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Leaky cell model of hard spheres.

Thomas G Fai1, Jamie M Taylor2, Epifanio G Virga3

  • 1Department of Mathematics and Volen Center for Complex Systems, Brandeis University, Waltham, Massachusetts 02453, USA.

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Summary

We calculated free volumes for hard sphere packings on lattices using a leaky cell model. This reveals phase transitions and coexistence in crystalline materials.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Materials Science

Background:

  • Understanding the behavior of hard sphere packings is crucial in statistical mechanics and materials science.
  • Lattice models provide a simplified yet insightful framework for studying phase transitions and material properties.

Purpose of the Study:

  • To develop a method for calculating the partition function and pressure of hard sphere lattice packings.
  • To investigate the role of accessible free volume in determining the thermodynamic properties of these systems.
  • To explore phase transitions and potential coexistence in crystalline materials.

Main Methods:

  • Utilizing a leaky cell model to compute accessible free volumes, accounting for sphere mobility beyond local cages.
  • Applying elementary geometry for exact free volume calculations in 2D and 3D lattice packings.
  • Comparing results with established liquid models like Carnahan-Starling and Percus-Yevick.
  • Employing the common tangent construction to identify phase transitions.

Main Results:

  • Formulas for free volumes in various lattice packings were derived.
  • The leaky cell model provides a distinct approach to free volume calculation compared to liquid models.
  • Phase transitions were identified within the leaky cell regime for lattice packings.

Conclusions:

  • The accessible free volume is a key determinant of thermodynamic properties in hard sphere lattice packings.
  • The leaky cell model offers a valuable framework for understanding crystalline material behavior and phase transitions.
  • The study indicates the potential for phase coexistence in crystalline systems, a significant finding for materials science.