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 ${\mathcal{K}}_{\mathrm{X}}$. Here, we calculate $R_c$ and ${\mathcal{K}}_{\mathrm{X}}$ 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 ${\mathcal{K}}_{\mathrm{X}}=(I{U}^3{)}^{1/4}$ 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 ${\mathcal{K}}_{\mathrm{X}}$ and $R_c$ over eleven orders of magnitude. We decompose ${\mathcal{K}}_{\mathrm{X}}$ into a product of a kinetic contribution, involving atomic cluster attachment and diffusion, and a thermodynamic contribution. We show that the thermodynamic contribution to ${\mathcal{K}}_{\mathrm{X}}$ dominates the kinetic contribution over the range of cooling rates that we consider. The nucleation barrier $\Delta G_c\sim {\tilde{\gamma }}^3/\Delta {\tilde{\mu }}^2$, where $\tilde{\gamma }$ is the reduced effective liquid--crystal interfacial free energy and $\Delta \tilde{\mu }$ is the reduced bulk driving force, determines the magnitude of the thermodynamic contribution. The relative importance of $\tilde{\gamma }$ and $\Delta \tilde{\mu }$ 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.