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Solution of the phase problem in crystallography and application to dynamical electron diffraction

W F Tivol1

  • 1Wadsworth Center for Laboratories and Research, School of Public Health, Albany, NY 12201-0509, USA.

Acta Crystallographica. Section A, Foundations of Crystallography
|September 1, 1995
PubMed
Summary

Unitarity in scattering theory predicts unique phases from diffraction data. This study derives direct phasing methods from unitarity and explores applications in electron diffraction.

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Area of Science:

  • Physics
  • Crystallography
  • Materials Science

Background:

  • Unitarity is a core principle in scattering theory, crucial for determining scattering amplitude phases.
  • Complete knowledge of differential cross-sections or crystal diffracted intensities is key to predicting these phases.
  • Existing direct phasing methods, like the Sayre equation, are special cases of unitarity.

Purpose of the Study:

  • To demonstrate how unitarity can be used to derive direct phasing methods.
  • To explore the relationship between dynamical and kinematical scattering.
  • To discuss applications of these principles to electron diffraction.

Main Methods:

  • Derivation of direct phasing methods as a special case of unitarity (zero excitation error).
  • Analysis of dynamical and kinematical scattering.

Related Experiment Videos

  • Formulation of the scattering relationship S = exp(i tau nzK).

    • Main Results:

    • Unitarity provides a framework for predicting unique scattering phases.
    • Direct phasing methods are shown to be a consequence of unitarity under specific conditions.
    • A relationship connecting dynamical and kinematical scattering was established.

    Conclusions:

    • The study reinforces the fundamental role of unitarity in scattering theory.
    • The findings offer a unified perspective on direct phasing methods.
    • The principles are applicable to electron diffraction, including cases with non-zero excitation error.