Quantitative phase-field modeling of solidification in binary alloys with nonlinear phase coexistence curves

A formalism is presented for performing quantitative phase-field simulations of single-phase solidification in binary alloys with nonlinear solidus and liquidus curves. It is shown that, close to equilibrium, Gibbs free energy of an alloy phase can be approximated by the free energy function of a dilute ideal binary alloy, modified by effective temperature-dependent coefficients. This makes it possible to exploit a recent phase-field technique [ A. Karma Phys. Rev. Lett. 87 115701 (2001)] to model the free-boundary kinetics of single-phase solidification in binary alloys having nonlinear phase coexistence curves. Simulations of isothermal and nonisothermal dendritic solidification in an isomorphous binary alloy are used to demonstrate convergence of tip speed and radius for different values of the phase-field interface thickness. The effect linear versus nonlinear phase boundaries on dendritic tip speed is examined.