Calculation of Gibbs energy of ZrAlNi, ZrAlCu, AlNiCu and ZrAlNiCu liquid alloys based on quasiregular solution model

With the effects of electronic structure and atomic size being introduced, the mixing enthalpy as well as the Gibbs energy of the ternary ZrAlCu, NiAlCu, ZrNiAl and quaternary ZrAlNiCu systems are calculated based on quasiregular solution model. The computed results agree well with the experimental data. The sequence of Gibbs energies of different systems is: GZrAlNiCu < GZrAlNi < GZrAlCu < GCuAlNi. To ZrAlCu, NiAlCu and ZrNiAl, the lowest Gibbs energy locates in the composition range of XZr = 0.39–0.61, XAl = 0.38–0.61; XNi = 0.39–0.61, XAl = 0.38–0.60 and XZr = 0.32–0.67, XAl = 0.32–0.66, respectively. And to the ZrNiAlCu system with 66.67% Zr, the lowest Gibbs energy is obtained in the region of XAl = 0.63–0.80, XNi = 0.14–0.24.