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By C. Lu, A.W. Czanderna

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5 mg/cm 2 onto a QCM in his experiments. 94 x 104 kg/m 3 ) for gold films. As the mass of deposited material becomes appreciable and forms a uniform layer of finite thickness, the assumption that acoustic waves do not propagate in the film becomes less accept­ able. In an effort to rectify the difficulties, Miller and Bolef [13] took a different approach and treated the quartz film combination as a composite acoustic resonator. The deposited film is considered as an integral part of the vibrating system.

10 for compara­ tive purposes. 44 C. LU The range of validity of Eq. (47) was also experimentally tested for other materials. Figure 11 shows the experimental results for nickel and silver. The data for aluminum and copper are shown in Fig. 12. Bulk values of Z were used for all materials [21] to obtain the theoretical curves. Some of the data points represent consider­ able material on the quartz crystal. 7, the thickness of the aluminum film is about 70% of the quartz crystal thickness. The maximum mass load allowable on each quartz crystal in these experiments was mainly limited by the capability of the quartz crystal and its associated oscillator to remain in oscillation.

The frequency of this composite resonator is found to satisfy the following equation: FILM 1 QUARTZ CRYSTAL FILM 2 "f, N % M t "q f 2 r 2 U\ Fig. 14. A quartz crystal resonator with two surfaces coated with different materials. 50 C. LU tan 7T f = (ZiT! + Z2T2) ——— {(k| 6 /TTf) [Z1T1 + Z2T2+ 2 tanCrrf/2)] + Z x Ti Z 2 T 2 - l } (49) where k 26 is the electromechanical coupling factor; f = f c / f q j Tj = tan (TrfMi/Zj); Zj = Z f i / Z q ; Mj = P f i t f i / p q t q ; with i = 1 or 2 denot­ ing the two different film materials.

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