Thermodynamic principles for phase-field modeling of alloy solidification

• The thermodynamic principles for phase-field modeling are reviewed.
• The recent progress in the phase-field modeling of isothermal solidification of binary alloys are reviewed and analyzed theoretically.
• The importance to solve directly the additional constraints in the modeling system self-consistently in thermodynamics is highlighted.
• The relation between the free energy functional and the grand potential functional are discussed.

Phase-field modeling is not only a powerful simulation tool to predict the microstructure evolution but also a useful theoretical method to study the interface kinetics. In this paper, the thermodynamic principles for and the recent progress in the phase-field modeling of isothermal solidification of binary alloys are reviewed. Different phase-field models with or without the condition of equal concentrations or equal diffusion potentials are reformulated from the entropy/free energy functional or the thermodynamic extremal principle. Their physics behind, problems and relation to the sharp interface models are analyzed. The importance to solve directly the additional constraints in the modeling system self-consistently in thermodynamics is highlighted.