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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.

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.


  1. 1.

    De Yoreo, J. J. et al. Crystallization by particle attachment in synthetic, biogenic, and geologic environments. Science 349, aaa6760 (2015).

    Article  Google Scholar 

  2. 2.

    Loh, N. D. et al. Multistep nucleation of nanocrystals in aqueous solution. Nat. Chem. 9, 77–82 (2017).

    CAS  Article  Google Scholar 

  3. 3.

    Li, B., Zhou, D. & Han, Y. Assembly and phase transitions of colloidal crystals. Nat. Rev. Mater. 1, 15011 (2016).

    CAS  Article  Google Scholar 

  4. 4.

    Henzler, K. et al. Supersaturated calcium carbonate solutions are classical. Sci. Adv. 4, eaao6283 (2018).

    Article  Google Scholar 

  5. 5.

    Chen, J., Sarma, B., Evans, J. M. B. & Myerson, A. S. Pharmaceutical crystallization. Cryst. Growth Des. 11, 887–895 (2011).

    CAS  Article  Google Scholar 

  6. 6.

    John, S. Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486–2489 (1987).

    CAS  Article  Google Scholar 

  7. 7.

    Choi, J.-H. et al. Exploiting the colloidal nanocrystal library to construct electronic devices. Science 352, 205–208 (2016).

    CAS  Article  Google Scholar 

  8. 8.

    Noorduin, W. L., Grinthal, A., Mahadevan, L. & Aizenberg, J. Rationally designed complex, hierarchical microarchitectures. Science 340, 832–837 (2013).

    CAS  Article  Google Scholar 

  9. 9.

    Ten Wolde, P. R. & Frenkel, D. Enhancement of protein crystal nucleation by critical density fluctuations. Science 277, 1975–1978 (1997).

    Article  Google Scholar 

  10. 10.

    Ducrot, É., He, M., Yi, G.-R. & Pine, D. J. Colloidal alloys with preassembled clusters and spheres. Nat. Mater. 16, 652–657 (2017).

    CAS  Article  Google Scholar 

  11. 11.

    Zhang, T. H. & Liu, X. Y. How does a transient amorphous precursor template crystallization. J. Am. Chem. Soc. 129, 13520–13526 (2007).

    CAS  Article  Google Scholar 

  12. 12.

    Tan, P., Xu, N. & Xu, L. Visualizing kinetic pathways of homogeneous nucleation in colloidal crystallization. Nat. Phys. 10, 73–79 (2013).

    Article  Google Scholar 

  13. 13.

    Kenneth, G. L. The physics of snow crystals. Rep. Prog. Phys. 68, 855–895 (2005).

    Article  Google Scholar 

  14. 14.

    Ye, X. et al. Quasicrystalline nanocrystal superlattice with partial matching rules. Nat. Mater. 16, 214–219 (2017).

    CAS  Article  Google Scholar 

  15. 15.

    Xia, Y. et al. Self-assembly of self-limiting monodisperse supraparticles from polydisperse nanoparticles. Nat. Nanotechnol. 6, 580–587 (2011).

    CAS  Article  Google Scholar 

  16. 16.

    Lin, H. et al. Clathrate colloidal crystals. Science 355, 931–935 (2017).

    CAS  Article  Google Scholar 

  17. 17.

    Batista, C. A., Larson, R. G. & Kotov, N. A. Nonadditivity of nanoparticle interactions. Science 350, 1242477 (2015).

    Article  Google Scholar 

  18. 18.

    De Yoreo, J. J. & Sommerdijk, N. A. J. M. Investigating materials formation with liquid-phase and cryogenic TEM. Nat. Rev. Mater. 1, 16035 (2016).

    Article  Google Scholar 

  19. 19.

    Park, J. et al. 3D structure of individual nanocrystals in solution by electron microscopy. Science 349, 290–295 (2015).

    CAS  Article  Google Scholar 

  20. 20.

    Liao, H.-G., Cui, L., Whitelam, S. & Zheng, H. Real-time imaging of Pt3Fe nanorod growth in solution. Science 336, 1011–1014 (2012).

    CAS  Article  Google Scholar 

  21. 21.

    Sutter, E. et al. In situ microscopy of the self-assembly of branched nanocrystals in solution. Nat. Commun. 7, 11213 (2016).

    CAS  Article  Google Scholar 

  22. 22.

    Schneider, N. M. et al. Electron–water interactions and implications for liquid cell electron microscopy. J. Phys. Chem. C. 118, 22373–22382 (2014).

    CAS  Article  Google Scholar 

  23. 23.

    Kim, J., Ou, Z., Jones, M. R., Song, X. & Chen, Q. Imaging the polymerization of multivalent nanoparticles in solution. Nat. Commun. 8, 761 (2017).

    Article  Google Scholar 

  24. 24.

    Agarwal, U. & Escobedo, F. A. Mesophase behaviour of polyhedral particles. Nat. Mater. 10, 230–235 (2011).

    CAS  Article  Google Scholar 

  25. 25.

    Jones, M. R. et al. DNA-nanoparticle superlattices formed from anisotropic building blocks. Nat. Mater. 9, 913–917 (2010).

    CAS  Article  Google Scholar 

  26. 26.

    Fraser, D. P., Zuckermann, M. J. & Mouritsen, O. G. Simulation technique for hard-disk models in two dimensions. Phys. Rev. A 42, 3186–3195 (1990).

    CAS  Article  Google Scholar 

  27. 27.

    Savage, J. R., Blair, D. W., Levine, A. J., Guyer, R. A. & Dinsmore, A. D. Imaging the sublimation dynamics of colloidal crystallites. Science 314, 795–798 (2006).

    CAS  Article  Google Scholar 

  28. 28.

    Liu, W. et al. Diamond family of nanoparticle superlattices. Science 351, 582–586 (2016).

    CAS  Article  Google Scholar 

  29. 29.

    Sauter, A. et al. On the question of two-step nucleation in protein crystallization. Faraday Discuss. 179, 41–58 (2015).

    CAS  Article  Google Scholar 

  30. 30.

    Lutsko, J. F. & Nicolis, G. Theoretical evidence for a dense fluid precursor to crystallization. Phys. Rev. Lett. 96, 046102 (2006).

    Article  Google Scholar 

  31. 31.

    Auer, S. & Frenkel, D. Prediction of absolute crystal-nucleation rate in hard-sphere colloids. Nature 409, 1020–1023 (2001).

    CAS  Article  Google Scholar 

  32. 32.

    Donev, A., Burton, J., Stillinger, F. H. & Torquato, S. Tetratic order in the phase behavior of a hard-rectangle system. Phys. Rev. B 73, 054109 (2006).

    Article  Google Scholar 

  33. 33.

    Timmermans, J. Plastic crystals: a historical review. J. Phys. Chem. Solids 18, 1–8 (1961).

    CAS  Article  Google Scholar 

  34. 34.

    Liu, B. et al. Switching plastic crystals of colloidal rods with electric fields. Nat. Commun. 5, 3092 (2014).

    Article  Google Scholar 

  35. 35.

    Boles, M. A., Engel, M. & Talapin, D. V. Self-assembly of colloidal nanocrystals: from intricate structures to functional materials. Chem. Rev. 116, 11220–11289 (2016).

    CAS  Article  Google Scholar 

  36. 36.

    Gruebele, M., Dave, K. & Sukenik, S. Globular protein folding in vitro and in vivo. Annu. Rev. Biophys. 45, 233–251 (2016).

    CAS  Article  Google Scholar 

  37. 37.

    Nikoobakht, B. & El-Sayed, M. A. Preparation and growth mechanism of gold nanorods (NRs) using seed-mediated growth method. Chem. Mater. 15, 1957–1962 (2003).

    CAS  Article  Google Scholar 

  38. 38.

    O’Brien, M. N., Jones, M. R., Brown, K. A. & Mirkin, C. A. Universal noble metal nanoparticle seeds realized through iterative reductive growth and oxidative dissolution reactions. J. Am. Chem. Soc. 136, 7603–7606 (2014).

    Article  Google Scholar 

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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.

Author information




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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