Interfacial Free Energy Controlling Glass-Forming Ability of Cu-Zr Alloys

Glass is a freezing phase of a deeply supercooled liquid. Despite its simple definition, the origin of glass forming ability (GFA) is still ambiguous, even for binary Cu-Zr alloys. Here, we directly study the stability of the supercooled Cu-Zr liquids where we find that Cu64Zr36 at a supercooled temperature shows deeper undercoolability and longer persistence than other neighbouring compositions with an equivalent driving Gibbs free energy. This observation implies that the GFA of the Cu-Zr alloys is significantly affected by crystal-liquid interfacial free energy. In particular, the crystal-liquid interfacial free energy of Cu64Zr36 in our measurement was higher than that of other neighbouring liquids and, coincidently a molecular dynamics simulation reveals a larger glass-glass interfacial energy value at this composition, which reflects more distinct configuration difference between liquid and crystal phase. The present results demonstrate that the higher crystal-liquid interfacial free energy is a prerequisite of good GFA of the Cu-Zr alloys.

thermophysical parameters used in this study. Density of supercooled liquids was measured by image analysis during cooling in ESL. The boundary of the sample image was fitted by 6 th order Lengendre polynomial which was a well-known method 1, 2 .
Viscosity measurements were carried out using the resonant oscillation drop method 3,4 .
The resonant oscillation of the samples at different temperatures was induced by applying the ac electric field, and the decay time-constant of the oscillation was obtained by the fitting of decay function. Specific heat can be obtained by Stephan-Boltzmann (SB) law, , since the liquids cool down radiatively under high vacuum in the ESL. From the SB law, we can get an accurate ratio of C p /ε T . If total hemispherical emissivity (ε T ) is given, the C p can be calculated. However, the ε T has not been reported for Cu-Zr liquids so far. Therefore, in this study, we used spectral emissivity which is used to measure sample temperature. Then, fusion enthalpy (ΔH f ) was calculated by multiplying C p and temperature rising T from the recalescence temperature T r on nucleating to the plateau temperature T s in Figure 1 in the main text.  conditions. This thermal relaxation was to ensure the atomic configurations on the free surfaces to reach equilibrium. After relaxation, system was quickly quenched to T = 50 K at a cooling rate of 250 K/ns. MD simulation continues to run for additional 1 ns at T = 50 K to obtain equilibrium potential energy of the system with free surfaces, then we move the two free surfaces together to form an interface at T = 50 K, followed by a relaxation of 6 ns with NPT ensemble (only control the box size along y-axis to ensure a zero pressure) using periodic boundary conditions. The interfacial energy is then defined

Calculations of glass-glass interfacial energies of
where E Interfacial is the total potential energy of the system with one interface, E Bulk is the total potential energy of the system before cutting and A the cross-section area in perpendicular to y-axis. To calculate the interfacial energy of amorphous alloys at high temperatures, we quickly raise the temperature of the system to 800 K from 50 K and then relax the system isothermally at 800 K for 12 ns under hydrostatic pressure of 3 GPa. We performed three runs for each composition for a better statistics. Since large internal stress might build up within system during solidification under large supercooling, it is not unreasonable to apply 3 GPa pressure in current calculation. From self-diffusivity as a function of external hydrostatic pressure, it is confirmed that the external hydrostatic pressure 3 GPa will not fundamentally change the self-diffusion behavior of atoms in those alloys. Similar technique has been used in the study of the thermal stability of interfacial energy 11 . Figure S1 illustrates an equilibrium atomic configuration of a selected composition Cu 64 Zr 36 amorphous alloy at T = 50 K, where blue and yellow spheres indicate Cu and Zr atoms, respectively. Figure S2 shows the potential energies of Cu and Zr in a selected Cu 64 Zr 36 amorphous alloy as a function of the position relative to interface at T = 50 K.
The potential energy of each component was normalized by its potential energy in bulk amorphous alloys. It is clear that an increase of the potential energy in the interface will result in an excess interfacial energy, mainly due to the structural change in the interface region. Figure