Phase-Field Modeling of Liquid Phases with Ordering

A strong negative enthalpy of mixing can lead to ordering in liquid solutions. To describe ordering in liquids, different thermodynamic descriptions of liquid phases have been developed in the CALPHAD approach, including the associate model and the modified quasichemical model. In this study, we show that the key to directly incorporate these liquid phase models and their corresponding CALPHAD-type free energy formulations in phase-field simulations, is to identify the internal processes and to properly define the internal thermodynamic variables. The free energy of the liquid phase can then be converted to a function of component compositions and internal variables, and the evolution of the internal variables will be determined via Allen-Cahn-type relaxation equations. We demonstrate this modeling strategy using the formation of stoichiometric phases from liquid phases in Na-Sb and Na-Sn systems. This study will pave the way for predicting microstructure evolution in liquids with ordering using phase-field simulations.