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Three-dimensional atomic structure and local chemical order of medium- and high-entropy nanoalloys

Nature volume 624, pages 564–569 (2023)Cite this article

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Abstract

Medium- and high-entropy alloys (M/HEAs) mix several principal elements with near-equiatomic composition and represent a model-shift strategy for designing previously unknown materials in metallurgy1,2,3,4,5,6,7,8, catalysis9,10,11,12,13,14 and other fields15,16,17,18. One of the core hypotheses of M/HEAs is lattice distortion5,19,20, which has been investigated by different numerical and experimental techniques21,22,23,24,25,26. However, determining the three-dimensional (3D) lattice distortion in M/HEAs remains a challenge. Moreover, the presumed random elemental mixing in M/HEAs has been questioned by X-ray and neutron studies27, atomistic simulations28,29,30, energy dispersive spectroscopy31,32 and electron diffraction33,34, which suggest the existence of local chemical order in M/HEAs. However, direct experimental observation of the 3D local chemical order has been difficult because energy dispersive spectroscopy integrates the composition of atomic columns along the zone axes7,32,34 and diffuse electron reflections may originate from planar defects instead of local chemical order35. Here we determine the 3D atomic positions of M/HEA nanoparticles using atomic electron tomography36 and quantitatively characterize the local lattice distortion, strain tensor, twin boundaries, dislocation cores and chemical short-range order (CSRO). We find that the high-entropy alloys have larger local lattice distortion and more heterogeneous strain than the medium-entropy alloys and that strain is correlated to CSRO. We also observe CSRO-mediated twinning in the medium-entropy alloys, that is, twinning occurs in energetically unfavoured CSRO regions but not in energetically favoured CSRO ones, which represents, to our knowledge, the first experimental observation of correlating local chemical order with structural defects in any material. We expect that this work will not only expand our fundamental understanding of this important class of materials but also provide the foundation for tailoring M/HEA properties through engineering lattice distortion and local chemical order.

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Fig. 1: The 3D atomic structure and lattice distortion of M/HEA nanoparticles.
Fig. 2: 3D strain tensor measurements of the M/HEA nanoparticles.
Fig. 3: Experimental observation of the correlation between CSRO and twinning in MEAs.
Fig. 4: The twin-formation energy (ETF) calculated from the experimental 3D atomic coordinates and species of the MEAs.

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Data availability

All the raw and processed experimental data are available on GitHub (https://github.com/AET-MEA-HEA/Supplementary-Data-Codes).

Code availability

All the MATLAB source codes for the 3D reconstruction, atom tracing and data analysis of this paper are available on GitHub (https://github.com/AET-MEA-HEA/Supplementary-Data-Codes).

References

  1. 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).

    Article  CAS  Google Scholar 

  2. 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).

    Article  Google Scholar 

  3. Gludovatz, B. et al. A fracture-resistant high-entropy alloy for cryogenic applications. Science 345, 1153–1158 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  4. 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).

    Article  ADS  CAS  PubMed  Google Scholar 

  5. Miracle, D. B. & Senkov, O. N. A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448–511 (2017).

    Article  ADS  CAS  Google Scholar 

  6. Yang, T. et al. Multicomponent intermetallic nanoparticles and superb mechanical behaviors of complex alloys. Science 362, 933–937 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  7. George, E. P., Raabe, D. & Ritchie, R. O. High-entropy alloys. Nat. Rev. Mater. 4, 515–534 (2019).

    Article  ADS  CAS  Google Scholar 

  8. Ren, J. et al. Strong yet ductile nanolamellar high-entropy alloys by additive manufacturing. Nature 608, 62–68 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  9. Xie, P. et al. Highly efficient decomposition of ammonia using high-entropy alloy catalysts. Nat. Commun. 10, 4011 (2019).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  10. Batchelor, T. A. A. et al. High-entropy alloys as a discovery platform for electrocatalysis. Joule 3, 834–845 (2019).

    Article  CAS  Google Scholar 

  11. Xin, Y. et al. High-entropy alloys as a platform for catalysis: progress, challenges, and opportunities. ACS Catal. 10, 11280–11306 (2020).

    Article  CAS  Google Scholar 

  12. Löffler, T., Ludwig, A., Rossmeisl, J. & Schuhmann, W. What makes high‐entropy alloys exceptional electrocatalysts? Angew. Chem. Int. Ed. 60, 26894–26903 (2021).

    Article  Google Scholar 

  13. Sun, Y. & Dai, S. High-entropy materials for catalysis: a new frontier. Sci. Adv. 7, eabg1600 (2021).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  14. Yao, Y. et al. High-entropy nanoparticles: synthesis-structure-property relationships and data-driven discovery. Science 376, eabn3103 (2022).

    Article  CAS  PubMed  Google Scholar 

  15. Koželj, P. et al. Discovery of a superconducting high-entropy alloy. Phys. Rev. Lett. 113, 107001 (2014).

    Article  ADS  PubMed  Google Scholar 

  16. Sarkar, A. et al. High entropy oxides for reversible energy storage. Nat. Commun. 9, 3400 (2018).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  17. 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).

    Article  CAS  Google Scholar 

  18. Jiang, B. et al. High figure-of-merit and power generation in high-entropy GeTe-based thermoelectrics. Science 377, 208–213 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  19. Tsai, M.-H. & Yeh, J.-W. High-entropy alloys: a critical review. Mater. Res. Lett. 2, 107–123 (2014).

    Article  Google Scholar 

  20. He, Q. & Yang, Y. On lattice distortion in high entropy alloys. Front. Mater. 5, 42 (2018).

    Article  ADS  Google Scholar 

  21. Zou, Y., Maiti, S., Steurer, W. & Spolenak, R. Size-dependent plasticity in an Nb25Mo25Ta25W25 refractory high-entropy alloy. Acta Mater. 65, 85–97 (2014).

    Article  ADS  CAS  Google Scholar 

  22. Owen, L. R. et al. An assessment of the lattice strain in the CrMnFeCoNi high-entropy alloy. Acta Mater. 122, 11–18 (2017).

    Article  ADS  CAS  Google Scholar 

  23. Song, H. et al. Local lattice distortion in high-entropy alloys. Phys. Rev. Mater. 1, 023404 (2017).

    Article  Google Scholar 

  24. Lee, C. et al. Lattice distortion in a strong and ductile refractory high-entropy alloy. Acta Mater. 160, 158–172 (2018).

    Article  ADS  CAS  Google Scholar 

  25. Li, J. et al. Heterogeneous lattice strain strengthening in severely distorted crystalline solids. Proc. Natl Acad. Sci. USA 119, e2200607119 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  26. Chen, B. et al. Correlating dislocation mobility with local lattice distortion in refractory multi-principal element alloys. Scr. Mater. 222, 115048 (2023).

    Article  CAS  Google Scholar 

  27. Zhang, F. X. et al. Local Structure and Short-Range Order in a NiCoCr Solid Solution Alloy. Phys. Rev. Lett. 118, 205501 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  28. 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).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  29. Ma, Y. et al. Chemical short-range orders and the induced structural transition in high-entropy alloys. Scr. Mater. 144, 64–68 (2018).

    Article  CAS  Google Scholar 

  30. 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).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  31. Ding, Q. et al. Tuning element distribution, structure and properties by composition in high-entropy alloys. Nature 574, 223–227 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  32. 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).

    Article  ADS  Google Scholar 

  33. Zhang, R. et al. Short-range order and its impact on the CrCoNi medium-entropy alloy. Nature 581, 283–287 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  34. Chen, X. et al. Direct observation of chemical short-range order in a medium-entropy alloy. Nature 592, 712–716 (2021).

    Article  ADS  CAS  PubMed  Google Scholar 

  35. 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).

    Article  ADS  CAS  PubMed  Google Scholar 

  36. Miao, J., Ercius, P. & Billinge, S. J. L. Atomic electron tomography: 3D structures without crystals. Science 353, aaf2157 (2016).

    Article  PubMed  Google Scholar 

  37. Ritchie, R. O. The conflicts between strength and toughness. Nat. Mater. 10, 817–822 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  38. Gludovatz, B. et al. Exceptional damage-tolerance of a medium-entropy alloy CrCoNi at cryogenic temperatures. Nat. Commun. 7, 10602 (2016).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  39. 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).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  40. Ma, E. & Wu, X. Tailoring heterogeneities in high-entropy alloys to promote strength–ductility synergy. Nat. Commun. 10, 5623 (2019).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  41. Varvenne, C., Luque, A. & Curtin, W. A. Theory of strengthening in fcc high entropy alloys. Acta Mater. 118, 164–176 (2016).

    Article  ADS  CAS  Google Scholar 

  42. Lu, K., Lu, L. & Suresh, S. Strengthening materials by engineering coherent internal boundaries at the nanoscale. Science 324, 349–352 (2009).

    Article  ADS  CAS  PubMed  Google Scholar 

  43. 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).

    Article  ADS  CAS  Google Scholar 

  44. 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).

    Article  CAS  Google Scholar 

  45. Nellaiappan, S. et al. High-entropy alloys as catalysts for the CO2 and CO reduction reactions: experimental realization. ACS Catal. 10, 3658–3663 (2020).

    Article  CAS  Google Scholar 

  46. Pedersen, J. K. et al. Bayesian optimization of high-entropy alloy compositions for electrocatalytic oxygen reduction. Angew. Chem. Int. Ed. 60, 24144–24152 (2021).

    Article  CAS  Google Scholar 

  47. 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).

    Article  ADS  CAS  PubMed  Google Scholar 

  48. Cruz-Martínez, H. et al. NiPdPt trimetallic nanoparticles as efficient electrocatalysts towards the oxygen reduction reaction. Int. J. Hydrogen Energy 44, 12463–12469 (2019).

    Article  Google Scholar 

  49. 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).

    Article  CAS  PubMed  Google Scholar 

  50. Yao, Y. et al. Carbothermal shock synthesis of high-entropy-alloy nanoparticles. Science 359, 1489–1494 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  51. Xu, R. et al. Three-dimensional coordinates of individual atoms in materials revealed by electron tomography. Nat. Mater. 14, 1099–1103 (2015).

    Article  ADS  CAS  PubMed  Google Scholar 

  52. Chen, C.-C. et al. Three-dimensional imaging of dislocations in a nanoparticle at atomic resolution. Nature 496, 74–77 (2013).

    Article  ADS  CAS  PubMed  Google Scholar 

  53. Johnson, C. L. J. et al. Effects of elastic anisotropy on strain distributions in decahedral gold nanoparticles. Nature Mater. 7, 120–124 (2008).

    Article  ADS  CAS  Google Scholar 

  54. De Fontaine, D. The number of independent pair-correlation functions in multicomponent systems. J. Appl. Crystallogr. 4, 15–19 (1971).

    Article  ADS  Google Scholar 

  55. Li, T. et al. Denary oxide nanoparticles as highly stable catalysts for methane combustion. Nat. Catal. 4, 62–70 (2021).

    Article  CAS  Google Scholar 

  56. 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).

    Article  ADS  CAS  PubMed  Google Scholar 

  57. Yang, Y. et al. Atomic-scale identification of the active sites of nanocatalysts. Preprint at https://arxiv.org/abs/2202.09460 (2023).

  58. Scott, M. C. et al. Electron tomography at 2.4-ångström resolution. Nature 483, 444–447 (2012).

    Article  ADS  CAS  PubMed  Google Scholar 

  59. 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).

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  60. Yang, Y. et al. Determining the three-dimensional atomic structure of an amorphous solid. Nature 592, 60–64 (2021).

    Article  ADS  CAS  PubMed  Google Scholar 

  61. Yuan, Y. et al. Three-dimensional atomic packing in amorphous solids with liquid-like structure. Nat. Mater. 21, 95–102 (2022).

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  62. Pham, M., Yuan, Y., Rana, A., Osher, S. & Miao, J. Accurate real space iterative reconstruction (RESIRE) algorithm for tomography. Sci. Rep. 13, 5624 (2023).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  63. Lloyd, S. Least squares quantization in PCM. IEEE Trans. Inf. Theory 28, 129–137 (1982).

    Article  MathSciNet  Google Scholar 

  64. Yang, Y. et al. Deciphering chemical order/disorder and material properties at the single-atom level. Nature 542, 75–79 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  65. Brünger, A. T. et al. Crystallography & NMR system: a new software suite for macromolecular structure determination. Acta Crystallogr. D 54, 905–921 (1998).

    Article  ADS  PubMed  Google Scholar 

  66. Zhou, J. et al. Observing crystal nucleation in four dimensions using atomic electron tomography. Nature 570, 500–503 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  67. Pelz, P. M. et al. Simultaneous successive twinning captured by atomic electron tomography. ACS Nano 16, 588–596 (2022).

    Article  CAS  PubMed  Google Scholar 

  68. Stein, O., Jacobson, A., Wardetzky, M. & Grinspun, E. A smoothness energy without boundary distortion for curved surfaces. ACM Trans. Graph. 39, 18 (2020).

    Article  Google Scholar 

  69. Zunger, A., Wei, S., Ferreira, L. G. & Bernard, J. E. Special quasirandom structures. Phys. Rev. Lett. 65, 353–356 (1990).

    Article  ADS  CAS  PubMed  Google Scholar 

  70. 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).

    Article  ADS  Google Scholar 

  71. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  72. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

    Article  ADS  CAS  Google Scholar 

  73. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  ADS  CAS  PubMed  Google Scholar 

  74. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).

    Article  ADS  CAS  Google Scholar 

  75. 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).

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Division of Materials Sciences and Engineering under award no. DE-SC0010378. The ADF-STEM imaging with TEAM 0.5 was performed at the Molecular Foundry, which is supported by the Office of Science, Office of Basic Energy Sciences of the US DOE under contract no. DE-AC02-05CH11231. J.D. was supported by the Natural Science Foundation of China (grant no. 12004294) and the HPC platform of Xi’an Jiaotong University.

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Author notes

  1. These authors contributed equally: Saman Moniri, Yao Yang, Jun Ding

Authors and Affiliations

  1. Department of Physics and Astronomy and California NanoSystems Institute, University of California, Los Angeles, Los Angeles, CA, USA

    Saman Moniri, Yao Yang, Yakun Yuan, Jihan Zhou, Long Yang, Fan Zhu, Yuxuan Liao & Jianwei Miao

  2. Center for Alloy Innovation and Design, State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, China

    Jun Ding

  3. Department of Materials Science and Engineering, University of Maryland, College Park, MD, USA

    Yonggang Yao & Liangbing Hu

  4. National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Peter Ercius

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Contributions

J.M. initiated and directed the project; Y. Yao and L.H. synthesized the samples; J.Z., P.E. and J.M. discussed and/or carried out the AET experiments; Y. Yang, Y. Yuan, S.M. and J.M. performed image reconstruction, atom tracing and classification for the AET experiments. S.M., Y. Yang, Y. Yuan, L.Y., F.Z., Y.L., J.D. and J.M. analysed the data and interpreted the results; J.D. performed the DFT calculations and molecular dynamics simulations with input from S.M., Y. Yang, Y. Yuan and J.M.; J.M., S.M. and Y. Yang wrote the paper. All authors commented on the paper.

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Correspondence to Jianwei Miao.

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Extended data figures and tables

Extended Data Fig. 1 EDS maps of the HEA nanoparticles.

a, Low-resolution ADF-STEM image of the nanoparticles. Scale bars, 20 nm. b-i, EDS maps showing the distribution of Co (b), Ni (c), Ru (d), Rh (e), Pd (f), Ag (g), Ir (h) and Pt (i) in the nanoparticles.

Extended Data Fig. 2 3D precision estimation.

a, b, Comparison between a representative experimental (after denoising) (a) and a multi-slice calculated image (b) of MEA-3. The multi-slice images were convolved with a Gaussian function to match the incoherence effects in the experimental images. Scale bar, 2 nm. c, Histogram of the deviation of the 3D atomic positions between the experimental atomic model and that obtained from 55 multi-slice images. The root-mean-square deviation of the histogram is 19.5 pm.

Extended Data Fig. 3 Experimental 3D atomic models of the other six M/HEA nanoparticles.

a-f, Experimental atomic models of four MEAs and two HEAs, named MEA-3 (a), MEA-4 (b), MEA-5 (c), MEA-6 (d), HEA-3 (e) and HEA-4 (f), in which the yellow circles represent the atoms along the twin boundaries in (a-c) and grey circles indicate the atoms on the grain boundary in (c). Scale bar, 1 nm.

Extended Data Fig. 4 Twin boundaries and dislocations in the M/HEAs.

a-e, The twin boundaries of three representative MEAs (a, twin-free; b, single twin; c, double twins) and two HEAs (d, single twin; e, double twins), showing more diffuse twin boundaries in the HEAs with each boundary spreading to the neighbouring atomic layers. The twin order parameter of 1 and −1 represents a hcp (i.e., twinning) and fcc structure, respectively. f, Two Shockley partial dislocations in MEA-5 with opposite Burgers vectors \(\frac{a}{6}\left[121\right]\) and \(\frac{a}{6}[\bar{1}\,\bar{2}\bar{1}]\), as the gliding process was frozen near the boundary during the rapid cooling process of the nanoparticle. g, A screw dislocation in MEA-2 with the Burgers vector \(\frac{a}{2}[110]\), where the zigzag lines in light blue show the characteristic feature of the screw dislocation. h, A Shockley partial dislocation in HEA-4 with the Burgers vector \(\frac{a}{6}\left[121\right]\), which exists near the boundary of the nanoparticle. i, A screw dislocation in HEA-3 with the Burgers vector \(\frac{a}{2}[110]\). Scale bars, 1 nm (a); and 5 Å (f).

Extended Data Fig. 5 3D distribution of the other four CSRO parameters of twin-free MEA-1 and double-twinned MEA-2.

a-d, 3D distribution of \({\alpha }_{{\rm{NiNi}}}\), \({\alpha }_{{\rm{PdPd}}}\), \({\alpha }_{{\rm{PtPt}}}\), and \({\alpha }_{{\rm{NiPd}}}\) in MEA-1, showing the formation of local chemical-order pockets. e-h, Histogram of the average \({\alpha }_{{\rm{NiNi}}}\), \({\alpha }_{{\rm{PdPd}}}\), \({\alpha }_{{\rm{PtPt}}}\), and \({\alpha }_{{\rm{NiPd}}}\) values for each atomic layer along the [111] direction in MEA-1. i-l, 3D distribution of \({\alpha }_{{\rm{NiNi}}}\), \({\alpha }_{{\rm{PdPd}}}\), \({\alpha }_{{\rm{PtPt}}}\), and \({\alpha }_{{\rm{NiPd}}}\) in MEA-2 (the twins labelled as yellow planes), exhibiting more heterogeneous CSRO than twin-free MEA-1 (a-d). m-p, Histogram of the average \({\alpha }_{{\rm{NiNi}}}\), \({\alpha }_{{\rm{PdPd}}}\), \({\alpha }_{{\rm{PtPt}}}\), and \({\alpha }_{{\rm{NiPd}}}\) values for each atomic layer along the [111] direction in MEA-2. Scale bar, 1 nm.

Extended Data Fig. 6 3D distribution of the six CSRO parameters in double-twinned MEA-3.

a-f, 3D distribution of \({\alpha }_{{\rm{NiNi}}}\), \({\alpha }_{{\rm{PdPd}}}\), \({\alpha }_{{\rm{PtPt}}}\), \({\alpha }_{{\rm{NiPd}}}\), \({\alpha }_{{\rm{NiPt}}}\), and \({\alpha }_{{\rm{PdPt}}}\), where the twins are labelled as yellow planes. g-l, Histogram of the average \({\alpha }_{{\rm{NiNi}}}\), \({\alpha }_{{\rm{PdPd}}}\), \({\alpha }_{{\rm{PtPt}}}\), \({\alpha }_{{\rm{NiPd}}}\), \({\alpha }_{{\rm{NiPt}}}\), and \({\alpha }_{{\rm{PdPt}}}\) values for each atomic layer along the [111] direction, where the yellow bars indicate the twin positions. Scale bar, 1 nm.

Extended Data Fig. 7 Twin formation energy (ETF) calculated from experimental 3D atomic coordinates of double-twinned MEA-3.

a-c, Calculation of ETF of the double-twinned MEA by fixing one twin (top yellow circles) and moving the other twin along the [111] direction, in which the three representative atomic configurations show a twin separation by 0 (i.e., a single twin) (a), 9 (b), and 13 atomic layers (c). d, Histogram of ETF as a function of the twin separation. The experimentally determined twin separation is 9 atomic layers (yellow bar), which is next to the minimum ETF with a twin separation of 10 layers. Scale bar, 1 nm.

Extended Data Fig. 8 3D distribution of the six CSRO parameters in twin-free HEA-1.

a-f, 3D distribution of \({\alpha }_{11}\), \({\alpha }_{22}\), \({\alpha }_{33}\), \({\alpha }_{12}\), \({\alpha }_{13}\), and \({\alpha }_{23}\), which are more heterogeneous than those of the twin-free MEAs (Fig. 3a,b, Extended Data Fig. 5a–d). g-l, Histograms of the average \({\alpha }_{11}\), \({\alpha }_{22}\), \({\alpha }_{33}\), \({\alpha }_{12}\), \({\alpha }_{13}\), and \({\alpha }_{23}\) values for the atomic layer along the [111] direction. Scale bar, 1 nm.

Extended Data Fig. 9 3D distribution of the six CSRO parameters in double-twinned HEA-2.

a-f, 3D distribution of \({\alpha }_{11}\), \({\alpha }_{22}\), \({\alpha }_{33}\), \({\alpha }_{12}\), \({\alpha }_{13}\), and \({\alpha }_{23}\), exhibiting greater local chemical fluctuations than the double-twinned MEA (Fig. 3e,f, Extended Data Figs. 5i–l and 6a–f). g-l, Histograms of the average \({\alpha }_{11}\), \({\alpha }_{22}\), \({\alpha }_{33}\), \({\alpha }_{12}\), \({\alpha }_{13}\), and \({\alpha }_{23}\) values of the atomic layer along the [111] direction. m, Histogram of the average values for the six CSRO parameters of a DFT-calculated bulk HEA, twin-free HEA-1, and double-twinned HEA-2. Scale bar, 1 nm.

Extended Data Table 1 Metal precursors used for the synthesis of M/HEA nanoparticles
Full size table
Extended Data Table 2 AET data collection, processing, reconstruction, refinement and statistics of the ten M/HEA nanoparticles
Full size table
Extended Data Table 3 Unpaired t-test on the 3D atomic displacements of MEA-1, MEA-2, HEA-1 and HEA-2
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Moniri, S., Yang, Y., Ding, J. et al. Three-dimensional atomic structure and local chemical order of medium- and high-entropy nanoalloys. Nature 624, 564–569 (2023). https://doi.org/10.1038/s41586-023-06785-z

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