Quantifying the Kinetic and Thermodynamic Origins of the Glass-Forming Ability in Metals

Abstract

The glass-forming ability (GFA) of a metallic liquid can be quantified by the critical cooling rate $R_c$, below which it crystallizes upon cooling. $R_c$ is determined by the competition between $R$ and the crystallization rate $\mathcal{K}_{\rm X}$. Here, we calculate $R_c$ and $\mathcal{K}_{\rm X}$ in model pure metals and alloys with BCC/B2 and FCC equilibrium crystal structures. Using classical nucleation theory and independently calculated crystal growth rates, we evaluate $\mathcal{K}_{\rm X}=(IU^3)^{1/4}$ at $T=0.8T_m$, where $I$ and $U$ are the nucleation and growth rates and $T_m$ is the melting temperature. We find a strong positive correlation between $\mathcal{K}_{\rm X}$ and $R_c$ over eleven orders of magnitude. We decompose $\mathcal{K}_{\rm X}$ into a product of a kinetic contribution, involving atomic cluster attachment and diffusion, and a thermodynamic contribution. We show that the thermodynamic contribution to $\mathcal{K}_{\rm X}$ dominates the kinetic contribution over the range of cooling rates that we consider. The nucleation barrier $ΔG_c \sim \tildeγ^3/Δ\tildeμ^2$, where $\tildeγ$ is the reduced effective liquid--crystal interfacial free energy and $Δ\tildeμ$ is the reduced bulk driving force, determines the magnitude of the thermodynamic contribution. The relative importance of $\tildeγ$ and $Δ\tildeμ$ depends on the material: a large interfacial free energy can suppress nucleation in some systems, whereas a weak bulk driving force can inhibit crystallization in others. Analyses of the structural and chemical order show that better glass formers have enhanced structural frustration, more icosahedral-like and less crystal-like local environments, and a larger chemical-order mismatch between the supercooled liquid and crystal phases.