Alternative theoretical derivation of response function for coated shear-mode quartz piezoelectric crystals

Abstract

In recent years piezoelectric crystals have been developed as chemical sensors. The principle of detection by a piezoelectric crystal is based on the fact that the frequency of an oscillating crystal can be decreased by a foreign material on its surface. The fundamental work of Sauerbrey provides a model for the theory of this phenomenon. This paper describes a mathematical model based on energetics which provides an alternative description of how piezoelectric crystals work. The Eigen frequency and the frequency change can be obtained from the proposed mathematical model. The relationship between Sauerbrey's expression and that proposed here can be deduced by the use of an expanding MacLaurin series.