A Multiple-Lognormal Model of Normal Grain Growth
In the literature, grain growth models of two kinds are found: (a) “single grain” descriptions; grain growth is described for a single, freely growing grain, where the grain boundary movement resulting from the boundary curvature causes the change of the grain size. Simple arguments show that the diameter of a single free grain varies with the square root of the time. Sometimes with argument, but generally without, it is concluded from this single-grain behavior that the average grain size shows the same time dependence. Even modern textbooks1 treat grain growth in this way, and (b) statistical models;2-6 some authors have introduced the effect of the distribution of shapes and sizes. Smith2 suggested a natural tendency of these distributions to be fixed. Assuming a lognormal distribution of shapes as well as of sizes, Feltham3 was the first to present a quantitative statistical description of the grain growth process.
KeywordsLognormal Distribution Cumulative Frequency Median Diameter Sinter Time Topological Parameter
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