Dense crystalline packings of ellipsoids

Area of Science:

• Condensed matter physics
• Materials science
• Crystallography

Background:

• Ellipsoids are fundamental models for nonspherical particles in various systems.
• The densest packing of congruent hard ellipsoids remains an unsolved problem in condensed matter physics.
• Understanding high-density phases is crucial for many materials systems.

Purpose of the Study:

• To discover new dense crystalline packings of congruent hard ellipsoids.
• To investigate the properties and stability of these novel packings.
• To explore the implications for self-assembly and condensed matter systems.

Main Methods:

• Computational discovery of crystalline structures.
• Analysis of packing density and symmetry.
• Thermodynamic stability analysis.
• Phase diagram construction for self-dual ellipsoids.

Main Results:

• Discovery of a novel family of dense crystalline packings of self-dual ellipsoids.
• Identification of a quasi-square-triangular (SQ-TR) tiling arrangement.
• Achieved packing densities exceeding the previously known densest crystal (SM2) for specific aspect ratios.
• Maximal packing density of approximately 0.75806 achieved at aspect ratio α=93/64.
• Demonstrated thermodynamic stability of the SQ-TR phase at high densities.

Conclusions:

• The discovered SQ-TR crystal represents a new paradigm for dense packing of nonspherical particles.
• These findings provide organizing principles for the self-assembly of colloidal and granular systems.
• The study advances the understanding of phase behavior in condensed matter systems involving anisotropic particles.