient of a long bar is nearly zero.^ These 



2 20 



01 23456789 10 



DEPTH OF OPTICAL AXES IN MILLIMETERS 



Fig. 1 — Temperature coefficient of a perpendicularly cut crystal for 

 varying ratios of width to length. 



long bar type crystals have been used to a small extent to control 



oscillators and to stabilize the pass bands of filters. Their small use 



is attributable to the fact that they vibrate at low frequencies and are 



difficult to excite in an oscillator circuit. 



The AT and BT high-frequency shear crystals and the CT and DT 



low-frequency shear crystals are other low temperature coefficient 



crystals and they are discussed in detail in section II. These crystals 



are cut with their planes at specified angles with respect to the crystal- 



lographic axes and all of them involve a single rotation about an axis 



which is parallel or approximately parallel to one of the crystallographic 



axes. It is shown in section III that such crystals are not the only 



zero coefficient crystals of these types that can be obtained, for if we 



allow three rotations about the crystallographic axes a whole surface 



of zero temperature coefficient crystals can be found. These crystals 



^ Matsumara and Kansaki, "On the Temperature Coefficient of Frequency of Y 

 Waves in X Cut Quartz Plates," Reports of Radio Researches and Works in Japan, 

 March 1932. 



