Electron Statistical Dynamical Diffuse Scattering in Crystals Containing Short-Range-Order Point Defects

Abstract

A formal statistical dynamical theory is developed to calculate diffuse scattering produced by short-range order (SRO) in a distorted crystal structure with consideration of atomic thermal vibrations. Diffuse scattering not only produces fine details in diffraction patterns but also introduces a non-local imaginary potential function that reduces the intensities of the Bragg reflected beams. The distribution of the diffusely scattered electrons and the Fourier coefficients of the absorption potential are directly related to a dynamic form factor S(Q,Q'), which has been calculated with consideration of SRO in the distorted lattices. The statistical structure average on imperfections is performed analytically and the final result is correlated to Cowley's short-range-order parameters. The theory is formulated in the Bloch-wave scheme (Bethe theory) for the convenience of numerical calculation in transmission electron diffraction. A rigorous theoretical proof is given to show that the inclusion of a complex potential in the dynamical calculation automatically recovers the contributions made by the high-order diffuse scattering, although the calculation is done using the equation derived for single diffuse scattering. This simply expands the capability of conventional single diffuse scattering theories. Therefore, the complex potential has a much richer meaning than the conventional interpretation of absorption effect.