572 BELL SYSTEM TECHNICAL JOURNAL 



that value was a good median for the range of frequencies then used in 

 electrical communication. For use in a clock any other frequency would 

 answer just as well, so the inherent stability of the resonator should be given 

 first consideration. 



One of the inhibitions imposed on the design of quartz resonators has 

 grown out of the dwindling available supply of large pieces of perfect crystal 

 quartz. Where large quantity production is involved this is an important 

 consideration, but for the small numbers required in a few observatories 

 and national laboratories it should not be a limiting factor. 



Except for whatever added difficulties might be entailed in the mounting, 

 it seems reasonable that a large resonator should be more stable than a very 

 small one. The most fundamental reason for this is the proportionate 

 change in effective size that would result from the transfer of any surface 

 material including even the quartz itself. 



Every substance is supposed to have some vapor pressure although in some 

 cases it is very minute. However, we are concerned with very minute 

 effects, and it is worthwhile to consider what would happen if there were any 

 evaporation or condensation of material. The possibility of this being an 

 important effect is evident when we reahze that the removal of a single layer 

 of molecules from the end of a resonator one centimeter long would increase 

 its frequency by about five parts in a hundred million. The effect on 

 frequency would vary about inversely as the effective length, which favors 

 a large crystal. Such a transfer of material could be inhibited to some 

 extent by operating at a low temperature and by seeking equilibrium between 

 the quartz material of the resonator and other quartz material within the 

 same envelope. Of ourse, other materials than quartz may be involved in 

 similar surface phenomena and should be thoroughly studied and controlled. 

 This has a strong bearing, of course, on the use of conductive materials 

 deposited on a resonator for the purpose of electrical coupling to it. 



The slightest trace of surface contamination has a deleterious effect on the 

 damping coefficient. Professor K. S. Van Dyke in 1935 made a series of 

 measurements on resonators of uniform shape and size but constructed with 

 a considerable range of surface treatments'^. In the construction of different 

 resonators used in these tests he used different grades of abrasive and 

 various amounts of etching with hydrofluoric acid. In these experiments he 

 operated them under varying degrees of refinement with regard to 

 contamination of the surfaces and found that the highest Q was obtain- 

 able only after the utmost care was exercised in keeping the surfaces 

 free from foreign material. The effect is so striking, in fact, that it leads 

 one to wonder whether there is any actual elastic hysteresis in the material 

 of quartz crystal, or whether the minute energy losses observed are entirely 



