Classifying Crystals of Rounded Tetrahedra and Determining Their Order Parameters Using Dimensionality Reduction

Area of Science:

• Materials Science
• Computational Physics
• Crystallography

Background:

• Understanding the phase behavior of non-spherical particles is crucial for designing novel materials.
• Hard spherotetrahedra offer a tunable model system interpolating between spheres and tetrahedra.

Purpose of the Study:

• To investigate the phase behavior and packing structures of hard spherotetrahedra using simulations.
• To identify novel dense packings and understand self-assembly mechanisms.

Main Methods:

• Molecular dynamics simulations were employed to study the phase behavior.
• Principal component analysis of bond orientational order parameters (q̅l) was used to characterize local environments.

Main Results:

• 13 close-packed structures were identified, some denser than previously reported, including quasicrystal approximants.
• All identified structures are stable below close packing, with a 14th plastic crystal phase observed.
• Self-assembly into ordered structures occurs at the tetrahedron and sphere extremes, but not in intermediate rounded-edge regimes.
• Specific linear combinations of bond orientational order parameters, like q̅4 - q̅6 and q̅4 - q̅8, effectively distinguish different crystal structures.

Conclusions:

• Hard spherotetrahedra exhibit rich phase behavior with previously undiscovered dense packings.
• The study highlights the importance of particle shape in dictating self-assembly and packing efficiency.
• Developed order parameter combinations offer a powerful tool for analyzing complex particle systems.