The effect of temperature, interaction range, and pair potential on the formation of dodecagonal quasicrystals in core-corona systems

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 anda repulsive square shoulder of diameter = 1.40. In the current work, we examine theformation of this quasicrystal using bond orientational order parameters, correlation functionsand 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 = 1.30 and 1.44. 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 freeenergy calculations, we demonstrate that the quasicrystal is thermodynamically stable in the
square-shoulder and linear-ramp system.
Keywords: dodecagonal quasicrystal, free energy, phase diagram