Defect formation and coarsening in hexagonal 2D curved crystals

Prior research has shown that defect behavior in flat crystal systems follows predictable patterns based on grain boundary interactions and thermal quenching. However, no prior work had resolved how curvature affects defect formation and coarsening in two-dimensional curved structures. This gap motivated the investigation of how geometric constraints influence defect density and distribution in 2D curved crystals. Existing knowledge suggests that grain boundaries form through crystal impingement in flat systems, but this process may not apply to curved geometries. The uncertainty around curvature-driven defect dynamics led to a need for experimental and theoretical analysis of curved crystal systems. No prior work had explored whether high-curvature regions act as defect traps during coarsening. The absence of data on dislocation and disclination behavior in curved systems created a need for this study. This paper addresses the lack of understanding about how curvature modifies defect formation and coarsening mechanisms in 2D curved crystals.

This study aims to investigate how curvature influences defect formation and coarsening in two-dimensional curved crystal structures. The specific problem is the lack of understanding of how geometric constraints affect the density and spatial distribution of defects during phase transitions. The motivation stems from the observation that flat crystal systems exhibit distinct defect formation mechanisms not applicable to curved geometries. The research seeks to determine whether curvature alters the onset and progression of defect formation during crystallization. A key question is whether high-curvature regions serve as traps for defect diffusion during coarsening. The study also explores whether dislocation density remains geometry-insensitive during early coarsening stages. The goal is to clarify how curved substrates modify defect dynamics compared to flat systems.

The study employs computational simulations to model defect formation and coarsening in 2D curved crystals. The approach involves quenching a liquid into a crystalline phase on curved substrates. The researchers track defect density and distribution during phase transitions using numerical simulations. They analyze how curvature affects the spatial inhomogeneity of defect formation at the onset of crystallization. The study compares defect behavior in curved systems with that in flat systems to identify geometric dependencies. The researchers monitor grain boundary motion and defect annihilation during annealing processes. They examine how dislocations and disclinations respond to curvature-driven forces during coarsening. The methods include tracking the diffusion of linear defect arrays toward high-curvature regions and their absorption by disclinations.

The study finds that defect formation in curved 2D crystals is strongly influenced by curvature, leading to inhomogeneous defect density at the onset of phase transitions. A single growing crystal can produce varying defect densities depending on its initial position and orientation relative to the substrate. Quenching the liquid into the crystal phase results in curved polycrystalline structures with complex defect arrays. During annealing, grain boundary motion and defect annihilation increase crystalline order through curvature-driven mechanisms. Linear defect arrays diffuse toward high-curvature regions and are absorbed by disclinations. At early coarsening stages, dislocation density remains insensitive to geometry, while disclination populations are strongly affected by curvature. High-curvature regions act as traps for defect diffusion, including disclinations and domain walls. These findings suggest that curvature significantly modifies defect dynamics compared to flat systems.

The authors conclude that curvature strongly influences defect formation and coarsening in 2D curved crystals. The onset of phase transitions leads to inhomogeneous defect density, which depends on the crystal's initial position and orientation. Quenching produces curved polycrystalline structures with complex defect arrays. During annealing, grain boundary motion and defect annihilation increase crystalline order through curvature-driven mechanisms. Linear defect arrays diffuse toward high-curvature regions and are absorbed by disclinations. At early coarsening stages, dislocation density remains insensitive to geometry, while disclination populations are strongly affected by curvature. High-curvature regions act as traps for defect diffusion, including disclinations and domain walls. These findings suggest that curvature significantly modifies defect dynamics compared to flat systems.