Physical description of a viscoelastically loaded AT-cut quartz resonator

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Abstract
In this work, the electrical admittance of this plane-parallel resonator loaded on one face with a viscoelastic medium is described directly in terms of the physical properties of the system. This description is based on the detailed matrix equations for the piezoelectric quartz and includes the piezoelectric effect of the quartz transducer and the shear modulus and viscosity of the overlayer. This physically based analysis has proven invaluable in relating the admittance behavior directly to the materials’ properties. Initial comparisons of the theory with experimental data are given, including the appearance of even harmonics as described by Benes [E. Benes, J. Appl. Phys. 56, 608 (1984)] for the asymmetrically loaded resonator. Additionally, measurements on a series of perfluoropolyether fluids of differing molecular weights indicate that they cannot be described as simple viscous liquids in the MHz range. The assignment of a frequency-dependent viscosity with a relaxation time proportional to the molecular weight resolves some of the discrepancies. Because this study relates the complete admittance spectrum of the loaded resonator to the overlayer material properties, it opens the possibility of studying more than just the changes in resonant frequency. A detailed analysis of the resonance spectrum using an impedance analyzer would provide data which can be fit to the material’s properties and would be particularly helpful with viscoelastic media.