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arXiv · 2509.06755

Transitional patterns on a spherical surface: from scars to domain defects of mixed lattices

Wenyu Liu·Han Xie·Yu Du·Baohui Li·Jeff Z. Y. Chen·Yao Li
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Abstract

The system of mixed hexagonal and square lattices on a spherical surface is examined, with an emphasis on the exploration of the disclination patterns that form in the square-rich regime. To demonstrate the possible outcomes, the Hertzian potential energy is used as a model for pairwise molecular interactions, which is known to support coexistent hexagonal and square lattices. Through molecular dynamics simulations, we show that at least four different disclination morphologies arise in a square-rich background: triangular defect domains composed of hexagonal lattices arranged in a cubic formation, bridged cubic state, linear scar disclinations with no hexagon content, and open scar disclinations containing a significant amount of hexagonal lattice in the open regions. Order parameters are also introduced to highlight the significance of the bridged and open-scar disclinations, both being the new morphologies reported in this study. The fact that the bridged state is an energetically preferred one is further demonstrated by a separate elastic energy model, which confirms its prevalence over the unbridged cubic state.

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Wenyu Liu, Han Xie, Yu Du, Baohui Li, Jeff Z. Y. Chen, Yao Li. 2025-09-08. Transitional patterns on a spherical surface: from scars to domain defects of mixed lattices. https://arxiv.org/abs/2509.06755

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