Theoretical Interpretation of the QCM Response

The shear mode resonator consists of a thin disk of AT-cut quartz crystal with electrodes coated on both sides. The application of a voltage between these electrodes results in a shear deformation of the crystal due to its piezoelectric properties. The crystal can be electrically excited into a 

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The geometry of the system consisting of a quartz crystal in contact with the outer medium is schematically shown in Fig. 2. The z-axis is plotted perpendicular to the plane of contact - the plane z = 0 coinciding with the unconstrained face of the quartz resonator, and the plane z = d is its constrained face. The thickness of the quartz crystal is d. 

When an ac voltage is applied between the electrodes, the motion of the AT cut quartz crystal can be described by a system of two coupled dilferential equations, which constitute the wave equation for elastic displacements, u z,t) = u z,03) exp(ioit), and the equations that establish 

Schematic sketch of the quartz crystal resonator in contact with a liquid. The contacting medium is a thin film rigidly attached to the crystal surface from one side, aXz = d. The opposite surface of the crystal (z = 0) is unconstrained, d is the thickness of the quartz crystal. 

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