Hidden order in amorphous structures: Extraction of nearest neighbor networks of amorphous Nd–Fe alloys with Gabriel graph analyses

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)].