Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion

A phase-field model is developed for simulating quantitatively microstructural pattern formation in solidification of dilute binary alloys with coupled heat and solute diffusion. The model reduces to the sharp-interface equations in a computationally tractable thin-interface limit where (i) the width of the diffuse interface is about one order of magnitude smaller than the radius of curvature of the interface but much larger than the real microscopic width of a solid-liquid interface, and (ii) kinetic effects are negligible. A recently derived antitrapping current [A. Karma, Phys. Rev. Lett. 87, 115701 (2001)] is used in the solute conservation equation to recover precisely local equilibrium at the interface and to eliminate interface stretching and surface diffusion effects that arise when the solutal diffusivities are unequal in the solid and liquid. Model results are first compared to analytical solutions for one-dimensional steady-state solidification. Two-dimensional thermosolutal dendritic growth simulations with vanishing solutal diffusivity in the solid show that both the microstructural evolution and the solute profile in the solid are accurately modeled by the present approach. Results are then presented that illustrate the utility of the model for simulating dendritic solidification for the large ratios of the liquid thermal to solutal diffusivities (Lewis numbers) typical of alloys.