Effective site-energy model: A thermodynamic approach applied to size-mismatched alloys

Abstract

We present a novel energetic model that takes into account atomistic relaxations to describe the thermodynamic properties of ${A}_{c}{B}_{1\ensuremath{-}c}$ binary alloys. It requires the calculation of the energies on each site of a random solid solution after relaxation as a function of both the local composition and the nominal concentration. These site energies are obtained by molecular static simulations using $N$-body interatomic potentials derived from the second-moment approximation (SMA) of the tight-binding scheme. This new model allows us to determine the effective pair interactions (EPIs) that drive the short-range order (SRO) and to analyze the relative role of the EPIs' contribution to the mixing enthalpy, with respect to the contribution due to the lattice mismatch between the constituents. We apply this formalism to Au-Ni and Ag-Cu alloys, both of them tending to phase separate in the bulk and exhibiting a large size mismatch. Rigid-lattice Monte Carlo (MC) simulations lead to phase diagrams that are in good agreement with both those obtained by off-lattice SMA-MC simulations and the experimental ones. While the phase diagrams of Au-Ni and Ag-Cu alloys are very similar, we show that phase separation is mainly driven by the elastic contribution for Au-Ni and by the EPIs' contribution for Ag-Cu. Furthermore, for Au-Ni, the analysis of the SRO shows an inversion between the tendency to order and the tendency to phase separate as a function of the concentration.