Generalized small set of ordered structures method for the solid-solution phase of high-entropy alloys

We present a generalization of the small set of ordered structures (SSOS) method that is especially suitable for high-throughput density-functional theory (DFT) calculations of high-entropy alloys in solid-solution phase. Using equiatomic quinary high-entropy alloys with fcc lattice structure, we show that the solution of the existing SSOS method is not unique. In fact, there are six solutions each containing three special ordered structures (SOS) when the range of atomistic pair correlations is up to second-nearest neighbors (NN). We also demonstrate that the SSOS method can be extended to consider atomic pair correlations up to the third NN. In this case, there are 24 solutions each containing six SOS and a negative weight. By increasing the number of SOS to seven to get rid of the negative weight, we show that there are 444 solutions. We further propose an averaging scheme to deal with the nonuniqueness of the generalized SSOS method. The generalized SSOS method allows fast, accurate calculations of ground-state energies of equiatomic high-entropy alloys, thus ideally suitable for high-throughput DFT calculations.