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Related Experiment Videos

About the Coulomb potential in crystals.

P Becker1, P Coppens

  • 1Laboratoire de Minéralogie et Cristallographie, Université Pierre et Marie Curie, Paris, France.

Acta Crystallographica. Section A, Foundations of Crystallography
|April 1, 1990
PubMed
Summary

The study addresses the singularity in the crystal Coulomb potential

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Area of Science:

  • Solid State Physics
  • Crystallography
  • Materials Science

Background:

  • The Coulomb potential is crucial for understanding crystal properties.
  • Its Fourier series expansion presents challenges, particularly the V(0,0,0) component.
  • This component impacts comparisons between different compounds and reactivity studies.

Purpose of the Study:

  • To discuss the singularity in the crystal Coulomb potential's Fourier series expansion.
  • To present methods for calculating the V(0,0,0) component.
  • To derive sum rules for crystal multipolar moments.

Main Methods:

  • Fourier series expansion of the Coulomb potential in crystals.
  • Development of methods to calculate the V(0,0,0) singularity.
  • Derivation of sum rules using crystal structure factors.

Main Results:

  • Identified and discussed the singularity of the V(0,0,0) component in the crystal Coulomb potential.
  • Presented calculable methods for this singular term.
  • Derived sum rules relating crystal multipolar moments to structure factors.

Conclusions:

  • The V(0,0,0) component's singularity is a key factor in crystal potential analysis.
  • The derived sum rules offer insights into dielectric properties.
  • This work facilitates accurate comparisons of crystalline materials and reactivity predictions.

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