Quantitative phase-field modeling of solute trapping in rapid solidification

Abstract A quantitative phase-field model is developed for prediction of solute trapping for solidification velocities relevant to the additive manufacturing. An anti-trapping flux is proposed to generate a chemical potential jump independent of the interface width and consistent with the sharp interface continuous growth (CG) model. The thin-interface analysis up to the second order is implemented to quantitatively parametrize the phase-field model based on the material properties for both full and zero solute drag limits of the CG model. As a benchmark example, the experimental data on Si-9at.%As (Kittl et al., Acta Materialia, 2000) is used to compare the partition coefficient and kinetic undercooling predicted by this phase-field model with those of the CG model. Our results, especially with the full-drag limit, present a very good agreement with the experimental data and theoretical models for solidification velocities up to the diffusive velocity. Unlike other phase-field models, this proposed model predicts accurate partition coefficient and kinetic undercooling for a wide range of solidification velocities, and the results are less sensitive to the diffusive interface width, enabling quantitative simulations in larger length scales. The model performance in prediction of the cellular growth is highlighted by showing that the primary dendritic arm spacing is also weakly dependent on the diffusive interface width.