On the Monte Carlo simulation of curvature-driven growth

The kinetics of shrinking of an island grain embedded in a matrix as a function of the grain boundary properties is simulated using a Monte Carlo (MC) technique where the probability of switching of a grain boundary site is scaled according to the product of the boundary energy and mobility. Careful investigation of the simulation results shows that the correct implementation is one where the MC simulation time, the time of visit to a grain boundary site during the simulation is scaled according to the product of the boundary energy and mobility. Simulations in which the site is visited all the time, but the flip probability is scaled according to the product of the boundary energy and mobility, do not yield the correct results expected for curvature-driven boundary migration. The mechanistic differences between the two approaches are described.