Aperiodic crystals and beyond

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.

33 pages, many pictures

References in corpus (6)

• Homometric model sets and window covariograms
• Can Kinematic Diffraction Distinguish Order from Disorder?
• A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns
• Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies
• Pinwheel patterns and powder diffraction
• Close-packed dimers on the line: diffraction versus dynamical spectrum

Cited by in corpus (1)

• Diffraction Patterns of Layered Close-packed Structures from Hidden Markov Models