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.

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Early investigations on quartz crystal resonators indicated, that for small mass change, the frequency shift is linearly proportional to the added mass. The accuracy of mass determination was later improved somewhat by using the so−called ’’period measurement’’ technique, which assumes a linear relationship between added mass and change in period of oscillation. However, recent studies indicate that for large mass load, the elastic properties of the deposited material have to be taken into consideration. Based on the theory of one−dimensional acoustic composite resonators, an equation relating the resonant frequency of the composite system to the mass and acoustic impedance of deposited material can be derived. The equation shows that materials with different acoustic impedances will obey different mass−frequency relations. The experimental data for a number of materials with different elastic properties are shown to be in excellent agreement with the theoretical predictions to a mass load as large as 50×10−3 g/cm2. The results indicate that if the acoustic impedance of the deposited material is known, quartz crystal resonantors can be used for measuring a large deposited mass to a remarkable accuracy by using the proper formula.