Entropy strikes again: stabilizing quasicrystals of hard spheres


Tuesday, February 27, 2024
15:00 - 17:00


Quasicrystals are exotic materials that break the traditional rules of crystallography. Like crystals, quasicrystals are highly ordered, and composed of a limited number of repeated units. However, unlike crystals, they are aperiodic, and can possess `forbidden' symmetries not found in typical crystals. Since their controversial discovery in the 1980s, quasicrystals have been found in a variety of metal alloys, as well as in a growing number of soft-matter systems, including nanoparticles, polymers, and micelles.

In this talk, we will explore how a phase as complex as a quasicrystal can be stabilized by entropy alone, starting from perhaps the simplest soft-matter model available: hard spheres. Using packing and entropy arguments, we predict that binary mixtures of hard spheres deposited onto a flat plane should form a dodecagonal quasicrystal at high densities. Simulations then confirm that these systems can indeed spontaneously self-assemble into the predicted quasicrystal... as well as into another unexpected quasicrystal with octagonal symmetry! Free-energy calculations on the dodecagonal quasicrystal reveal the reason for its stability: the configurational entropy arising from the high number of possible realizations that make up the same quasicrystal phase. Finally, I will briefly highlight recent experiments demonstrating the self-assembly of a granular quasicrystal of millimeter-sized steel spheres.

[1]Self-assembly of dodecagonal and octagonal quasicrystals in hard spheres on a plane, E. Fayen, M. Impéror-Clerc, L. Filion, G. Foffi, and F. Smallenburg, Soft Matter 19, 2654 (2023)
[2]A hard-sphere quasicrystal stabilized by configurational entropy, E. Fayen, L. Filion, G. Foffi, F. Smallenburg, Physical Review Letters 132, 048202 (2024).
[3]Quasi-crystalline order in vibrated granular matter,
A. Plati, R. Maire, E. Fayen, F. Boulogne, F. Restagno, F. Smallenburg, G. Foffi,
Nature Physics (2024) https://doi.org/10.1038/s41567-023-02364-1


Condensed Matter Theory group


UvA - Faculty of Science

Room number



Group Seminar


computational physics, condensed matter theory, soft matter


Frank Smallenburg (Université Paris-Saclay)

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