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).
Google Scholar
Cantor, B., Chang, I. T. H., Knight, P. & Vincent, A. J. B. Microstructural development in equiatomic multicomponent alloys. Mater. Sci. Eng. A 375–377, 213–218 (2004).
Google Scholar
Gludovatz, B. et al. A fracture-resistant high-entropy alloy for cryogenic applications. Science 345, 1153–1158 (2014).
Google Scholar
Li, Z., Pradeep, K. G., Deng, Y., Raabe, D. & Tasan, C. C. Metastable high-entropy dual-phase alloys overcome the strength-ductility trade-off. Nature 534, 227–230 (2016).
Google Scholar
Miracle, D. B. & Senkov, O. N. A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448–511 (2017).
Google Scholar
Yang, T. et al. Multicomponent intermetallic nanoparticles and superb mechanical behaviors of complex alloys. Science 362, 933–937 (2018).
Google Scholar
George, E. P., Raabe, D. & Ritchie, R. O. High-entropy alloys. Nat. Rev. Mater. 4, 515–534 (2019).
Google Scholar
Ren, J. et al. Strong yet ductile nanolamellar high-entropy alloys by additive manufacturing. Nature 608, 62–68 (2022).
Google Scholar
Xie, P. et al. Highly efficient decomposition of ammonia using high-entropy alloy catalysts. Nat. Commun. 10, 4011 (2019).
Google Scholar
Batchelor, T. A. A. et al. High-entropy alloys as a discovery platform for electrocatalysis. Joule 3, 834–845 (2019).
Google Scholar
Xin, Y. et al. High-entropy alloys as a platform for catalysis: progress, challenges, and opportunities. ACS Catal. 10, 11280–11306 (2020).
Google Scholar
Löffler, T., Ludwig, A., Rossmeisl, J. & Schuhmann, W. What makes high‐entropy alloys exceptional electrocatalysts? Angew. Chem. Int. Ed. 60, 26894–26903 (2021).
Google Scholar
Sun, Y. & Dai, S. High-entropy materials for catalysis: a new frontier. Sci. Adv. 7, eabg1600 (2021).
Google Scholar
Yao, Y. et al. High-entropy nanoparticles: synthesis-structure-property relationships and data-driven discovery. Science 376, eabn3103 (2022).
Google Scholar
Koželj, P. et al. Discovery of a superconducting high-entropy alloy. Phys. Rev. Lett. 113, 107001 (2014).
Google Scholar
Sarkar, A. et al. High entropy oxides for reversible energy storage. Nat. Commun. 9, 3400 (2018).
Google Scholar
Li, W., Liu, P. & Liaw, P. K. Microstructures and properties of high-entropy alloy films and coatings: a review. Mater. Res. Lett. 6, 199–229 (2018).
Google Scholar
Jiang, B. et al. High figure-of-merit and power generation in high-entropy GeTe-based thermoelectrics. Science 377, 208–213 (2022).
Google Scholar
Tsai, M.-H. & Yeh, J.-W. High-entropy alloys: a critical review. Mater. Res. Lett. 2, 107–123 (2014).
Google Scholar
He, Q. & Yang, Y. On lattice distortion in high entropy alloys. Front. Mater. 5, 42 (2018).
Google Scholar
Zou, Y., Maiti, S., Steurer, W. & Spolenak, R. Size-dependent plasticity in an Nb25Mo25Ta25W25 refractory high-entropy alloy. Acta Mater. 65, 85–97 (2014).
Google Scholar
Owen, L. R. et al. An assessment of the lattice strain in the CrMnFeCoNi high-entropy alloy. Acta Mater. 122, 11–18 (2017).
Google Scholar
Song, H. et al. Local lattice distortion in high-entropy alloys. Phys. Rev. Mater. 1, 023404 (2017).
Google Scholar
Lee, C. et al. Lattice distortion in a strong and ductile refractory high-entropy alloy. Acta Mater. 160, 158–172 (2018).
Google Scholar
Li, J. et al. Heterogeneous lattice strain strengthening in severely distorted crystalline solids. Proc. Natl Acad. Sci. USA 119, e2200607119 (2022).
Google Scholar
Chen, B. et al. Correlating dislocation mobility with local lattice distortion in refractory multi-principal element alloys. Scr. Mater. 222, 115048 (2023).
Google Scholar
Zhang, F. X. et al. Local Structure and Short-Range Order in a NiCoCr Solid Solution Alloy. Phys. Rev. Lett. 118, 205501 (2017).
Google Scholar
Ding, J., Yu, Q., Asta, M. & Ritchie, R. O. Tunable stacking fault energies by tailoring local chemical order in CrCoNi medium-entropy alloys. Proc. Natl Acad. Sci. USA 115, 8919–8924 (2018).
Google Scholar
Ma, Y. et al. Chemical short-range orders and the induced structural transition in high-entropy alloys. Scr. Mater. 144, 64–68 (2018).
Google Scholar
Li, Q. J., Sheng, H. & Ma, E. Strengthening in multi-principal element alloys with local-chemical-order roughened dislocation pathways. Nat. Commun. 10, 3563 (2019).
Google Scholar
Ding, Q. et al. Tuning element distribution, structure and properties by composition in high-entropy alloys. Nature 574, 223–227 (2019).
Google Scholar
Zhang, R., Chen, Y., Fang, Y. & Yu, Q. Characterization of chemical local ordering and heterogeneity in high-entropy alloys. MRS Bull. 47, 186–193 (2022).
Google Scholar
Zhang, R. et al. Short-range order and its impact on the CrCoNi medium-entropy alloy. Nature 581, 283–287 (2020).
Google Scholar
Chen, X. et al. Direct observation of chemical short-range order in a medium-entropy alloy. Nature 592, 712–716 (2021).
Google Scholar
Walsh, F., Zhang, M., Ritchie, R. O., Minor, A. M. & Asta, M. Extra electron reflections in concentrated alloys do not necessitate short-range order. Nat. Mater. 22, 926–929 (2023).
Google Scholar
Miao, J., Ercius, P. & Billinge, S. J. L. Atomic electron tomography: 3D structures without crystals. Science 353, aaf2157 (2016).
Google Scholar
Ritchie, R. O. The conflicts between strength and toughness. Nat. Mater. 10, 817–822 (2011).
Google Scholar
Gludovatz, B. et al. Exceptional damage-tolerance of a medium-entropy alloy CrCoNi at cryogenic temperatures. Nat. Commun. 7, 10602 (2016).
Google Scholar
Zhang, Z. et al. Dislocation mechanisms and 3D twin architectures generate exceptional strength-ductility-toughness combination in CrCoNi medium-entropy alloy. Nat. Commun. 8, 14390 (2017).
Google Scholar
Ma, E. & Wu, X. Tailoring heterogeneities in high-entropy alloys to promote strength–ductility synergy. Nat. Commun. 10, 5623 (2019).
Google Scholar
Varvenne, C., Luque, A. & Curtin, W. A. Theory of strengthening in fcc high entropy alloys. Acta Mater. 118, 164–176 (2016).
Google Scholar
Lu, K., Lu, L. & Suresh, S. Strengthening materials by engineering coherent internal boundaries at the nanoscale. Science 324, 349–352 (2009).
Google Scholar
Otto, F. et al. The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high-entropy alloy. Acta Mater. 61, 5743–5755 (2013).
Google Scholar
Pedersen, J. K., Batchelor, T. A. A., Bagger, A. & Rossmeisl, J. High-entropy alloys as catalysts for the CO2 and CO reduction reactions. ACS Catal. 10, 2169–2176 (2020).
Google Scholar
Nellaiappan, S. et al. High-entropy alloys as catalysts for the CO2 and CO reduction reactions: experimental realization. ACS Catal. 10, 3658–3663 (2020).
Google Scholar
Pedersen, J. K. et al. Bayesian optimization of high-entropy alloy compositions for electrocatalytic oxygen reduction. Angew. Chem. Int. Ed. 60, 24144–24152 (2021).
Google Scholar
Xie, S. et al. Atomic layer-by-layer deposition of Pt on Pd nanocubes for catalysts with enhanced activity and durability toward oxygen reduction. Nano Lett. 14, 3570–3576 (2014).
Google Scholar
Cruz-Martínez, H. et al. NiPdPt trimetallic nanoparticles as efficient electrocatalysts towards the oxygen reduction reaction. Int. J. Hydrogen Energy 44, 12463–12469 (2019).
Google Scholar
Wu, D. et al. Noble-metal high-entropy-alloy nanoparticles: atomic-level insight into the electronic structure. J. Am. Chem. Soc. 144, 3365–3369 (2022).
Google Scholar
Yao, Y. et al. Carbothermal shock synthesis of high-entropy-alloy nanoparticles. Science 359, 1489–1494 (2018).
Google Scholar
Xu, R. et al. Three-dimensional coordinates of individual atoms in materials revealed by electron tomography. Nat. Mater. 14, 1099–1103 (2015).
Google Scholar
Chen, C.-C. et al. Three-dimensional imaging of dislocations in a nanoparticle at atomic resolution. Nature 496, 74–77 (2013).
Google Scholar
Johnson, C. L. J. et al. Effects of elastic anisotropy on strain distributions in decahedral gold nanoparticles. Nature Mater. 7, 120–124 (2008).
Google Scholar
De Fontaine, D. The number of independent pair-correlation functions in multicomponent systems. J. Appl. Crystallogr. 4, 15–19 (1971).
Google Scholar
Li, T. et al. Denary oxide nanoparticles as highly stable catalysts for methane combustion. Nat. Catal. 4, 62–70 (2021).
Google Scholar
Tian, X. et al. Correlating the three-dimensional atomic defects and electronic properties of two-dimensional transition metal dichalcogenides. Nat. Mater. 19, 867–873 (2020).
Google Scholar
Yang, Y. et al. Atomic-scale identification of the active sites of nanocatalysts. Preprint at https://arxiv.org/abs/2202.09460 (2023).
Scott, M. C. et al. Electron tomography at 2.4-ångström resolution. Nature 483, 444–447 (2012).
Google Scholar
Dabov, K., Foi, A., Katkovnik, V. & Egiazarian, K. Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. Image Process. 16, 2080–2095 (2007).
Google Scholar
Yang, Y. et al. Determining the three-dimensional atomic structure of an amorphous solid. Nature 592, 60–64 (2021).
Google Scholar
Yuan, Y. et al. Three-dimensional atomic packing in amorphous solids with liquid-like structure. Nat. Mater. 21, 95–102 (2022).
Google Scholar
Pham, M., Yuan, Y., Rana, A., Osher, S. & Miao, J. Accurate real space iterative reconstruction (RESIRE) algorithm for tomography. Sci. Rep. 13, 5624 (2023).
Google Scholar
Lloyd, S. Least squares quantization in PCM. IEEE Trans. Inf. Theory 28, 129–137 (1982).
Google Scholar
Yang, Y. et al. Deciphering chemical order/disorder and material properties at the single-atom level. Nature 542, 75–79 (2017).
Google Scholar
Brünger, A. T. et al. Crystallography & NMR system: a new software suite for macromolecular structure determination. Acta Crystallogr. D 54, 905–921 (1998).
Google Scholar
Zhou, J. et al. Observing crystal nucleation in four dimensions using atomic electron tomography. Nature 570, 500–503 (2019).
Google Scholar
Pelz, P. M. et al. Simultaneous successive twinning captured by atomic electron tomography. ACS Nano 16, 588–596 (2022).
Google Scholar
Stein, O., Jacobson, A., Wardetzky, M. & Grinspun, E. A smoothness energy without boundary distortion for curved surfaces. ACM Trans. Graph. 39, 18 (2020).
Google Scholar
Zunger, A., Wei, S., Ferreira, L. G. & Bernard, J. E. Special quasirandom structures. Phys. Rev. Lett. 65, 353–356 (1990).
Google Scholar
Krexner, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 49, 14251–14269 (1994).
Google Scholar
Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).
Google Scholar
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).
Google Scholar
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Google Scholar
Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).
Google Scholar
Zhou, X. W., Johnson, R. A. & Wadley, H. N. G. Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers. Phys. Rev. B 69, 144113 (2004).
Google Scholar