Grain size distribution and topology in 3D grain growth simulation with large-scale Monte Carlo meth

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Three-dimensional normal grain growth was appropriately simulated using a Potts model Monte Carlo algorithm.The quasi-stationary grain size distribution obtained from simulation agreed well with the experimental result of pure iron.The Weibull function with a parameter β=2.77 and the Yu-Liu function with a parameter v =2.71 fit the quasi-stationary grain size distribution well.The grain volume distribution is a function that decreased exponentially with increasing grain volume.The distribution of boundary area of grains has a peak at S/=0.5,where S is the boundary area of a grain and is the mean boundary area of all grains in the system.The lognormal function fits the face number distribution well and the peak of the face number distribution is f=10.The mean radius of f=faced grains is not proportional to the face number,but appears to be related by a curve convex upward.In the 2D cross-section,both the perimeter law and the Aboav-Weaire law are observed to hold.
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