Short- and medium-range order in a ${\text{Zr}}_{73}{\text{Pt}}_{27}$ glass: Experimental and simulation studies

The structure of a ${\text{Zr}}_{73}{\text{Pt}}_{27}$ metallic glass, which forms a ${\text{Zr}}_5{\text{Pt}}_3$ (${\text{Mn}}_5{\text{Si}}_3$-type) phase having local atomic clusters with distorted icosahedral coordination during the primary crystallization, has been investigated by means of x-ray diffraction and combining ab initio molecular-dynamics (MD) and reverse Monte Carlo (RMC) simulations. The ab initio MD simulation provides an accurate description of short-range structural and chemical ordering in the glass. A three-dimensional atomistic model of 18 000 atoms for the glass structure has been generated by the RMC method utilizing both the structure factor $S\left(k\right)$ from x-ray diffraction experiment and the partial pair-correlation functions from ab initio MD simulation. Honeycutt and Andersen index and Voronoi cell analyses, respectively, were used to characterize the short- and medium-range order in the atomistic structure models generated by ab initio MD and RMC simulations. The ab initio results show that an icosahedral type of short-range order is predominant in the glass state. Furthermore, analysis of the atomic model from the constrained RMC simulations reveals that the icosahedral-like clusters are packed in arrangements having higher-order correlations, thus establishing medium-range topological order up to two or three cluster shells.

Figure 1

(Color online) (a) Total structure factor $S\left(k\right)$ and (b) pair-correlation function of ${\text{Zr}}_{73}{\text{Pt}}_{27}$ metallic glass obtained from the ab initio MD simulations compared with those from HEXRD measurements.

Figure 2

(Color online) (a) Structure factor $S\left(k\right)$ of amorphous ${\text{Zr}}_{73}{\text{Pt}}_{27}$. $S\left(k\right)$ from RMC is compared to that from x-ray diffraction experiment. Partial pair-correlation functions $g_{ij}\left(r\right)$ from MD and RMC simulations for (b) Zr-Pt, (c) Zr-Zr, and (d) Pt-Pt.

Figure 3

Distribution of local coordination numbers in glass ${\text{Zr}}_{73}{\text{Pt}}_{27}$ calculated from the MD and RMC models. (a) Zr-centered distribution functions and (b) Pt-centered distribution functions.

Figure 4

(Color online) Icosahedral clusters of metallic glass alloy ZrPt from MD simulation. (a) Pt-centered, (b) Zr-centered, (c) interpenetrating icosahedra, (d) vertex-connected, (e) Face-sharing icosahedra, and (f) Medium-range order made up of icosahedra in glass ${\text{Zr}}_{73}{\text{Pt}}_{27}$. Yellow and white spheres denote Zr and Pt atoms, respectively.

Figure 5

(Color online) Population of the HA index in the liquid and glass ${\text{Zr}}_{73}{\text{Pt}}_{27}$ from the ab initio MD simulation when the sample is cooled from 3000 K liquid to the amorphous state at 200 K.

Figure 6

(Color online) Distribution of Voronoi clusters around Pt and Zr atoms in ${\text{Zr}}_{73}{\text{Pt}}_{27}$ amorphous alloy.

Figure 7

The calculated frequency density of ${\widehat{W}}_6$ distributions for 14 types of the most abundant polyhedra from Voronoi indexes. The vertical lines indicate the ${\widehat{W}}_6$ values for the ideal icosahedral $\left(-0.169\right)$, fcc $\left(-0.013\right)$, and bcc (0.013) structures, as indicated in the figure. Note that $⟨0,0,12,0⟩$ barely spans the ${\widehat{W}}_6$ value for an icosahedron.

Figure 8

Difference between the cluster-cluster PCFs $g_{\alpha \beta }\left(r\right)$ and the total PCF $g\left(r\right)$, i.e., $\Delta g_{\alpha \beta }\left(r\right)$, among the cluster belonging to groups A, B, and C, respectively. Clusters in group A are $⟨0,2,8,2⟩$, $⟨0,0,12,0⟩$, and $⟨0,1,10,2⟩$; clusters in group B are $⟨0,4,4,3⟩$, $⟨0,4,4,4⟩$, and $⟨0,4,4,5⟩$; and clusters in group C are $⟨0,2,8,1⟩$, $⟨0,2,8,3⟩$, $⟨0,2,8,4⟩$, $⟨0,3,6,2⟩$, $⟨0,3,6,3⟩$, $⟨0,3,6,4⟩$, $⟨0,3,6,5⟩$, and $⟨0,1,10,3⟩$.

Figure 9

Distribution of the clusters having Voronoi indices of (a) $⟨0,0,12,0⟩$, (b) $⟨0,2,8,2⟩$, and (c) $⟨0,1,10,2⟩$ (left: total; middle: Pt centered; right: Zr centered).

Figure 10

Difference between the cluster-cluster PCFs $g_{\alpha \beta }\left(r\right)$ and the total PCF $g\left(r\right)$, i.e., $\Delta g_{\alpha \beta }\left(r\right)$, among the cluster belonging to group A ($\alpha ,\beta =\text{a},\text{b},\text{c}$, where a represents $⟨0,0,12,0⟩$ clusters, b represents $⟨0,2,8,2⟩$ clusters, and c represents $⟨0,1,10,2⟩$ clusters).