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Tetragonal sphere packings: minimal densities and subunits.

W Fischer1

  • 1Institut für Mineralogie, Petrologie und Kristallographie der Philipps-Universität Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany. drwerner.fischer@staff.uni-marburg.de

Acta Crystallographica. Section A, Foundations of Crystallography
|June 24, 2005
PubMed
Summary

This study calculated minimal sphere-packing densities for 382 tetragonal symmetry packings. The findings provide coordinates for visualizing these dense sphere arrangements.

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Area of Science:

  • Crystallography
  • Materials Science
  • Geometry

Background:

  • Sphere packing is a fundamental problem in geometry and materials science.
  • Understanding dense packings is crucial for various applications, including crystallography and materials design.
  • Tetragonal symmetry presents unique challenges and opportunities in sphere arrangement.

Purpose of the Study:

  • To systematically calculate the minimal sphere-packing densities for all known homogeneous sphere packings with tetragonal symmetry.
  • To provide a comprehensive catalog of these packings for further research and application.
  • To facilitate the visualization and analysis of dense sphere arrangements.

Main Methods:

  • Computational analysis of 382 distinct homogeneous sphere packings.

Related Experiment Videos

  • Determination of minimal packing densities using established geometric and mathematical principles.
  • Tabulation of coordinates for representative sphere positions within each packing type.

    • Main Results:

    • Calculated minimal sphere-packing densities for all 382 tetragonal homogeneous sphere packings.
    • Provided tabulated coordinates enabling graphic representation of each packing type.
    • Identified and listed 1- and 2-periodic subunits within these packings.

    Conclusions:

    • The study establishes a definitive set of minimal densities for tetragonal sphere packings.
    • The provided data serves as a valuable resource for researchers in geometry, crystallography, and materials science.
    • This work contributes to the fundamental understanding of dense packing structures.