# High-Temperature Liquid-Liquid Phase Transition in Glass-Forming Liquid Pd43 Ni20 Cu27P10
## 3 Results and Discussion
### AIMD Simulations
#### 3.2.2 Atomic Structures  
We now turn our attention to the microscopic details of the structural transition of LLPT. The atomic structure was analyzed with pair distribution function, Voronoi polyhedra, bond order orientation, and bond angle distribution on the data obtained from AIMD simulations. The calculated total pair distribution function (PDF) and partial PDFs (PPDFs, \(g_{\mathrm{ij}}\)) of liquid Pd\({}_{43}\)Ni\({}_{20}\)Cu\({}_{27}\)P\({}_{10}\) at different temperatures are displayed in Figure 4. For clarity, only the PPDFs of three atom pairs are shown here since the other seven pairs show similar PPDFs with Ni-Cu and Cu-P. The PPDFs for the other atom pairs are shown in Figure S4. From Figure 4a, it can be seen that the intensity of the first peak of the total PDF, \(g_{\mathrm{total}}\)(r), is gradually increased with the decrease of the temperature. At the same time, the second peak begins to split at around 800 K, indicating a certain degree of correlation between the connections and atomic clusters. As indicated by the red dotted lines in Figure 4b-d, the second peak of nine PPDFs, except the \(g_{\mathrm{P}}\)-p, begins to split from a single peak into two subpeaks when the liquid is cooled down below around 1000 K. The split of the second peak for P-P pair becomes obvious as the temperature decreases below 700 K. To view the change of the structure, the nearest neighbor distance, \(r_{1}\), is obtained from a Gaussian peak fitting for the first peak of PPDF, and the results are shown in Figure 5a. For demonstration, the Gaussian peak fitting for the first peak of PPDF for the Ni-Cu atom pair is presented in Figure 5b. Clearly, at temperatures above 900 K, the \(r_{1}\) for all the atom pairs remains nearly unchanged. However, atom pairs of Ni-Pd, Ni-Ni, Ni-Cu, and Cu-P show apparent variations when the temperature is decreased below 900 K, which is quite close to the LLPT temperature. The \(r_{1}\) for Ni-Pd and Cu-P increases first and then decreases as the temperature decreases. However, the \(r_{1}\) for Ni-Ni and Ni-Cu has an obvious abnormal decrease between 1000 K and 900 K. From Figure 5b, it can be seen that the first peak of PPDF for the Ni-Cu atom pair has a noticed left shift at 900 K when compared with the case of 1000 K, indicating that the \(r_{1}\) of 900 K is smaller than that of 1000 K.  
Figure 3: Temperature-dependent variation of (**a**) density and (**b**) enthalpy per atom for Pd\({}_{43}\)Ni\({}_{20}\)Cu\({}_{27}\)P\({}_{10}\) liquid obtained from the AIMD simulations, where the purple curve denotes the results of the FDSC test at the cooling rate of 2100 K/s shown in Figure 2. The fitting lines are shown together with the dots. To gain further insights into the atomic local structure from a geometrical perspective, the changes in the cluster were analyzed using the Voronoi tessellation method [(43)]. Voronoi polyhedra (VP) analysis is an efficient method for analyzing local atomic environments and clusters in liquids and glasses. The Voronoi index is expressed as <\(n_{3}\)\(n_{4}\)\(n_{5}\), \(n_{6}\)>, where \(n_{i}\) represents the number of \(i\)-edged faces. Figure 6 shows the temperature dependence of the fraction of the dominant six VPs centered on Pd, Cu, Ni, and P atoms. It is worth noting that after LLPT, the fraction of the icosahedral-like VP with dense atomic packing, including <0 0 12 0> and <0 1 102>, has a marked growth (Figure 6a), and some studies have shown that the icosahedral cluster is the main factor for the formation of metallic glass. VP, such as  
Figure 4: Total and partial PDFs in Pd\({}_{43}\)Ni\({}_{20}\)Cu\({}_{27}\)P\({}_{10}\) liquid at various temperatures. (**a**) Total, (**b**) Ni-Cu partial, (**c**) Cu-P partial, and (**d**) P-P partial. For clarity, the curve is shifted by 1 successively from the bottom to the top. Figure 5: (**a**) Change of the nearest neighbor distance of different atomic pairs with temperature.