Simultaneous determination of thin-film inertia and shear stiffness using thickness-twist and face-shear modes of an AT-cut quartz resonator

Abstract

We propose the use of thickness-twist (TT) and face-shear (FS) vibration modes of an AT-cut quartz crystal plate resonator for simultaneous determination of the inertia and stiffness of a thin film deposited on a crystal surface. A theoretical analysis using Mindlin's first-order theory for crystal plates is performed to demonstrate the idea. Expressions for the stiffness ratio and mass ratio between the thin film and the resonator are presented in terms of frequency shifts of FS and TT modes, which are experimentally measurable. A numerical example is given.

Keywords:

• mechanics
• elastic waves
• sensors

Acknowledgements

This work was supported by grants from the National Natural Science Foundation of China (Numbers 10932004, 11072116, and 10772087); the Doctoral Program Fund of Ministry of Education of China (Number 2009 305110003/JW); and the Zhejiang Provincial Science Fund for Distinguished Young Scholars (No. LR12A02001). Additional supports were from the Sir Y.K. Pao Chair Professorship and the K.C. Wong Magna Fund through Ningbo University, and the K.C. Wong Education Foundation in Hong Kong. This work was also supported in part by the US Army Research Laboratory/US Army Research Office under agreement number W911NF-10-1-0293.