Defect formation and coarsening in hexagonal 2D curved crystals.

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.