Quasicrystals as superposed waves. Stability and entropy

Abstract

International audience2D and 3D quasicrystalline structures are derived from an energy minimization method as a sum of density waves. The quasicrystalline stability against the occurrence of defects is controlled by the density difference between retained sites and possible defects. The relative stabilities of octagonal, decagonal, dodecagonal and icosahedral quasicrystals are compared. Sevenfold and elevenfold symmetry are shown to be quite instable. In the case of dodecagonal quasicrystals, the comparison between different solutions reveals their different densities and defects so their respective entropies are compared as well as their elastic and acoustic properties. Different quasicrystalline structures with a given symmetry can be produced by this method which reveals and classifies low energy defects