Measurements of structural and chemical order in $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ and $\mathrm{Z}{\mathrm{r}}_{77}\mathrm{R}{\mathrm{h}}_{23}$ liquids

The short-range order (SRO) and medium-range order of electrostatically levitated $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ and $\mathrm{Z}{\mathrm{r}}_{77}\mathrm{R}{\mathrm{h}}_{23}$ liquids are presented based on a combination of high-energy x-ray diffraction and time-of-flight neutron diffraction studies. The atomic structures of the $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ liquids were determined as a function of temperature from constrained reverse Monte Carlo simulations using x-ray and elastic neutron scattering measurements and two partial pair-distribution functions obtained from molecular dynamics (MD) simulations. Analysis of both the Faber-Ziman and Bhatia-Thornton partial structure factors shows that the $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ and $\mathrm{Z}{\mathrm{r}}_{77}\mathrm{R}{\mathrm{h}}_{23}$ liquids have similar topological SRO. Interestingly, the chemical SRO appears to be much more strongly tied to the topological order in the $\mathrm{Z}{\mathrm{r}}_{77}\mathrm{R}{\mathrm{h}}_{23}$ liquid than in the $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$. These results demonstrate that the combination of experimental scattering measurements with MD results provides a powerful approach for obtaining details of chemical and topological ordering in metallic glasses and liquids.

Figure 1

Total $S$($q$)s measured for levitated liquid (a) $\mathrm{Z}{\mathrm{r}}_{77}\mathrm{R}{\mathrm{h}}_{23}$ and (b) $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ using both x-ray (solid black line) and neutron (open red circles) scattering. Each temperature is vertically offset by 2 for clarity.

Figure 2

Example $S$($q$) for $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ at $1293{}^{\circ }\mathrm{C}$ out to $32{\AA }^{-1}$ showing the range of the NOMAD instrument.

Figure 3

Neutron (solid black line) and x-ray (dashed-dotted red line) scattering in the low-$q$ region at $\sim 1110{}^{\circ }\mathrm{C}$ for $\mathrm{Z}{\mathrm{r}}_{77}\mathrm{R}{\mathrm{h}}_{23}$ (top) and $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ (bottom) liquids (vertically offset by 0.5 for clarity). The dotted blue lines are guides to the eye to emphasize the prepeak that appears in $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ from neutron scattering.

Figure 4

Results of CRMC (solid black line) fits to experimental (open red circles) results for $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ liquid at $1110{}^{\circ }\mathrm{C}$ for (a) $S$($q$)$-1$ and (b) $g$($r$) for both neutron (top curves) and x-ray (bottom curves) scattering (the neutron results are offset by 2 for clarity).

Figure 5

Comparisons of the PPDFs from MD (open blue circles) and CRMC (solid black line) for (a) $g_{\mathrm{ZrZr}}\left(r\right)$, (b) $g_{\mathrm{ZrPt}}\left(r\right)$, and (c) $g_{\mathrm{PtPt}}\left(r\right)$. The largest differences were observed with $g_{\mathrm{PtPt}}\left(r\right)$.

Figure 6

Comparisons of the PSFs from MD (open blue circles) and CRMC (solid black line) for (a) $S_{\mathrm{ZrZr}}\left(q\right)$, (b) $S_{\mathrm{ZrPt}}\left(q\right)$, and (c) $S_{\mathrm{PtPt}}\left(q\right)$. The largest differences were observed with $S_{\mathrm{PtPt}}\left(q\right)$.

Figure 7

(a) Capped and (b) diagonal interpenetrating icosahedra. The center of each icosahedron is represented by a blue sphere. A red line connects the centers of neighboring interpenetrating icosahedra.

Figure 8

(a) $S$($q$) and (b) $g$($r$) Bhatia-Thornton partials for $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ (solid lines) and $\mathrm{Z}{\mathrm{r}}_{77}\mathrm{R}{\mathrm{h}}_{23}$ (open symbols) at $1106{}^{\circ }\mathrm{C}$. The topological order (NN) is similar between both alloys.

Figure 9

Comparisons of $g_{NN}\left(r\right)$ between $\mathrm{Z}{\mathrm{r}}_{77}\mathrm{R}{\mathrm{h}}_{23}$ (open gray circles) and $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ for different CRMC results. Similar topological order is found if $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ is constrained with both the Zr-Zr and Zr-Pt partials from MD (solid red line), but the agreement is much better if $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ is constrained with only Zr-Pt from MD (dashed blue line). In both cases, the simulations are additionally constrained with both x-ray and neutron measurements.

Figure 10

Frequency of the dominant VIs at $1106{}^{\circ }\mathrm{C}$ for (a) Zr-centered and (b) Pt-centered structures. Temperature dependent indices are provided in the Supplemental Material [65].

Figure 11

Identification of a phase mixture of β-Zr (asterisks) and $\mathrm{Z}{\mathrm{r}}_5\mathrm{R}{\mathrm{h}}_3$ (open circles) crystalline phases that crystallized from a supercooled (more than $200{}^{\circ }\mathrm{C}$) $\mathrm{Z}{\mathrm{r}}_{77}\mathrm{R}{\mathrm{h}}_{23}$ liquid.