Theoretical considerations of extra equal-thickness fringes around a dislocation outcrop observed with an X-ray plane wave

An analytical interpretation is presented of extra half-line equal-thickness fringes observed at a dislocation outcrop in X-ray and electron micrographs of wedge-shaped crystals taken at off-Bragg conditions. Extra fringes arc well explained as the interference of two wavefields deduced from Takagi's equations for dynamical diffraction in distorted crystals. Theoretical discussions given in the present paper confirm the experimentally obtained rule of Δn = h. b (h is the diffracting vector and b the Burgers vector of a dislocation), which determines the extra number of fringes, Δn, at the dislocation outcrop. When h. b≠ integer, it is predicted that a discontinuous shift will occur in the position of equal-thickness fringes along the topographic image of a dislocation.