Generalization of a nonstandard approach in dynamic diffraction theory to the case of deformed crystal

A nonstandard X-ray diffraction theory for crystals taking lattice deformation into account is generalized in this paper. The vector of atomic-plane displacement is introduced in a model of crystal polarizability in analogy with the Takagi generalized dynamic theory. The solution of the wave equation is sought using the technique of expanding the field amplitude and vector operators in terms of the Fourier polarizability component χ _H in accordance with the multiscale method. It is shown that, in the general case, taking lattice distortions into account requires consideration of various characteristic spatial regions for the diffraction equation. This corresponds wholly to the basic idea of the multiscale method. The particular case of the displacement field depending on a single scale is considered. If a relative change in deformation occurs at a length on the order of the extinction length in this case, then equations generalizing the Takagi equations to the case of arbitrary diffraction geometry are obtained as a result.