Evaluation of electromechanical coupling factor for a piezoelectric quartz crystal in liquid phase

Abstract

Based on the Butterworth–Van Dyke (BVD) equivalent circuit model for a quartz crystal, the general equations upon the series resonant-frequency f s, and parallel resonant-frequency f p, were obtained by solving the quadratic equation of frequency at susceptance B=0. Consequently, the electromechanical coupling factor ( K) in liquid was first evaluated by using f s and f p. In sucrose solutions, it was seen that K 2 decreases as ( ρη) 1/2 increases, where ρ and η were the density and viscosity of the solution, respectively. It was also interesting to find that K 2 linearly correlates with ( ρη) 1/2 of the media. The regression equation was K 2=−1.216×10 −6( ρη) 1/2+5.204×10 −6, correlation coefficient r 2=0.9954. Regardless of unknown reason for this linear relationship, it was evident that the values of K 2 showed apparent difference when a quartz crystal worked in different media.