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

ABSTRACT

The relative stability of three-dimensional icosahedral quasicrystals in multi-component systems has been investigated based on a phenomenological 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 energy to high accuracy. Compared with traditional approaches, the advantage of the projection method has also been discussed in detail. A rigorous and systematic computation demonstrates that three-dimensional icosahedral quasicrystal and two-dimensional decagonal quasicrystal are both stable phases in such a simple multi-component coupled-mode Swift-Hohenberg model. The result extends the two-length scales interaction mechanism of stabilising quasicrystals from single-component to multi-component systems.

GRAPHICAL ABSTRACT

KEYWORDS:

• Icosahedral quasicrystals
• two-length scales
• coupled-mode swift-Hohenberg model
• phase diagrams
• projection method

PACS:

• 61.44.Br
• 61.44.Fw
• 64.60.Bd
• 02.70.Hm

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11771368], Hunan Science Foundation of China [grant number 2018JJ2376], Youth Project Hunan Provincial Education Department of China [grant number 18B057] and Project of Scientific Research Fund of Hunan Provincial Science and Technology Department [grant number 2018WK4006].