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Related Experiment Videos

Hexagonal and trigonal sphere packings. II. Bivariant lattice complexes.

H Sowa1, E Koch

  • 1Institut für Mineralogie, Petrologie und Kristallographie der Philipps-Universität Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany. heidrun.sowa@t-online.de

Acta Crystallographica. Section A, Foundations of Crystallography
|February 18, 2004
PubMed
Summary

This study details 109 types of homogeneous sphere packings within the hexagonal crystal family, including novel types with contact number 10 and unique interpenetrating arrangements. These findings expand our understanding of crystal structures and sphere packing geometries.

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Area of Science:

  • Crystallography
  • Materials Science
  • Geometry

Background:

  • Sphere packing is fundamental to understanding crystal structures and material properties.
  • The hexagonal crystal family encompasses numerous complex lattice configurations.
  • Previous research has cataloged various sphere packing types, but gaps remain.

Purpose of the Study:

  • To systematically derive all homogeneous sphere packings corresponding to the 26 bivariant lattice complexes of the hexagonal crystal family.
  • To identify and characterize novel sphere packing types and interpenetrating arrangements.
  • To relate these derived packings to known frequently occurring structure types.

Main Methods:

  • Derivation of sphere packings based on point configurations of hexagonal crystal family lattice complexes.

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  • Classification of sphere packings into distinct types.
  • Analysis of symmetry and density properties of the identified packings.
  • Identification of interpenetrating sphere packing arrangements.

    • Main Results:

    • 109 distinct homogeneous sphere packing types were identified.
    • A novel sphere packing type with a contact number of 10 was discovered.
    • Seven sphere packing types exhibit cubic symmetry at minimal density.
    • Three types of interpenetrating sphere packings and one of interpenetrating 6(3) sphere layers were found, with the latter being previously unknown.

    Conclusions:

    • The systematic derivation provides a comprehensive catalog of sphere packings for the hexagonal crystal family.
    • The discovery of new packing types, including interpenetrating layers, advances the field of crystallography.
    • These findings offer insights into the formation and properties of crystalline materials.