Defects Enhance Stability in 12-fold Symmetric Soft-Matter Quasicrystals

Quasicrystals are materials that exhibit long-range order without translational periodicity. In soft matter, the most commonly observed quasicrystal has 12-fold symmetry and consists of tilings made out of squares and triangles. Intriguingly, both in experiments and simulations, these tilings nearly always appear with many point defects. These defects can be decomposed into squares, triangles, and an additional tile: a rhombus. In this Letter, we explore how rhombus tiles change the entropy of square-triangle 12-fold quasicrystals. We introduce a novel lattice-based Monte Carlo simulation method that uses open boundaries to allow the concentration of different tile types to fluctuate. Our simulations show that rhombus tiles significantly increase the configurational entropy of the quasicrystal phase, enhancing its stability. These findings highlight the critical role of defects in stabilizing soft-matter quasicrystals.