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本文叙述了分形理论中镍基高温合金定向凝固固－液界面研究中的应用。从分形的基本理论出发，论证了定向凝固固－液界面是一种不规则的分形结构，并用分形维数的新方法定量地描述了固－液界面的生长形态，给出了界面分形维数与凝固速率之间的关系。发现随着凝固速率的增加，固－液界面的分形维数呈指数规律增加。而且，从热力学角度对分形维数不仅仅是单纯描述不规则图形的几何参量，而是对一个依赖于凝固参数而变化的态函数做了较为深入的讨论。
This article describes the fractal theory of nickel-base superalloy directional solidification solid-liquid interface research. Based on the basic theory of fractal, the solid-liquid interface of directional solidification is an irregular fractal structure. The fractal dimension of the solid-liquid interface is quantitatively described by a new method of fractal dimension. The interface fractal dimension And the relationship between the solidification rate. It is found that the fractal dimension of the solid-liquid interface increases exponentially as the solidification rate increases. Moreover, from the thermodynamic point of view, the fractal dimension is not only a simple description of geometric parameters of irregular shapes, but a more in-depth discussion of a state function that depends on the parameters of solidification.