Phase field formulations for modeling the Ostwald ripening in two-phase systems

Phase field formulations have been constructed for modeling Ostwald ripening in two-phase systems. The microstructural evolution and the kinetics of Ostwald ripening were studied by numerically solving the time-dependent Ginzburg-Landau (TDGL) equations. The simulated microstructures are in a striking resemblance with experimental observations. The shape accommodation of second phase particles occurs as the volume fraction increases. It was observed that these two-phase systems reach the steady state or scaling state after a short transient time and the scaling functions are independent of time for all volume fractions of the second phase. The kinetics of Ostwald ripening in a two-phase mixture have been studied over a range of volume fractions of the coarsening phase. It was found that the coarsening kinetics of second phase particles follows the power growth law R-t(m) - R-o(m) = kt with m = 3, which is independent of the volume fraction of the coarsening phase. The kinetic coefficient k increases significantly as the volume fraction of the coarsening phase increases. (C) 1998 Published by Elsevier Science B.V.