Graph-Theory Approach to Element Miscibility and Alloy Design

With 118 currently known elements, hence millions of possible quinary combinations, understanding and discovering potentially beneficial mixtures is challenging. Possible stable mixtures, however, are vital for alloy design or realization of new materials. Thermodynamically favorable interactions can also lead to enhanced materials properties. We apply graph theory to map relation in key thermodynamic parameters between elements, therefore revealing possible favorable (miscible) pairs and their congeners. Using closeness centrality and Lipschitz-Hölder exponent, we define miscibility across the whole period table, albeit at ambient conditions. Whereas most metals have fair solubility, hyper- and hypo- centrality (high and low solubility respectively) clusters are identified. We confirm our graph-based approach in understanding miscibility by comparing results to CALPHAD and Miedema's model. Unlike the heuristic models, the graph-based approach is amenable to machine learning enabling prediction at extreme environments by extrapolating known scaling laws.