Designing aperiodic to periodic interfaces

TL;DR

This paper introduces a method for designing coherent interfaces between aperiodic and periodic structures using hexagonal tilings, expanding understanding of symmetry sharing and lattice decoration.

Contribution

It presents a novel class of hexagonal aperiodic tilings derived from golden-mean modifications, and methods for creating aperiodic to periodic interfaces.

Findings

New hexagonal aperiodic tilings with single edge-lengths

Vertices can be viewed as decorations of a periodic triangular lattice

Methods for designing coherent aperiodic to periodic interfaces

Abstract

Symmetry sharing facilitates coherent interfaces which can transition from periodic to aperiodic structures. Motivated by the design and construction of such systems, we present hexagonal aperiodic tilings with a single edge-length which can be considered as decorations of a periodic lattice. We introduce these tilings by modifying an existing family of golden-mean trigonal and hexagonal tilings, and discuss their properties in terms of this wider family. Then, we show how the vertices of these new systems can be considered as decorations or sublattice sets of a periodic triangular lattice, before introducing methods to designing coherent aperiodic to periodic interfaces.