Stability of Two-Dimensional Soft Quasicrystals

TL;DR

This paper investigates the stability of various two-dimensional soft quasicrystals using a numerical projection method to compute free energies, revealing conditions under which different quasicrystals are stable or metastable.

Contribution

It introduces a unified numerical framework to accurately compute free energies of 2D soft quasicrystals, enabling detailed phase diagram construction for the Lifshitz-Petrich model.

Findings

Dodecagonal and decagonal quasicrystals can be stable phases.

Octagonal quasicrystal remains metastable.

Phase diagrams show stability regions for different quasicrystals.

Abstract

The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal and octagonal quasicrystals, are obtained for a simple model, i.e. the Lifshitz-Petrich free energy functional, of soft quasicrystals with two length-scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.