A phase-field model bridging near-equilibrium and far-from-equilibrium alloy solidification

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Mapping to the appropriate Gibbs–Thomson (G–T) condition is essential for phase-field modeling to produce reliable and realistic solidification microstructures. However, existing phase-field models face challenges in simultaneously satisfying both near-equilibrium and far-from-equilibrium G–T conditions. This limitation restricts the applicability of phase-field methods in scenarios with a wide range of interface velocities, such as those observed in additive manufacturing. In this work, we propose a phase-field model that bridges both regimes by redefining each interfacial concentration field into two components: a conservative term representing long-range diffusion and a non-conservative term accounting for short-range redistribution within the diffuse interface. This formulation makes the model fully variational and analytically traceable through thin-interface analysis, allowing for accurate mapping to the G–T condition and determining model parameters. A key advancement of this model is the inclusion of free energy dissipation for short-range redistribution fluxes in the thin-interface limit, providing the necessary degree of freedom to reconcile both near-equilibrium and far-from-equilibrium G–T conditions. This capability is demonstrated by applying the model to simulate banded structures, effectively capturing the transition between near-equilibrium and far-from-equilibrium states.