Phase Field Model for Non-equilibrium Interface Conditions

This article presents a new phase-field formulation for non-equilibrium interface conditions in rapid phase transformations. With a particular way of defining concentration fields, the classical sharp and diffuse (thick) interface theories are unified into the present phase-field model. Each point inside the diffuse interface is comparable to the classical sharp interface model, governed by phase boundary migration and short-range atomic exchanges and connected by long-range diffusion. Their thermodynamic forces and fluxes are following the Onsager reciprocal relation and consistent with the classical irreversible thermodynamics. Furthermore, we establish the balance of driving forces and energy dissipations for both the diffuse interface and the single point inside it. The model is then validated by rapid solidification of Al-Cu alloys. With an effective mobility of considering non-equilibrium long-range diffusion, the model represents the main characteristics of non-equilibrium interface kinetics, i.e., solute trapping and solute drag. Especially, we reproduce the complete trapping at the high-velocity regime and provide a thermodynamic consistent description of the partial drag phenomena at the low-velocity region. Moreover, the dissipation analysis indicates that even the far-from-equilibrium diffuse interface is composed of numerous representative volume elements near the equilibrium, providing a new understanding of non-equilibrium interfaces.