Unified formula describing the impedance dependence of a quartz oscillator on gas pressure

Abstract

The impedance dependence of a tuning-fork-shaped quartz oscillator on gas pressure is theoretically analyzed on the basis of a string-of-beads model of the quartz oscillator. The theoretical results are numerically compared with experimental data. The analysis has been already carried out in molecular flow and viscous flow region. In this paper, the impedance behavior in the intermediate flow region is formulated by making use of the theory of slip effect. Furthermore, by the formal extension of this formula to the molecular flow region, a single formula describing the impedance dependence on gas pressure over the whole pressure region is obtained. This formula is found to be in good agreement with experimental data. However, there is still a slight discrepancy (<20%) between the two in the intermediate flow region. This shows the limit of the slip theory. For this reason, the Millikan’s empirical formula is adopted in the intermediate flow region. The unified formula obtained thusly is in numerical agreement with experimental data for various kinds of gases.

Hydrogen Sensing Characteristics of a Quartz Oscillator

“…Finally, from equations (1), (2), and (3), the expression on the impedance of the quartz oscillator can be summarized for the molecular and the viscous flow region as follows (Kokubun K. et al, 1987):…”

“…The calculation is based on equations (4) and (7) depending on the nature of gas flow. The pressure around the border between the molecular and viscous flow region was obtained by fitting of equations (4) and (7) to the experimental results (Kokubun K. et al, 1987). It should be noted that the pressure reading from the quartz friction pressure gauge depends on the kinds of gas measured because the electrical impedance of the quartz oscillator, which is the source for the pressure reading, depends on the viscosity and molecular weight of the measured gas.…”

“…The pressure reading from this quartz friction pressure gauge is derived from the impedance-converted-voltage through pressure calculation (Kokubun K. et al, 1987). The calculation is based on equations (4) and (7) depending on the nature of gas flow.…”

Controlling the quality factor of a tuning-fork resonance between 9 and 300 K for scanning-probe microscopy

“…The mechanical resonance is intrinsically stable and the crystal's piezo-electric effect allows for direct electronic interfacing. Quartz tuning forks have proven to be extremely useful as sensors for temperature [1,2], mass [3], pressure [7,5,6,4], and friction [8,9,10,12,13,15,14,11,17,16]. Due to their high mechanical quality factor Q between 10 3 to 10 5 they are very sensitive to environmental changes.…”

Unified theory of gas damping of flexible microcantilevers at low ambient pressures

“…Clearly, a unified theory to accurately predict the gas damping of microcantilevers over different flow regimes would be very desirable. 7 In this work, we develop a Boltzmann equation based semianalytical model to predict the gas damping of rectangular microcantilevers oscillating in the free-molecular, the transition and even the low pressure slip-flow regimes and validate the approach with detailed experimental results.…”