The temperature effect of AT-cut input quartz parameters on QCM effective properties calculated with equivalent circuit models

In what follows, AT-cut quartz crystal microbalance (QCM) effective properties for two commercial QCM substrates, are calculated as a function of temperature, while varying the degree of implementation regarding the temperature dependence of input quartz parameters in the transmission line (TL) model. Results for the effective quartz viscosity, oscillation area and external capacitance, are in qualitative agreement per property, irrespective of the implemented, input quartz parameter set for the calculations. However, the effective quartz thickness accounts for the quartz thermal expansion effect, only when quartz density is temperature adjusted, whereas quantitative deviations in the effective oscillation area, are qualitatively explained in the light of literature correlations, which relate the implemented input quartz parameter set, with inherent QCM energy dissipation metrics, and the magnitude of energy trapping. Moreover, the varying degree of input quartz parameter adjustment with temperature, yields qualitative and quantitative deviations from the expected response, in terms of a QCM quality metric, the C-0/C-1 ratio. Results suggest that the precision in the determination of the static capacitance C-0 and the QCM effective properties incorporated therein, can be improved, with potential improvements in relevant, liquid or gas phase QCM applications.