The influence of geometry on the local and global packing of particles is important to many fundamental and applied research themes, such as the structure and stability of liquids, crystals and glasses. Here we show by experiments and simulations that a binary mixture of hard-sphere-like nanoparticles crystallizing into a MgZn2 Laves phase in bulk spontaneously forms icosahedral clusters in slowly drying droplets. Using advanced electron tomography, we are able to obtain the real-space coordinates of all the spheres in the icosahedral clusters of up to about 10,000 particles. The local structure of 70–80% of the particles became similar to that of the MgCu2 Laves phase. These observations are important for photonic applications. In addition, we observed in simulations that the icosahedral clusters nucleated away from the spherical boundary, which is distinctly different from that of the single species clusters. Our findings open the way for particle-level studies of nucleation and growth of icosahedral clusters, and of binary crystallization.
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All data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.
Computer simulations were performed using HOOMD-blue, available at http://glotzerlab.engin.umich.edu/hoomd-blue/.
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D.W., E.B.v.d.W. and A.v.B. acknowledge partial financial support from the European Research Council under the European Union’s Seventh Framework Programme (FP-2007-2013)/ERC Advanced Grant Agreement 291667 HierarSACol. T.D. and M.D. acknowledge financial support from the Industrial Partnership Programme, ‘Computational Sciences for Energy Research’ (grant number 13CSER025), of the Netherlands Organization for Scientific Research (NWO), which was co-financed by Shell Global Solutions International BV G.M.C. was also financially supported by NWO. S.B. acknowledges financial support from ERC Consolidator Grant Number 815128 REALNANO. T.A. acknowledges a post-doctoral grant from the Research Foundation Flanders (FWO, Belgium). C.B.M. and Y.W. acknowledge support for materials synthesis from the Office of Naval Research Multidisciplinary University Research Initiative Award ONR N00014-18-1-2497. G. A. Blab is gratefully acknowledged for 3D printing numerous truncated tetrahedra, which increased our understanding of the connection between the binary icosahedral cluster and Laves phase structures. N. Tasios is sincerely thanked for providing the code for the diffraction pattern calculation. M. Hermes is sincerely thanked for providing interactive views of the structures in this work. We thank G. van Tendeloo, M. Engel, J. Wang, S. Dussi, L. Filion, E. Boattini, S. Paliwal, N. Tasios, B. van der Meer, I. Lobato, J. Wu and L. Laurens for fruitful discussions. We acknowledge the EM Square centre at Utrecht University for the access to the microscopes.
The authors declare no competing interests.
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Supplementary methods, Tables 1 and 2, Figs. 1–13 and refs. 1–12.
Crystal structure of the MgZn2 Laves phase.
Crystal structure of the MgCu2 Laves phase.
Crystal structure of the MgNi2 Laves phase.
An experimental binary icosahedral cluster supraparticle composed of 2,609 nanocrystals, with a size ratio of 0.78.
A simulated binary icosahedral cluster supraparticle composed of 5,001 HS-like particles with a size ratio of 0.78, after compression.
Cluster made up of the first eight shells from the centre of symmetry, of a simulated binary icosahedral cluster supraparticle composed of 5,001 HS-like particles with a size ratio of 0.78, after compression.
Cluster made up of the first eight shells from the centre of symmetry, of an experimental binary icosahedral cluster supraparticle composed of 2,609 nanocrystals.
Pentagonal tubes composed of alternating pentagons of L and S particles, in a simulated binary icosahedral cluster supraparticle composed of 5,001 HS-like particles with a size ratio of 0.78, after compression.
Pentagonal tubes composed of alternating pentagons of L and S particles, in an experimental binary icosahedral cluster supraparticle composed of 2,609 nanocrystals.
HAADF-STEM tilt series of an experimental binary icosahedral cluster supraparticle with a diameter of 110 nm, consisting of 2,609 nanocrystals.
Three-dimensional representation and orthoslices views of the reconstructed binary icosahedral cluster supraparticle with a diameter of 110 nm by SSR algorithm. Large PbSe nanocrystals and small CdSe nanocrystals are coloured in cyan and red, respectively.
HAADF-STEM tilt series of an experimental binary icosahedral cluster supraparticle with a diameter of 187 nm, consisting of 9,898 nanocrystals.
Three-dimensional representation and orthoslices views of the reconstructed binary icosahedral cluster supraparticle with a diameter of 187 nm by SSR algorithm. Large PbSe nanocrystals and small CdSe nanocrystals are coloured in cyan and red, respectively.
A video showing the nucleation of a binary icosahedral cluster in computer simulation (Ntot = 5,001). Different crystalline domains are shown in different colours. Particles not belonging to the binary icosahedral cluster are reduced in size for visual clarity.
Coordinates of six experimental supraparticles and two simulated supraparticles composed of Ntot = 3,501 and Ntot = 5,001 HS-like particles.
Coordinates of a simulated supraparticles composed of Ntot = 10,002 HS-like particles.
Plots of the fraction of crystalline particles as a function of the radial distance from the centre of the supraparticle (Ntot = 5,001) at different molecular dynamics times.
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Wang, D., Dasgupta, T., van der Wee, E.B. et al. Binary icosahedral clusters of hard spheres in spherical confinement. Nat. Phys. 17, 128–134 (2021). https://doi.org/10.1038/s41567-020-1003-9
Nature Communications (2021)