Abstract
Lattice mismatch has long constrained alloy compositional design. Governed by the Hume-Rothery rules, severe atomic radius differences (δ) between the constituent elements of nano-alloys can lead to excessive lattice distortions or even phase separation. Therefore, synthesizing alloy nanoparticles with large δ-factors (>15%) is almost impossible, restricting structural and functional tunability. Here, we report a general plasma-assisted carbothermal flash sintering (PCFS) synthesis strategy to obtain sub-5 nm high-entropy alloys (HEAs) nanoparticles with δ-factors exceeding 15%. Plasma treatment helps compensate for the entropy reduction caused by high-δ, while non-equilibrium ultrafast synthesis prevents slow nucleation under thermodynamic steady-state conditions. Utilizing high-entropy to introduce medium-sized bridging elements, large atoms (lanthanides, >180 pm) and small atoms (Al) are successfully accommodated in a single-phase nanolattice with ordered lattice distortions. The resulting quasi-periodic lattice distortions (QPLD) formed via stress relief minimize structural defects and enable anomalous electronic and thermal transport properties. These nanoscale HEAs achieve an exceptional electromagnetic interference (EMI) shielding efficiency of ~99% at a thickness of only ~1.8 μm, which is two orders of magnitude thinner than conventional materials. This general strategy unlocks thousands of possible element combinations, providing a broad materials platform for advanced electronics, energy, and device applications.
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References
Liu, J. & Zhang, J. Nanointerface chemistry: lattice-mismatch-directed synthesis and application of hybrid nanocrystals. Chem. Rev. 120, 2123–2170 (2020).
Mizutani, U., Sato, H. & Massalski, T. B. The original concepts of the Hume-Rothery rule extended to alloys and compounds whose bonding is metallic, ionic, or covalent, or a changing mixture of these. Prog. Mater. Sci. 120, 100719 (2021).
Hume-Rothery, W. & Powell, H. M. On the theory of super-lattice structures in alloys. Z. f.ür. Kristallographie-Crystalline Mater. 91, 23–47 (1935).
Miracle, D. B. & Senkov, O. N. A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448–511 (2017).
Takrori, F. M. & Ayyad, A. Surface energy of metal alloy nanoparticles. Appl. Surf. Sci. 401, 65–68 (2017).
Halperin, W. P. Quantum size effects in metal particles. Rev. Mod. Phys. 58, 533–606 (1986).
George, E. P., Raabe, D. & Ritchie, R. O. High-entropy alloys. Nat. Rev. Mater. 4, 515–534 (2019).
Yeh, J.-W. Physical metallurgy of high-entropy alloys. JOM 67, 2254–2261 (2015).
Wang, H. et al. Multifunctional high entropy alloys enabled by severe lattice distortion. Adv. Mater. 36, 2305453 (2024).
Zeng, Y. et al. High-entropy mechanism to boost ionic conductivity. Science 378, 1320–1324 (2022).
He, Q. F. et al. A highly distorted ultraelastic chemically complex Elinvar alloy. Nature 602, 251–257 (2022).
Lee, C. et al. Strength can be controlled by edge dislocations in refractory high-entropy alloys. Nat. Commun. 12, 5474 (2021).
Jiang, B. et al. High-entropy-stabilized chalcogenides with high thermoelectric performance. Science 371, 830–834 (2021).
Wang, B. et al. General synthesis of high-entropy alloy and ceramic nanoparticles in nanoseconds. Nat. Synth. 1, 138–146 (2022).
Cao, G. et al. Liquid metal for high-entropy alloy nanoparticles synthesis. Nature 619, 73–77 (2023).
Yao, Y. et al. Computationally aided, entropy-driven synthesis of highly efficient and durable multi-elemental alloy catalysts. Sci. Adv. 6, eaaz0510 (2020).
Minamihara, H. et al. Continuous-flow reactor synthesis for homogeneous 1 nm-sized extremely small high-entropy alloy nanoparticles. J. Am. Chem. Soc. 144, 11525–11529 (2022).
Ai, Y. et al. Ultra-small high-entropy alloy nanoparticles: efficient nanozyme for enhancing tumor photothermal therapy. Adv. Mater. 35, 2302335 (2023).
Wang, Y. et al. Unconventional interconnected high-entropy alloy nanodendrites for remarkably efficient c−c bond cleavage toward complete ethanol oxidation. Angew. Chem. Int. Ed. 64, e202420752 (2025).
Li, H. et al. Fast site-to-site electron transfer of high-entropy alloy nanocatalyst driving redox electrocatalysis. Nat. Commun. 11, 5437 (2020).
Mori, K. et al. Hydrogen spillover-driven synthesis of high-entropy alloy nanoparticles as a robust catalyst for CO2 hydrogenation. Nat. Commun. 12, 3884 (2021).
Hao, J. et al. Unraveling the electronegativity-dominated intermediate adsorption on high-entropy alloy electrocatalysts. Nat. Commun. 13, 2662 (2022).
Liu, Y.-H. et al. Toward controllable and predictable synthesis of high-entropy alloy nanocrystals. Sci. Adv. 9, eadf9931 (2023).
Yao, Y. et al. Carbothermal shock synthesis of high-entropy-alloy nanoparticles. Science 359, 1489–1494 (2018).
Yao, Y. et al. Extreme mixing in nanoscale transition metal alloys. Matter 4, 2340–2353 (2021).
Yeh, J.-W. et al. Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes. Adv. Eng. Mater. 6, 299–303 (2004).
Mansoori, G. A., Carnahan, N. F., Starling, K. E. & Leland, T. W. Jr. Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres. J. Chem. Phys. 54, 1523–1525 (1971).
Ye, Y. F., Wang, Q., Lu, J., Liu, C. T. & Yang, Y. High-entropy alloy: challenges and prospects. Mater. Today 19, 349–362 (2016).
Campbell, C. T. Electronic perturbations. Nat. Chem. 4, 597–598 (2012).
Liu, X., Zhang, J. & Pei, Z. Machine learning for high-entropy alloys: Progress, challenges and opportunities. Prog. Mater. Sci. 131, 101018 (2023).
Lundberg, S. M. & Lee, S. I. in 31st Annual Conference on Neural Information Processing Systems (NIPS). (2017).
Wang, H. et al. Deformation-induced crystalline-to-amorphous phase transformation in a CrMnFeCoNi high-entropy alloy. Sci. Adv. 7, eabe3105 (2021).
Cui, M. et al. Multi-principal elemental intermetallic nanoparticles synthesized via a disorder-to-order transition. Sci. Adv. 8, eabm4322 (2022).
Zhou, J. et al. Boridene: Two-dimensional Mo4/3B2-x with ordered metal vacancies obtained by chemical exfoliation. Science 373, 801–805 (2021).
Dey, A., Chroneos, A., Braithwaite, N. S. J., Gandhiraman, R. P. & Krishnamurthy, S. Plasma engineering of graphene. Appl. Phys. Rev. 3, 021301 (2016).
Pacchioni, G. & Freund, H.-J. Controlling the charge state of supported nanoparticles in catalysis: lessons from model systems. Chem. Soc. Rev. 47, 8474–8502 (2018).
Ubaru, S., Międlar, A., Saad, Y. & Chelikowsky, J. R. Formation enthalpies for transition metal alloys using machine learning. Phys. Rev. B 95, 214102 (2017).
Widom, M. Modeling the structure and thermodynamics of high-entropy alloys. J. Mater. Res. 33, 2881–2898 (2018).
Widom, M. & Gao, M. First principles calculation of the entropy of liquid aluminum. Entropy 21, 131 (2019).
Tyson, W. R. & Miller, W. A. Surface free energies of solid metals: estimation from liquid surface tension measurements. Surf. Sci. 62, 267–276 (1977).
Molleman, B. & Hiemstra, T. Size and shape dependency of the surface energy of metallic nanoparticles: unifying the atomic and thermodynamic approaches. Phys. Chem. Chem. Phys. 20, 20575–20587 (2018).
Pauling, L. Atomic radii and interatomic distances in metals. J. Am. Chem. Soc. 69, 542–553 (1947).
Powell, C. J. Recommended Auger parameters for 42 elemental solids. J. Electron. Spectrosc. Relat. Phenom. 185, 1–3 (2012).
Jones, L. & Nellist, P. D. Identifying and correcting scan noise and drift in the scanning transmission electron microscope. Microsc. Microanalysis 19, 1050–1060 (2013).
Oni, A. A. et al. Large area strain analysis using scanning transmission electron microscopy across multiple images. Appl. Phys. Lett. 106, 011601 (2015).
Subhash, B. et al. Resolving atomic-scale structure and chemical coordination in high-entropy alloy electrocatalysts for structure-function relationship elucidation. ACS Nano 17, 22299–22312 (2023).
Wang, Y. et al. Layered double hydroxide nanosheets with multiple vacancies obtained by dry exfoliation as highly efficient oxygen evolution electrocatalysts. Angew. Chem. Int. Ed. 56, 5867–5871 (2017).
Paggel, J. J., Miller, T. & Chiang, T. Quantum-well states as fabry-Perot modes in a thin-film electron interferometer. Science 283, 1709–1711 (1999).
Volokitin, Y. et al. Quantum-size effects in the thermodynamic properties of metallic nanoparticles. Nature 384, 621–623 (1996).
Ching, W.-Y. et al. Fundamental electronic structure and multiatomic bonding in 13 biocompatible high-entropy alloys. npj Comput. Mater. 6, 45 (2020).
Li, K. et al. High-entropy strategy to achieve electronic band convergence for high-performance thermoelectrics. J. Am. Chem. Soc. 146, 14318–14327 (2024).
Lv, H. et al. Functional nanoporous graphene superlattice. Nat. Commun. 15, 1295 (2024).
Zhao, P. et al. Ultrahigh thermal robustness of high-entropy spectrally selective absorbers for next-generation concentrated solar power system. Adv. Funct. Mater. 34, 2411316 (2024).
Choi, C. et al. Reconfigurable heterogeneous integration using stackable chips with embedded artificial intelligence. Nat. Electron. 5, 386–393 (2022).
Li, R. et al. Review on polymer composites with high thermal conductivity and low dielectric properties for electronic packaging. Mater. Today Phys. 22, 100594 (2022).
Apell, P. & Ljungbert, Å A general non-local theory for the electromagnetic response of a small metl particle. Phys. Scr. 26, 113–118 (1982).
Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 12327804, 52231007, T2321003, 22088101, 22405050), the National Key Research Program of China (No. 2024YFA1208902, 2024YFA1408000, 2021YFA1200600), the Science and Technology Commission of Shanghai Municipality (No. 24ZR1406400), and Shanghai Municipal Education Commission (No. 24KXZNA06).
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Y.D., X.Z., and B.L. contributed equally to this work. Y.D., X.Z., R.C., and H.L. conceptualized and designed experiments, directed research, and participated in manuscript writing. Y.D., X.Z., B.L., Z.W., E.Z., and H.Z. conducted material synthesis and performed various characterizations, involving SEM, TEM, XRD, XPS, and XAFS. Y.D., Y.L., H.Z., and J.C. designed and conducted experiments on electricity, heat, and electromagnetism. Y.D., H.Z., and X.X. carried out DFT simulations and trained machine learning models. All authors contributed to data interpretation, discussions, and manuscript preparation.
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Du, Y., Zhou, X., Li, B. et al. Sub-5 nm high-entropy nanoalloys beyond the hume-rothery limit. Nat Commun (2026). https://doi.org/10.1038/s41467-026-69681-w
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DOI: https://doi.org/10.1038/s41467-026-69681-w
