Virtual diffraction analysis of dislocations and dislocation networks in discrete dislocation dynamics simulations

This work proposes a data-analytics-based method to correlate diffraction peak broadening to dislocation density in relaxed dislocation networks. The model relies on two key developments: the generation of virtual diffraction signatures of dislocated crystals and the development of a surrogate model to predict dislocation density from diffraction profiles. First, two algorithms are introduced for the generation of diffraction profiles from discrete dislocation dynamics (DDD) simulations. Both algorithms leverage the full-field spectral computation of the elastic strain fields generated in the presence of dislocations. However, the two algorithms differ in their treatment of correlations in the elastic strain field; the impact of this difference on the shape of diffraction peaks is emphasized. A database containing 220 virtual diffraction profiles is generated from networks of dislocations in Al using the correlation-dependent algorithm. This dataset is employed to train and test a surrogate model. Predictions consistently yield dislocation densities within a 90% confidence interval of +30% to -41%, which is an improvement over prior dislocation density prediction methods. It is thus demonstrated that the simultaneous use of virtual diffraction and data analytics can yield alternative models for the analysis of diffraction line profiles in which uncertainty can be quantified for complex dislocation networks.