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X-ray Crystallography02:18

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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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Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane...
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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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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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Crystal Field Theory
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Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other...
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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Interpolation method for pair correlations in classical crystals.

Stanislav O Yurchenko1, Nikita P Kryuchkov, Alexei V Ivlev

  • 1Bauman Moscow State Technical University, 2nd Baumanskaya str. 5, 105005 Moscow, Russia.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|May 10, 2016
PubMed
Summary
This summary is machine-generated.

Anharmonicity effects on crystal pair correlation functions are improved using a novel shortest-graph approach. This method accurately models finite-temperature and lattice discreteness effects for better crystal structure analysis.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Anharmonicity significantly influences the pair correlation function (PCF) in classical crystals.
  • Existing models often struggle to accurately capture these anharmonic effects, especially at finite temperatures.
  • The shortest-graph approach provides a framework for PCF analysis but requires refinement for anharmonicity.

Purpose of the Study:

  • To enhance the shortest-graph approach for calculating the pair correlation function in classical crystals.
  • To incorporate anharmonic corrections arising from finite temperatures and hard-sphere-like interactions.
  • To develop an analytical interpolation method for improved PCF accuracy.

Main Methods:

  • Improved shortest-graph approach incorporating Gaussian representation of correlation peaks.
  • Inclusion of anharmonic corrections from finite-temperature phonon spectra.
  • Development and application of an analytical interpolation method.
  • Validation using molecular dynamics simulations.

Main Results:

  • Identified two key effects modifying correlation peaks: finite-temperature phonon spectra at large distances and lattice discreteness at short distances.
  • The proposed analytical interpolation method accurately describes these modifications.
  • Verified the method's accuracy for 2D and 3D crystals with various interactions (Yukawa, inverse-power-law, pseudo-hard-sphere).

Conclusions:

  • The enhanced shortest-graph approach provides accurate PCF calculations for anharmonic crystals.
  • The method successfully captures deviations from Gaussian forms due to lattice discreteness and temperature.
  • Demonstrated capability in calculating phase diagrams, exemplified by a 3D Yukawa system.