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Accelerating computational modeling and design of high-entropy alloys

A preprint version of the article is available at arXiv.


High-entropy alloys, with N elements and compositions {cν = 1,N} in competing crystal structures, have large design spaces for unique chemical and mechanical properties. Here, to enable computational design, we use a metaheuristic hybrid Cuckoo search (CS) to construct alloy configurational models on the fly that have targeted atomic site and pair probabilities on arbitrary crystal lattices, given by supercell random approximates (SCRAPs) with S sites. Our Hybrid CS permits efficient global solutions for large, discrete combinatorial optimization that scale linearly in a number of parallel processors, and linearly in sites S for SCRAPs. For example, a four-element, 128-site SCRAP is found in seconds—a more than 13,000-fold reduction over current strategies. Our method thus enables computational alloy design that is currently impractical. We qualify the models and showcase application to real alloys with targeted atomic short-range order. Being problem-agnostic, our Hybrid CS offers potential applications in diverse fields.

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Fig. 1: Hybrid CS-optimized 250-atom cell for a bcc equiatomic ABCDE solid-solution alloy with zero SRO for three neighbor shells around each atom.
Fig. 2: Hybrid CS and CS function values versus iterations (objective evaluations) to reach the optimum for six functions.
Fig. 3: Hybrid CS performance.
Fig. 4: Hybrid CS versus MC-only optimization for a 54-atom bcc SCRAP.
Fig. 5: Eform versus SRO for Cu0.75Au0.25 in 108-site SCRAP.
Fig. 6: SCRAPs results for refractory bcc TaNbMo, TaNbMoW and TaNbMoWV.

Data availability

Supporting data for all data plotted in the Figs. 16 (as well as Supplementary Figs. 1–4) are available as source data in spreadsheets, in the Supplementary Information (see additional information) and at Code Ocean50 and Source data are provided with this paper.

Code availability

Interactive open-source codes are available via Code Ocean for Hybrid-CS SCRAPs50 and for Hybrid CS for 1D functions51. For open-source codes (and data) for Hybrid CS SCRAPs or 1D functions, see


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R.S. was supported in part by D.D.J.’s F. Wendell Miller Professorship at ISU. Work at Ames Laboratory (by R.S., A.S., P.S. and D.D.J.) was funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Science & Engineering Division. Ames Laboratory is operated for the US DOE by Iowa State University under contract no. DE-AC02-07CH11358. G.B. was funded by the National Science Foundation through award no. 1944040.

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Authors and Affiliations



D.D.J. proposed and supervised the project. R.S. wrote the SCRAPs generation code using the hybrid CS algorithm. R.S. and A.S. did initial testing. D.D.J. developed the linear-scaling parallel algorithm and scaling analysis. P.S. and R.S. implemented SCRAPs optimization with parallelization and catalogged timings. P.S. completed DFT and phonon calculations, and performed analysis with D.D.J. P.S. got the code running on Code Ocean. R.S., A.S., P.S. and G.B. drafted the initial manuscript, then D.D.J. prepared the final manuscript with approval from all the authors.

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Correspondence to Duane D. Johnson.

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The authors declare no competing interests.

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Peer review information Fernando Chirigati was the primary editor on this Article and managed its editorial process and peer review in collaboration with the rest of the editorial team. Nature Computational Science thanks the anonymous reviewers for their contribution to the peer review of this work.

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Singh, R., Sharma, A., Singh, P. et al. Accelerating computational modeling and design of high-entropy alloys. Nat Comput Sci 1, 54–61 (2021).

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