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Structure of the hard sphere solid.

Charles Radin¹, Lorenzo Sadun

¹Department of Mathematics, University of Texas, Austin, TX 78712, USA. radin@math.utexas.edu

Physical Review Letters

|February 9, 2005

Summary

Near densest packing, hexagonal close-packed (hcp) structures exhibit higher entropy due to reduced neighbor motion interference. This finding clarifies the dynamics of sphere packing and entropy in condensed matter systems.

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Area of Science:

Condensed matter physics
Statistical mechanics
Materials science

Background:

Understanding the relationship between structure and entropy is crucial in condensed matter physics.
Dense packing of spheres is a fundamental problem with applications in materials science and granular physics.
Previous studies have explored various dense packing configurations but often overlook dynamic properties.

Purpose of the Study:

To investigate the entropic properties of different densest packing structures under perturbation.
To identify the structural characteristics that lead to higher entropy in sphere packing.
To elucidate the role of inter-particle motion correlations in determining system entropy.

Main Methods:

Computational simulations were used to model sphere packing structures.
Perturbations were applied to ideal hexagonal close-packed (hcp) and other densest packing structures.
Analysis focused on quantifying entropy and examining correlations in the motion of nearest neighbors.

Main Results:

Perturbations of the hexagonal close-packed (hcp) structure resulted in higher entropy compared to other densest packing arrangements.
Significant differences in entropy were attributed to variations in the correlations between nearest-neighbor motions.
The hcp structure demonstrated less impingement between random motions of adjacent spheres.

Conclusions:

The hexagonal close-packed (hcp) structure is dynamically favored near densest packing due to its unique inter-neighbor motion characteristics.
Entropy in dense sphere systems is intrinsically linked to the detailed correlations of particle dynamics.
These findings provide insights into the stability and behavior of materials with close-packed structures.

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