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Determining the three-dimensional atomic structure of an amorphous solid


Amorphous solids such as glass, plastics and amorphous thin films are ubiquitous in our daily life and have broad applications ranging from telecommunications to electronics and solar cells1,2,3,4. However, owing to the lack of long-range order, the three-dimensional (3D) atomic structure of amorphous solids has so far eluded direct experimental determination5,6,7,8,9,10,11,12,13,14,15. Here we develop an atomic electron tomography reconstruction method to experimentally determine the 3D atomic positions of an amorphous solid. Using a multi-component glass-forming alloy as proof of principle, we quantitatively characterize the short- and medium-range order of the 3D atomic arrangement. We observe that, although the 3D atomic packing of the short-range order is geometrically disordered, some short-range-order structures connect with each other to form crystal-like superclusters and give rise to medium-range order. We identify four types of crystal-like medium-range order—face-centred cubic, hexagonal close-packed, body-centred cubic and simple cubic—coexisting in the amorphous sample, showing translational but not orientational order. These observations provide direct experimental evidence to support the general framework of the efficient cluster packing model for metallic glasses10,12,13,14,16. We expect that this work will pave the way for the determination of the 3D structure of a wide range of amorphous solids, which could transform our fundamental understanding of non-crystalline materials and related phenomena.

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Fig. 1: Determining the 3D atomic structure of a multi-component glass-forming nanoparticle with AET.
Fig. 2: SRO of the glass-forming nanoparticle.
Fig. 3: Connectivity and distribution of MROs in the glass-forming nanoparticle.
Fig. 4: Quantitative characterization of MROs.
Fig. 5: 3D atomic packing of four representative MROs.

Data availability

The raw and processed experimental data are available at The 3D atomic coordinates of the glass-forming nanoparticle have been deposited in the Materials Data Bank ( with MDB ID NiRh00001.

Code availability

The MATLAB source codes for the RESIRE reconstruction and data analysis used in this work are available at


  1. 1.

    Zallen, R. The Physics of Amorphous Solids (Wiley, 1998).

  2. 2.

    Elliott, S. R. Physics of Amorphous Materials (Longman Scientific & Technical, 1990).

  3. 3.

    Andrady, A. L. & Neal, M. A. Applications and societal benefits of plastics. Phil. Trans. R. Soc. B 364, 1977–1984 (2009).

    CAS  Google Scholar 

  4. 4.

    Carlson, D. E. & Wronski, C. R. Amorphous silicon solar cell. Appl. Phys. Lett. 28, 671–673 (1976).

    ADS  CAS  Google Scholar 

  5. 5.

    Zachariasen, W. H. The atomic arrangement in glass. J. Am. Chem. Soc. 54, 3841–3851 (1932).

    CAS  Google Scholar 

  6. 6.

    Bernal, J. D. & Mason, J. Packing of spheres: co-ordination of randomly packed spheres. Nature 188, 910–911 (1960).

    ADS  Google Scholar 

  7. 7.

    Scott, G. D. Packing of equal spheres. Nature 188, 908–909 (1960).

    ADS  MATH  Google Scholar 

  8. 8.

    Finney, J. L. Random packings and structure of simple liquids. I. Geometry of random close packing. Proc. R. Soc. Lond. A 319, 479–493 (1970).

    ADS  CAS  Google Scholar 

  9. 9.

    Nelson, D. R. & Spaepen, F. Polytetrahedral order in condensed matter. Solid State Phys. 42, 1–90 (1989).

    CAS  Google Scholar 

  10. 10.

    Miracle, D. B. A structural model for metallic glasses. Nat. Mater. 3, 697–702 (2004).

    ADS  CAS  Google Scholar 

  11. 11.

    Sheng, H. W., Luo, W. K., Alamgir, F. M., Bai, J. M. & Ma, E. Atomic packing and short-to-medium-range order in metallic glasses. Nature 439, 419–425 (2006).

    ADS  CAS  Google Scholar 

  12. 12.

    Miracle, D. B., Egami, T., Flores, K. M. & Kelton, K. F. Structural aspects of metallic glasses. MRS Bull. 32, 629–634 (2007).

    CAS  Google Scholar 

  13. 13.

    Cheng, Y. Q. & Ma, E. Atomic-level structure and structure-property relationship in metallic glasses. Prog. Mater. Sci. 56, 379–473 (2011).

    CAS  Google Scholar 

  14. 14.

    Miracle, D. B. A physical model for metallic glass structures: an introduction and update. JOM 64, 846–855 (2012).

    CAS  Google Scholar 

  15. 15.

    Hirata, A. et al. Geometric frustration of icosahedron in metallic glasses. Science 341, 376–379 (2013).

    ADS  CAS  Google Scholar 

  16. 16.

    Chen, M. W. A brief overview of bulk metallic glasses. NPG Asia Mater. 3, 82–90 (2011).

    Google Scholar 

  17. 17.

    Klement Jun, W., Willens, R. H. & Duwez, P. Non-crystalline structure in solidified gold–silicon alloys. Nature 187, 869–870 (1960).

    ADS  Google Scholar 

  18. 18.

    Greer, A. L. Metallic glasses. Science 267, 1947–1953 (1995).

    ADS  CAS  Google Scholar 

  19. 19.

    Peker, A. & Johnson, W. L. A highly processable metallic glass: Zr41.2Ti13.8Cu12.5Ni10.0Be22.5. Appl. Phys. Lett. 63, 2342–2344 (1993).

    ADS  Google Scholar 

  20. 20.

    Inoue, A. Stabilization of metallic supercooled liquid and bulk amorphous alloys. Acta Mater. 48, 279–306 (2000).

    ADS  CAS  Google Scholar 

  21. 21.

    Wang, W. H., Dong, C. & Shek C. H. Bulk metallic glasses. Mater. Sci. Eng. Rep. 44, 45–89 (2004).

    Google Scholar 

  22. 22.

    Giacovazzo, C. et al. Fundamentals of Crystallography 3rd edn (Oxford Univ. Press, 2011).

  23. 23.

    Egami, T. & Billinge, S. J. L. Underneath the Bragg Peaks: Structural Analysis of Complex Materials (Pergamon, 2003).

  24. 24.

    Kelton, K. F. et al. First X-ray scattering studies on electrostatically levitated metallic liquids: demonstrated influence of local icosahedral order on the nucleation barrier. Phys. Rev. Lett. 90, 195504 (2003).

    ADS  CAS  Google Scholar 

  25. 25.

    Zhong, L., Wang, J., Sheng, H., Zhang, Z. & Mao, S. X. Formation of monatomic metallic glasses through ultrafast liquid quenching. Nature 512, 177–180 (2014).

    ADS  CAS  Google Scholar 

  26. 26.

    Hwang, J. et al. Nanoscale structure and structural relaxation in Zr50Cu45Al5 bulk metallic glass. Phys. Rev. Lett. 108, 195505 (2012).

    ADS  Google Scholar 

  27. 27.

    Hirata, A. et al. Direct observation of local atomic order in a metallic glass. Nat. Mater. 10, 28–33 (2011).

    ADS  CAS  Google Scholar 

  28. 28.

    Pekin, T. C. et al. Direct measurement of nanostructural change during in situ deformation of a bulk metallic glass. Nat. Commun. 10, 2445 (2019).

    ADS  PubMed  PubMed Central  Google Scholar 

  29. 29.

    Tang, X. P., Geyer, U., Busch, R., Johnson, W. L. & Wu, Y. Diffusion mechanisms in metallic supercooled liquids and glasses. Nature 402, 160–162 (1999).

    ADS  CAS  Google Scholar 

  30. 30.

    Sachdev, S. & Nelson, D. R. Order in metallic glasses and icosahedral crystals. Phys. Rev. B 32, 4592–4606 (1985).

    ADS  CAS  Google Scholar 

  31. 31.

    Tang, C. & Harrowell, P. Anomalously slow crystal growth of the glass-forming alloy CuZr. Nat. Mater. 12, 507–511 (2013).

    ADS  CAS  Google Scholar 

  32. 32.

    Cheng, Y. Q., Ma, E. & Sheng, H. W. Atomic level structure in multicomponent bulk metallic glass. Phys. Rev. Lett. 102, 245501 (2009).

    ADS  CAS  Google Scholar 

  33. 33.

    Hu, Y. C., Li, F. X., Li, M. Z., Bai, H. Y. & Wang, W. H. Five-fold symmetry as indicator of dynamic arrest in metallic glass-forming liquids. Nat. Commun. 6, 8310 (2015).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  34. 34.

    Ding, J. & Ma, E. Computational modeling sheds light on structural evolution in metallic glasses and supercooled liquids. npj Comput. Mater 3, 9 (2017).

    ADS  Google Scholar 

  35. 35.

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

    ADS  CAS  Google Scholar 

  36. 36.

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

    Google Scholar 

  37. 37.

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

    ADS  CAS  Google Scholar 

  38. 38.

    Goris, B. et al. Three-dimensional elemental mapping at the atomic scale in bimetallic nanocrystals. Nano Lett. 13, 4236–4241 (2013).

    ADS  CAS  Google Scholar 

  39. 39.

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

    ADS  CAS  Google Scholar 

  40. 40.

    Haberfehlner, G. et al. Formation of bimetallic clusters in superfluid helium nanodroplets analysed by atomic resolution electron tomography. Nat. Commun. 6, 8779 (2015).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  41. 41.

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

    ADS  CAS  Google Scholar 

  42. 42.

    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).

    CAS  Google Scholar 

  43. 43.

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

    ADS  CAS  Google Scholar 

  44. 44.

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

    ADS  CAS  Google Scholar 

  45. 45.

    Kim, J. Y. et al. Utilization of high entropy alloy characteristics in Er-Gd-Y-Al-Co high entropy bulk metallic glass. Acta Mater. 155, 350–361 (2018).

    ADS  CAS  Google Scholar 

  46. 46.

    Liu, X. J. et al. Metallic liquids and glasses: atomic order and global packing. Phys. Rev. Lett. 105, 155501 (2010).

    ADS  CAS  Google Scholar 

  47. 47.

    Wu, Z. W., Li, M. Z., Wang, W. H. & Liu, K. X. Hidden topological order and its correlation with glass-forming ability in metallic glasses. Nat. Commun. 6, 6035 (2015).

    ADS  CAS  Google Scholar 

  48. 48.

    Spaepen, F. A microscopic mechanism for steady state inhomogeneous flow in metallic glasses. Acta Metall. 25, 407–415 (1977).

    CAS  Google Scholar 

  49. 49.

    Argon, A. S. Plastic-deformation in metallic glasses. Acta Metall. 27, 47–58 (1979).

    CAS  Google Scholar 

  50. 50.

    Johnson, W. L. Thermodynamic and kinetic aspects of the crystal to glass transformation in metallic materials. Prog. Mater. Sci. 30, 81–134 (1986).

    CAS  Google Scholar 

  51. 51.

    Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001).

    ADS  CAS  Google Scholar 

  52. 52.

    Xu, Z., Sun, H., Zhao, X. & Gao, C. Ultrastrong fibers assembled from giant graphene oxide sheets. Adv. Mater. 25, 188–193 (2013).

    CAS  Google Scholar 

  53. 53.

    Takeuchi, A. & Inoue, A. Quantitative evaluation of critical cooling rate for metallic glasses. Mater. Sci. Eng. A 304–306, 446–451 (2001).

    Google Scholar 

  54. 54.

    Bordeenithikasem, P. et al. Determination of critical cooling rates in metallic glass forming alloy libraries through laser spike annealing. Sci. Rep. 7, 7155 (2017); author correction 8, 17898 (2018).

    ADS  PubMed  PubMed Central  Google Scholar 

  55. 55.

    Ercius, P., Boese, M., Duden, T. & Dahmen, U. Operation of TEAM I in a user environment at NCEM. Microsc. Microanal. 18, 676–683 (2012).

    ADS  CAS  Google Scholar 

  56. 56.

    Lewis, J. P. Fast normalized cross-correlation. In Vision Interface 1995 120–123 (1995).

  57. 57.

    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).

    ADS  MathSciNet  Google Scholar 

  58. 58.

    Miao, J., Sayre, D. & Chapman, H. N. Phase retrieval from the magnitude of the Fourier transform of non-periodic objects. J. Opt. Soc. Am. A 15, 1662–1669 (1998).

    ADS  Google Scholar 

  59. 59.

    Pryor, A. et al. GENFIRE: a generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging. Sci. Rep. 7, 10409 (2017).

    ADS  PubMed  PubMed Central  Google Scholar 

  60. 60.

    Gilbert, P. Iterative methods for the three-dimensional reconstruction of an object from projections. J. Theor. Biol. 36, 105–117 (1972).

    CAS  Google Scholar 

  61. 61.

    Rogers, S. S., Waigh, T. A., Zhao, X. & Lu, J. R. Precise particle tracking against a complicated background: polynomial fitting with Gaussian weight. Phys. Biol. 4, 220–227 (2007).

    ADS  CAS  Google Scholar 

  62. 62.

    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 

  63. 63.

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

    MathSciNet  MATH  Google Scholar 

  64. 64.

    Pryor, A., Ophus, C. & Miao, J. A streaming multi-GPU implementation of image simulation algorithms for scanning transmission electron microscopy. Adv. Struct. Chem. Imaging 3, 15 (2017).

    PubMed  PubMed Central  Google Scholar 

  65. 65.

    Steinhardt, P. J., Nelson, D. R. & Ronchetti, M. Bond-orientational order in liquids and glasses. Phys. Rev. B 28, 784–805 (1983).

    ADS  CAS  Google Scholar 

  66. 66.

    Lechner, W. & Dellago, C. Accurate determination of crystal structures based on averaged local bond order parameters. J. Chem. Phys. 129, 114707 (2008).

    ADS  Google Scholar 

  67. 67.

    Yu, H. B. & Samwer, K. Atomic mechanism of internal friction in a model metallic glass. Phys. Rev. B 90, 144201 (2014).

    ADS  Google Scholar 

  68. 68.

    Warren, B. E. X-Ray Diffraction (Dover Publications, 1990).

  69. 69.

    Cowley, J. M. X‐Ray measurement of order in single crystals of Cu3Au. J. Appl. Phys. 21, 24–30 (1950).

    ADS  CAS  Google Scholar 

  70. 70.

    Lee, C. Y. An algorithm for path connections and its applications. IEEE Trans. Electron. Comput. EC-10, 346–365 (1961).

    MathSciNet  Google Scholar 

  71. 71.

    Larsen, P. M., Schmidt, S. & Schiøtz, J. Robust structural identification via polyhedral template matching. Model. Simul. Mater. Sci. Eng. 24, 055007 (2016).

    ADS  Google Scholar 

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We thank J. Ding for discussions, H. B. Yu for providing a molecular-dynamics-simulated atomic model of the Cu65Zr35 metallic glass, and D. J. Kline and M. R. Zachariah for assistance with the temperature measurements. This work was primarily supported by STROBE: A National Science Foundation Science & Technology Center under grant number DMR 1548924. This work was also supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Division of Materials Sciences and Engineering under award number DE-SC0010378 (data acquisition and 3D image reconstruction) and the NSF DMREF programme under award number DMR-1437263. J.M. acknowledges partial support from an Army Research Office MURI grant on Ab-Initio Solid-State Quantum Materials: Design, Production and Characterization at the Atomic Scale. Y. Yao and L.H. are supported by the National Science Foundation (award number 1635221).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 number DE-AC02—05CH11231.

Author information




J.M. conceived the idea and directed the project; Y. Yao and L.H. synthesized the samples; J.Z., P.E., A.K.S. and J.M. discussed and/or carried out the experiments; M.P., Y. Yuan, A.R., S.J.O. and J.M. developed the RESIRE algorithm. Y. Yang, F.Z., Y. Yuan, D.J.C., J.Z., D.S.K., X.T. and J.M. performed image reconstruction, atom tracing and classification, analysed the data and/or interpreted the results; J.M., Y. Yang, J.Z. and F.Z. wrote the manuscript. All authors commented on the manuscript.

Corresponding author

Correspondence to Jianwei Miao.

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The authors declare no competing interests.

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Peer review information Nature thanks Simon Billinge, Paul Voyles, Yong Yang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 Cooling rate measurement, EDX and EELS maps of the nanoparticles.

a, The cooling rate for the average (Taverage) and maximum (Tmax) temperature curves was measured to be 51,000 K s−1 (slope of the red line) and 69,000 K s−1 (slope of the green line), respectively. b, Low-resolution ADF-STEM image of the nanoparticles. cj, EDX maps showing the distribution of Ni (c), Co (d), Ru (e), Rh (f), Pd (g), Ag (h), Ir (i) and Pt (j). k, EDX spectrum of all the elements shown in cj; cps, counts per second. l, Low-resolution ADF-STEM image of a large area, with the white square indicating the aggregation of several nanoparticles used for the EELS measurement. m, ADF-STEM image of the region in the white square in l. np, EELS maps show the distribution of Co (n), Ni (o) and O (p) in the same region. q, EELS spectrum obtained from np. No oxygen signal was detected in the EELS map or spectrum. Scale bars, 20 nm (b); 100 nm (l); and 10 nm (o).

Extended Data Fig. 2 Analysis of seven multi-component metallic nanoparticles.

ag, Representative ADF-STEM images of particles 1–7, respectively. Scale bar, 2 nm. hn, Local BOO parameters for all atoms in particles 1–7, where the dashed red curves correspond to a normalized BOO parameter of 0.5. The percentage at the top of each panel shows the fraction of disordered atoms in each particle. o, Local BOO parameters of a 3D atomic model cropped from a molecular-dynamics-simulated Cu65Zr35 metallic glass67 used as a reference, from which a normalized BOO parameter of 0.5 (dashed red curve) was chosen as a cut-off to separate crystal nuclei from amorphous structure. For a fair comparison, the 3D atomic model was cropped to have a similar 3D shape and size to the experimental nanoparticle (particle 1). pv, PDFs of all atoms in particles 1–7, respectively. With decreasing fraction of disordered atoms in the nanoparticles, the peaks in the PDFs become narrower and new peaks corresponding to different crystal planes appear.

Extended Data Fig. 3 Experimental tomographic tilt series of a multi-component glass-forming nanoparticle (particle 1).

55 raw ADF-STEM images of the nanoparticle with a tilt range from −69.4° to +72.6°. The 2D power spectra of the images are shown in the insets, where the amorphous halo is visible. Some crystalline features are visible in several experimental images and the 2D power spectra. Scale bar, 2 nm.

Extended Data Fig. 4 Angular errors in the experimental images and verification of the experimental 3D atomic model using multi-slice simulations.

a, Angular errors in the experimental images determined by an angular refinement procedure (Methods), where the colour dots and lines represent the deviation of the three Euler angles (ϕ, θ and φ) from the correct ones (0°) at each tilt angle. These angular errors were taken into account in the multi-slice simulations. b, The angular errors were correctly refined in the 3D reconstruction of the 55 multi-slice images using RESIRE (Methods). After the angular refinement, the largest error is only 0.2°. c, d, Comparison between a representative experimental (after denoising) (c) and a multi-slice (d) image at 0°. To account for the source size and incoherence effects, each multi-slice image was convolved with a Gaussian function (Methods). e, Histogram of the deviation of the atomic positions between the experimental atomic model and that obtained from 55 multi-slice images. The peak, mean and root-mean-square deviation of the histogram are 6 nm, 15 nm and 21 pm, respectively. Scale bar, 2 nm.

Extended Data Fig. 5 3D distribution of the crystal nuclei in the glass-forming nanoparticle, partial coordination numbers and Voronoi polyhedra of the solute-centre clusters.

a, 3D distribution of the atoms with a normalized BOO parameter ≥0.5, revealing that 15.46% of the total atoms form crystal nuclei in the nanoparticle. b, Normalized partial coordination numbers of type-1, -2 and -3 atoms. c, 3D distribution of the 2,682 solute centres (red dots) that are between the first (3.78 Å) and the second (6.09 Å) minimum of the PDF curve (Fig. 1g). d, Ten most abundant Voronoi polyhedra of the solute-centre clusters.

Extended Data Fig. 6 Identification of MROs with a 1-Å radius cut-off.

a, Histogram of the four types of MRO—fcc- (blue), hcp- (red), bcc- (green) and sc-like (purple)—as a function of size (that is, the number of solute centres). b, Population of the solute-centre atoms for the four types of MRO. cj, Representative fcc- (c), hcp- (e), bcc- (g) and sc-like (i) MROs, containing 23, 18, 10 and 27 solute centres (large red spheres), respectively. The solute centres are orientated along the fcc (d), hcp (f), bcc (h) and sc (j) zone axes.

Extended Data Fig. 7 Identification of MROs with a 0.5-Å radius cut-off.

a, Histogram of the four types of MRO—fcc- (blue), hcp- (red), bcc- (green) and sc-like (purple)—as a function of size. b, Population of the solute-centre atoms for the four types of MRO. cj, Representative fcc- (c), hcp- (e), bcc- (g) and sc-like (i) MROs, containing 15, 10, 8 and 8 solute centres (large red spheres), respectively. The solute centres are orientated along the fcc (d), hcp (f), bcc (h) and sc (j) zone axes.

Extended Data Fig. 8 Tomographic tilt series of an amorphous CuTa thin film.

ADF-STEM images of a portion of the CuTa thin film. The insets show the 2D power spectra of the experimental images, in which the amorphous halo are clearly visible. Scale bar, 2 nm.

Extended Data Fig. 9 Determination of the 3D atomic structure of the amorphous CuTa thin film.

a, Large-field-of-view image of amorphous CuTa. b, Magnified image of the region in the white square in a. c, Average 2D power spectrum of all the experimental images. d, 3D atomic model of a portion of the CuTa thin film with a total of 1,808 Cu (gold) and 12,774 Ta (blue) atoms, determined from the tilt series shown in Extended Data Fig. 8 (Methods). Because the CuTa film is thinner than ~6 nm, 40 experimental images are sufficient to produce a good 3D reconstruction. e, A 2-Å-thick internal slice of the 3D reconstruction of the amorphous CuTa thin film, showing the disordered atomic structure. f, Local BOO parameters of the 3D atomic model, where only 0.47% of the total atoms with a normalized BOO parameter ≥0.5 form crystal nuclei. g, PDF of the disordered atoms with a normalized BOO parameter <0.5. Scale bars, 30 nm (a) and 2 nm (b, e).

Extended Data Table 1 AET data collection, processing, reconstruction, refinement and statistics

Supplementary information

Supplementary Information

This file contains details regarding the Data and Source Code Package and Supplementary Figures 1-4.

Video 1

Temperature measurement of the carbothermal shock process by a high-speed Phantom Miro M110 camera. The movie shows the colormap of the temperature distribution with an interval of 55 ms and a pixel size of 25 μm, where the inhomogeneity is due to the difference of the local heat transfer.

Video 2

Progressive slices of the 3D reconstruction of the multi-component glass-forming nanoparticle, showing the disordered nature of the nanoparticle and that the majority of type 3 atoms (red blobs) are distributed in the second coordination shell. Each slice corresponds to 0.347 Å thick.

Video 3

Experimental 3D atomic model of the multi-component glass-forming nanoparticle with type 1, 2 and 3 atoms in green, blue and red, respectively, which exhibits disordered atomic structure. Compared with type 1 and 2 atoms, type 3 atoms are more uniformly distributed in the 9-nm-diameter nanoparticle.

Video 4

3D distribution of the four types of the MROs in the multi-component glass-forming nanoparticle, where fcc-, hcp-, bcc- and sc-like MROs are in blue, red, green and purple, respectively. To better visualize the networks, only those with eight solute centre atoms or more are shown.

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

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