Robust minimal matching rules for quasicrystals

TL;DR

This paper introduces a unified framework for identifying minimal matching rules in quasicrystals from diffraction data, enabling robust analysis of atomic arrangements and defect tolerance.

Contribution

It presents a novel method for extracting minimal matching rules directly from diffraction data, applicable to both theoretical models and real quasicrystals.

Findings

Provides precise atomic density calculations.

Robustly tolerates structural defects.

Applicable to tiling models and experimental data.

Abstract

We propose a unified framework for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching rules, directly from the phased diffraction data. The construction yields precise values for the spatial density of distinct atomic positions and tolerates the presence of defects in a robust way.