A hard-sphere quasicrystal stabilized by configurational entropy

Abstract

Due to their aperiodic nature, quasicrystals are one of the least understood phases in statistical physics. One significant complication they present in comparison to their periodic counterparts is the fact that any quasicrystal can be realized as an exponentially large number of different tilings, resulting in a significant contribution to the quasicrystal entropy. Here, we use free-energy calculations to demonstrate that it is this configurational entropy which stabilizes a dodecagonal quasicrystal in a binary mixture of hard spheres on a plane. Our calculations also allow us to quantitatively confirm that in this system all tiling realizations are essentially equally likely, with free-energy differences less than 0.0001$k_{B}T$ per particle -- an observation that could be the related to the observation of only random tilings in soft matter quasicrystals. Owing to the simplicity of the model and its available counterparts in colloidal experiments, we believe that this system is a excellent candidate to achieve the long-awaited quasicrystal self-assembly on the micron scale.

Contains an SI as ancillary file

References in corpus (5)

• Determination of phase diagrams via computer simulation: Methodology and applications to water, electrolytes and proteins
• Self-Assembly of Monatomic Complex Crystals and Quasicrystals with a Double-Well Interaction Potential
• Quasicrystalline Nanocrystal Superlattice with Partial Matching Rules
• Soft quasicrystals - Why are they stable?
• Stabilizing quasicrystals composed of patchy colloids by narrowing the patch width

Cited by in corpus (9)

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• Quasicrystal bulk and surface energies from density functional theory
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• Beating the aliasing limit with aperiodic monotile arrays
• Atomistic mechanisms of dynamics in a two-dimensional dodecagonal quasicrystal
• Defects Enhance Stability in 12-fold Symmetric Soft-Matter Quasicrystals
• A patchy-particle 3-dimensional octagonal quasicrystal
• Inflation rules for a chiral pentagonal quasiperiodic tiling of stars and hexes