Computer simulation of Zener pinning

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Abstract
In this paper we describe analytical and computer models of the inhibition of grain growth in two and three dimensions. In two dimensions (thin films), all the models agree that the ratio of the stagnant grain size R to the particle size r is proportional to f −½, where f is the volume fraction of particles. In three dimensions the analytical models are only valid when f < 1% and then R/r oc f −1. The computer model for f > 1% gives the result R/r oc f −1/3. Experimental data from the literature support these conclusions and there is some evidence that there is a discontinuity in R/r at f≈1%.