# High-Temperature Liquid-Liquid Phase Transition in Glass-Forming Liquid Pd43 Ni20 Cu27P10
## 2 Experimental and Simulation Details  
To prepare the master alloy of Pd\({}_{43}\)Ni\({}_{20}\)Cu\({}_{27}\)P\({}_{10}\), the mixture of pure Pd (99.99%), Cu (99.99%), and Ni-P pre-alloy (99.99%) was melted in the arc-melting furnace in a high-purity argon atmosphere (see raw materials information in Table S1 in the Supporting Information). For chemical homogeneity, the master alloy was remelted more than five times. Then, the melt-spun ribbons, with a thickness of 20-30 \(\upmu\)m and a width of 1 mm, were prepared by a single-roll melt-spinning method under a high-purity argon atmosphere.  
The amorphous structure of the melt-spun ribbon samples was characterized by XRD, as shown in Figure S1. The thermal stabilities of amorphous alloys, including glass transition temperature (\(T_{g}\)), Curie temperature (\(T_{c}\)), crystallization onset temperature (\(T_{x}\)), melting temperature (\(T_{m}\)), and liquidus temperature (\(T_{l}\)) were determined by DSC at a heating rate of 0.67 K/s. The qualitative assessment of the content of constituent elements in the Pd\({}_{43}\)Ni\({}_{20}\)Cu\({}_{27}\)P\({}_{10}\) amorphous alloy was performed using energy dispersive spectroscopy (EDS) (Figure S2). The results of the qualitative analysis confirmed a homogeneous distribution for all component atoms. Figure S3 gives the semi-quantitative atomic percentage of each element in the Pd\({}_{43}\)Ni\({}_{20}\)Cu\({}_{27}\)P\({}_{10}\) amorphous strip, which is quite close to the desired constitution.  
METTLER TOLEDO Flash DSC 2+ (Mettler Toledo, Zurich, Switzerland) with a maximum heating and cooling rate of 40,000 K/s was used during the experiment. FDSC samples were prepared by cutting thin metallic glass ribbons into around 50 \(\times\) 50 \(\upmu\)m\({}^{2}\) to around 100 \(\times\) 100 \(\upmu\)m\({}^{2}\) pieces weighing 1-5 \(\upmu\)g under a stereo microscope and then transferred using an electrostatic hairbrush to the central area of the chip sensor. The sample was repeatedly heated from room temperature to 900 \({}^{\circ}\)C at a heating rate of 500 K/s and then cooled to room temperature with an interval of 1 s. We cycled more than 10 times at different cooling rates (400 K/s, 500 K/s, 800 K/s, 1000 K/s, 1500 K/s, 2000 K/s, and 2100 K/s), during which the sample was continuously purged with pure argon to avoid oxidation.  
AIMD simulations were performed by using the Vienna Ab initio Simulation Package (VASP) based on density functional theory (DFT) [39]. The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional was adopted to describe electron exchange and correlation functions [40]. The projector augmented-wave (PAW) pseudopotentials were used, and for the accuracy of calculation, the energy cutoff was uniformly set to be 520 eV. The canonical ensemble (NVT), namely, constant number of atoms, volume, and temperature, was used, and the Nose-Hoover thermostat was utilized to adjust the temperature. Only \(\Gamma\) point was applied to sample the Brillouin zone. To integrate [PERSON]'s equations of motion, the velocity Verlet algorithm was used with a timestep of 3 fs.  
An initial random structure of 200 atoms (including 86 Pd, 40 Ni, 54 Cu, and 20 P atoms) in a cubic simulation box with periodic boundary conditions was completely melted at 1500 K and relaxed for 5000 timesteps. To obtain the vitreous structure, the melt was quenched to 300 K stepwisely with a cooling rate of 4 \(\times\) 10\({}^{13}\) K/s. For every 100 K, the volume of the simulation box was adjusted to ensure that the average total pressure was close to 0 (within \(\pm\) 0.5 kbar). Then, the system was run for additional 5000 timesteps, and the last 4500 timesteps were used for trajectory production and property analysis.