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Related Concept Videos

X-ray Crystallography02:18

X-ray Crystallography

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
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Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Inferring planar disorder in close-packed structures via ε-machine spectral reconstruction theory: examples from

D P Varn1, G S Canright, J P Crutchfield

  • 1Complexity Sciences Center and Physics Department, University of California, Davis, One Shields Avenue, Davis, California 95616, USA. dpv@complexmatter.org

Acta Crystallographica. Section A, Foundations of Crystallography
|June 20, 2013
PubMed
Summary
This summary is machine-generated.

The ε-machine spectral reconstruction theory (εMSR) successfully analyzes X-ray diffraction patterns to reveal stacking structures in close-packed crystals. This method accurately models both ordered and disordered materials, providing insights into crystal defects.

Keywords:
X-ray diffractioncomputational mechanicsdiffuse scatteringone-dimensional disorderplanar faultspolytypes

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Area of Science:

  • Materials Science
  • Crystallography
  • Data Analysis

Background:

  • X-ray diffraction is crucial for analyzing crystal structures.
  • Planar-faulted, close-packed structures present challenges in pattern analysis.
  • Previous work introduced the ε-machine spectral reconstruction theory (εMSR) for pattern inference.

Purpose of the Study:

  • To apply the εMSR algorithm to simulated diffraction patterns from close-packed crystals.
  • To evaluate εMSR's effectiveness in reconstructing stacking structures with varying degrees of disorder.
  • To define and discuss length parameters for characterizing long-range order in layered materials.

Main Methods:

  • Application of the εMSR algorithm to simulated X-ray diffraction data.
  • Analysis of reconstructed stacking structures and their statistical properties.
  • Definition and calculation of length parameters from the ε-machine model.

Main Results:

  • εMSR accurately reproduces stacking structure statistics for memory lengths up to three.
  • For longer memory lengths, εMSR generates models capturing key features like multiple faults and crystal structures.
  • The algorithm successfully identifies stacking structure even in highly disordered crystals.

Conclusions:

  • εMSR is a powerful tool for inferring and modeling stacking structures from diffraction data.
  • The method demonstrates robustness across a range of crystal disorder.
  • Defined length parameters offer a means to quantify long-range order in layered materials.