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Quasi-crystalline order in vibrating granular matter

Nature Physics volume 20, pages 465–471 (2024)Cite this article

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Abstract

Quasi-crystals are aperiodic structures with crystallographic properties that are not compatible with that of a single unit cell. Their discovery in a metallic alloy more than four decades ago has required a full reconsideration of our definition of a crystal structure. Quasi-crystalline structures have also been discovered at much larger length scales in different microscopic systems for which the size of the elementary building blocks ranges from the nanometre to the micrometre scale. Here we report the first experimental observation of spontaneous quasi-crystalline self-assembly at the millimetre scale. This result is obtained in a fully athermal system of macroscopic spherical grains vibrating on a substrate. Starting from a liquid-like disordered phase, the grains begin to locally arrange into three types of square and triangle tile that eventually align, forming an eight-fold symmetric quasi-crystal that has been predicted in simulation but not yet experimentally observed in non-atomic systems. These results not only demonstrate an alternative route for the spontaneous assembly of quasi-crystals but are of fundamental interest for the connection between equilibrium and non-equilibrium statistical physics.

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Fig. 1: Numerical results obtained with EDMD of a collisional model.
Fig. 2: Experimental results: time evolution.
Fig. 3: Experimental results: self-assembled structure.

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Data availability

Raw datasets generated during this study are available from the corresponding author on reasonable request. Source data are provided with this paper.

Code availability

The code of the EDMD simulations is available via GitHub at https://github.com/Syrocco/EDMD-QC8. The DEM simulations are implemented through the LAMMPS package available at https://www.lammps.org/.

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Acknowledgements

We thank A. Puglisi and A. Gnoli for their invaluable help in setting up this project and for their comments on the manuscript. We also thank M. Impéror-Clerc, L. Filion, A. Jagannathan and F. Sciortino for carefully reading and commenting on our paper and S. Cabaret for the design of the quasi-2D cell. This work has been done with the support of Investissements d’Avenir of LabEx PALM (grant no. ANR-10-LABX-0039-PALM) and of the Agence Nationale de la Recherche (ANR), grant ANR-18-CE09-0025.

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Authors and Affiliations

  1. Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, Orsay, France

    A. Plati, R. Maire, E. Fayen, F. Boulogne, F. Restagno, F. Smallenburg & G. Foffi

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Contributions

G.F. and F.S. conceived the work and supervised the research. A.P, F.R., F.B. and G.F. designed the experiment. A.P. performed the experimental research and analysed the experimental data. A.P., E.F. and R.M. designed the simulations. A.P. and R.M. performed the simulations and analysed the data from the simulations. A.P., F.S. and G.F. wrote the paper. All authors reviewed and commented on the paper and the Supplementary Information.

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Correspondence to A. Plati or G. Foffi.

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Nature Physics thanks Joshua Dijksman, Eva Noya and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–14 and discussion.

Supplementary Video 1

Spatial configuration, structure factor, reconstructed tiling and bond orientation histogram as a function of time.

Source data

Source Data Fig. 1

Full data sources for Fig. 1 in a multiple-tab Excel file.

Source Data Fig. 2

Full data sources for Fig. 2 in a multiple-tab Excel file.

Source Data Fig. 3

Full data sources for Fig. 3 in a multiple-tab Excel file.

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Plati, A., Maire, R., Fayen, E. et al. Quasi-crystalline order in vibrating granular matter. Nat. Phys. 20, 465–471 (2024). https://doi.org/10.1038/s41567-023-02364-1

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