Using the scheme of Delaunay and Gabriel graphs, we analyzed the amorphous structures of computationally created Nd–Fe alloys for several composition ratios based on melt quench simulations with finite temperature first-principles molecular dynamics. By the comparison of the radial distribution functions of the whole system and those derived from the Delaunay and Gabriel graphs, it was shown that the Gabriel graphs represent the first nearest neighbor networks well in the examined amorphous systems. From the Gabriel graph analyses, we examined the coordination structures of amorphous Nd–Fe alloys statistically. We found that the ranges of distributions of coordination numbers are wider at the lower Nd composition ratios. The angular distributions among three adjacent atoms were also analyzed, and it was found that the steeper the angular distributions become the higher the Nd composition ratios are. These features mean that the orders in the amorphous system become stronger as the Nd ratio increases, which corresponds to the appearance of crystalline grain boundary phases at high Nd composition ratios [T. T. Sasaki et al., Acta Mater. 115, 269–277 (2016)].

中文翻译：

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非晶态结构的隐藏顺序：利用Gabriel图分析提取非晶态Nd-Fe合金的最近邻域网络

使用Delaunay和Gabriel图的方案，我们基于有限温度第一性原理分子动力学的熔融淬火模拟，分析了几种组成比的计算创建的Nd-Fe合金的非晶态结构。通过比较整个系统的径向分布函数以及从Delaunay和Gabriel图得到的径向分布函数，可以看出，Gabriel图很好地表示了所检查的非晶系统中的第一个最近邻网络。从Gabriel图分析中，我们统计地检查了非晶Nd-Fe合金的配位结构。我们发现，在较低的Nd组成比下，配位数的分布范围较宽。还分析了三个相邻原子之间的角分布，并且发现，角分布越陡，则Nd组成比越高。这些特征意味着，随着Nd比的增加，非晶态系统中的有序化变得更强，这对应于高Nd组成比下的晶界相的出现[TT Sasaki等。，Acta Mater。115，269-277（2016）]。