Vacancy defects in square-triangle tilings and their implications for quasicrystals formed by square-shoulder particles

TL;DR

This study explores how point-like defects in square-triangle quasicrystals increase configurational entropy, stabilizing the phase, with implications for soft-matter quasicrystal design and understanding defect roles.

Contribution

It introduces a Monte Carlo simulation for defect entropy in square-triangle tilings and links defect concentration to phase stability in soft-matter quasicrystals.

Findings

Defects significantly increase configurational entropy.

Higher defect concentration stabilizes the quasicrystal phase.

Entropy gain is amplified by mixing different defect types.

Abstract

Almost all observed square-triangle quasicrystals in soft-matter systems contain a large number of point-like defects, yet the role these defects play in stabilizing the quasicrystal phase remains poorly understood. In this work, we investigate the thermodynamic role of such defects in the widely observed 12-fold symmetric square-triangle quasicrystal. We develop a new Monte Carlo simulation to compute the configurational entropy of square-triangle tilings augmented to contain two types of irregular hexagons as defect tiles. We find that the introduction of defects leads to a notable entropy gain, with each defect contributing considerably more than a conventional vacancy in a periodic crystal. Intriguingly, the entropy gain is not simply due to individual defect types but isamplified by their combinatorial mixing. We then apply our findings to a microscopic model of core-corona particles interacting via a square-shoulder potential. By combining the configurational entropy with vibrational free-energy calculations, we predict the equilibrium defect concentration and confirm that the quasicrystalline phase contains a higher concentration of point-defects than a typical periodic crystal. These results provide a new understanding of the prominence of observed defects in soft-matter quasicrystals.