Improved multi-order parameter and multi-component model of polycrystalline solidification

Abstract

• The grain boundary energy can be predicted even at larger undercoolings by tuning the coefficient of the new introduced interpolation function. • The kinetic coefficient can be adjusted to match the grain boundary migration situation encountered during solid state transition. • A self-consistent nucleation method was successfully incorporated into the model through introduction of noise effects. Accurate nucleation driving force is used and temperature dependent noise amplitude expression is given. • Through employing the parabolic free energy fitting technique, the developed model can be effectively used to study the entire solidification process for a variety of alloys. Temperature dependent phase field parameters selection strategy is proposed and proved. • Two solid phases nucleation of Al-Cu alloy is realized through self-consistent noise term. This approach is suitable to study multiple solid phase solidification phenomena. In this paper, we present an improved multi-order parameter model for multi-component model of polycrystalline solidification. We introduce an interpolation function in the phase field dynamical equation to obtain controllable grain boundary energy at large undercooling. The same interpolation function is also employed in the kinetics coefficient to allow for better control of grain boundary migration. Temperature dependent phase field parameters and noise terms are consistently coupled into the dynamics of a binary system in a manner that allows for quantitative simulations in the thin interface limit. The model is applied to multi-phase solidification in Al-Cu alloy, where a parabolic fitting method is employed to model the free energy of Al-Cu phases and two-phase nucleation is demonstrated in directional solidification.