Nucleation plays a critical role in many physical and biological phenomena that range from crystallization, melting and evaporation to the formation of clouds and the initiation of neurodegenerative diseases1,2,3. However, nucleation is a challenging process to study experimentally, especially in its early stages, when several atoms or molecules start to form a new phase from a parent phase. A number of experimental and computational methods have been used to investigate nucleation processes4,5,6,7,8,9,10,11,12,13,14,15,16,17, but experimental determination of the three-dimensional atomic structure and the dynamics of early-stage nuclei has been unachievable. Here we use atomic electron tomography to study early-stage nucleation in four dimensions (that is, including time) at atomic resolution. Using FePt nanoparticles as a model system, we find that early-stage nuclei are irregularly shaped, each has a core of one to a few atoms with the maximum order parameter, and the order parameter gradient points from the core to the boundary of the nucleus. We capture the structure and dynamics of the same nuclei undergoing growth, fluctuation, dissolution, merging and/or division, which are regulated by the order parameter distribution and its gradient. These experimental observations are corroborated by molecular dynamics simulations of heterogeneous and homogeneous nucleation in liquid–solid phase transitions of Pt. Our experimental and molecular dynamics results indicate that a theory beyond classical nucleation theory1,2,18 is needed to describe early-stage nucleation at the atomic scale. We anticipate that the reported approach will open the door to the study of many fundamental problems in materials science, nanoscience, condensed matter physics and chemistry, such as phase transition, atomic diffusion, grain boundary dynamics, interface motion, defect dynamics and surface reconstruction with four-dimensional atomic resolution.
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All the raw and processed experimental data can be freely downloaded at www.physics.ucla.edu/research/imaging/nucleation. All the seven experimental atomic models with 3D coordinates of particles 1, 2 and 3 have been deposited in the Materials Data Bank (MDB, www.materialsdatabank.org) with their MDB IDs provided in Extended Data Table 1.
All the MATLAB source codes for image reconstruction and data analysis of this work are freely available at www.physics.ucla.edu/research/imaging/nucleation.
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We thank W. A. Goddard III, J. Rudnick, A. Foi, L. Azzari and P. Sautet for discussions and T. Duden for assistance with experiments. This work was primarily supported by STROBE (a National Science Foundation Science and Technology Center) under grant no. DMR 1548924. We also acknowledge support by the Office of Basic Energy Sciences of the US DOE (DE-SC0010378) and the NSF DMREF program (DMR-1437263). 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.
Nature thanks Jim Lutsko, Peter Vekilov and the other anonymous reviewer(s) for their contribution to the peer review of this work.
The authors declare no competing interests.
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Extended data figures and tables
a, b, 3D atomic models (Pt in blue and Fe in red) of particle 1, obtained from two independent experimental measurements. c, d, Pt-rich cores cropped from the atomic models shown in a and b, respectively. e, f, The same atomic layer of the nanoparticle along the  direction (Pt in blue and Fe in red), obtained from the two independent measurements. Scale bar, 1 nm. g, Histogram of the deviation of the common atoms between the two independent measurements. By dividing the common atoms by the average number of atoms in the two measurements, we estimated that 95.4% of the atoms are consistent. The average deviation between the two independent measurements is 37 pm. According to the statistical analysis of error propagation, the precision of the AET measurement is 37 pm / √2 = 26 pm. (See Methods for details.).
a, ADF-STEM image of the FePt nanoparticles on a Si3N4 substrate. b–d, Energy-dispersive X-ray spectroscopy images showing the distribution of Fe (b), Pt (c), and both Fe and Pt atomic nanoclusters (d) between FePt nanoparticles; b–d were acquired simultaneously with the ADF-STEM image in a. e, Fitted spectrum of Fe (K edges) and Pt (L edges) from the region labelled with ellipses in b–d; c.p.s., counts per second. Scale bar, 10 nm.
a, b, 3D atomic models (Pt in blue and Fe in red) of particle 3 with a total annealing time of 9 min and 16 min, respectively, determined by AET. c, d, The Pt-rich core of the nanoparticle remained the same between the two annealing times. The light and dark grey projections show the whole nanoparticle and the core, respectively. e, f, The same atomic layer of the nanoparticle along the  direction at the two annealing times (Pt in and Fe in red), where a fraction of the surface and subsurface atoms were rearranged due to the annealing process, but the Pt-rich core of the nanoparticle did not change. Scale bar, 1 nm.
a, b, The distribution of the nucleation sites (dots) in particle 1 obtained from two independent measurements, where the lighter colour dots are closer to the front side and the darker dots are closer to the back side of the nanoparticle. The <100> and <111> facets are in green and magenta, respectively. c, Histogram of the nucleation site distribution in particle 1. Compared to particles 2 and 3, particle 1 has more nucleation sites at the subsurface, because many nuclei in particle 1 are relatively large and their cores are at a distance of more than one unit cell from the surface. d, e, The distribution of the nucleation sites (dots) in particle 3 with an annealing time of 9 min and 16 min, respectively. f, Histogram of the nucleation site distribution in particle 3. g, The order parameter of the nucleus core as a function of the effective number of atoms for particles 2 and 3. h, The sphericity of the nuclei as a function of the effective number of atoms for particles 2 and 3. i, j, The sphericity of the nuclei in the MD simulations of a Pt nanoparticle (i; heterogeneous nucleation) and a bulk Pt system (j; homogeneous nucleation) as a function of the effective number of atoms.
a–d, Four representative growing nuclei in particle 2 with a total annealing time of 9 min, 16 min and 26 min, respectively. The atomic models show Fe (red) and Pt atoms (blue) with an order parameter ≥0.3, and the 3D contour maps show the distribution of an order parameter of 0.7 (red), 0.5 (purple) and 0.3 (light blue). Dividing and merging nuclei are observed in b–d. e–h, Another four representative growing nuclei in particle 2 with a total annealing time of 9 min, 16 min and 26 min, where the 3D contour maps show the distribution of an order parameter of 0.7 (red), 0.5 (purple), 0.3 (light blue), 0.2 (green) and 0.1 (grey). No atomic model is displayed if a corresponding common nucleus was not identified at a specific annealing time. Another five growing nuclei in particle 3 similar to those in e–h are not shown here.
a–e, Five representative fluctuating nuclei in particle 2 with a total annealing time of 9 min, 16 min and 26 min, respectively. The atomic models show Fe (red) and Pt atoms (blue) with an order parameter ≥0.3, and the 3D contour maps show the distribution of an order parameter of 0.7 (red), 0.5 (purple) and 0.3 (blue). Merging and dividing nuclei are observed in e. f–k, Another six representative fluctuating nuclei in particle 2 with a total annealing time of 9 min, 16 min and 26 min. The 3D contour maps show the distribution of an order parameter of 0.7 (red), 0.5 (purple), 0.3 (light blue), 0.2 (green) and 0.1 (grey). No atomic model is displayed if a corresponding common nucleus was not identified at a specific annealing time.
Extended Data Fig. 7 Experimental observation of dissolving nuclei and radial average order parameter distributions of nine representative nuclei.
a–d, Four dissolving nuclei in particle 2 with a total annealing time of 9 min, 16 min and 26 min. The 3D contour maps show the distribution of an order parameter of 0.7 (red), 0.5 (purple), 0.3 (light blue), 0.2 (green) and 0.1 (grey). No atomic model is displayed if a corresponding common nucleus was not identified at a specific annealing time. e–m, The order parameter distributions for four growing nuclei (e–h), four fluctuating nuclei (i–l) and one dissolving nucleus (m) in particle 2. The dots represent the experimentally measured data and the curves are fits of equation (1).
Extended Data Fig. 8 Nucleation dynamics in the liquid–solid transition of a Pt nanoparticle, obtained by MD simulations with the interface force field.
a, A representative growing nucleus, where the atomic models show the Pt atoms with an order parameter ≥0.3 and the 3D contour maps show the distribution of an order parameter of 0.7 (dark blue), 0.5 (light blue) and 0.3 (cyan). b, c, Two representative fluctuating nuclei, where merging and dividing nuclei are observed in c. d, A representative dissolving nucleus, which dissolved at 245 ps. e–h, Radial average order parameter distributions of the four nuclei shown in a–d, respectively, where the dots were obtained by time-averaging ten consecutive MD snapshots with 1-ps time intervals and the curves are fits of equation (1) using a constant background.
Extended Data Fig. 9 Nucleation dynamics in the liquid–solid transition of a bulk Pt system, obtained by MD simulations with the embedded-atom-method potential.
a, A representative growing nucleus, where the atomic models show the Pt atoms with an order parameter ≥0.3 and the 3D contour maps show the distribution of an order parameter of 0.7 (dark blue), 0.5 (light blue) and 0.3 (cyan). b, c, Two representative fluctuating nuclei, where merging and dividing nuclei are observed in c. d, A representative dissolving nucleus, which dissolved at 140 ps. e–h, Radial average order parameter distributions of the four nuclei shown in a–d, respectively, where the dots were obtained by time-averaging ten consecutive MD snapshots with 1-ps time intervals and the curves are fits of equation (1) using a constant background.
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Zhou, J., Yang, Y., Yang, Y. et al. Observing crystal nucleation in four dimensions using atomic electron tomography. Nature 570, 500–503 (2019). https://doi.org/10.1038/s41586-019-1317-x
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