Roughness effect on the frequency of a quartz-crystal resonator in contact with a liquid

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Abstract
The problem of coupling of the shear oscillations of a quartz crystal bounded by a rough surface with damped waves in a liquid has been investigated. The shift of the resonance frequency of a quartz crystal due to either random roughness or periodical corrugation has been considered. A relation between the shift and a correlation function of roughness has been found. It has been shown that the roughness effect is most pronounced in the low viscosity limit. It has been demonstrated that the results of quartz-crystal microbalance measurements can provide valuable information on the average height and the correlation length of surface roughness.