A Study of the Crystallizations Possible on the Surface of a Spherical Droplet Using Coulomb Interactions Between Point Charges

Abstract

Sets of charges interacting under coulomb force are relaxed to equilibrium on the surface of a sphere in order to study the symmetries and geometries of crystals confined to a spherical surface. The equilibrium configurations and point groups are obtained for charge number varying between N = 32 and N = 108 and tabulated for all known configurations with N less than 108. General properties are discussed. It is found that five-fold symmetry is quite common although two-fold symmetry is most common. Seven-fold symmetry does not occur. An approximate formula for the total energy is derived. The nature of and symmetry of isoenergy subsets is discussed. Continuity of the configuration between consecutive charge numbers of quite different symmetries is demonstrated for several cases. Crystallization on sphere, Spherical geometry, Spherical polyhedrons, Molecules on a spherical surface.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1990
Accession Number
ADA276455

Entities

People

  • Burt V. Bronk
  • Robert H. Frickel

Organizations

  • Edgewood Chemical Biological Center

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Charged Particles
  • Classification
  • Continuity
  • Crystallization
  • Crystals
  • Engineering
  • Equations
  • Geometry
  • Governments
  • Molecules
  • Particles
  • Reflection
  • Security
  • Symmetry
  • Technical Information Centers
  • Three Dimensional
  • Triangles

Readers

  • Graph Algorithms and Convex Optimization.
  • Materials Science and Engineering.
  • Plasma Physics.