Physical space description of decorated quasicrystals

TL;DR

This paper introduces a physical space method for analyzing decorated quasicrystals using average unit cell formalism, enabling classical crystallography techniques and reducing parameters needed for structure refinement.

Contribution

It presents a systematic, physical space approach for decorated quasicrystals based on average unit cell formalism, applicable to experimental data analysis.

Findings

Explicit calculation of structure factors for decorated quasicrystals

Development of an algorithm for pattern analysis

Application to Sturmian sequence-based quasicrystals

Abstract

In this paper the systematic method of dealing with the arbitrary decorations of quasicrystals is presented. The method is founded on the average unit cell formalism and operates in the physical space only, where each decorating atom manifests itself just by an additional component of the displacement density function in the average unit cell. Such approach allows us to use almost all classical crystallography algorithms for structure refining based on experimental data and may meaningly decrease the number of parameters which have to be fit. Further help for such analysis may be the use of proposed recently average Patterson function, here applied to decorated sets. As an example we present a description of a class of decorated quasicrystals based on Sturmian sequence of two interatomic spacings: we calculate explicitly structure factor, the shape of average Patterson function and give an algorithm for pattern analysis.