Densest local sphere-packing diversity. II. Application to three dimensions

Area of Science:

• Condensed Matter Physics
• Materials Science
• Computational Physics

Background:

• Understanding sphere packing is fundamental in various scientific disciplines.
• Previous work established methods for finding densest packings in d-dimensional space.
• Local packings of spheres near a central sphere are of particular interest.

Purpose of the Study:

• To determine the densest local packings of N identical spheres in three dimensions (R(3)).
• To analyze the properties, symmetries, and characteristics of these packings.
• To develop a realizability condition for pair correlation functions and an upper bound for infinite sphere packings.

Main Methods:

• Utilized a previously established method for finding putative densest packings.
• Analyzed packings for N up to 1054 spheres in R(3).
• Employed knowledge of R(min)(N) for constructing conditions and bounds applicable in any dimension.

Main Results:

• Identified diverse symmetries in densest local packings, including tetrahedral and icosahedral.
• Found that densest local packings differ significantly from minimal-energy configurations of Lennard-Jones potentials.
• Observed that local packings resemble subsets of the densest infinite packings (Barlow packings) with fewer coordination shells.

Conclusions:

• Densest local sphere packings exhibit significant variability and unique symmetries.
• These findings have implications for nucleation theory and the understanding of disordered systems.
• The study provides a realizability condition for pair correlation functions and an upper bound on maximal infinite packing density.