Aperiodic crystals and their atomic structures in superspace : an introduction

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van Smaalen, Sander:
Aperiodic crystals and their atomic structures in superspace : an introduction.
In: Rendiconti Lincei. Scienze Fisiche e Naturali. Bd. 34 (1 September 2023) Heft 3 . - S. 681-688.
ISSN 1720-0776
DOI: https://doi.org/10.1007/s12210-023-01167-z

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Abstract

Aperiodic crystals are ordered matter without three-dimensional (3D) translational symmetry. They encompass quasicrystals, incommensurate composite crystals and incommensurately modulated structures. Their crystal structures are described by the so-called superspace theory, in which hidden periodicity is uncovered as translational symmetry in a space of dimensions higher than three. Here, I give an introduction to the structural features of aperiodic crystals and to the superspace theory for describing those structures. Applications, in particular t-plots, are demonstrated for the charge-density wave (CDW) materials Er₂Ir₃Si₅ and EuAl₄.