Fast prediction of phase equilibrium at varying temperatures for use in multi-component phase field models

A new method for temperature-dependent phase equilibrium prediction for use in multi-component phase field models of solidification is proposed. The method consists of two parts. First, the convex hull method is applied to predict the phase equilibrium at a single temperature. Second, a set of linear equations is developed to extend the equilibrium calculation over a range of temperatures. These linear equations are derived as an extension of the equation used for solidification of binary alloys in approximating the equilibrium state of multi-component systems. Phase field simulations of solidification of a Ti-Al-V-Fe alloy are performed to demonstrate the effectiveness of the present approach under isothermal and continuous cooling conditions. The results are compared against Thermo-Calc calculations, and indicate that a high accuracy of equilibrium prediction is achieved at a single and multiple temperatures, thus demonstrating that this approach can be successfully applied to the multi-component phase field models.