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

利用最小生成树(MST)对凝固组织的均匀性和空间分布进行了分析。首先阐明了MST分析对于生成的二维点空间模式的有效性。对于相关图案，边缘的归一化平均值及其MST的标准差给出了确定结构图案的信息。通过对铸件边缘长度和边缘角度的统计，得到了局部结点分布的信息。傅立叶变换分析还提供了组织长程有序化的有用信息。定向凝固镍基高温合金中一次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，并具有正方形晶格图案的特征。研究了快速凝固合金的形核点分布。形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，这种分布变得无序。

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.