# Stability of three-dimensional icosahedral quasicrystals in multi-component systems

## TL;DR

This paper investigates the stability of 3D icosahedral quasicrystals in multi-component systems using a coupled-mode Swift-Hohenberg model and a projection method, demonstrating their stability and extending the understanding of quasicrystal stabilization mechanisms.

## Contribution

It introduces a systematic computational approach to analyze quasicrystal stability in multi-component systems, extending the length-scale interaction mechanism.

## Key findings

- 3D icosahedral quasicrystals are stable in the model.
- The projection method accurately computes free energies.
- Multi-component interactions stabilize quasicrystals.

## Abstract

The relative stability of three-dimensional icosahedral quasicrystals in multi-component systems has been investigated based on a coupled-mode Swift-Hohenberg model with two-length-scales. A recently developed projection method, which provides a unified numerical framework to study periodic crystals and quasicrystals, is used to compute free energies to high accuracy. Compared with traditional approaches, the advantage of the projection method has been also discussed detailedly. A rigorous and systematical computation demonstrates that three-dimensional icosahedral quasicrystal, two-dimensional decagonal quasicrystal are stable phases in such a simple multi-component coupled-mode Swift-Hohenberg model. The result extends the multiple length-scales interaction mechanism which can stabilize quasicrystals from single-component to multi-component systems.