Dislocation density tensor identification by coupling micromechanics and X-ray diffraction line broadening

An inverse approach to dislocation microstructure analysis is presented, able to provide dislocation density, character of the activated dislocations and range of the corresponding distortion field. It is based on the coupling between the micromechanical dislocation theory (providing the distortion field within a given crystal) with X-ray line profile analysis (relating a distortion field with the broadening of diffraction line profiles). In particular, lattice distortion is calculated by using both the dislocation density tensor (expressing the incompatibility of the microstructure) and the general Greenʹs function formalism (characterizing the interaction between lattice spatial positions) whereas a Fourier treatment is used to evaluate the X-ray diffraction line broadening. Within the proposed formalism, the case of a periodic arrangement of dislocations is analysed, and numerical simulations, compared with high resolution X-ray diffraction, are shown to provide results quantitatively compatible with literature data both on dislocation density, arrangement and mean distance.