Abstract
Predicting the synthetic accessibility of multi-principal element alloys (MPEAs) across the global chemical space remains a challenge. In this study, we show that the synthesizability of MPEAs across broad compositional and structural spaces can be predicted using a physical model that expresses the total energy of any MPEA as a linear combination of energies from lower-dimensional subsystems. The model is validated with a large computational dataset and supported by the experimental synthesis of multiple MPEAs, achieving mean absolute errors near or below 7 meV/atom on a density functional theory dataset of 135,791 MPEAs spanning 28 metals and up to ten components. Its accuracy is comparable to state-of-the-art deep learning models while maintaining interpretability through cluster-expansion theory. Moreover, we show that the stability of high-entropy alloys can be predicted using a linear combination of energies from lower-dimensional systems with low errors, indicating a flatter energy landscape at high compositional complexity.
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Acknowledgements
This work is supported by startup funding from Florida State University (B.O.). Additional support was provided by the American Chemical Society Petroleum Research Fund (ACS-PRF # 68184-DNI10) (L.W. and B.O.). Computational resources were provided by ACCESS (B.O.), the National Energy Research Scientific Computing Center (NERSC), a U.S. DOE Office of Science User Facility supported under Contract No. DE-AC02-05CH11231 (B.O.), and the Research Computing Center at Florida State University (B.O.). The Department of Energy’s Office of Energy Efficiency and Renewable Energy at the National Renewable Energy Laboratory also supported computation and data processing (B.O.). The experimental work of this paper was supported by the Toyota Research Institute, Inc. (B.S., Z.Y., and C.A.M.) and the U.S. Army DEVCOM ARL Army Research Office (ARO) Energy Sciences Competency (Electrochemistry) Program award W911NF-23-1-0285 (Z.Y. and C.A.M.). The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Army or the U.S. Government.
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B.O. supervised and planned all aspects of the research. B.O. and L.W. designed the computations and generated all computational results; B.O., L.W., and Z.H. analyzed the data and generated all figures; B.S. and Z.Y. did chemical synthesis and analysis; L.W., B. S., Z.Y., Y.Z., C.A.M., and B.O. contributed to the writing.
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C.A.M. has financial interests in Mattiq Inc. which could potentially benefit from the outcomes of this research. Northwestern University has financial interests relative to intellectual property related to this research. As a result of these interests, Northwestern University could ultimately potentially benefit financially from the outcomes of this research.
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Wang, L., Shen, B., He, ZD. et al. Universal framework for efficient estimation of stability in multi-principal element alloys. Nat Commun (2026). https://doi.org/10.1038/s41467-026-69585-9
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DOI: https://doi.org/10.1038/s41467-026-69585-9
