Competing Hexagonal and Square Lattices on a Spherical Surface

TL;DR

This paper investigates how soft-core particles form competing hexagonal and square lattices on spherical surfaces, revealing new defect patterns and providing insights into geometric incompatibilities in natural and engineered systems.

Contribution

It introduces molecular dynamics simulations of Hertzian particles to identify novel disclination patterns arising from lattice competition on curved surfaces.

Findings

Discovery of domain and counter-domain defects in coexisting lattice patterns.

Identification of geometric incompatibilities affecting lattice arrangements on spheres.

Insights applicable to biological systems and architectural designs.

Abstract

The structural properties of packed soft-core particles provide a platform to understand the cross-pollinated physical concepts in solid-state- and soft-matter physics. Confined on spherical surface, the traditional differential geometry also dictates the overall defect properties in otherwise regular crystal lattices. Using molecular dynamics simulation of the Hertzian model as a tool, we report here the emergence of new types of disclination patterns: domain and counter-domain defects, when hexagonal and square patterns coexist. A new angle is presented to understand the incompatibility between tiling lattice shapes and the available spherical areal shapes, which is common in nature -- from molecular systems in biology to backbone construction in architectures.