An extended two-state model for grain growth during gas phase production of powders

We have investigated a Monte-Carlo treatment of particle-growth by evaporation–condensation based on a combination of a two-state Potts, or Ising, model with the Metropolis algorithm for the acceptance/rejection of simulated growth steps. The effects of initial size-distribution and lattice occupancy on particle-growth through Ostwald ripening via evaporation–condensation have been explored and the sensitivity of the results to model-parameters, such as interaction energy, temperature and second-nearest-neighbour weightings has been investigated.From an initial random distribution of particles, the predicted growth follows a square root dependence on time, consistent with well known analytical treatments. When the temperature parameter was examined, a critical temperature Tc was found. Below Tc the rate of particle-growth increased with increasing T; but above Tc the growth-rate decreased with increase in T. The correspondence, in the absence of second-nearest-neighbour interactions, of the computed Tc with the analytically determined value demonstrates the robustness of our procedures.The effects of evaporation–condensation on the size-distribution, characterized by a mean size 〈R〉 and r.m.s. deviation δ, have received particular consideration. It is predicted that, for three different initial particle size distributions, with the same initial mean size, growth by evaporation–condensation will lead to convergence of the normalized δ/〈R〉 versus time or δ/〈R〉 versus 〈R〉 curves. Counter-intuitively, a narrow initial size-distribution is not maintained by particles growing by evaporation–condensation.Finally, we have developed a simple technique for incorporating diffusive phenomena into this model by incorporating distance dependence into the probability of migration. This has reduced the necessary computational time and enabled us to compare the dependence of the δ/〈R〉 versus 〈R〉 relationship for different values of the characteristic distance. Remarkably and somewhat unexpectedly, we find that for a wide range of model-parameters the normalized deviation is effectively independent of this characteristic distance.