THE LAGUERRE MODEL OF GRAIN-GROWTH IN 2 DIMENSIONS .2. EXAMPLES OF COARSENING SIMULATIONS

The basic concepts of a deterministic scheme for simulating grain grow th or foam coarsening in two dimensions have been presented in Part I. Implementation of the corresponding Laguerre (or weighted Voronoi) di agram in computer manageable practical terms is now presented. The int ernal constituents of the model are discussed first and include the in itial configurations of the cellular network, obtained from different schemes. An internal clock is designed and an arbitrary dimensionless parameter is introduced to provide a relative weight to the rates of c hange of the generating circle positions with those of their sizes. A criterion for evaluating robustness and consistency of simulations is also presented. Actual simulation experiments are subsequently describ ed as conducted from a range of initial structures built from differen t numbers of cells--up to 10(5). The essential theoretical attributes of normal grain growth were found to be recoverable in all simulations , notably statistical self-similarity, parabolic kinetic law, and inde pendence from initial structures. It was also found that varying the r elative rates of change of circle positions with radii (via the corres ponding internal parameter mentioned above) resulted in size and shape distributions ranging from foam-like to polycrystal-like behaviours. It is claimed finally that the present model can be extended to three dimensions without any basic difficulty.