Modelling frequency fluctuations caused by adsorbing and desorbing masses in a UHF quartz resonator enclosed in a crystal holder

Resonator frequency fluctuations due to adsorption and desorption of molecules on plate electrodes are studied using the principle of mass-loading effects of adsorbed molecules. The study is based on a 525-MHz, AT-cut quartz resonator enclosed in a HC-18 crystal holder. The maximum root mean square of pressure fluctuations at 300 K is estimated to be on the order of 10^-9 torr, and hence would not be a factor in frequency fluctuations, if the crystal holder pressure is a few orders higher. Equations relating the surface adsorption rates of crystal holder to pressure are found to be quadratic polynomial functions of the adsorption rates. Calculations based on these equations show that a contaminant gas with a higher desorption energy creates larger changes in pressure when the temperature is varied. The autocorrelation and spectral-density function of resonator frequency fluctuations are derived. The spectral density of frequency fluctuations at 1 Hz is studied as a function of pressure, temperature, and desorption energy of molecules. The noise levels as indicated by the spectral density of frequency fluctuations at 1 Hz are found to be lower for contaminant gases with lower desorption energies, and higher for gases at lower pressures