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X-ray Crystallography02:18

X-ray Crystallography

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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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A perfect crystal, in theory, has a uniform structure with the same unit cell and lattice points throughout. However, any deviation from this periodic arrangement is known as an imperfection or defect. These defects can be categorized into three types: point, line, and plane defects.Point defects occur when there is a deviation from the ideal due to missing atoms, displaced atoms, or additional atoms. These imperfections might occur due to imperfect packing during crystallization or because of...
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In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
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Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
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Non-stoichiometric defects refer to a type of defect in the crystal structure of a compound where the ratio of its constituent elements deviates from the ideal stoichiometric ratio. There are two main types of non-stoichiometric defects: metal excess defects and metal deficiency defects.Metal excess defects occur when there is a slight surplus of metal ions than what is required by the stoichiometric ratio of the compound. For example, heating a sodium chloride crystal in sodium vapor results...
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Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction
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Strain distributions and diffraction peak profiles from crystals with dislocations.

Vladimir M Kaganer1, Karl K Sabelfeld2

  • 1Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, Germany.

Acta Crystallographica. Section A, Foundations and Advances
|September 2, 2014
PubMed
Summary

This study compares dislocation arrangements and strain distributions using Monte Carlo simulations. Results show good agreement between diffraction profiles and strain distributions when long-range order is absent.

Keywords:
Monte Carlo methodsdislocationspeak profilespowder diffractionstrain

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Crystallography

Background:

  • Dislocation arrangements significantly influence material properties.
  • Understanding strain distributions is crucial for predicting material behavior.
  • Existing approximations like Stokes-Wilson and Krivoglaz-Wilkens model these effects.

Purpose of the Study:

  • To directly calculate diffraction profiles for various dislocation models using Monte Carlo methods.
  • To compare these calculated profiles with strain distributions.
  • To analytically derive strain distributions for uncorrelated defects.

Main Methods:

  • Direct calculation of diffraction profiles via Monte Carlo simulation.
  • Comparison with strain distributions corresponding to the Stokes-Wilson approximation.
  • Analytical derivation of strain distributions for uncorrelated defects.

Main Results:

  • Diffraction profiles and strain distributions show close agreement in the absence of long-range order.
  • Analytical calculations provide strain distributions for uncorrelated defects.
  • Stokes-Wilson and Krivoglaz-Wilkens approximations yield identical diffraction profiles for straight dislocations.

Conclusions:

  • The Monte Carlo method accurately models diffraction profiles related to dislocation arrangements.
  • Absence of long-range order is key for the agreement between strain and diffraction profiles.
  • The study validates and refines approximations for modeling defect-induced strain and diffraction.