A dynamical diffraction theory of X-rays for a largely distorted crystal. 1. Fundamental equations

A new dynamical theory of X-ray diffraction is given for a largely distorted crystal. The wave field inside the crystal is described using a kind of modified Bloch waves with amplitude modulation, assuming that the modulation is 'slowly varying' not in the sub-micron level but in the nanometer level. Therefore, the present theory is applicable to very heavy lattice distortion compared with the previous dynamical theory. The present theory is based on the Maxwell's wave equation for the electric field, in which the electric field appearing in the electric polarization term is approximated to the transverse component of the electric field. The results give a set of fundamental equations for the wave filed about the Fourier coefficients and the local variation of the Bloch waves. It is equivalent to, in a perfect crystal, the fundamental equation given by Laue's dynamical theory, and also it leads to Takagi's equations for the electric displacement. (author)