Convex Hull Aware Active Search for Phase Stability in High-Dimensional Composition Spaces

High-entropy ceramics have a variety of clean-energy applications including catalysis, thermoelectrics, and batteries. Building a library of stable, high-entropy ceramics is a critical first step for eventually discovering exceptional compositions. As such, considerable efforts have been made in producing high-throughput screening methods for identifying single-phase compositions. A convex hull is required for assessing the stability of a composition; despite ongoing efforts, it remains incredibly costly—and often infeasible—to produce an accurate free energy convex hull in many dimensions.<br/><br/>For this purpose, we have devloped convex-hull aware active search to efficiently produce the free energy convex hull. In each iteration of the active search algorithm, we choose the composition that is expected to give the most information about the hull. As such, we do not waste calculations trying to accurately model irrelevant compositions that are clearly above the hull. Often, large swaths of composition space are far above the hull, and by ignoring them, our algorithm allows for efficient exploration. Since Bayesian methods are employed, the uncertainty in the hull is naturally resolved as a function of composition, allowing for intelligent decisions based on the produced predictions. We offer this method as a tool for effectively building a library of stable, high-entropy ceramics. As a proof of concept, we calculate the free energy convex hull for the senary (Pb,Sn,Ge)(S,Se,Te), a relevant composition space for thermoelectrics.