Validation of the frequency shift of thickness-shear-mode resonators in liquids - determination of the activation energy of viscosity

High-Temperature Properties of Langasite

Materials such as langasite (La3Ga5SiO14) and related compounds are promising candidates for piezoelectric applications at high temperatures. In particular, langasite does not exhibit phase transformations up to the melting point of 1470 °C. Langasite was investigated with respect to potential applications in high temperature resonator devices. In contrast to current resonator materials, we have observed bulk oscillations at temperatures of up to 750 °C in langasite devices. At 700 °C the mass load response for 0.78 mm thick resonators is approximately 0.10 µg/Hz.

At elevated temperatures, the bulk resistivity of the resonator devices cannot be neglected due to attenuation of the resonance signal. Therefore, the temperature dependence of the electrical properties of langasite resonator devices, including bulk resistivity, capacity and resonance frequency were measured and are presented. The electrical conductivity is characterized by an activation energy of 105 kJ/mol. In order to confirm langasites stability with respect to oxidation-reduction reactions, we examined the oxygen diffusivity by measuring 18O tracer profiles by SIMS. The diffusivity along the Y-axis is given by D = 5-10−5 exp(-140 kJ/mol / RT) cm2/s in the temperature range from 500 to 800 °C. Langasite shows low oxygen diffusion coefficients with respect to other materials which might be investigated using a langasite microbalance. This would, for example, enable oxygen diffusion kinetics to be examined in YBa2Cu3O6 at 600 °C by means of 18O/16O exchange.

An extended Butterworth-Van Dyke model for quartz crystal microbalance applications in viscoelastic fluid media

An extended Butterworth-Van Dyke (EBVD) model with frequency-independent parameters for the characterization of a resonant compound formed by a quartz crystal in contact with a finite viscoelastic layer contacting a semi-infinite viscoelastic medium is extracted by analysis of the lumped element model. The formulation of the EBVD model is compared with the complete expression of the electrical admittance of the loaded quartz derived from the transmission line model (TLM). Relative deviations between them do not exceed 3% around 1% bandwidth near resonance. An extended Martin & Granstaff's model and an explicit expression for the frequency shift that supposes an extension of Kanazawa's model for viscoelastic media are obtained. An analysis of the errors associated with the extraction of shear parameters of the coating for different materials prove that, to obtain an error less than 5% in the shear parameters determination, the viscoelastic contribution, defined as the relative error in the thickness computed from the frequency shift by Sauerbrey equation, must be greater than a limit that depends on Q, which is defined as the ratio of the shear storage modulus (G') to shear loss modulus (G"). In the materials studied, polymers in the transition range or in the rubbery state with Q = 1 and 10, the viscoelastic contribution must be higher than 15% and 50%, respectively, for a 5% limit error in the shear parameters extraction. A criterion for a practical determination of the appropriate viscoelastic regimes is indicated.