Pendellö/sung fringes in stroboscopic X-ray section topography of weakly excited quartz resonators

Abstract

The theory for slightly distorted crystals [Kato (1963). J. Phys. Soc. Jpn, 18, 1785-1791] is applied to the case of quartz AT-cut resonators to interpret stroboscopic section topographs. Features in the diffraction process such as ray trajectories, phase changes and intensities of diffracted waves are drawn from this theory. Furthermore, it is shown that extra Pendellö/sung fringes appearing on section topographs with increasing acoustic vibration can be directly related to the vibration amplitude within a precision of about 0-3 Å. Experimental images are compared with Kato's theoretical profiles and simulated images obtained by solving Takagi's [Acta Cryst. (1962), 15, 1311-1312] equations. The results lead to the conclusion that stroboscopic X-ray topography is a precise method to measure the vibration amplitude in weakly excited resonators.