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Geometrical characterization of hard-sphere systems
P Richard1, L Oger, J P Troadec
1Groupe Matière Condensée et Matériaux, UMR CNRS 6626, Université de Rennes I, 35042 Rennes Cedex, France.
Summary
Molecular dynamics simulations reveal that hard-sphere crystallization occurs in a narrow packing fraction range. Beyond this, systems exist as fluids or glasses, geometrically characterized by Voronoï tessellation.
Area of Science:
- Physics
- Materials Science
- Computational Chemistry
Background:
- Understanding the phase behavior of simple systems like hard spheres is fundamental to statistical mechanics.
- The transition between fluid, glass, and crystalline states is crucial for materials design.
Purpose of the Study:
- To geometrically characterize hard-sphere systems across their phase diagram.
- To identify the specific packing fraction (η) ranges for fluid, glass, and crystalline states.
- To analyze the evolution of order during crystallization using Voronoï tessellation.
Main Methods:
- Large-scale molecular dynamics simulations of hard spheres.
- Geometric analysis using Voronoï tessellation.
- Characterization of structural order with an order parameter (Q(6)) based on spherical harmonics.
Main Results:
- Crystallization of disordered hard-sphere packings is observed only within a limited range of packing fraction.
- For other packing fractions, the system exists as a stable or metastable fluid or a glass.
- The study tracked changes in Voronoï tessellation statistics during crystallization, quantifying order emergence.
Conclusions:
- The geometric properties of Voronoï tessellations effectively distinguish between fluid, glass, and crystalline phases in hard-sphere systems.
- A narrow window of packing fraction facilitates crystallization, with deviations leading to amorphous states.
- The order parameter Q(6) provides a quantitative measure for the onset of structural order in these systems.