Using computer simulations, we study the phase behavior of a model system of colloidal hard disks with a diameter σ and a soft corona of width 1.4σ. The particles interact with a hard core and a repulsive square-shoulder potential. We calculate the free energy of the random-tiling quasicrystal and its crystalline approximants using the Frenkel-Ladd method. We explicitly account for the configurational entropy associated with the number of distinct configurations of the random-tiling quasicrystal. We map out the phase diagram and find that the random tiling dodecagonal quasicrystal is stabilised by entropy at finite temperatures with respect to the crystalline approximants that we considered, and its stability region seems to extend to zero temperature as the energies of the defect-free quasicrystal and the crystalline approximants are equal within our statistical accuracy.

Using Monte Carlo simulations and free-energy calculations, we investigate the phase behaviour of a two-dimensional core-corona system. We model this system as particles consisting of an impenetrable hard core of diameter σ surrounded by a purely repulsive soft corona of diameter δ = 1.95σ. At low densities, we observe the spontaneous formation of a phase with a stripe texture as well as a honeycomb-like phase driven by both energy and entropy considerations. At high densities, we find that a two-dimensional analogue of the periodic sigma phase, considered as an approximant of dodecagonal quasicrystals, is energetically stabilised with respect to two distinct dodecagonal quasicrystals, namely, a square-triangle tiling and a square-triangle-shield tiling. We also find the formation of stable hexagonal phases at three distinct density ranges, which are energetically driven, i.e. by minimising the overlap of coronas. Furthermore, our calculations show that the low-density dodecagonal quasicrystal that was previously reported by Dotera et al., [Nature, 2014, 506, 208] is kinetically formed in the coexistence region between the honeycomb and the medium-density hexagonal phase.

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 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=1.27σ,1.40σ, and 1.60σ, 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.

Using computer simulations, we investigate the phase behavior of a system of particles interacting with a remarkably simple repulsive square-shoulder pair potential and report the formation of a novel (and stable) pyrochlorelike crystal phase. The lattice structure of the pyrochlorelike phase formed in our simulations possesses two inherent length scales corresponding to the inter- and intratetrahedral neighbors. We show that it can be used to fabricate a photonic crystal which displays complete photonic band gaps in both the direct and inverted dielectric structures.

A two-dimensional dodecagonal quasicrystal was previously reported by Dotera et al (2014 Nature 506 208) in a system of particles interacting with a hard core of diameter σ and a repulsive square shoulder of diameter [Formula: see text]. In the current work, we examine the formation of this quasicrystal using bond orientational order parameters, correlation functions and tiling distributions. We find that this dodecagonal quasicrystal forms from a fluid phase. We further study the effect of the width of the repulsive shoulder by simulating the system over a range of values of δ. For the range of densities and temperatures considered, we observe the formation of the dodecagonal quasicrystal between [Formula: see text] and [Formula: see text]. We also study the effect of shape of the interaction potential by simulating the system using three other interaction potentials with two length scales, namely hard-core plus a linear ramp, modified exponential, or Buckingham (exp-6) potential. We observe the presence of the quasicrystal in all three systems. However, depending on the shape of the potential, the formation of the quasicrystal takes place at lower temperatures (or higher interaction strengths). Using free-energy calculations, we demonstrate that the quasicrystal is thermodynamically stable in the square-shoulder and linear-ramp system.