Self-assembly of dodecagonal and octagonal quasicrystals in hard spheres on a plane

TL;DR

This study demonstrates that simple binary mixtures of hard spheres on a plane can reliably self-assemble into dodecagonal and octagonal quasicrystals, providing an accessible model for exploring quasicrystal formation.

Contribution

It introduces a minimal colloidal model system that spontaneously forms two distinct quasicrystal phases, expanding understanding of quasicrystal self-assembly in simple particle systems.

Findings

Binary hard sphere mixtures form quasicrystals on a plane.

Both dodecagonal and octagonal quasicrystals are observed.

The octagonal phase's tile composition can be tuned continuously.

Abstract

Quasicrystals are fascinating structures, characterized by strong positional order but lacking the periodicity of a crystal. In colloidal systems, quasicrystals are typically predicted for particles with complex or highly specific interactions, which makes experimental realization difficult. Here, we propose an ideal colloidal model system for quasicrystal formation: binary mixtures of hard spheres sedimented onto a flat substrate. Using computer simulations, we explore both the close-packing and spontaneous self-assembly of these systems over a wide range of size ratios and compositions. Surprisingly, we find that this simple, effectively two-dimensional model systems forms not only a variety of crystal phases, but also two quasicrystal phases: one dodecagonal and one octagonal. Intriguingly, the octagonal quasicrystal consists of three different tiles, whose relative concentrations can be continuously tuned via the composition of the binary mixture. Both phases form reliably and rapidly over a significant part of parameter space, making hard spheres on a plane an ideal model system for exploring quasicrystal self-assembly on the colloidal scale.