Generalized Kanzaki-Krivoglaz model of lattice relaxations in concentrated size-mismatched substitutional alloys applied to Cu-Au and Fe-Pt systems

A generalization of the Kanzaki-Krivoglaz model to concentrated alloys was developed and applied to Cu$_{1-x}$Au$_x$ and Fe$_{1-x}$Pt$_x$ alloys at x = 0.25, 0.5, and 0.75. This model is based on many-body cluster expansions of the configuration-dependent Kanzaki forces and force constants defined with respect to the ideal fcc lattice. The parameters of these expansions were directly fitted to the forces calculated from first-principles for a number of ordered structures at fixed concentration and volume. The Kanzaki forces are dominated by nearest-neighbor terms, which are strongly asymmetric between the atomic species. This asymmetry leads to a non-pairwise effective interaction with a long-range elastic singularity. The ability to capture this singular non-pairwise interaction accurately is a major advantage of the generalized Kanzaki-Krivoglaz model. The comparison of the predicted stable phases and ordering temperatures with experiment is generally favorable; while the prediction for Cu$_{0.25}$Au$_{0.75}$ is wrong due to a known failure of semi-local functionals, the remaining discrepancies for Cu$_{0.5}$Au$_{0.5}$ and Fe$_{0.25}$Pt$_{0.75}$ are attributed to the contributions from the strong tetragonal striction in the L1$_0$ phase and of magnetic disorder, respectively.