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By C. Lu, A.W. Czanderna
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Additional resources for Applications of Piezoelectric Quartz Crystal Microbalances
Example text
22), Vf is the acoustic wave velocity in the film and tf is the film thickness. Thus, ff can be considered as the mechanical resonant frequency of the film when it is freely suspended. By 34 C. LU retaining terms only to the second order after a series expansion of the trigonometric functions in Eq. (21) and making a few more approximations, Miller and Bolef showed that Eq. (21) can be reduced to Eq. (14) for small added mass. Miller and Bolefs model and interpretation were certainly more realistic for uniformly deposited films of well-defined thickness, while Stockbridge T s argument appeared to be more appropriate for extremely thin or aggregated films.
LU C. Quartz Crystal Microbalances for Special Environments The crystal holder shown in Fig. 17 is suitable for near room temperature operation. If external thermal input to the mass sensing crystal is properly controlled, its temperature will not be much different from that of the water-cooled crystal holder. Since the temperature coefficient of standard AT-cut quartz crystals is very small near room temperature, the frequency change due to small temperature variations can be ignored. However, when a QCM is operated at a temperature much different (either higher or lower) from room temperature, the effect of a small temperature change to resonant frequency can be quite large even with a quartz crystal of optimal cut.
44) Equation (44) shows that films with different acoustic impedance, or elastic properties, will obey different mass-frequency relations. It can be easily verified that Eq. (29) is only a special case of Eq. (44) with Z = 1. This means that Eq. (44) is valid only for a perfect match of the acoustic impedance between the deposited material and quartz crystal. e. where Af/fq is much less than unity, Eq. (44) reduces to the original Sauerbrey equation [Eq. (15)]. The fact that Eq. (44) is derived from a simple but physically sound model, and Eqs.