Highly efficient tree search algorithm for irreducible site-occupancy configurations

We present a universal and extremely efficient tree search algorithm for irreducible site-occupancy configurations (implemented in disorder code) that partially avoids the barrier from the combinatorial explosion and allows us to model the compositionally complex materials. The tree search algorithm is developed based on our original algorithm and is leveraging the idea of stopping descending further down the branches of the tree that do not meet the requirements. Meanwhile, the wrongly counted degeneracies of the irreducible site-occupancy configurations, caused by the skipping of some branches of the tree, can be corrected by a degeneracy correction procedure. Using binary face-centered cubic alloys, ternary body-centered cubic alloys, and quaternary simple cubic alloys as examples, we demonstrate that, compared with our original algorithm, the overall efficiency of the tree search algorithm is improved by more than 2 times for binary site occupancy, 70 times for ternary site occupancy, and 50 times for quaternary site occupancy, which is far beyond other similar algorithms. The tree search algorithm developed here can be broadly useful for the modeling of high-entropy alloys and provides support for other methods, such as special quasirandom structures and small set of ordered structures, that require enumerating a set of site-occupancy configurations.