Efficient sampling method for multi-component ZrCu(Al) metallic glasses

Abstract

We investigate multi-component metallic glass systems using a hybrid Molecular Dynamics (MD) and Variance-Constrained Semi-Grand Canonical approach. This method enables us to generate samples with properties consistent with experimental observations, at deeply supercooled states that are typically inaccessible with conventional MD simulations. Using a realistic interatomic potential, we investigate the dynamics, kinetic stability, and rheology of a ZrCuAl metallic glass, together with the widely studied ZrCu system, in the low-temperature glassy regime, specifically, for ZrCu below its experimental glass-transition temperature. Our results demonstrate how the hybrid method enhances relaxation and provides a generic framework for modeling realistic complex metallic glasses in close agreement with experimental observations.

Figures (5)

• Figure 1: The deviation $\lVert C^{SGC}-C^{target} \rVert$ of the simulated composition in SGC from the target a) Zr$_{50}$Cu$_{50}$ and b) Zr$_{46}$Cu$_{46}$Al$_{8}$. The optimal differences in chemical potential $\Delta\mu$ for the target compositions are those that minimize this deviation. For the Zr$_{50}$Cu$_{50}$, the corresponding value is $\Delta\mu_{Zr-Cu}=-2.69$ eV, indicated by vertical black line. For the Zr$_{46}$Cu$_{46}$Al$_{8}$, the optimal values are $\Delta\mu_{Zr-Cu}=-2.69$ eV, and $\Delta\mu_{Zr-Al}=-1.9$ eV, marked by a white cross in the two-dimensional plot. The colorbar represents the deviation, from low (blue) to high (red).
• Figure 2: Temperature dependence of the potential energy per atom for the binary Zr$_{50}$Cu$_{50}$ (red lines) and the ternary Zr$_{46}$Cu$_{46}$Al$_{8}$ (blue lines), obtained from cooling simulations using both conventional MD and hybrid MD+VC SGC methods. The dependencies overlap at high temperatures, where atomic dynamics are fast. As the temperature decreases, the trends diverge, indicating that the hybrid approach enables the system to access lower-energy states more effectively.
• Figure 3: Relaxation times obtained from conventional MD and hybrid MD+VC SGC simulations as a function of inverse temperature for the a) binary and b) ternary systems. The solid lines represent fits to the VFT function. The VFT fit of MD relaxation times was extrapolated to the value of $100$$s$ to determine the glass transition temperature $T_g$. For ZrCu, $T_g=633$$K$, and for ZrCuAl, $T_g=772$$K$, which are indicated by a vertical dashed line. The estimated acceleration of the dynamics in $T_g$ by the hybrid approach is approximately eight orders of magnitude for the binary system and ten orders of magnitude for the ternary system.
• Figure 4: Heat capacity as a function of temperature determined during the regular MD heating ($10^{11}$$K/s$) of a) Zr$_{50}$Cu$_{50}$ and b) Zr$_{46}$Cu$_{46}$Al$_{8}$ samples resulting from MD and MD+VC SGC cooling procedures. The insets show the temperature dependency of the enthalpy per atom obtained from heating, which derivative allowed for heat capacity determination.
• Figure 5: a) Stress-strain curves for samples obtained from MD and MD+VC SGC cooling procedures. Samples prepared with MD+VC SGC scheme exhibit drastic stress drop. b) Example of shear bands for ternary ZrCuAl MG. The shear band is more diffuse for samples prepared with conventional MD simulations (left panel), while it is well-defined for samples generated via MD+VC SGC (right panel). The colorbar indicates the non-affine squared displacements $D^2_{min}$ from the unstrained configuration.