Analysis for uniformity and spatial distribution structure of solidification structures using minimal spanning tree

利用最小生成树（MST）分析了凝固组织的均匀性和空间模式分布。首先阐明了MST分析对生成的二维点空间格局的有效性。图中各边的归一化均值及其标准差为确定结构的模式提供了信息。局部节点分布信息由MST的边长和边角直方图获得。傅里叶变换分析也提供了关于结构的长范围排序的有用知识。单向凝固镍基高温合金初生枝晶的空间分布规律。当温度梯度较小时，枝晶的空间分布受抑制规律支配。当温度梯度较大时，枝晶图案变得规则，具有方形点阵图案的特征。研究了快速凝固合金的形核点分布。成核点的空间分布具有一定的规律性，但随着熔体过热度的增加，成核点的空间分布具有随机性。

Analysis for uniformity and spatial pattern distribution of solidification structures is investigated using minimal spanning tree (MST). The validity of MST analysis is at first clarified for the generated 2-dimensional point spatial patterns. The normalized mean values of edges and its standard variation of MST for the concerning pattern give the information for determining the pattern of the structure. The information on local node distribution is obtained from the histgrums of edge length and edge angle of MST.Fourie transform analysis also gives useful knowledge about the long range ordering of structures.The spatial pattern of primary dendrites in the unidirectionally solidified Ni-based superalloy. The spatial distribution of dendrites is dominated by an inihibitition rule when temperature gradient is small. When temperature gradient is large, dendrite pattern becomes regular and has the characteristics of a square lattice pattern. The nucleation point distribution of rapidly solidified alloys are also investigated. The regularity is found in the spatial pattern of nucleation points, though the pattern becomes random with increase of superheat of the melts.