A method based on the centroid of segregation points: A Voronoi polygon application to solidification of alloys

A new method for controlling segregation delicately based on the centroid of independent segregation points in an alloy macrostructure is established using Voronoi polygon method. Voronoi polygon area is found to nearly obey the log-normal distribution, which shows that a polygon may reflect a new solidifying unit. The relationship between Voronoi polygon characteristics and carbon segregation extent (segregation ratio) is investigated at different locations. In a pure columnar grain zone, the segregation extent worsens as the Voronoi polygon size decreases; in an equiaxed grain zone, this extent worsens as the size increases. A near-equilibrium solidification model for polygons under different conditions is studied, and the results are consistent with the aforementioned finding of segregation ratio. Compared with a secondary arm spacing, the fractal dimension of the solidification structure may be a better method to describe the characteristics of the solidification structure and the size change of Voronoi polygons as to relevant segregation. Thus, this study proposes a new experimental method that depicts the macrostructure from a different perspective, i.e., the segregation point instead of the solidification structure. The formation of Voronoi polygons created by segregation points during solidifying should be divided into two stages, i.e., appearance of the segregation point and determination of the polygon's outline. The segregation extent can be controlled by altering the size of the relevant Voronoi polygon, which is a unique alternative strategy for improving the uniformity of element distribution rather than simultaneously considering nucleus formation, solidification structure growth, and liquid flow as to the complex process of segregation formation.