Non-Crystalline Compact Packings of Hard Spheres of Two Sizes: Bipyramids and the Geometry of Common Neighbours (Preprint)

Abstract

Insight into the efficient filling of space in systems of binary spheres is explored using bipyramids consisting of 3-to-8 n tetrahedra sharing a common pair of spheres. Compact packings are sought in bipyramids consisting of larger hard spheres of unit radius and smaller hard spheres of radius between .001 and 1. Seventy-seven distinct compact bipyramids are found. The number of distinct compact bipyramids increases with the number n of constituent tetrahedra. No compact bipyramids are found for R greater than 0.9473 and for R between 0.8493 and 0.7434. A topological instability eliminates compact packings for R less than 0.1547. Pentagonal bipyramids cover a larger range in R than any other compact bipyramids studied.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 2009
Accession Number
ADA501735

Entities

People

  • Daniel Miracle
  • Peter Harrowell

Organizations

  • Air Force Research Laboratory

Tags

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  • Air Platforms

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Air Force Research Laboratories
  • Chemistry
  • Crystal Structure
  • Crystals
  • Department Of Defense
  • Dihedral Angle
  • Geometry
  • Instability
  • Manufacturing
  • Materials
  • Military Research
  • Particles
  • Sequences
  • Topology
  • United States

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  • Materials Science and Engineering.
  • Mathematics or Statistics
  • Quantum Chemistry

Technology Areas

  • Space