Aperiodic crystals and their atomic structures in superspace: an introduction

Abstract

AbstractAperiodic 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 Er$$_2$$ 2 Ir$$_3$$ 3 Si$$_5$$ 5 and EuAl$$_4$$ 4 . Graphical abstract