Vibration modes analysis by X-ray topography in quartz and langasite resonators

This paper presents the results of the vibration modes measurements by X-ray topography in SC-cut quartz and Y-cut unpolished langasite resonators. A comparison of these results with X-ray diffraction topography images on AT-cut quartz resonators and Y-cut polished langasite resonators pointed out the behavior of mass-loading effect with plate orientation angle and with the surface state of the piezoelectric substrate. The results are compared with electrical measurements performed on the same resonators. 5 MHz Sawyer, plan parallel SC-cut quartz and Y-cut unpolished langasite resonators, with 14 mm plate diameter and various electrode thickness and diameters have been investigated on fundamental, third and fifth overtones. The study on SC-cut quartz resonators and unpolished Y-cut langasite resonators pointed out a good agreement with the results obtained on the same resonators by electrical measurements. The conclusion is that the SC-cut quartz resonator characteristics present a similarly harmonic dependence with those of the Y-cut langasite resonators thus revealing the stress-compensated feature of the Y-cut in langasite crystal.