Experimental and ab initio structural studies of liquid ${\text{Zr}}_2\text{Ni}$

High-energy x-ray diffraction and ab initio molecular-dynamics simulations demonstrate that the short-range order in the deeply undercooled ${\text{Zr}}_2\text{Ni}$ liquid is quite nuanced. The second diffuse scattering peak in the total structure factory sharpens with supercooling, revealing a shoulder on the high-$Q$ side that is often taken to be a hallmark of increasing icosahedral order. However, a Voronoi tessellation indicates that only approximately 3.5% of all the atoms are in an icosahedral or icosahedral-like environment. In contrast, a Honeycutt-Andersen analysis indicates that a much higher fraction of the atoms is in icosahedral (15%–18%) or distorted icosahedral (25%–28%) bond-pair environments. These results indicate that the liquid contains a large population of fragmented clusters with pentagonal and distorted pentagonal faces, but the fully developed icosahedral fragments are rare. Interestingly, in both cases, the ordering changes little over the 500 K of cooling. All metrics show that the nearest-neighbor atomic configurations of the most deeply supercooled simulated liquid (1173 K) differ topologically and chemically from those in the stable C16 compound, even though the partial pair distributions are similar. The most significant structural change upon decreasing the temperature from 1673 to 1173 K is an increase in the population of Zr in Ni-centered clusters. The structural differences between the liquid and the C16 increase the nucleation barrier, explaining glass formation in the rapidly quenched alloys.

Figure 1

(Color online) (a) Experimental total scattering factor $\left[S\left(Q\right)\right]$ for the liquid ${\text{Zr}}_2\text{Ni}$ alloy. The inset figure shows the detail of the second peak. (b) The reduced distribution function by x-ray (circle) and by ab initio MD simulations (line). The pink-dashed line is the MD data of 198 atoms model at $T=1573\text{K}$. The different scattering factors for Zr and Ni have been included in the simulation data.

Figure 2

(Color online) The partial pair-correlation functions by ab initio MD simulations. The dashed lines are at the maximum of the pair-correlation functions of the liquids to compare with that of the C16 alloy at 1273 K.

Figure 3

(Color online) Populations of the 20 most frequent Voronoi indices for (a) total, (b) Zr center, and Ni center (c). The indices are sorted by the CN as shown in the top of the figure. The Voronoi populations of (d) icosahedral and icosahedral-like clusters and (e) C16-like clusters $⟨0,2,8,0,0⟩$ and $⟨0,0,12,3,0⟩$ as a function of temperature.

Figure 4

(Color online) (a) A HA index analysis of the liquid, showing little change with temperature; the HA for the liquid is very different from that for the C16 at 1255 K. DICOS indicates a distorted icosahedral and ICOS indicates icosahedral bond pairs. (b) BOO analysis of the liquid also shows little change with temperature. As for the HA analysis, the BOO for the liquid is quite different from that for the C16 phase, indicating different local structures. $Q_l$ is normalized such that ${\sum }_{\text{even}l}{Q}_l=5$, characteristics of random configuration.

Figure 5

(Color online) The population difference of the local chemical distributions of the Zr and Ni clusters between $T=1173$ and 1673 K. The blue square indicates the decrease in population, while the red one indicates the increase in population, e.g., for the Zr-centered cluster with eight Zr neighbors and five Ni neighbors, (8:5), the population decreases $\sim 1.1\%$, and for the Ni-centered cluster with nine Zr neighbors and three Ni neighbors, (9:3), the population increases $\sim 5.0\%$, when temperature decreases from 1673 to 1173 K.