A Study of the Crystallizations Possible on the Surface of a Spherical Droplet Using Coulomb Interactions Between Point Charges
Technical rept. Jul 1988-Jul 1989
CHEMICAL RESEARCH DEVELOPMENT AND ENGINEERING CENTER ABERDEEN PROVING GROUND MD
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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.
- Physical Chemistry
- Atomic and Molecular Physics and Spectroscopy