Bulk acoustic wave modes in quartz for sensing measurand-induced mechanical and electrical property changes

Abstract

It is well known that a measurand in a gas, liquid or solid medium can cause significant changes in the mechanical (mass, elasticity, viscosity) and/or electrical (conductivity, permittivity) properties of the medium. In the case of quartz (α-SiO 2) bulk acoustic wave sensors, the standard approach is to employ the AT-cut thickness-shear mode (TSM) to monitor the presence of the measurand. Although this mode exhibits excellent temperature stability and can operate efficiently in a liquid medium, it is not necessarily the most sensitive mode to monitor mechanical and/or electrical changes induced by the measurand in the medium. It is the purpose of the present paper to determine the sensitivity of the shear acoustic modes in various orientations in quartz so that one may choose the mode that is most sensitive to the mechanical and/or electrical property changes caused by the measurand. The coupled elastic wave equation and Maxwell’s equations are solved simultaneously to obtain five bulk and electromagnetic wave velocities and the associated mechanical and electrical fields quantities for the span of all doubly rotated orientations in quartz. Variational approximation techniques from prior studies are then used to predict the sensitivity of acoustic shear modes in doubly rotated quartz to measurand induced mechanical and electrical property changes in the sensing medium. Those orientations and modes which are most sensitive to measurand-induced mechanical and/or electrical property changes in gas and liquid environment are identified.