Defect formation and coarsening in hexagonal 2D curved crystals

Abstract

In this work we study the processes of defect formation and coarsening of two-dimensional (2D) curved crystal structures. These processes are found to strongly deviate from their counterparts in flat systems. In curved backgrounds the process of defect formation is deeply affected by the curvature, and at the onset of a phase transition the early density of defects becomes highly inhomogeneous. We observe that even a single growing crystal can produce varying densities of defects depending on its initial position and local orientation with regard to the substrate. This process is completely different from flat space, where grain boundaries are formed due to the impingement of different propagating crystals. Quenching the liquid into the crystal phase leads to the formation of a curved polycrystalline structure, characterized by complex arrays of defects. During annealing, mechanisms of geodesic curvature-driven grain boundary motion and defect annihilation lead to increasing crystalline order. Linear arrays of defects diffuse to regions of high curvature, where they are absorbed by disclinations. At the early stage of coarsening the density of dislocations is insensitive to the geometry while the population of isolated disclinations is deeply affected by curvature. The regions with high curvature act as traps for the diffusion of different structures of defects, including disclinations and domain walls.

Mesostructure of Ordered Corneal Nano-nipple Arrays: The Role of 5–7 Coordination Defects

“…The combination of the two in the 5–7 configuration forms a dislocation, similar to dislocations in other 2D crystal structures with and without curvature (e.g. refs 24, 25, 26, 27, 28, 29, 30, 31, 32). The surprising result of the study was that the 5–7 coordination defects are aligned in rows forming grain boundaries between adjacent crystals/domains with perfect structure, also similar to grain boundaries in other 2D hexagonal structures (e.g.…”

“…While the results of this study are of significant importance in the analysis and understanding of the intriguing nanostructure in nipple arrays of butterfly eyes, the findings are also equally important in the broader context of symmetry breaking 5- and 7-fold defects and their distribution in numerous other and seemingly unrelated structures referenced earlier24252627282930313233343536373839404142434445464748. The type of 5- and 7-coordination defect and combinations thereof to form higher order defects have been observed in 2D structure systems such as magnetic bubble arrays, block copolymers, convection patterns, charge distributions, graphene, etc.…”

Defect patterns on the curved surface of fish retinae suggest mechanism of cone mosaic formation

“…The biological example of grain boundary formation during initial patterning in zebrafish retinae also poses interesting physical questions. A primary concern in the existing physics literature has been the existence of grain boundaries in the ground state of crystals on curved surfaces [24-26, 34, 49-50]; although some aspects of the kinetics of crystal growth have also been considered [51][52], the question of how the growth geometry affects the positioning of defects has received little attention [40,53]. For example, in which growth geometries does crystallization produce defect distributions that are close to the ground state without defect motion?…”

Phase nucleation in curved space

“…Although experiments and theoretical calculations have contributed to unveil equilibrium configurations and energetics of topological defects in curved space, dynamical processes like crystallization and melting still remain marginally explored [29][30][31][32] .…”