Rules for Computing Symmetry, Density and Stoichiometry in a Quasi-Unit-Cell Model of Quasicrystals

TL;DR

This paper presents a method to determine the density, stoichiometry, and symmetry of quasicrystals using a quasi-unit cell model, linking atomic decorations to tiling structures.

Contribution

It introduces a practical approach to calculate key properties of quasicrystals from their atomic decoration within the quasi-unit cell framework.

Findings

Provides a simple method for density calculation

Establishes relationships between atomic decorations and tiling models

Enables accurate symmetry and stoichiometry determination

Abstract

The quasi-unit cell picture describes the atomic structure of quasicrystals in terms of a single, repeating cluster which overlaps neighbors according to specific overlap rules. In this paper, we discuss the precise relationship between a general atomic decoration in the quasi-unit cell picture atomic decorations in the Penrose tiling and in related tiling pictures. Using these relations, we obtain a simple, practical method for determining the density, stoichiometry and symmetry of a quasicrystal based on the atomic decoration of the quasi-unit cell taking proper account of the sharing of atoms between clusters.