Pattern coarsening in a 2D hexagonal system

Abstract

We have studied the ordering dynamics of a two-dimensional system which consists of a single layer of spherical block copolymer microdomains in a thin film. We follow the annealing process after a quench from the disordered state by electron microscopy and time-lapse atomic force microscopy. At late times the orientational correlation length ξ6 of the microdomain lattice exhibits a t 1/4 temporal power law. We compare the time evolution of the densities of dislocations, disclinations and the dislocation orientational correlation function. While most disclinations condense into dislocations and most dislocations condense into "grain boundaries", the dynamics appear to involve the interplay of disclinations and lines of dislocations. Rather than isolated grains shrinking, the most frequently observed process is the collapse of a smaller grain which resides on the boundary of two larger grains.

Crystallization dynamics on curved surfaces

“…Here the different structures of defects that participate in the dynamics of crystallization are dislocations, pleats (linear arrays of dislocations with variable distance between them [14]), free disclinations, and scars (linear arrays of dislocations and disclinations with a net topological charge) [9]. During crystallization in flat space, the domain structure is dominated by triple points (regions where three grains meet) [32], [33]; isolated disclinations are absent [34][35][36]. However, due to curvature, here the triple points become unstable and the mechanism of domain growth produces scars and pleats (see Fig.…”

“…Since defect structures mainly decorate domain walls, a characteristic length scale ξ , defined in terms of ρ ds as ξ ∼ d/ρ ds , provides a measure of the average domain size [32][33][34][35]. Here d ∼ 2a is the average distance between dislocations along a domain wall.…”

“…Through the triangulation, it is possible to obtain structural parameters such as the particle's first neighbors, degree of crystallinity, or topological defects [32][33][34][35]. Once the positions of the particles are determined, the analysis starts by calculating each particle's first neighbors.…”

Coarsening dynamics of topological defects in thin permalloy films

“…The topic of coarsening dynamics of topological defects in diverse systems ranging from liquid crystals [1][2][3][4] to biosystems [5] and cosmology [6] has attracted considerable interest as it is related to properties of symmetry-breaking phase transitions. As the system is quenched from a hightemperature disordered phase to a low-temperature ordered phase, the symmetry of the disordered phase is broken and topological defects are generated, subsequently exhibiting slow coarsening dynamics [7].…”

Hexagonal phase ordering in strongly segregated copolymer films

“…Experiments on block copolymer thin films have been able to capture time evolution of pattern defects and orientation domain coarsening [14][15][16]. They find in the case of a spherical or cylindrical phase that gives rise to hexagonally ordered films, the correlation length ξ characterizing the size of grains of similar orientation grows roughly according to the power law t 1/4 , at least after some initial transient behavior.…”