Characterization of maximally random jammed sphere packings: Voronoi correlation functions

Area of Science:

• Statistical Mechanics
• Materials Science
• Computational Physics

Background:

• Understanding the structure of jammed sphere packings is crucial for materials science.
• Local statistics like Minkowski functionals are insufficient to distinguish complex packing structures.
• Maximally random jammed (MRJ) sphere packings represent a key class of disordered solids.

Purpose of the Study:

• To characterize the structure of MRJ sphere packings using advanced statistical descriptors.
• To differentiate MRJ packings from equilibrium hard-sphere liquids and Poisson point processes.
• To investigate nonlocal structural correlations within MRJ packings.

Main Methods:

• Computation of Minkowski functionals (volume, surface area, integrated mean curvature) for Voronoi cells.
• Introduction and evaluation of nonlocal descriptors: Minkowski functional correlation functions and cell-cell probability density functions.
• Comparison of these descriptors for MRJ packings, equilibrium hard spheres, and Poisson point processes.

Main Results:

• Local Minkowski functionals are insensitive to global structural differences.
• Nonlocal correlation functions reveal significant structural information, outperforming standard pair-correlation functions.
• MRJ packings show strong anticorrelations in Voronoi volumes, indicating suppressed large-scale volume fluctuations.
• Correlation functions successfully distinguish MRJ packings from equilibrium liquids and random processes.
• Preliminary analysis suggests the presence of distorted icosahedral structures in MRJ packings.

Conclusions:

• Nonlocal correlation functions are essential for characterizing the complex structure of jammed sphere packings.
• MRJ sphere packings possess unique structural signatures not captured by local statistics alone.
• These findings advance our understanding of glassy systems and disordered materials.