Formation of a stable colloidal quasicrystal with negligible phason strain

Quasicrystals occur in systems comprised of building blocks ranging from atoms to molecules to nanoparticles,suggesting that there are mechanisms for quasicrystal formation and stabilization independent of building block type or size. Yet, mechanisms of quasicrystal formation have only been clearly demonstrated in alloys, where quasicrystals grow imperfectly with phason strain, and only perfect themselves later into a high-quality quasicrystal with negligible strain. Such formation mechanism leading to high-quality quasicrystals has not been reported in other types of quasicrystals, such as soft matter quasicrystals consisting of colloids or polymers. Here, we study the formation of a colloidal dodecagonal quasicrystal (DQC) in a hard tetrahedron system via Monte Carlo simulations. We find that phason strain remains small during DQC growth and only weakly relaxes further, resulting in a high-quality DQC with negligible phason strain directly from the melt. We also observe that a quasicrystal approximant with inherent phason strain transform to the DQC via continuous phason strain relaxation. These results demonstrate that the DQC can be stable over approximants and be grown with high structural quality as in alloy quasicrystals.