Theory of X-Ray Diffraction by a Distorted Crystal

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Abstract
Based on the quantum theory of X-ray diffraction by a perfect crystal (M. Ashkin and M. Kuriyama, J. Phys. Soc. Japan 21 (1966) 1549), a diffraction theory for a distorted crystal has been developed. The scattering amplitude for the case of a single Bragg reflection has been obtained in terms of a lattice sum including the displacement of each atom. A basic assumption for this formulation is that there is no overlap of the electron wave functions of the displaced atoms. The existing basic assumption in the dynamical theory for a distorted crystal, that the local distortion in the crystal must change very slowly so that the local wave field can be described by the dynamical theory for a perfect crystal, has been successfully avoided in the present formulation. A criticism is also made of the so-called “Fourier” expansion of polarizability or electron distribution in the distorted crystal, which has been important for the dynamical theory.