Monte Carlo simulations of grain growth and Zener pinning

This paper describes computer simulations of Zener pinning in two and three dimensional grain growth, in the presence of dispersions of shaped particles. The two dimensional simulations are embedded on square or hexagonal lattices of 2000 × 2000 Potts elements. In these simulations, if they are large enough, the grain growth exponent is n = 0.38 for the initial growth and stagnation occurs at a grain size which is proportional to the particle size and proportional to f−1/2 where f is the area fraction of particles. In three dimensions the simulations are embedded on simple or face-centered cubic lattices with up to 235 × 235 × 235 Potts elements. In these simulations, the kinetics are similar to those in two dimensions (n = 0.38) and the stagnant grain size is proportional to ƒ−1/3. The stagnant grain shape does not depend strongly on the particle shape (sphere, needle or plate), but the grain size exhibits a mild dependence on the precipitate shape. However, these three dimensional simulations are often not big enough to give reliable results and, in particular, they violate the principle that the grain size should be proportional to the particle size. This problem becomes more acute as the volume fraction of particles decreases. The ranges of allowable volume fractions and particle sizes in a simulation of given size are discussed.