A Dynamical Theory of Diffraction for a Distorted Crystal

A dynamical theory of X-ray and electron diffraction for a distorted crystal which has been briefly explained elsewhere (Acta cryst. 15 (1962) 1311) is presented in more detail. The fundamental equations for both the X-ray and electron cases are deduced from the Maxwell or the Schrodinger equations, respectively, inside crystalline media which may contain distortions. A method of solution of the equations using the Riemann function is given together with the following general results; (1) the intensities and integrated intensities, with respect to the incident angle, of the transmitted and diffracted rays at a point on the exit surface are given by integrals over the entrance surface, (2) a theoretical basis for the column approximation in the electron case is provided, (3) the intensities of the X-ray projection topographs (traverse pattern) is not dependent upon the type of the incident waves but upon the total intensity to which the crystal is exposed. The limit of the applicability of the present theo...