Phase behaviour of quasicrystal forming systems of core-corona particles

Using Monte Carlo simulations and free-energy calculations, we study the phase behaviour of a two-dimensional system of particles interacting with a hard core of diameter $σ H D$ and a repulsive square shoulder potential. The interest in this system lies in the formation of quasicrystals of different symmetries at specific square-shoulder widths δ as previously reported by Dotera et al. [Nature 506, 208 (2014)]. However, an insight into other possible periodic phases formed in these systems and the thermodynamic stability of both the periodic and quasicrystal phases is yet to be addressed. Here, we study the phase behaviour and map out the phase diagrams for three different shoulder widths $δ = 1.27 σ H D , 1.40 σ H D$⁠, and $1.60 σ H D$⁠, where octadecagonal, dodecagonal, and decagonal quasicrystals were previously reported. In addition, we verify the thermodynamic stability of these quasicrystals with respect to their periodic approximants. In general, we find that the system at all three shoulder widths forms hexagonal phases in two distinct density ranges due to the two characteristic length scales in the interaction potential. Further, we find that the dodecagonal and octadecagonal quasicrystals are stable in between two crystal phase regimes. In contrast, the decagonal quasicrystal is not bounded by a low-density crystal phase regime due to the lower density of this quasicrystal. From the free-energy calculations, we find indications that the decagonal and dodecagonal quasicrystals are thermodynamically stable with respect to their approximants, and the octadecagonal quasicrystal is stabilised by a configurational entropy contribution.