Periodic dislocation configuration analysis by lattice distortion evaluation: micromechanical approach and X-ray diffraction line broadening

Abstract

This work concerns dislocation microstructure analysis in order to assess stored elastic energy using Fourier coefficients of diffraction lines. These coefficients are related to the lattice distortion heterogeneity evaluated using a micromechanical approach. The lattice distortion formulation is based on dislocation density and Green's function tensors. The first tensor, which is a state quantity, characterizes the distortion incompatibility, while the second one characterizes the interaction phenomena between spatial positions. The proposed approach considers a given dislocation configuration in order to calculate the exact associated fields in a deterministic way. Periodic dislocation distributions were examined and the lattice distortion was calculated as a function of the distance H between two successive dislocations (dislocation density). A short‐range interaction effect was found for two values: H = 50 and 100 Å. Then Fourier coefficients of {h00}, {hhh} and {hkl} diffraction lines were estimated. It was observed that the sensitivity of the Fourier coefficients to H depends strongly on the choice of the diffraction vector. Since the dislocation configurations were crystallographically defined, the contrast factor is included directly in our approach. For the considered slip system, it is shown that the screw periodical distribution has a higher Fourier coefficient variation than the periodical edge dislocations.

Anisotropic elasticity of multilayered crystals deformed by a biperiodic network of misfit dislocations

“…6 Periodic boundary conditions are ubiquitous in describing crystalline states theoretically and computationally. 7,8 In this paper, we develop a theoretical framework that accounts for the elastic properties of observed periodic dislocation arrays in multilayered structures.…”