Phase-field Modeling Of Non-equilibrium Solidification Of Binary And Multi-component Alloys

Non-equilibrium solidification technology has been developed rapidly in recent years and new meta-stable materials have been widely prepared.Solidification is a considerable complicated process,which contain not only the phenomenon of heat transfer,mass transfer,liquid flow,crystallization latent heat release and constituent undercooling on macro-scale,but also the process of nucleation,grain growth,ripening and solute redistribution in the front of interface on a micro-scale.Solidification is generally carried out under high temperature condition and thus hard to be observed and measured directly.There must be a lot of difficulties if the research of solidification only proceeds experimentally.The simulation method provides another way for studying solidification.As a rapid development simulation technology for phase-transformation,phase-field method has developed to be an efficient tool for simulation of solidification.However,there still exist some open problems in phase-field modeling,such as the complex additional constraints and the method to introduce non-equilibrium solute diffusion effect.In this thesis,the thermodynamic extremal principle was applied to phase-field modeling of non-equilibrium solidification to solve the above problems.The main research contents and conclusions are as follows.1.The additional constraints in binary alloy system can be solved self-consistently by the thermodynamic extremal principle,and the kinetic cross couplings between propagation of non-conserved phase-field and diffusion fluxes of conserved solute molar fraction can be derived naturally in the phase-field model.The model follows the Onsager’s reciprocal relation.2.Considering the case of 1-D steady-state growth and neglecting solute diffusion in solid,the current phase-field model was analyzed theoretically.It was found that solute trapping in the current phase-field model is similar to that in sharp-interface model.The effective mobility method introduces simultaneously non-equilibrium solute diffusion into both long-range solute diffusion and short-range solute redistribution.In this case,the present model is able to predict an abruptly concurrent occurrence of diffusionless solidification and absence of solute drag.3.The current phase-field model was applied to non-equilibrium solidification of Si-9at.%As binary alloy.Through the calculations of solute partition coefficient and solute drag factor,the results were consistent with that of the theoretical analysis.4.An extension of the phase-field model for binary alloys to multi-component alloys shows that two sets of phase-field model can be obtained,one of which is much simpler than all the previous phase-field models for multi-component alloys.Under equilibrium condition,one can see that the interface and bulk contributions can be decoupled completely,indicating that it is feasible to increase the simulation efficiency by the “thin interface limit” analysis.5.Applying the phase-field model for multi-component alloys to non-equilibrium solidification of Al-Si-Cu ternary alloys indicates that if the interaction between the components is strong,anomalous solute trapping and anomalous solute profiles within the diffuse interface could occur,thus highlighting the importance of interaction among the component elements in multi-component alloys.