Shifts of frequency and bandwidth of quartz crystal resonators coated with samples of finite lateral size

• Published in: Journal of applied physics 2007-06, Vol.101 (11)
• Main Authors: Herrscher, M., Ziegler, C., Johannsmann, D.
• Format: Article
• Language: English
• ISSN: 0021-8979; 1089-7550
• DOI: 10.1063/1.2729451

Recently, the viscoelastic properties of polymeric materials were probed by pushing a hemispherical cap of the respective material against the front surface of a quartz crystal resonator and measuring the induced shift of frequency and bandwidth, Δf and ΔΓ, as a function of the contact area, Ac.1 The shift of the resonance parameters was found to be proportional to the contact area, with the constant of proportionality containing the sample’s shear modulus. Confining the contact area to a small spot in the center of the plate is central to this approach, because the resonator would otherwise be overdamped. However, more detailed experiments have shown that there are small deviations from the proportionality of the frequency shift to the contact area. In particular, the ratio of ΔΓ and Δf (the “D-f ratio”), which should reflect intrinsic material properties, was found to slightly depend on contact area. Employing a finite element method simulation, two hypotheses were tested for the nontrivial area dependence of Δf and ΔΓ, which are, first, scattering of the acoustic wave from the acoustically heterogeneous surface and, second, a change of the lateral amplitude distribution, (“energy trapping”) induced by loading the crystal in the center only. It can be concluded that scattering affects the D-f ratio only at very small contact radii (