Numerical simulation of two-dimensional late-stage coarsening for nucleation and growth

Abstract

Numerical simulations of two-dimensional late-stage coarsening for nucleation and growth or Ostwald ripening are performed at area fractions 0.05 to 0.4 using the monopole and dipole approximations of a boundary integral formulation for the steady state diffusion equation. The simulations are performed using two different initial spatial distributions. One is a random spatial distribution, and the other is a random spatial distribution with depletion zones around the particles. We characterize the spatial correlations of particles by the radial distribution function, the pair correlation functions, and the structure function. Although the initial spatial correlations are different, we find time-independent scaled correlation functions in the late stage of coarsening. An important feature of the late-stage spatial correlations is that depletion zones exist around particles. A log-log plot of the structure function shows that the slope at small wave numbers is close to 4 and is -3 at very large wave numbers for all area fractions. At large wave numbers we observe oscillations in the structure function. We also confirm the cubic growth law of the average particle radius. The rate constant of the cubic growth law and the particle size distribution functions are also determined. We find qualitatively good agreement between experiments and the present simulations. In addition, the present results agree well with simulation results using the Cahn-Hilliard equation.