Structural Origins of the Excellent Glass Forming Ability of ${\mathrm{Pd}}_{40}{\mathrm{Ni}}_{40}{\mathrm{P}}_{20}$

We report a hybrid atomic packing scheme comprised of a covalent-bond-mediated “stereochemical” structure and a densely packed icosahedron in a bulk metallic glass ${\mathrm{Pd}}_{40}{\mathrm{Ni}}_{40}{\mathrm{P}}_{20}$. The coexistence of two atomic packing models can simultaneously satisfy the criteria for both the charge saturation of the metalloid element and the densest atomic packing of the metallic elements. The hybrid packing scheme uncovers the structural origins of the excellent glass forming ability of ${\mathrm{Pd}}_{40}{\mathrm{Ni}}_{40}{\mathrm{P}}_{20}$ and has important implications in understanding the bulk metallic glass formation of metal-metalloid alloys.

Figure 1

(a) Simulated temperature-dependent pair correlation function of ${\mathrm{Pd}}_{40}{\mathrm{Ni}}_{40}{\mathrm{P}}_{20}$ from 2000 to 300 K. The shoulder peak and subpeaks are marked by the arrowheads. (b),(c) The generalized and partial radial distribution functions of ${\mathrm{Pd}}_{40}{\mathrm{Ni}}_{40}{\mathrm{P}}_{20}$. The experimental data are shown as a dotted line, and the calculated peaks of the hybrid packing assemblies are marked by solid lines. (d) The pDOS of ${\mathrm{Pd}}_{40}{\mathrm{Ni}}_{40}{\mathrm{P}}_{20}$ for P, Ni, and Pd. $\mathbf{A}$, $\mathbf{B}$, $\mathbf{C}$, and $\mathbf{D}$ are marked as the different bands for the discussion in the main text.

Figure 2

(a) The isosurface of charge density of the band $\mathbf{C}$, as shown in Fig. 1d. (b) The isosurface of charge density of the bands $\mathbf{A}$ and $\mathbf{B}$ in Fig. 1d. (c) The histogram of P-centered Voronoi polyhedra of ${\mathrm{Pd}}_x{\mathrm{Ni}}_{80-x}{\mathrm{P}}_{20}$ ($x=0,20,40,60$) glasses using charge density ${\rho }_m=0.21,0.18,0.15,0.12\mathrm{e}/{\AA }^3$ as the cutoff parameters, respectively. (d) Histogram of Ni-centered Voronoi polyhedra for ${\mathrm{Pd}}_x{\mathrm{Ni}}_{80-x}{\mathrm{P}}_{20}$ ($x=0,20,40,80$) glasses. The frequencies are normalized by the atomic number of P. $R_{\mathrm{cutoff}}=3.5\mathrm{Angstrom}$.

Figure 3

Typical atomic configuration of glassy ${\mathrm{Pd}}_{40}{\mathrm{Ni}}_{40}{\mathrm{P}}_{20}$. The connection between P-centered TTPs and Ni-centered icosahedra is highlighted, illustrating a topological order between the two clusters. FS, ES, and VS denote the face, edge, and vertex sharing methods between P-centered clusters. The dashed circles delineate the Ni-centered icosahedronlike polyhedra.

Figure 4

(a) The typical atomic configuration of P-centered $⟨0,3,6,0⟩$ and $⟨0,4,4,0⟩$ clusters as well as the relationship between the two types of clusters. Site 1 denotes the vertices of the trianglar prism, and site 2 denotes the side atoms of the trigonal prism. (b) The hybrid packing between one Ni-centered polyhedron and two P-centered clusters. The inset is the planform view of the Ni-centered polyhedron with the Voronoi index of $⟨0,2,8,2⟩$. Sites $\mathbf{A}$ and $\mathbf{B}$ represent a special atom site for the switch from $⟨0,3,6,0⟩$ to $⟨0,4,4,0⟩$ for the P-centered trigonal prism structure and from a symmetric icosahedronlike polyhedron to a low-symmetric atomic cluster. (c) The bond-angle distributions of Ni-vertex and P-vertex angles that reflect the correlation between two neighboring P-centered clusters and the Ni-centered polyhedron. (d) The packing methods between the local ordering clusters. The solute Ni atoms are the dark gray (green) ones.