Modes of Motion in Quartz Crystals, the Effects of Coupling and Methods of Design

ITH the recent extended use of Quartz crystals in oscillators and electrical networks has come a need for a comprehensive view of the various types of crystal cuts. In addition there has been a need for illustration of some of the methods employed in choosing the proper cut for a given requirement, the manner in which quartz crystals vibrate and the basic principles governing the choice of a design to use certain cuts most advantageously. In particular one of the greatest problems associated with the recent large scale production of crystals for oscillator purposes has been that of obtaining crystals the activity and frequency of which would not vary to any large degree over a wide range in temperature. It is the intention of this chapter to present a physical picture of the manner in which quartz crystals vibrate in their simplest forms and then to show what has been learned from these simple forms that will apply to the more complex combinations of motion. The motion of a bar or plate is determined almost wholly by its dimensions and the particular type of wave generated, or frequency applied, and very little upon the driving system if the coupling to the driving system is small. In the case of quartz the coupling between the electric and mechanical system is small and hence we may study the motion of rods and plates without always considering the effect of changes due to the method of excitation (i.e., piezo-electric). However the ease of exciting and measuring a particular mode does depend on the piezo-electric constant driving it.