Stability of icosahedral quasicrystals in a simple model with two-length scales

The phase behaviour of a free energy functional with two length scales is examined by comparing the free energy of different candidate phases including three-dimensional icosahedral quasicrystals. Accurate free energy of the quasicrystals has been obtained using the recently developed projection method. The results reveal that the icosahedral quasicrystal and body-centred-cubic spherical phase are the stable ordered phases of the model. Furthermore, the difference between the results obtained from the projection method and the one-mode approximation has been analyzed in detail. The present study extends previous results on two-dimensional systems, demonstrating that the interactions between density waves at two length scales can stabilize two- and three-dimensional quasicrystals.