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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.
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...
Determination of Crystal Structures01:29

Determination of Crystal Structures

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...
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...
Scanning Electron Microscopy01:07

Scanning Electron Microscopy

A scanning electron microscope (SEM) is used to study the surface features of a sample by using an electron beam that scans the sample surface in a two-dimensional manner. Typically, areas between ~1 centimeter to 5 micrometers in width can be imaged. SEM can be used to image bacteria, viruses, tissues as well as larger samples like insects. Conventional SEM gives a magnification ranging from 20X to 30,000X and spatial resolution of 50 to 100 nanometers.
Fundamental Principles
Accelerated...
Transmission Electron Microscopy01:15

Transmission Electron Microscopy

In 1931, physicist Ernst Ruska—building on the idea that magnetic fields can direct an electron beam just as lenses can direct a beam of light in an optical microscope—developed the first prototype of the electron microscope. This development led to the development of the field of electron microscopy. In the transmission electron microscope (TEM), electrons are produced by a hot tungsten element and accelerated by a potential difference in an electron gun, which gives them up to 400 keV in...
Electron Microscope Tomography and Single-particle Reconstruction01:07

Electron Microscope Tomography and Single-particle Reconstruction

Transmission electron microscopy (TEM) can be used to determine the 3D structure of biological samples with the help of techniques such as electron microscope tomography and single-particle reconstruction. While single-particle reconstruction can examine macromolecules and macromolecular complexes in vitro conditions only, tomography permits the study of cell components or small cells in vivo.
Electron Tomography
Electron tomography can be performed either in TEM or STEM (scanning transmission...

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Updated: Jun 18, 2026

Quantitative Atomic-Site Analysis of Functional Dopants/Point Defects in Crystalline Materials by Electron-Channeling-Enhanced Microanalysis
07:24

Quantitative Atomic-Site Analysis of Functional Dopants/Point Defects in Crystalline Materials by Electron-Channeling-Enhanced Microanalysis

Published on: May 10, 2021

Position averaged convergent beam electron diffraction: theory and applications.

James M Lebeau1, Scott D Findlay, Leslie J Allen

  • 1Materials Department, University of California, Santa Barbara, CA 93106-5050, USA.

Ultramicroscopy
|November 27, 2009
PubMed
Summary
This summary is machine-generated.

Position-averaged convergent beam electron diffraction patterns offer a simple method to determine sample thickness, tilt, and polarity. This technique enhances electron microscopy analysis without complex algorithms.

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Published on: August 22, 2017

Area of Science:

  • Materials Science
  • Solid State Physics
  • Electron Microscopy

Background:

  • Convergent beam electron diffraction (CBED) patterns are sensitive to probe position and instrumental aberrations.
  • Existing methods for analyzing CBED patterns can be complex and require pattern-matching algorithms.

Purpose of the Study:

  • To develop a simplified method for determining specimen thickness, tilt, and polarity using CBED.
  • To demonstrate the applicability of position-averaged CBED for routine analysis in electron microscopy.

Main Methods:

  • Incoherent averaging of CBED patterns over multiple probe positions.
  • Experimental and simulated CBED pattern analysis for various materials.
  • Comparison of frozen phonon and absorptive models for thermal diffuse scattering.

Main Results:

  • Position-averaged CBED patterns are independent of lens aberrations and source size.
  • Accurate determination of specimen thickness (±10%), tilt (±1 mrad), and polarity is achievable.
  • Measurements can be performed via visual comparison, eliminating the need for pattern-matching algorithms.
  • The absorptive model is suitable for analyzing thicker samples (>50 nm).

Conclusions:

  • Position-averaged CBED provides a robust and straightforward approach for quantitative analysis of specimen parameters.
  • This method complements atomic resolution scanning transmission electron microscopy (STEM) imaging.
  • The technique is valuable for materials characterization and quality control in electron microscopy.