Self-assembly of quasi-crystals on a human scale

Image in real space, structure factor, quasi-crystalline mosaic reconstructed after approximately 170 hours of experiments.

The physicists from the Laboratory of Solid State Physics (CNRS/Université Paris-Saclay) have demonstrated that quasi-crystals, the ordered aperiodic structures, are not confined to the atomic or microscopic domain but can spontaneously form on the millimeter scale.

Quasi-crystals constitute a category of ordered and non-periodic solids. Their discovery by Shechtman and colleagues in 1982 (Nobel Prize in Chemistry in 2011) has profoundly altered our understanding of crystalline structure and order in solids. Due to their mechanical, elastic, thermal, and optical properties, they hold significant potential for technological advancements in the fields of metallurgy, electronics, as well as optics and photonics.

Until now, the self-assembly of quasi-crystals has been limited to atomic, nanometric, and micrometric scales. At these scales, thermal agitation plays a predominant role in the formation of these groundbreaking structures. However, no quasi-crystal had been observed at a larger scale, where thermal agitation is absent.

Physicists from the Laboratory of Solid State Physics (LPS) at CNRS/Université Paris-Saclay, through collaboration between the Soft Interfaces and Theory teams, have successfully generated quasi-crystals using millimeter-sized steel balls. By placing a single layer of balls on a vibrating metal plate, they confirmed the emergence of a quasi-crystal under conditions previously predicted by statistical equilibrium mechanics.

The trick is to use two slightly different sizes of balls, as the smaller ones can pass underneath the larger ones—a technique previously employed with colloidal systems but never before with macroscopic systems. Initially, this might suggest that vibrations simply play the role of thermal agitation, but the researchers demonstrated that the underlying dynamics of self-assembly are distinct and more complex. It is rooted in the realm of non-equilibrium statistical physics, a domain attempting to go beyond simple thermal agitation and is much less understood. This work is published in the journal Nature Physics on January 19, 2024.

This result opens a new avenue for self-assembly that could be of interest to a broad range of researchers in fundamental physics (equilibrium and non-equilibrium statistical mechanics) and applied physics (granular systems and active matter). In practical applications, just as atomic crystals can be designed to produce specific electronic properties, it has been demonstrated that granular crystals can function as a switch, rectifier, and logical element for sound conduction.


Soft Interfaces group (MMOI)
Theory group (THEO)


LabEx PALM (grant no. ANR-10-LABX0039-PALM) and of
Agence Nationale de la Recherche (ANR), grant ANR-18-CE09-0025.


A. Plati , R. Maire, E. Fayen, F. Boulogne   , F. Restagno   , F. Smallenburg    & G. Foffi : Quasi-crystalline order in vibrating granular matter. Nature Physics 2024,