Monte Carlo simulations of particle/boundary interactions

By simulating a single boundary moving through an array of particles we are able to model Zener pinning with volume fractions from f = 10(-4) to f = 10(-2). Thus we are able to use the analytical predictions (in a volume fraction regime that is statistically significant) to test the computer model. Single boundaries are modelled which possess constant curvature and migrate via the same grain growth algorithm as other Monte Carlo simulations of grain growth. In the absence of particles the boundaries show a linear relationship between driving force, Fd, and velocity,v. With the inclusion of particles, at high values of grain curvature, R. v is proportional to che net driving force. Immobility of the boundary defines a pinned state and critical values of r and R are determined. A plot of log((R)/(r)) vs. log(f) gives a gradient, n = 0.45 +/- 0.01.