Structural models of quasicrystals.

Microscopic models of quasicrystals

Cluster Models of Decagonal Tilings and Quasicrystals

Two different relaxed versions of Gummelt’s aperiodic cluster covering rules are considered. These relaxed covering rules produce certain random tiling type structures, which are precisely characterized, along with their relationships to various other random tiling ensembles. One variant of the relaxed covering rules allows for a natural realization in terms of a vertex cluster. It is shown wit...

a structural survey of the polish posters

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Geometric Models for Quasicrystals I. Delone Sets of Finite Type

This paper studies three classes of discrete sets X in R n which have a weak translational order imposed by increasingly strong restrictions on their sets of interpoint vectors X ? X. A nitely generated Delone set is one such that the abelian group X ? X] generated by X ? X is nitely generated, so that X ? X] is a lattice or a quasilattice. For such sets the abelian group X] is nitely generated...

Quasicrystals

The discretely diffracting aperiodic crystals termed quasicrystals, discovered at NBS in the early 1980s, have led to much interdisciplinary activity involving mainly materials science, physics, mathematics, and crystallography. It led to a new understanding of how atoms can arrange themselves, the role of periodicity in nature, and has created a new branch of crystallography.