Short-range-order types in binary alloys: a reflection of coherent phase stability

The short-range order (SRO) present in disordered solid solutions is classified according to three characteristic system-dependent energies: (1) formation enthalpies of ordered compounds, (2) enthalpies of mixing of disordered alloys, and (3) the energy of coherent phase separation (the composition-weighted energy of the constituents each constrained to maintain a common lattice constant along an A/B interface). These energies are all compared against a common reference, the energy of incoherent phase separation (the composition-weighted energy of the constituents each at their own equilibrium volumes). Unlike long-range order (LRO), short-range order is determined by energetic competition between phases at a fixed composition , and hence only coherentphase-separated states are of relevance for SRO. We find five distinct SRO types, and give examples showing each of these five types, including Cu-Au, Al-Mg, GaP-InP, Ni-Au, and Cu-Ag. The SRO is calculated from first principles using the mixed-space cluster expansion approach combined with Monte Carlo simulations. Additionally, we examine the effect of inclusion of coherency strain in the calculation of SRO, and specifically examine the appropriate functional form for accurate SRO calculations.