Investigation of film-thickness determination by oscillating quartz resonators with large mass load

Abstract

A one-dimensional acoustical composite-resonator model is used to study the behavior of a quartz-crystal resonator with large mass load. On the basis of this model, it is found that the exact relationship between the frequency shift and the added mass depends on the acoustic impedance of the deposited material. The experimental data for three materials (silver, copper, and lead) with different acoustic impedances are shown to be in good agreement with the theoretical predictions. The validity and limitations of the presently used equations for thickness determination by quartz-crystal resonators are also discussed.

Sublimation Rate of TNT Microcrystals in Air

“…In general, the substance under investigation should have good adhesion to the QCM surface, should be homogeneously spread, and should be sufficiently rigid. 12,13 QCM may lose its high sensitivity in the absence of good adhesion or undergo additional frequency shifts in the case of soft sample due to dissipation of oscillation energy. 14,15 Large errors in the measurement may occur in the case of thick nonrigid layers due to the acoustic wave absorption by the soft load.…”

Solid particle erosion mechanisms of protective coatings for aerospace applications

“…For thick films such as those studied here, the effect of the coating elasticity on the system's acoustic impedance must be taken into account. Therefore, the mass change of the coated samples was calculated from the Z-Match method proposed by Lu and Lewis [183] which relates m L to the observed change in oscillation frequency through:…”

“…Because the Sauerbrey equation does not take into account the change in elastic properties caused by the deposited film, the Z-Match method [183] is used for thick coatings where,…”

Thermophysical Properties of Penetrants in Polymers via a Piezoelectric Quartz Crystal Microbalance

“…The parameter ff is considered as the resonant frequency of the film if it were oscillating (Lu and Czandema, 1984). Lu and Lewis (1972) indicated that for precise mass determinations, the elastic properties of deposited material have to be taken into consideration. In the equation derived by Lu and Lewis, the resonant frequency of the composite system is determined by tIle acoustic properties of both the quartz crystal and the deposited film.…”

“…The Sauerbrey relation, Equation (28) was found to be valid up to a frequency change of about 2 % of the uncoated crystal frequency. Beyond that range the analytical expression developed by Lu and Lewis (1972) must be used.…”