Pendellösung Fringes in Bragg Case in a Crystal of Finite Thickness

Abstract

The dynamical theory of electron and X-ray diffraction for a distorted crystal, developed by Takagi, is applied to the Bragg case in a crystal of finite thickness. A crystal is divided into the front regions and back regions to which Green’s integral formula is applied. The transmitted and diffracted waves are represented in the integral forms in each region in a distorted crystal. The wave functions are analytically obtained in a perfect crystal of finite thickness and are calculated in the regions near an incident point. The waves are expressed by the superposition of several groups of Pendellösung fringes originating at different points. The diffracted wave has a strong intensity at the point to which comes the diffracted wave through the direct reflection of transmitted wave by the net plane at rear surface.