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Beyond Atomic Sizes and Hume-Rothery Rules: Understanding and Predicting High-Entropy Alloys

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Abstract

High-entropy alloys constitute a new class of materials that provide an excellent combination of strength, ductility, thermal stability, and oxidation resistance. Although they have attracted extensive attention due to their potential applications, little is known about why these compounds are stable or how to predict which combination of elements will form a single phase. In this article, we present a review of the latest research done on these alloys focusing on the theoretical models devised during the last decade. We discuss semiempirical methods based on the Hume-Rothery rules and stability criteria based on enthalpies of mixing and size mismatch. To provide insights into the electronic and magnetic properties of high-entropy alloys, we show the results of first-principles calculations of the electronic structure of the disordered solid-solution phase based on both Korringa–Kohn–Rostoker coherent potential approximation and large supercell models of example face-centered cubic and body-centered cubic systems. We also discuss in detail a model based on enthalpy considerations that can predict which elemental combinations are most likely to form a single-phase high-entropy alloy. The enthalpies are evaluated via first-principles “high-throughput” density functional theory calculations of the energies of formation of binary compounds, and therefore it requires no experimental or empirically derived input. The model correctly accounts for the specific combinations of metallic elements that are known to form single-phase alloys while rejecting similar combinations that have been tried and shown not to be single phase.

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Notes

  1. In this article, we reserve the term HEA for systems that are single-phase solid solutions despite the fact that the term is often used more generally for alloys that, while being multi-component and concentered, may actually exhibit multiple phases—on some (typically microstructural) length-scale.

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Acknowledgements

This research was supported by the U.S. Department of Energy, Basic Energy Sciences, Division of Materials Sciences and Engineering (M.C.T., G.M.S., J.R.M., and A.R.L.). This research used resources of the Oak Ridge Leadership Computing Facility at Oak Ridge National Laboratory, which is supported by the Office of Science of the Department of Energy under Contract DE-AC05-00OR22725. The work of M.D. was supported by the Laboratory Directed Research and Development Program at Lawrence Livermore National Laboratory under tracking code No. 13-ERD-044. Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344.

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Authors and Affiliations

  1. Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA

    M. Claudia Troparevsky, James R. Morris, Andrew R. Lupini & G. Malcolm Stocks

  2. Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN, 37996, USA

    James R. Morris

  3. Physical and Life Sciences, Lawrence Livermore National Laboratory, Livermore, CA, 94551, USA

    Markus Daene

  4. Pittsburgh Supercomputing Center, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Yang Wang

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  1. M. Claudia Troparevsky
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Correspondence to M. Claudia Troparevsky.

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Troparevsky, M.C., Morris, J.R., Daene, M. et al. Beyond Atomic Sizes and Hume-Rothery Rules: Understanding and Predicting High-Entropy Alloys. JOM 67, 2350–2363 (2015). https://doi.org/10.1007/s11837-015-1594-2

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