The influence of spatial grain size correlation and topology on normal grain growth in two dimensions

In this paper two-dimensional grain growth has been simulated by the program Surface Evolver, and the influence of grain size correlation and topology on normal grain growth in two dimensions has been studied. The paper is an extension to two dimensions of the treatment in the accompanying paper discussing one-dimensional grain growth. Two-dimensional grain structures initially of 10 4 random Voronoi grains have been coarsened until approx. 2000 grains were left. It is demonstrated that a size correlation between neighbouring grains exists in a two-dimensional grain structure, and a spatial grain size correlation function relating the average size of all neighbours to grains of size R to R itself is defined. It is demonstrated that both the distribution function and the correlation function approaches a quasi stationary state when the mean grain size has roughly doubled compared to its initial value. The results are in agreement with corresponding results obtained for one-dimensional grain growth simulations. A modification of Hillert's mean field theory incorporating the correlation effect has also been developed and compared to the simulated results.