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

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.