Towards interfacing dark-field X-ray microscopy to dislocation dynamics modeling

Deformation gradient tensor fields are reconstructed in three dimensions (mapping all 9 tensor components) using synthetic Dark-Field X-ray Microscopy data. Owing to the unique properties of the microscope, our results imply that the evolution of deformation fields can now be imaged non-destructively, in situ, and within deeply embedded crystalline elements. The derived regression framework and sampling scheme operate under the kinematic diffraction approximation and are well-suited for studying microstructure evolution during plastic deformation. We derive the deformation conditions under which diffraction vectors extracted from DFXM images can be uniquely associated to the deformation gradient tensor field of the sample. The analysis concludes that the inverse deformation gradient tensor field must feature limited higher order spatial derivatives over line segments defined by the X-ray beam thickness and the diffracted ray path. The proposed algorithms are validated against numerical simulations for realistic noise levels. Reconstructions of a simulated single straight-edge dislocation show that the Burgers vector components can be recovered with an error of $<$2%. The mean absolute error of the reconstructed elastic distortion field was found to be $<10^{-6}$. By taking the curl of the elastic distortion field, local dislocation densities are derived, yielding a reconstructed dislocation core position with sub-pixel accuracy. The significance of directly measuring the elastic distortion and the dislocation density tensor fields is discussed in the context of continuum theory of dislocations. Such measurements can also be interfaced with continuum dislocation dynamics by providing data that can guide the development and validation, thus extending the relevant models to finite strain regimes.