Response-function-optimized phase field modeling of solute trapping and solute drag in rapid alloy solidification

Abstract

Quantitative prediction of rapid solidification microstructures requires phase field models that represent the velocity dependence of interfacial properties, including solute partitioning, kinetic liquidus response, solute drag, and kinetic undercooling. These response functions control both microsegregation and morphology selection, but are difficult to prescribe accurately in phase field simulations that employ large interfaces for numerical efficiency. We introduce an optimization-based calibration strategy that embeds target sharp-interface response functions into a dilute alloy phase field formulation by treating the interfacial diffusivity interpolation function as a response-matching degree of freedom. The optimized diffusivity functions are obtained from one-dimensional steady-state phase field solutions, constrained to reproduce prescribed continuous-growth-model targets for velocity-dependent solute trapping and drag-modified liquidus kinetics. We demonstrate the calibrated model's accuracy and versatility in dilute Al-Cu by reproducing the prescribed response functions for intermediate solute drag coefficients relevant to rapid solidification. Two-dimensional directional-solidification simulations are conducted to isolate the effect of drag at fixed composition, thermal gradient, and pulling velocity. We show that increasing solute drag shifts the solidification morphology from dendritic/cellular growth to mixed dendritic-banded structures, and finally to predominantly banded growth. We extend the formulation to dilute multicomponent alloys, enabling independent specification of equilibrium partition coefficients and liquidus slopes for multiple solute species. The framework provides a route for incorporating experimentally, theoretically, or atomistically informed nonequilibrium interface kinetics into quantitative phase field simulations of rapidly solidified alloys.