Figure 3: Formation energies of ideal solid solutions in all binary subsystems of the Ir–Re–W alloy system, obtained via various methods.
Over mechanically stable regions, all three calculation methods considered agree. However, the proposed inflection-detection method provides the smoothest extrapolation behaviour into mechanically unstable regions, unlike formation energies obtained with symmetry-constrained relaxations (in which the structure’s space group is not allowed to change during relaxations). At the same time, the inflection-detection method avoids full relaxation towards nearby mechanically stable phases (marked in parentheses), unlike relaxations allowing for symmetry breaking (where the relaxed structures are allowed to have a lower symmetry than the corresponding unrelaxed ones). The resulting inflection-detection predictions for pure elements agree remarkably well with the widely used SGTE values29 and more recent estimates20. (Formation energies are reported relative to each element’s most stable crystal structure.)
