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Most stable structure for hard spheres.

Hans Koch¹, Charles Radin, Lorenzo Sadun

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 11, 2005

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The hard sphere model exhibits a liquid-solid phase transition. This study compares methods for determining the stability of the face-centered cubic versus hexagonal close-packed solid structures.

Area of Science:

Physics
Materials Science
Thermodynamics

Background:

The hard sphere model is a fundamental system in statistical mechanics.
It is known to exhibit a liquid-solid phase transition.
The resulting solid phase is typically either face-centered cubic (FCC) or hexagonal close-packed (HCP).

Purpose of the Study:

To contrast different theoretical approaches for determining the relative stability of FCC and HCP structures in the hard sphere model.
To extend existing methods for analyzing free energy differences between these solid phases.

Main Methods:

Review and comparison of existing theoretical frameworks for free energy calculations.
Application and extension of a specific free energy calculation method.

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Main Results:

Analysis of the strengths and limitations of various approaches.
Presentation of extended calculations for one method, providing insights into structural stability.

Conclusions:

The free energy differences between FCC and HCP in the hard sphere model are subtle.
The study provides a comparative analysis and an extension of methods to better understand this phase transition.