Partial structure investigation of the traditional bulk metallic glass ${\mathrm{Pd}}_{40}{\mathrm{Ni}}_{40}{\mathrm{P}}_{20}$

Local structures of ${\mathrm{Pd}}_{40}{\mathrm{Ni}}_{40}{\mathrm{P}}_{20}$ bulk metallic glass were investigated by combining anomalous x-ray scattering close to the Pd and Ni $K$ absorption edges, x-ray diffraction, neutron diffraction, and reverse Monte Carlo modeling, from which partial structure factors $S_{ij}\left(Q\right)$ and partial pair distribution functions $g_{ij}\left(r\right)$ as well as three-dimensional atomic configurations were carefully obtained around the constituent elements. A disagreement is found in the local structures with an ab initio molecular dynamics simulation by Guan et al., i.e., the existence of the P-P nearest-neighboring configurations is clarified in the present experimental result. From the Voronoi tessellation analysis, a preference of the pure icosahedral configurations is observed around the Ni atoms, whereas the local configurations around the Pd and P atoms are rather distorted icosahedra. A persistent homology analysis was carried out to identify meaningful shape characteristics of the intermediate-range atomic configuration of large rings.

Figure 1

From top to bottom, circles denote experimental data of ${\mathrm{\Delta }}_{\mathrm{Pd}}S\left(Q\right)$ and ${\mathrm{\Delta }}_{\mathrm{Ni}}S\left(Q\right)$ taken from AXS, and $S\left(Q\right)\mathrm{s}$ by XD and ND in the (a) whole $Q$ range measured and (b) in the low-$Q$ range up to 80 ${\mathrm{nm}}^{-1}$. Solid curves show the corresponding fits from RMC modeling. For clarity, the spectra are displaced upward by 3.

Figure 2

Circles represent experimental $g_N$ data and the solid curve shows the corresponding fit from RMC modeling.

Figure 3

$S_{ij}\left(Q\right)\mathrm{s}$ obtained from the RMC calculation. For clarity, the spectra are displaced upward by 3.

Figure 4

$g_{ij}\left(r\right)\mathrm{s}$ obtained from the RMC calculation. For clarity, the spectra are displaced upward by 3.

Figure 5

Selected partial bond angle distributions $\eta (cos{\theta }_{ijk})$. The ${\theta }_{ijk}$ values are given at the top of the figures.

Figure 6

Three-dimensional atomic representation obtained from the RMC calculation. The circles indicate the Ni-rich regions, and their diameter of 1.26 nm corresponds to a $Q$ value of 5 ${\mathrm{nm}}^{-1}$.

Figure 7

${\xi }_i$ of (a) Pd, (b) Ni, (c) P, and (d) all atoms in voxels with the size of 1.0161 nm.

Figure 8

The relation of ${\xi }_i$ values among (a) Pd-Ni, (b) Pd-P, and (c) Ni-P atoms. The dashed lines in (a) and (b) indicate the data fits of linear relations.

Figure 9

The persistence diagram for the ring structure ${\mathrm{D}}_1$ around (a) all atoms, (b) Pd, (c) Ni, and (d) P elements.