Computer simulation of topological evolution in 2-D grain growth using a continuum diffuse-interface field model

The local kinetics and topological phenomena during normal grain growth were studied in two dimensions by computer simulations employing a continuum diffuse-interface field model. The relationships between topological class and individual grain growth kinetics were examined, and compared with results obtained previously from analytical theories, experimental results and Monte Carlo simulations. It was shown that both the grain-size and grain-shape (side) distributions are time-invariant and the linear relationship between the mean radii of individual grains and topological class n was reproduced. The moments of the shape distribution were determined, and the differences among the data from soap froth, Potts model and the present simulation were discussed. In the limit when the grain size goes to zero, the average number of grain edges per grain is shown to be between 4 and 5, implying the direct vanishing of 4- and 5-sided grains, which seems to be consistent with recent experimental observations on thin films. Based on the simulation results, the conditions for the applicability of the familiar Mullins-Von Neumann law and the Hillert's equation were discussed.