Efficient local atomic packing in metallic glasses and its correlation with glass-forming ability

We have probed local atomic structure of Zr-Cu metallic glasses using time-of-flight neutron and synchrotron x-ray diffraction techniques with high resolution. Our results provide evidence for a scheme of efficient local atomic packing where atomic clusters encompass multiple types of atoms in the first coordination shell. We also demonstrate experimental evidence of a strong correlation between the number of unlike atom bonds and the glass-forming ability. Our findings may provide insights into a broad range of scientific problems where efficient space filling by packing spheres is essential.

Figure 1

(Color online) The reduced PDF $\left[G\left(r\right)\right]$ of a series of natural Cu-containing Zr-Cu glasses determined by (a) neutron and (b) x-ray diffractions. Also shown in (c) are the $G\left(r\right)\text{s}$ of the ${\text{Zr}}_{35.5}{\text{Cu}}_{64.5}$ glass obtained by neutron diffraction of Cu-isotope-substituted samples (with ${}^{65}\text{C}\text{u}$, ${}^{\text{Nat}}\text{C}\text{u}$, ${}^{\text{Zr}}\text{C}\text{u}$, and ${}^{63}\text{C}\text{u}$, respectively), and x-ray diffraction of the natural Cu-containing sample.

Figure 2

(Color online) The best fit of a linear combination of convoluted Gaussian functions to the $T_N\left(r\right)\text{s}$ of the ${\text{Zr}}_{35.5}{\text{Cu}}_{64.5}$ glass with Cu-isotope substitutions and to the $T_X\left(r\right)$ of the same alloy. Also shown are the extracted Zr-Zr, Zr-Cu, and Cu-Cu partials for ${\text{Zr}}_{35.5}{{}^{65}\text{C}\text{u}}_{64.5}$.

Figure 3

(Color) Comparison of the extracted partial-coordination numbers in this work with the literature data with respect to (a) Cu-Cu, (b) Cu-Zr, (c) Zr-Cu, and (d) Zr-Zr, respectively.

Figure 4

(Color) (a) Plots of $Z_{\text{CuCu}}$ vs $Z_{\text{CuZr}}$ and $Z_{\text{ZrCu}}$ vs $Z_{\text{ZrZr}}$ showing the correlation between partial-coordination numbers. The two solid lines represent the efficient local packing limit for Cu and Zr, respectively, as calculated from Eq. (4a, 4b). Letters a-f refer to ${\text{Zr}}_x{\text{Cu}}_{\left(100-x\right)}$ where $x=35.5$, 38.6, 44, 50, 54.5, and 60, respectively. (b) The experimental average coordination number and the total coordination numbers of Cu and Zr as a function of composition. The two solid straight lines mark the theoretical maximum coordination number for Cu around Zr (top) and vice versa (bottom), according to the Miracle model (Ref. 5). The insets represent structures of two types of Cu-centered clusters, i.e., (0,12,0) and (2,8,0) Voronoi polyhedra as would be seen in a and f, respectively. Orange and light blue balls represent Zr and Cu atoms, respectively.

Figure 5

(Color) Comparison of the extracted number of Zr-Cu bonds with the glass-forming ability indicators $\gamma \left[=T_x/\left(T_g+T_l\right)\right]$ and $T_{rg}\left(=T_g/T_l\right)$ as a function of alloy composition.