Design and Performance of Ultraprecise 2.5-mc Quartz Crystal Units

Abstract

A 2.5-mc crystal unit has been developed for use in a new, extremelu stable frequrncy standard oscillator. A well-balanced design was achieved by using a 30-mm-diameter, plano-conoex, polished quartz plate, coated with gold and operated on its fifth ooertone. The quartz plate is mounted on its quiescent edge in an eoacuaied bulb, and achieoes a Q of five to six million, represeniaiioe of the Q of the quartz itself. The temperature coefficient, current coefficient, frequency adjustmen: tolerance and frequency aging oj the crystal unit are all consistent with a frequency stability in the order of one part in 1010. It was necessary to deoelop polishing methods that would not disturb the crystal structure of the quartz plate and new methods of orienting the crystallographic a.res to achiere better temperature coefficient control. New methods of mounting the quartz plate werc found that aroid strain and reduce the e,{fects oj shock and cioralion. The new crystal unit makes possible oscillators characterized by excellent frequency stability, small and uniform aging and straightforward design. For periods up to one month, the frequency stability of such. standards compares Javorably with that of atomic [requenci) standards. I. I NTHODFCTIO:-\The quality of a quartz crystal frequency standard is determined by the crystal-controlled oscillator, and particularly by the mechanically vibrating, piezoelectrically excited quartz plate. Special quartz crystal resonators, characterized by high Q, excellent frequency stability under shock and vibration, and small change with time, have been developed for use in a new general-purpose, extremely stable frequency standard.The development of improved oven and oscillator circuits has contributed substantially to this improved standard, and will be reported in a separate urticle. Over-all performance of an experimental oscillator has heen reported briefly,' and similar oseillutors are in operation at the Xu-1193

Quartz and GaPO<inf>4</inf> pressure transducers for high resolution applications in high temperature: A simulation approach

“…These simulation results are in good agreement with the results found in the literature for quartz [17] and for GaP04 [5].…”

Material and resonator properties of langasite and langatate: a progress report

“…Of particular interest is the resonator quality factor -frequency product, Qf; the best value we have measured to date is 13.4 million for LGS and 16.0 million for LGT. Interestingly enough, this latter value is equal to the asymptotic value for natural quartz AT quartz resonators measured by Warner [24].…”

“…The maximum obtainable value for a given orientation and mode of vibration of a piezoelectric material constitutes a figure of merit for the material. This measure appears to have been introduced by Warner [24] in 1960. For resonators using AT-cut natural quartz, Warner obtained an estimated upper bound for Q.f of 16.106 based on measurements of carefully made resonators over a frequency range from a few hundred kilohertz to 100 MHz.…”

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“…Some 30 years ago Bommel [52] and later Warner [53] have shown that a material limit for AT-cuts reveals a dependence Q, * x, = 1.5 x 10" (74) whereas Seed has found for BT-cuts a two-times-larger value [54]. Recently Bidart and Chauvin [55] We have plotted all four relations (74)-(77) in Fig.…”