Hidden orders in amorphous structures: extraction of nearest neighbor networks of amorphous Nd-Fe alloys with Gabriel graph analyses

TL;DR

This study uses Gabriel graph analysis to identify and compare the nearest neighbor networks in amorphous Nd-Fe alloys, revealing composition-dependent structural variations and increased order with higher Nd content.

Contribution

It introduces Gabriel graph analysis as an effective method for extracting and analyzing nearest neighbor networks in amorphous metallic alloys.

Findings

Gabriel graphs accurately represent first nearest neighbor networks.

Coordination number distributions vary with alloy composition.

Higher Nd content correlates with increased structural order.

Abstract

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 vary depending on the composition ratio. The angular distributions among three adjacent atoms were also analyzed, and it was found that the angular distributions behave differently in the Nd-rich and Fe-rich samples. We found that the orders in the amorphous system becomes stronger as increasing the Nd ratio, which corresponds to the appearance of crystalline grain boundary phases at high Nd composition ratio [T. T. Sasaki et al., Acta Mater. 115, 269-277 (2016)].