An inverse approach to dislocation microstructure analysis was presented which was able to predict the dislocation density, the nature of the activated dislocations and the range of the corresponding distortion field. It was based upon a coupling between micro-mechanical dislocation theory (providing the distortion field within a given crystal) and X-ray line profile analysis (which related a distortion field to the broadening of diffraction-line profiles). In particular, the lattice distortion was calculated by using both the dislocation density tensor (which expressed the incompatibility of the microstructure) and the general Green’s function formalism (which characterized the interaction between lattice spatial positions). A Fourier treatment was used to evaluate the X-ray diffraction-line broadening. The case of a periodic arrangement of dislocations was analysed, within the proposed formalism. Numerical simulations, compared with high-resolution X-ray diffraction, were shown to provide results which were quantitatively compatible with published data on dislocation density, arrangement and mean distance.

Dislocation Density Tensor Identification by Coupling Micromechanics and X-Ray Diffraction Line Broadening. H.Bougrab, K.Inal, M.Leoni: Materials Science and Engineering A, 2005, 400-401, 142-5