Icosahedral superclusters in ${\mathrm{Cu}}_{64}{\mathrm{Zr}}_{36}$ metallic glass

The presence of superclusters based on Cu-centered icosahedra was studied via classical molecular dynamics simulations in ${\mathrm{Cu}}_{64}{\mathrm{Zr}}_{36}$ metallic glass. Medium-range order was identified by determining the nearest-neighbor histogram and bond-angle distribution of superclusters. A heterogeneous distribution of icosahedra was observed while other common cluster types are distributed homogeneously. The degree of superclustering, as quantified by the number of cap-sharing bonds per icosahedron, was found to depend only on the icosahedron fraction, irrespective of thermal history. This is further supported by a long-time annealing in the supercooled liquid regime, where the number of icosahedra significantly increases and the formation of superclusters is consequently enhanced. While distorted icosahedra are not found in the vicinity of full icosahedra, the Zr-centered ⟨0 0 12 4⟩ clusters show a high spatial correlation to Cu-centered icosahedra. This is indicative of early stages of crystallization into a ${\mathrm{Cu}}_2\mathrm{Zr}$ Laves phase.

Figure 1

(a) Fraction of the three most prominent VP in ${\mathrm{Cu}}_{64}{\mathrm{Zr}}_{36}$ metallic glass. Blue: Inherent structure after cooling at a rate of 0.01 K/ps. Red: Inherent structure after cooling at 0.1 K/ps. A steep increase in the FI fraction is observed when approaching the glass transition temperature $T_{\mathrm{g}}$ from the melt. The higher cooling rate generates a lower fraction of FI in the glass. (b) VP fractions during annealing at 800 K: The FI fraction increases during annealing, while no significant change of the other VP fractions is observed.

Figure 2

Potential energies (symbols) and histograms (bars) of ⟨0 2 8 2⟩ (red) and ⟨0 0 12 0⟩ (blue) for different local stoichiometries. The histograms were normalized by the total number of the respective VP. Due to its large fraction the statistical errors for the ⟨0 0 12 0⟩ VP are within the symbol size.

Figure 3

Number of cap-sharing bonds per icosahedron $n$ (symbols), compared to the statistical prediction $n_{\mathrm{s}}$ (black line) as a function of the FI fraction $f_{\mathrm{icos}}$. Every data point is calculated from the data points in Figs. 1 and 1. Note that even though the corresponding structures are at different temperatures the data all fall on a single curve.

Figure 4

Nearest-neighbor histograms for ⟨0 0 12 0⟩, ⟨0 2 8 2⟩, and ⟨0 3 6 4⟩ VP (symbols) at 50 K (a) as-cast and (b) after annealing, as well as (c) at 1000 K compared to the nearest-neighbor histograms of the random network model (lines). The ⟨0 0 12 0⟩ VP show an enhancement of the peak at 2.7 Å compared to the random network configuration in all three cases. In contrast, the other VP are well represented by the random structure.

Figure 5

Nearest-neighbor histogram for FI-DI neighbors, ${\mathrm{NNH}}_{\mathrm{FI}\text{−}\mathrm{DI}}$, (symbols) of the annealed sample. Both peaks are sharper than for the random network model (line) but the integrated-peak ratio is similar.

Figure 6

Nearest-neighbor histograms for Cu-centered FI and the Zr-centered ⟨0 0 12 4⟩ VP before and after annealing at 800 K. A strong spatial correlation is seen.

Figure 7

(a) Bond-angle distribution of icosahedral SCs at 50 K for the as-cast and annealed sample and at 1000 K. In the liquid state the number of 120°- and 180°-type bonds is reduced. The dashed lines indicate the natural abundance (5/11 and 10/11) for the cumulative histogram. (b) Fragment of an icosahedral supercluster to illustrate 60°-, 120°-, and 180°-type bonds (green: center atoms of FI; orange: cap-sharing bonds).