Influence of the thickness of tabs on the resonating properties of a quartz crystal

Abstract

The behavior of the resonant frequencies of a quartz crystal, coated with electrodes and tabs of the same material, is investigated both theoretically and experimentally. It is pointed out that, when the thicknesses of the tab exceeds the sum of the thickness of the electrodes, the tab behaves like a resonator acting independently of the resonator determined by the conventional electrodes. In the model, which describes this phenomenon, use is made of trapped energy theory on thickness-twist modes. The results of numerical calculations on the theoretical model developed in this paper are in excellent agreement with the results obtained form the experiments. The additional resonant frequencies created by the presence of the tab together with the resonant frequencies related to the electrodes could possibly be used in the field of simultaneous mass and temperature determination. The principle of such a method is given in the paper.

Effects of Mass Layer Nonuniformity on a Quartz-Crystal Microbalance

“…In the plane, we introduce a new coordinate system by (9) In this new coordinate system, the ellipses in (1) are transformed into circles described by (10) Equation (3) becomes (11) We then introduce a polar coordinate system defined by (12) We are only interested in modes that are independent of . Then,…”

“…This paper is concerned with a nonuniform mass layer on a QCR. While there have been a few published results on nonuniform mass layers or nonuniform electrodes either for QCMs [9], [10] or energy trapping in resonator applications [11]- [14], these analyses are all for strip resonators with mode and mass layer (or electrode) thickness variations depending on only one inplane coordinate. For an accurate understanding of the effect of nonuniform mass layers in real devices, a more sophisticated analysis with the mass layer thickness and mode variations depending on the inplane coordinates of the resonator plate is necessary.…”

Effects of a Mass Layer With Gradually Varying Thickness on a Quartz Crystal Microbalance

“…The specific choice of the thickness variation in (7) is also for the mathematical convenience below so that the problem is solvable. Corresponding to (7), from (3) , we have (8) where (9) Substitution of (8) into (5) gives (10) where we have denoted (11) is the frequency of the fundamental TSh mode of a crystal plate with a mass layer of a uniform thickness . We are interested in the so-called energy-trapped modes with the frequency within…”

“…This is what the present paper is concerned with. While there have been a few published results on nonuniform mass layers or nonuniform electrodes on QCRs either for mass sensing [9], [10] or for energy trapping in resonator applications [11]- [14], these analyses are all for strip resonators with modes and mass layer (or electrode) thickness variations depending on one in-plane coordinate only. For an accurate understanding of the effects of nonuniform mass layers, a more sophisticated analysis with the mass layer thickness and mode variation depending on both of the in-plane coordinates is necessary.…”