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采用分形理论定量地描述了定向凝固过程中固-液界面的形态,给出了固-液界面的分形维数与凝固速度、枝晶间距和试验合金中磷含量之间的关系发现随着凝固速率和合金中磷含量增大,固-液界面的分形线数呈指数规律增加。而且,结合分形理论和热力学理论论证了分形维数不仅仅是单纯描述不规则图形的几何参量,而且是一个依赖于凝固参数、化学成分变化的态函数
Fractal theory is used to quantitatively describe the solid-liquid interface morphology during directional solidification. The relationship between the fractal dimension of solid-liquid interface and solidification rate, dendrite spacing and phosphorus content in the experimental alloy is also obtained. The rate and the content of phosphorus in the alloy increase, and the fractal lines of the solid-liquid interface increase exponentially. Moreover, the fractal theory and thermodynamics theory demonstrate that the fractal dimension is not only a simple geometric parameter describing the irregular figure, but also a state function that depends on the solidification parameter and the chemical composition change