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Kinetic pathways of crystallization at the nanoscale


Nucleation and growth are universally important in systems from the atomic to the micrometre scale as they dictate structural and functional attributes of crystals. However, at the nanoscale, the pathways towards crystallization have been largely unexplored owing to the challenge of resolving the motion of individual building blocks in a liquid medium. Here we address this gap by directly imaging the full transition of dispersed gold nanoprisms to a superlattice at the single-particle level. We utilize liquid-phase transmission electron microscopy at low dose rates to control nanoparticle interactions without affecting their motions. Combining particle tracking with Monte Carlo simulations, we reveal that positional ordering of the superlattice emerges from orientational disorder. This method allows us to measure parameters such as line tension and phase coordinates, charting the nonclassical nucleation pathway involving a dense, amorphous intermediate. We demonstrate the versatility of our approach via crystallization of different nanoparticles, pointing the way to more general applications.

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Fig. 1: Gold triangular nanoprisms crystallize hierarchically in 3D to an unexpected hexagonal lattice.
Fig. 2: Energetics and in situ observation of the crystallization process.
Fig. 3: Multi-step crystallization of a nanoparticle superlattice via a dense, amorphous liquid state as the intermediate.
Fig. 4: Positional ordering originates from orientational disorder.

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Data availability

The data that support the findings of this study are available from the corresponding authors upon request.

Code availability

Custom Matlab codes for image processing and particle tracking as well as the algorithms for the particle interactions and the MC simulations are available from the corresponding authors upon request.


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The experiments and analysis of the experimental data presented in this research were supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under award no. DE-FG02-07ER46471 through the Materials Research Laboratory at the University of Illinois (the nanoprism system) and the National Science Foundation through award no. DMR-1752517 (the concave nanocube and nanosphere systems). The theoretical model and simulations presented in this research were supported by the National Science Foundation through award no. DMR-1610796 and based upon work supported as part of the Center for Bio-Inspired Energy Science, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences under Award DE-SC0000989. Z.W. gratefully acknowledges support from a Ryan Fellowship and the International Institute for Nanotechnology at Northwestern University. We thank J. Kim for useful discussions.

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Authors and Affiliations



Z.O. and Q.C. designed and performed the experiments and analysed the data on the nanoprism system. Z.W. and E.L. designed the theoretical model and performed the simulations. B.L. performed the experiments on the concave nanocube and nanosphere systems. Z.O., Z.W., E.L. and Q.C. wrote the manuscript.

Corresponding authors

Correspondence to Erik Luijten or Qian Chen.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Video Legends 1–9, Notes 1–13, Figures 1–28, Tables 1–4 and references.

Supplementary Video 1

Synchronized liquid-phase TEM video showing the lattice vibration inside a large-scale hexagonal superlattice formed by triangular nanoprisms.

Supplementary Video 2

Liquid-phase TEM video of individual prisms moving on the SiNx substrate and the stacking process of a pair of prisms.

Supplementary Video 3

Monte Carlo simulation of hexagonal superlattice formation from 1472 triangular prisms.

Supplementary Video 4

Liquid-phase TEM video showing the disassembly and reassembly of the lattice when the electron beam is turned off or on.

Supplementary Video 5

Single-column Monte Carlo simulation showing the fluctuation of prism orientations inside a column.

Supplementary Video 6

Synchronized liquid-phase TEM video showing the formation of a large-scale superlattice.

Supplementary Video 7

Monte Carlo simulation of the formation of side-by-side aggregates from 576 triangular prisms.

Supplementary Video 8

Liquid-phase TEM video showing the crystallization of gold concave nanocubes into simple cubic superlattices.

Supplementary Video 9

Liquid-phase TEM video showing the crystallization of nanospheres into face-centred cubic superlattices.

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Ou, Z., Wang, Z., Luo, B. et al. Kinetic pathways of crystallization at the nanoscale. Nat. Mater. 19, 450–455 (2020).

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