Solute trapping and solute drag in a phase-field model of rapid solidification

During rapid solidification, solute may be incorporated into the solid phase at a concentration significantly different from that predicted by equilibrium thermodynamics. This process, known as solute trapping, leads to a progressive reduction in the concentration change across the interface as the solidification rate increases. Theoretical treatments of rapid solidification using traditional sharp-interface descriptions require the introduction of separately derived nonequilibrium models for the behavior of the interfacial temperature and solute concentrations. In contrast, phase-field models employ a diffuse-interface description and eliminate the need to specify interfacial conditions separately. While at low solidification rates equilibrium behavior is recovered, at high solidification rates nonequilibrium effects naturally emerge from these models. In particular, in a previous study we proposed a phase-field model of a binary alloy [A. A. Wheeler et al., Phys. Rev. E 47, 1893 (1993)] in which we demonstrated solute trapping. Here we show that solute trapping is also possible in a simpler diffuse interface model. We show that solute trapping occurs when the solute diffusion length D-I/V is comparable to the diffuse interface thickness. Here V is the interface velocity and D-I characterizes the solute diffusivity in the interfacial region. We characterize the dependence of the critical speed for solute trapping on the equilibrium partition coefficient k(E) that shows good agreement with experiments by Aziz and co-workers [see M. J. Aziz, Metall. Mater. Trans. A 27, 671 (1996)]. We also show that in the phase-held model, there is a dissipation of energy in the interface region resulting in a solute drag, which we quantify by determining the relationship between the interface temperature and velocity.