Dynamical scattering image simulations for two-phase γ-γ′ microstructures: A theoretical model

We introduce an extension of the Darwin-Howie-Whelan (DHW) equations for the case of coherent L12 precipitates in an FCC matrix. The equations are similar in form to the conventional DHW equations and are sufficiently general to account for the different translational variants of the precipitate phase as well as for the displacement fields of arbitrary lattice defects. An approximate scheme to perform fast and accurate image simulations using a pre-computed list of scattering matrices is also introduced. Finally, the results of diffraction pattern and image simulations are shown for two synthetic microstructures for a Ni-Al alloy generated using phase field simulations. The dynamical scattering equations reveal that the precipitate phase superlattice beams can propagate through the disordered matrix, but they are fully decoupled from the fundamental waves.