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

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)].

Disordering the Disorder as the Route to a Higher Order: Incoherent Crystallization of Calcium Phosphate through Amorphous Precursors

“…From this perspective, amorphous materials could be seen not as the defective kin of their crystalline counterparts but, rather, as a gateway to complex structures and, thus, the materials of the future. This insight parallels the widely accepted hypothesis that there is an order intrinsic to every amorphous structure − as well as that there is more than one distinct structure associated with each amorphous material. , With their complex free energy profiles typified by an erratic distribution of closely related minima, they also resemble the energy landscape of proteins, which never occupy a single energy state twice, and may be a natural choice for material structures to interface with life, as opposed to more energetically defined and ordered crystals. When one adds to this that amorphous materials in a number of pharmaceutical, medical, and other − applications exhibit higher activities than their crystalline analogues, it could be concluded that interesting new products may result from fundamental research on synthesis and understanding of the structural evolution of order and disorder in these materials.…”

“…Temperature is another ambiguous parameter, correlating to some extent to the peculiar reversal from the exothermic to the endothermic crystallization process at approximately the physiological temperature . Henceforth, lowering the temperature may often, but not always, slow the crystallization of the amorphous phase. , Likewise, using specific ions in the reaction mixture, such as Mg 2+ , Sr 2+ , Si 4+ , Ni 2+ , Cu 2+ , Ga 3+ , or P 2 O 7 , − may inhibit the transition, but only for short periods of time, alongside often exhibiting a dual, concentration-dependent effect, as in the case of Zn 2+ . The use of low-pressure, high-energy methods for synthesis and storage can extend the stability of ACP, but these methods are incompatible with physiological conditions on which most biomedical applications depend.…”

First-principles determination of intergranular atomic arrangements and magnetic properties in rare-earth permanent magnets

“…Amorphous structures within a supercell can be obtained by first-principles molecular dynamics with the melt-quench approach [63]. Even though the distribution of interatomic distances is continuous in amorphous structures, it is possible to identify the nearest-neighbor pairs by utilizing Gabriel graphs [64,65]. The average of the interatomic distances for, e.g., the nearest-neighbor Nd-Fe pairs in amorphous Nd Other expressions of the Liechtenstein method [18] to calculate ij J have been given without using t -matrix in order to apply the method to first-principles schemes that do not directly use the concept of multiple scattering [66].…”

First-principles study of exchange coupling constants in Nd$_x$Fe$_{1-x}$ amorphous alloy

“…We have demonstrated that the Gabriel graph is suitable to describe nearest neighbor networks in amorphous systems in Ref. [25]. In the following analysis, we define the pairs of neighboring atoms as the atom pairs having Gabriel graph edges in between.…”

“…By comparing the J ij curves for different compositions, we observed that the J ij curves became steeper for large x. Moreover, we performed a combined analysis to examine the relationship between the exchange coupling constants with the local structures, using Gabriel graph analysis for amorphous systems [25]. We found that the average J ij for neighboring atom pairs became larger with an increase in the x value, which resulted in the modest decrease of the calculated Curie temperature of amorphous Nd x Fe 1−x depending on x.…”