Bond-orientational analysis of hard-disk and hard-sphere structures

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Materials Science

Background:

• Understanding the structural ordering of matter under external fields is crucial for materials design.
• Hard-disk and hard-sphere models provide fundamental insights into phase transitions and emergent structures.
• Shear flow can induce non-equilibrium crystalline structures not observed in equilibrium thermodynamics.

Purpose of the Study:

• To analyze the bond-orientational order in thermodynamic, random, and homogeneously sheared hard-disk and hard-sphere systems.
• To investigate the crystalline structures formed under shear, including two-dimensional (2D) and three-dimensional (3D) cases.
• To compare shear-induced structures with equilibrium freezing transitions and martensitic transformations.

Main Methods:

• Application of bond-orientational analysis to characterize local and global order parameters.
• Utilizing third-order rotational invariant analysis to identify specific crystalline symmetries.
• Employing Honeycutt-Andersen pair analysis and polyhedral analysis for detailed structural identification.

Main Results:

• Thermodynamic structures show a sharp increase in order at the freezing transition.
• Homogeneously sheared structures exhibit ordering at higher packing fractions than thermodynamic freezing due to suppressed nucleation.
• Shear flow in 2D hard disks induces fourfold order; in 3D hard spheres, it leads to body-centered-tetragonal (bct) structures and hexagonal-close-packed (hcp) structures due to stacking faults, with a coexistence of face-centered-cubic (fcc), bct, and hcp orders.

Conclusions:

• Shear-induced ordering in hard-sphere systems leads to complex crystalline structures, analogous to martensitic transformations.
• Dense, sheared hard-sphere systems display a coexistence of multiple crystalline orders (fcc, bct, hcp), not a single dominant phase.
• Advanced analytical techniques are essential for resolving the intricate structural details in sheared non-equilibrium systems.