Partitioning of Size-Mismatched Impurities to Grain Boundaries in 2d Solid Hard-Sphere Monolayers

Computational studies have been carried out to investigate the equilibrium partitioning of size-mismatched impurities between the bulk solid and grain boundary (GB) environments in 2d hard-sphere monolayers. The solvent repacking Monte Carlo method and a new variation were used to exchange varying numbers and types of particles under conditions of fixed particle fugacities, allowing efficient sampling of impurity particle distributions even within the bulk solid. Measurements of GB stiffness depression arising from the impurities were made via the capillary fluctuation method and found to agree with calculations based on the Gibbs adsorption isotherm, providing a test of the internal consistency of the results. The dependence of the excess concentration at the GB on factors, including impurity size (diameter ratios λ = 0.5-4 times the majority host particle diameter), impurity concentration, grain misorientation angle, and packing pressure, was studied. In general, the affinity of impurity particles for GB increased with the difference between their size and the host particles, and varied with grain misorientation angle with a dependence reflecting the excess free area at the GB. Impurities with λ = 4 were exceptions to both these trends, due to their ability to substitute efficiently for six-coordinate host particles within the bulk and for five-coordinate host particles at dislocations in the grain boundaries. Comparison with results from an experimental study of mixed colloidal monolayers raises questions about how kinetic effects during grain coarsening might produce less impurity segregation to the GB than equilibrium exchange.