Entropic formation of a thermodynamically stable colloidal quasicrystal with negligible phason strain

Significance Quasicrystals––ordered crystals lacking translational periodicity––occur in systems comprising building blocks ranging from atoms to nanoparticles. These quasicrystals can have the same structure despite the obvious differences in building-block type or size. Do they all form in the same way? Or do colloidal quasicrystals grow differently than atomic quasicrystals? We study the formation of a colloidal quasicrystal in a hard tetrahedron system, where structural ordering is solely governed by entropy. We observe that the colloidal quasicrystal forms with high structural quality when simulations begin in the melt. We also find that structural imperfections in approximant crystals can be repaired by the relaxation process observed during quasicrystal formation. This demonstrates that our quasicrystal is thermodynamically stable.