Solute trapping and the non-equilibrium phase diagram for solidification of binary alloys

A phase field model for the solidification of binary alloys is presented and analyzed. A matched asymptotic approach is used to recover the model’s leading order sharp interface motion. Equations for both the solute profile and free energy balance at the interface are derived, demonstrating solute trapping at large growth velocities and leading to a construction of the non-equilibrium phase diagram over a large range of growth conditions. A rigorous understanding of the interfacial conditions is provided, and comparisons are made to existing theories.