Classification, based on energetics, of ideal icosahedral clusters, and building blocks of icosahedral quasicrystals and approximant crystals

Abstract

We have classified, by their energy, compact finite clusters of icosahedral symmetry, composed of a single atom type, constituted by at most ten layers, and centered at an empty or occupied site with coordination number 12. The clusters are formed by adding one by one the best possible icosahedral layers in the surface potential minima and by relaxing numerically the cluster at each step. Polyatomic clusters are also considered. The energy is calculated from two-body pair potentials depending only upon the distance. Comparison is made between (1) the succession of layers inside these ideal icosahedral clusters, (2) the layers constituting the real clusters present in m 35 -approximant crystals and (3) the icosahedral local order in icosahedral quasicrystals as deduced from the ‘experimental’ atomic surfaces. After revisiting many m 35 -approximant crystals, we propose a characterization and a classification of local icosahedral order in crystallized matter and icosahedral quasicrystals.