Aperiodic crystals and beyond

TL;DR

This paper explores the broader concept of crystalline order beyond traditional periodic structures, including aperiodic and non-crystalline systems, questioning the current diffraction-based definition of crystals.

Contribution

It investigates the limits of the current crystal definition by examining non-crystalline ordered structures and proposing a more inclusive understanding of crystallinity.

Findings

Current definitions are limited to point-like diffraction patterns.

Aperiodic and non-crystalline structures challenge traditional crystal concepts.

The study emphasizes the need to reconsider what constitutes a crystal.

Abstract

Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order, encompassing both periodic and aperiodic crystals. The current definition of crystals rests on their essentially point-like diffraction. Considering a number of recently investigated toy systems, with particular emphasis on non-crystalline ordered structures, the limits of the current definition are explored.