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Schemes to determine the crystal potential under dynamical conditions using voltage variation.

Rez1

  • 1Department of Physics and Astronomy and Center for Solid State Science, Arizona State University, Tempe, AZ 85287-1504, USA. peter.rez@asu.edu

Acta Crystallographica. Section A, Foundations of Crystallography
|August 6, 2000
PubMed
Summary

Electron diffraction can now determine crystal potential directly. By measuring intensity differences at varying voltages, researchers can overcome dynamical diffraction challenges, enabling precise crystal structure analysis.

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Area of Science:

  • Materials Science
  • Crystallography
  • Condensed Matter Physics

Background:

  • X-ray diffraction routinely determines charge densities and crystal structures due to weak scattering.
  • Strong dynamical diffraction in high-energy electron diffraction hinders similar direct analysis.
  • Dynamical diffraction involves wave propagation and crystal potential scattering, influenced by voltage-dependent relativistic effects.

Purpose of the Study:

  • To develop a method for direct crystal potential determination using electron diffraction.
  • To overcome limitations imposed by strong dynamical diffraction in electron scattering.
  • To establish a relationship between diffracted intensities and crystal potential.

Main Methods:

  • Measuring electron diffracted intensities at two different voltages.

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  • Analyzing the relationship between intensity differences and crystal potential.
  • Utilizing first-order perturbation theory and exact calculations for validation.

    • Main Results:

    • The difference in diffracted intensities at two voltages is directly proportional to the crystal potential.
    • First-order perturbation theory calculations show negligible differences compared to exact calculations.
    • A simple procedure exists to recover the crystal potential if the full complex wave function is known.

    Conclusions:

    • Direct determination of crystal potential from electron diffraction is feasible.
    • Measuring intensity variations with voltage offers a new route to analyze crystal potentials.
    • This method holds promise for detailed crystallographic studies even under dynamical diffraction conditions.