On a simple derivation of the amplitudes of the electron beams transmitted and scattered by a crystal containing planar interfaces — images of subgrain boundaries

Abstract

AbstractA calculation is made of the amplitudes of the waves transmitted and scattered by a plate‐shaped foil formed by the superposition of two parallel plate‐shaped crystals. The diffraction vectors, the excitation errors, the extinction distances, the absorption lengths, and the phase‐angles of the Fourier coefficients of the internal potential are assumed to be different in the two crystals. The amplitudes can be readily derived from the corresponding expressions for a perfect plate‐shaped foil. These expressions are found by considering the transmitted and scattered beams to arise from the interference of two plane waves with slightly different wave vectors. The method can be generalized to a plate‐shaped foil formed by the superposition of more than two parallel crystals. Assuming the column approximation to be valid a brief discussion is given of the different types of images resulting from planar interfaces. The images due to low angle subgrain‐boundaries are discussed in some detail and observations are presented. These images are often complicated by the superpositions of “wedge crystal” pseudo‐periodic fringe patterns and the “moiré” type of fringe patterns which are strictly periodic.