基于Glicksman近期提出的平均N面体模型(ANHs),研究了拓扑分组下晶粒表面积的变化规律,导出了一个可由简单数学关系式近似表示的具有拓扑依赖性的晶粒长大速率方程.速率方程显示晶粒的表面积变化速率与其面数的平方根近似成线性关系.
The law of grain growth is one of the classic problems in materials science. In 1952, an exact formula named von Neumann relation was derived for grain growth in two-dimensional space that the growth rate of a grain depends only on its number of sides n. In three dimensions, topology-dependent rate equations of grain growth are usually proposed to describe the individual grain growth. Such equations can describe the mean growth rate of grains within the same topological class and can be used to derive general properties of polycrystals. In this paper, based on average N-hedra (ANHs) model proposed by Glicksman recently, the law of the change of grain surface area was studied and a topology-dependent rate equation of grain surface area change was derived. Both the contributions of the grain boundary motion and grain edges motion to the grain growth were considered in the derivation. This topology-dependent rate equation can be expressed through a simple relation that the change rate of grain surface area is proportional to the square root of the number of grain faces. This result can assist in a better understanding of the process of grain growth from a statistical point of view and is similar to the reported topology-dependent grain growth equations.
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