Effect of electrodes on force-frequency characteristics of rotated Y-cut quartz resonators

The change in the resonance frequency of the thickness-shear vibration of rotated Y-cut quartz resonators using various electrode materials was studied. We used a three-dimensional finite element method to calculate the strain distribution of a circular plate and the electrodes under a pair of diametrical forces so that the anisotropy of the blank can be accurately considered. The relationship between mass-loading and force-frequency (F-f) characteristics is obtained for several types of electrode material. The results show that, for some electrode materials, the change in the F-f coefficients induced by the initial strain field distribution in the electrode through the third-order elastic constants is significant, but for others, the variations are small. We also find that the change is proportional to the thickness of the electrode. Furthermore, different materials have different effects. For most metals, such as gold, silver, copper, aluminum and nickel, with the increase in thickness, the F-f coefficient increase. However, for chromium, the increase in thickness may result in a lower F-f coefficient.