Simulations of grain boundaries between ordered hard sphere monolayer domains: Orientation-dependent stiffness and its correlation with grain coarsening dynamics.

The properties of grain boundaries (GBs) between ordered 2-d domains of a hard-sphere monolayer have been investigated using grand canonical Monte Carlo simulations. The capillary fluctuation method was used to determine the GB stiffness over a range of pressures, misorientations, and inclinations. Stiffness was found to be sensitive to misorientation (mismatch in the orientation angle of neighboring grains) but not to depend on inclination (angle between the boundary and the grain orientation). Excess area per GB length was observed to follow the same trend as stiffness with respect to grain misorientation and GB inclination angles. Dynamical studies of the evolution of bicrystalline or multicrystalline monolayers with simple geometries show that the calculated angle-dependent stiffnesses correlate well with the rate at which the evolving grain structure decreases the lengths of various GBs, in agreement with recent experimental results on monolayers of colloidal microspheres.