Deep learning accelerated phase prediction of refractory multi-principal element alloys

The tunability of the mechanical properties of refractory multi-principal-element alloys (RMPEAs) makes them attractive for numerous high-temperature applications. It is well-established that the phase stability of RMPEAs controls their mechanical properties. In this study, we develop a deep learning framework that is trained on a CALPHAD-derived database and is predictive of RMPEA phases with high accuracy up to eight phases within the elemental space of Ti, Fe, Al, V, Ni, Nb, and Zr with an accuracy of approximately 90 %. We further investigate the causes for the low out-of-domain performance of the deep learning models in predicting phases of RMPEAs with new elemental sets and propose a strategy to mitigate this performance shortfall. While our proposed approach shows marginal improvement in accurately predicting the phases of RMPEAs with new elemental sets, we should emphasize that overcoming the out-of-domain problem remains largely challenging, particularly in materials science where there are missing elements or absent material classes in training data hindering predictions, thus slowing the discovery of new potential materials. Predicting phase competition is inherently difficult due to the very small differences in free energies (on the order of meV/atom) that govern competing phases. Current deep learning models, including ours, face significant limitations in capturing these subtle energy differences. Accordingly, more substantial future work is needed to fully address this challenge and achieve robust out-of-domain predictions in complex alloy systems.