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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Accurate lattice parameters from 3D electron diffraction data. I. Optical distortions.

Petr Brázda1, Mariana Klementová1, Yaşar Krysiak1,2

  • 1Department of Structure Analysis, Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, Prague 8, 18221, Czech Republic.

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Summary

Accurate lattice parameter determination using 3D electron diffraction (3D ED) is challenged by optical distortions. This study identifies a new parabolic distortion and offers methods to correct for it, improving accuracy.

Keywords:
3D electron diffractiondistortionslattice parametersparabolic distortionprecession electron diffraction

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Area of Science:

  • Materials Science
  • Crystallography
  • Electron Microscopy

Background:

  • Accurate determination of lattice parameters is crucial for materials characterization.
  • Transmission electron microscopy (TEM) using 3D electron diffraction (3D ED) is a powerful technique for this purpose.
  • However, optical distortions in TEM significantly limit the precision of lattice parameter measurements.

Purpose of the Study:

  • To investigate and quantify distortions affecting 3D ED data accuracy.
  • To identify novel distortions beyond known barrel-pincushion, spiral, and elliptical types.
  • To develop strategies for correcting these distortions and improving lattice parameter determination.

Main Methods:

  • Analysis of experimental 3D ED datasets from a transmission electron microscope.
  • Identification and characterization of various optical distortion types, including a newly observed parabolic distortion.
  • Development of computational methods to correct for distortions and refine lattice parameters.

Main Results:

  • Experimental data revealed barrel-pincushion, spiral, elliptical, and a novel parabolic distortion.
  • Parabolic distortion causes excitation-error-dependent shifts and splitting of reflections in precession electron diffraction.
  • All distortions except elliptical can be corrected using a single 3D ED dataset.
  • Elliptical distortion requires additional information, such as crystal Laue class or multi-crystal data, for unique determination.
  • Lattice parameter ratios can be determined with ~0.1% accuracy, and angles with <0.03° accuracy.

Conclusions:

  • Optical distortions are a major limitation in precise 3D ED lattice parameter determination.
  • A new parabolic distortion has been identified and characterized.
  • Methods for correcting various distortions, including the novel parabolic type, have been proposed.
  • The study demonstrates the potential of 3D ED for highly accurate crystallographic analysis when distortions are properly addressed.