Development of an innovative diffraction scattering theory of X‐rays and electrons in imperfect crystals.

Fundamental equations describing the X‐ray and electron diffraction scattering in imperfect crystals have been derived in the form of the matrix Fredholm–Volterra integral equation of the second kind. A theoretical approach has been developed using the perfect‐crystal Green function formalism. In contrast, another approach utilizes the wavefield eigenfunctions related to the diagonalized matrix propagators of the conventional Takagi–Taupin and Howie–Whelan equations. Using the Liouville–Neumann‐type series formalism for building up the matrix Fredholm–Volterra integral equation solutions, the general resolvent function solutions of the X‐ray and electron diffraction boundary‐valued Cauchy problems have been obtained. Based on the resolvent‐type solutions, the aim is to reveal the features of the diffraction scattering onto the crystal lattice defects, including the mechanisms of intra‐ and interbranch wave scattering in the strongly deformed regions in the vicinity of crystal lattice defect cores. Using the two‐stage resolvent solution of the second order, this approach has been supported by straightforward calculation of the electron bright‐ and dark‐field contrasts of an edge dislocation in a thick foil. The results obtained for the bright‐ and dark‐field profiles of the edge dislocation are discussed and compared with analogous ones numerically calculated by Howie & Whelan [Proc. R. Soc. A (1962), 267, 206]. [ABSTRACT FROM AUTHOR]