Enthalpies of formation for the Al–Cu–Ni–Zr quaternary alloys calculated via a combined approach of geometric model and Miedema theory

A method to extrapolate the thermodynamic properties of quaternary alloys from constitutive binary systems is presented. The method is based on Miedema's theory, and the asymmetry of thermodynamic properties of constitutive binary alloys is considered in the present model. The dependence of asymmetric constituent on the choice in Toop model has been overcome. This method has been applied to calculate the enthalpies of formation for ternary alloys. In the present work, the proposed method is used to calculate the mixing enthalpies of Al–Cu–Ni–Zr quaternary alloys and its constitutive subsystems. The good agreement between calculation and experimental data indicates that the present method is reasonable for predicting the thermodynamic properties of multi-component system.