EVOLUTION OF QUARTZ CRYSTAL CLOCK 533 



and in the years following was studied extensively by them'^* • ^^. They 

 found that when quartz and certain other crystals are stressed, an electric 

 potential is induced in nearby conductors and, conversely, that when such 

 crystals are placed in an electric field, they are deformed a small amount 

 proportional to the strength and polarity of that field. The first of these 

 effects is known as the direct piezoelectric effect and the latter as the inverse 

 effect. The amount of such deformation in quartz is extremely minute, a 

 static potential gradient of 1 esu (300 volts) per centimeter causing a 

 maximum extension or contraction, depending on the polarity, of only 

 6.8 X 10~^ cm per cm. If a crystal resonator is subjected to an alternating 

 electric field having the frequency for which the crystal is resonant, the 

 amplitude of motion will, of course, be multipHed many times. In prac- 

 tice, however, the actual amplitudes of motion are kept so small, by limiting 

 the applied electric field, that even with the largest crystals used they can 



0.175////f 25"^ 0.0288////f 420^ 



17 H 



-^W^ — VW—i 



1026 H 



GT CRYSTAL UNIT SQUARE ROD, 8.3 X 0.5 X 0.5 CM 



FREQUENCY 100 KG FREQUENCY 29.2 KG 



Fig. 7 — Equivalent electrical circuits for typical quartz crystal resonators. 



be observed only under a high powered microscope. This, in conjunction 

 with means for precise amplitude control, is one of the reasons for the 

 remarkable frequency stability of quartz crystal oscillators. 



In practice, a quartz resonator is mounted between conducting electrodes 

 which now most often consist of thin metallic coatings deposited on the 

 surface of the crystal by evaporation, chemical deposition or other suitable 

 means. Electrical connection is made to these coatings through leads 

 which also support the crystal mechanically. The resonators with which 

 we are chiefly concerned in this discussion have only two electrodes. 



If such a two-terminal resonator is connected into any circuit, it will 

 behave there as though it consisted of wholly electrical circuit elements, 

 usually of such low loss as can not be realized by other means. The equiv- 

 alent electric circuit for a quartz crystal resonator was first described^^ by 

 K. S. Van Dyke in 1925 and, for some significant cases, is illustrated in 

 Fig. 7. The part of such an equivalent circuit which in many cases cannot 

 be duplicated by any ordinary means is the inductance element containing 

 so Httle resistance. It is as though an electric resonator could be made and 

 utilized constructed of some supra-conducting material. 



