Can Kinematic Diffraction Distinguish Order from Disorder?

Abstract

Diffraction methods are at the heart of structure determination of solids. While Bragg-like scattering (pure point diffraction) is a characteristic feature of crystals and quasicrystals, it is not straightforward to interpret continuous diffraction intensities, which are generally linked to the presence of disorder. However, based on simple model systems, we demonstrate that it may be impossible to draw conclusions on the degree of order in the system from its diffraction image. In particular, we construct a family of one-dimensional binary systems which cover the entire entropy range but still share the same purely diffuse diffraction spectrum.

5 pages, 1 figure; two typos in the recursion relations for the autocorrelation coefficients were corrected

References in corpus (2)

• Diffractive point sets with entropy
• The singular continuous diffraction measure of the Thue-Morse chain

Cited by in corpus (15)

• Mathematical diffraction of aperiodic structures
• Kinematic Diffraction from a Mathematical Viewpoint
• Aperiodic crystals and beyond
• Diffraction of limit periodic point sets
• Surprises in aperiodic diffraction
• Scaling of diffraction intensities near the origin: Some rigorous results
• Planar dynamical systems with pure Lebesgue diffraction spectrum
• Close-packed dimers on the line: diffraction versus dynamical spectrum
• Some comments on pinwheel tilings and their diffraction
• Random point sets and their diffraction
• Substitution-based sequences with absolutely continuous diffraction
• A comment on the relation between diffraction and entropy
• Homometry in the light of coherent beams
• Inflation versus projection sets in aperiodic systems: The role of the window in averaging and diffraction
• Recent progress in mathematical diffraction