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Related Concept Videos

Symmetry Elements in a Crystal01:27

Symmetry Elements in a Crystal

Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...
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.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
The de Broglie Wavelength02:32

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
X-ray Diffraction of Biological Samples01:10

X-ray Diffraction of Biological Samples

X-ray diffraction or XRD is an analytical tool that utilizes X-rays to study ordered structures such as crystalline organic and inorganic samples, polycrystalline materials, proteins, carbohydrates, and drugs.
According to Bragg's law, when X-rays strike the sample positioned on a stage, the rays are  scattered by the electron clouds around the sample atoms. The  X-ray diffraction or scattering is caused by constructive interference of the X-ray waves that reflect off the internal crystal...

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Related Experiment Video

Updated: Jun 12, 2026

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
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Published on: October 11, 2016

The symmetry of precession electron diffraction patterns.

J-P Morniroli1, P Stadelmann, G Ji

  • 1Laboratoire de Métallurgie Physique et Génie des Matériaux, UMR CNRS 8517, USTL and ENSCL, Cité Scientifique, 59655 Villeneuve d'Ascq, France. Jean-Paul.Morniroli@univ-lille1.fr

Journal of Microscopy
|May 27, 2010
PubMed
Summary

Integrated beam intensity in microdiffraction reveals ideal crystal symmetry. This symmetry correlates with Laue classes in conventional patterns and point groups in unconventional patterns, aiding crystallographic analysis.

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Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
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Published on: October 11, 2016

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
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Picometer-Precision Atomic Position Tracking through Electron Microscopy

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Area of Science:

  • Crystallography
  • Materials Science
  • Electron Microscopy

Background:

  • Microdiffraction patterns provide crystallographic information.
  • Symmetry determination is crucial for understanding crystal structures.
  • Interpreting diffraction patterns requires careful analysis of beam positions and intensities.

Purpose of the Study:

  • To demonstrate the utility of integrated diffracted beam intensity for determining 'ideal' crystal symmetry.
  • To establish the relationship between this ideal symmetry and established crystallographic classifications.
  • To explore symmetry determination using both conventional and unconventional microdiffraction techniques.

Main Methods:

  • Analysis of integrated intensities of diffracted beams on microdiffraction precession patterns.
  • Comparison of inferred symmetry with conventional electron precession patterns (11 Laue classes).
  • Evaluation of symmetry on unconventional precession patterns obtained without 'descan' (centro- and non-centrosymmetrical point groups).

Main Results:

  • Integrated beam intensity accurately infers the 'ideal' symmetry of crystals.
  • The inferred ideal symmetry aligns with the 11 Laue classes for conventional patterns.
  • Unconventional precession patterns reveal connections to centro- and non-centrosymmetrical point groups.

Conclusions:

  • Integrated intensity analysis is a powerful tool for determining crystal symmetry from microdiffraction data.
  • This method bridges conventional and unconventional precession techniques for robust symmetry determination.
  • The findings enhance the interpretation of electron diffraction patterns in materials science and crystallography.