Polynomial regression and interpolation of thermodynamic data in Al-Si-Mg-Fe system

A numerical technique for constructing thermodynamic databases has been proposed. This technique offers accurate calculations of solidification temperature, phase fractions, and solute concentrations of specific alloys in quaternary systems. The thermodynamic data is extracted by calling the TQ-interface (Thermodynamic Calculation Interface) from Thermo-Calc software, and modeled through efficient computational approaches such as polynomial regression and interpolation. This method is described in three parts. First, the applicability of regression functions is demonstrated on the Al-Si binary phase diagram. Second, the way of combining polynomial regression and interpolation is applied to model the Al-Si-Mg ternary system. Finally, the A356 alloy, which belongs to the Al-Si-Mg-Fe system, is modeled by a series of sub-ternary systems using regression and interpolation. The valid accuracy of the method is demonstrated by comparing the present results with those calculated using Thermo-Calc software. The application of the TQ-interface to solidification processes in Scheil and lever-rule models is also included. The results indicate that this method can offer accurate thermodynamic parameters for the A356 alloy in Al-Si-Mg-Fe system and reduce CPU time significantly when applied to solidification simulation. Several problems and the corresponding strategies for high order functions, unsmooth variations of thermodynamic information and partition coefficients are discussed to improve this method. This technique can also be applied to other specific alloys with small variations of thermodynamic variables in quaternary systems.