Clusters in quasicrystals: tiling versus covering and porosity

Diffraction data and quasicrystallography provide average perfect quasiperiodic structures for quasicrystals. These patterns are prototypes of atomic clusters which may be used to model quasicrystal structures. Three alternative schemes are presented in this paper: (1) a perfect quasiperiodic arrangement that exhibits a hierarchical distribution of holes; (2) a dense random covering (DRC) structure; and (3) a long range ordered structures with successive layers of interpenetrating clusters.