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Mathematical diffraction of aperiodic structures.

Michael Baake1, Uwe Grimm

  • 1Fakultät für Mathematik, Universität Bielefeld, Germany. mbaake@math.uni-bielefeld.de

Chemical Society Reviews
|July 17, 2012
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Summary
This summary is machine-generated.

This review explores mathematical approaches to kinematic diffraction, focusing on non-periodic structures. It clarifies which matter distributions yield pure point diffraction and analyzes diffuse scattering for sharp Bragg peaks.

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Area of Science:

  • Materials Science
  • Solid State Physics
  • Mathematical Physics

Background:

  • The discovery of quasicrystals spurred mathematical developments in kinematic diffraction.
  • Understanding matter distributions that produce pure point diffraction (sharp Bragg peaks) is crucial.

Purpose of the Study:

  • To review key results in kinematic diffraction, emphasizing non-periodic structures.
  • To analyze diffuse scattering in continuous diffraction patterns.
  • To identify matter distributions leading to pure point diffraction.

Main Methods:

  • Mathematical approach using measures.
  • Analysis of characteristic examples of non-periodic structures.
  • Review of existing literature on diffraction theory.

Main Results:

  • Characterization of matter distributions for pure point diffraction.
  • Detailed analysis of different types of diffuse scattering.
  • Key results summarized with emphasis on non-periodic structures.

Conclusions:

  • Mathematical measures provide a robust framework for kinematic diffraction analysis.
  • Further study of continuous diffraction and diffuse scattering is necessary.
  • Non-periodic structures offer insights into diffraction phenomena beyond perfect crystals.