A boundary integration method for calculating diffraction intensity of crystalline materials with planar deformation

Abstract

Defects and strain states in crystals can be investigated using X-ray and neutron diffraction, two types of penetrating, non-destructive detection techniques. Various approximations are frequently employed to minimize the amount of computation in the practical calculations because the present Fourier transform approach, established by Warren, Averbach et al. based on the Kinematic diffraction theory, has a huge computational cost. This paper develops a numerical method to precisely calculate diffraction intensity by integrating kinematic diffraction amplitude over the boundary, which is applicable to crystals with planar deformation. The precision of this method is assessed by contrasting it with Wilson's analytical equations for the X-ray diffraction results of a single screw dislocation. As an example, the difference in diffraction spots on a single edge dislocation irradiated by different incident X-ray widths are calculated and analyzed. When compared to the X-ray diffraction spots of an ideal material with a dislocation core dug out, the results indicate that if lattice information close to the dislocation core is to be retrieved by X-ray diffraction, the X-ray irradiation area should be restricted.