The Effect of Thin Surface Films

First we consider the effect of a thin film, rigidly attached to an ideally flat crystal surface, on the response of the quartz crystal resonator (see Fig. 2). 

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For a homogeneous thin film with a thickness smaller than the wavelength of the shear oscillations, the shift of the resonance frequency can be expressed in terms of the change in surface mass density of the film, Amy (in g/cm ). This was given by Sauerbrey [6] as 

This equation coincides with Eq. (1) with Cm = Equation 

Equation (9) shows that the addition of mass rigidly attached to the surface of the quartz-crystal resonator leads to a decrease of the resonant frequency, but it does not influence the width of the resonance. 

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