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

The short-range order (SRO) present in disordered solid solutions is classi fied according to three characteristic system-dependent energies: (1) forma tion enthalpies of ordered compounds, (2) enthalpies of mixing of disordere d alloys, and (3) the energy of coherent phase separation (the composition- weighted energy of the constituents each constrained to maintain a common l attice constant along an AIS interface). These energies are all compared ag ainst a common reference, the energy of incoherent phase separation (the co mposition-weighted energy of the constituents each at their own equilibrium volumes). Unlike long-range order (LRO), short-range order is determined b y energetic competition between phases at a fired composition, and hence on ly coherent phase-separated states are of relevance for SRO. We find five d istinct SRO types, and give examples showing each of these five types, incl uding Cu-Au, AI-Mg, GaP-InP, Ni-Au, and Cu-Ag. The SRO is calculated from f irst principles using the mixed-space cluster expansion approach combined w ith Monte Carlo simulations. Additionally, we examine the effect of inclusi on of coherency strain in the calculation of SRO, and specifically examine the appropriate functional form for accurate SRO calculations.