Extension of Gladman's model for abnormal grain growth

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Abstract
We present a first principles model for abnormal grain growth in either two or three dimensions that has the virtue of simplicity on the one hand and of close agreement with recent computer simulations on the other. The model is based on Gladman's picture of one grain growing in a matrix of similar grains, retaining its shape as it grows. The grain must have a critical size advantage over its neighbors before the process is spontaneous. Once growth is under way the kinetics are identical to those in Hillert's classical model of grain growth. In the competition between abnormal growth of one grain and the normal growth in the matrix, the important parameters are the ratios γa/γm and μa/μm, where γ is the energy and μ is the mobility of a grain boundary and the subscripts a and m refer to abnormal and matrix, respectively. Values of these three factors: size advantage, energy advantage, and mobility advantage define the conditions under which abnormal grain growth may occur. The results agree closely with recent computer simulations and therefore permit interpolations to be made between computer answers. A hypothesis on the role of second phase particles as a trigger for abnormal grain growth is proposed.
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