532 BELL SYSTEM TECHNICAL JOURNAL 



hardness nearly equal to that of ruby and sapphire, and a rigidity of structure 

 such that it cannot be deformed beyond its elastic limit without fracture, 

 it might be expected to remain in a given shape indefinitely under ordinary 

 conditions of use. Because of its great chemical stability, its composition 

 is not easily modified by any ordinary environment. 



In addition to its inherent physical and chemical stability, the elastic 

 hysteresis in quartz is extremely small. For this reason, it requires only a 

 very small amount of energy to sustain oscillation and the period is only 

 very slightly affected by variable external conditions in the means for 

 driving it. 



A striking illustration of the importance of this property is indicated by 

 the number of periods that a resonant element will execute freely, that is, 

 without any sustaining forces whatever, during the time required for the 

 ampUtude to decrease to one-half of some prescribed value. For a good 

 electrical circuit consisting of an air core inductance and an air condenser, 

 this number is about 100; for a good tuning fork in vacuum, it is about 20C0. 

 For a good cavity resonator under standard conditions of temperature and 

 pressure, the number may be as high as 10,000. The best gravity pendu- 

 lums will swing freely from 2,000 to 20,000 times before they reach half 

 amplitude. The effect is most striking of all in quartz crystal, in which the 

 internal losses are extremely low. Professor Van Dyke has measured the 

 rate of decay of oscillations under a wide range of conditions'^^ and has found 

 that, as ordinarily mounted, nearly all of the losses are in the mounting or 

 in the surrounding atmosphere, if any, or in surface effects. Extremely small 

 amounts of surface contamination will more than double the decrement. 

 Recently^® Maynard Waltz and K. S. Van Dyke have measured the decre- 

 ment of one out of the first set of four zero coefficient ring crystals ever made''^ 

 and found that, vibrating freely in vacuum and favorably mounted, it would 

 execute more than a million vibrations before falling to half amplitude. 



The advantage of this property is immediately obvious because of the 

 relatively small amount of energy that must be supplied at each oscillation 

 to keep the resonator in motion. As already discussed in relation to the 

 pendulum, the amount that the rate of oscillation may be disturbed in a 

 given structure is proportional to this energy and, to first order, on the 

 departure from the ideal phase condition of the applied driving force. 



The properties just enumerated are sufficient to assure the superiority of 

 quartz crystal for the control element in a rate standard; no other vibrating 

 system known at the present time is so sharply resonant or so stable. How- 

 ever, one more property, its piezoelectric activity, has added greatly to the 

 convenience of its use in vacuum tube devices. 



The piezoelectric effect was discovered by the Curie brothers in 1880,'^ 



