Gibbs energy calculation of liquid Zr–Al–Ni and Zr–Al–Cu–Ni alloys with clusters

The Gibbs energies of liquid Zr–Al–Ni and Zr–Al–Ni–Cu alloys with multi-clusters are calculated based on the statistical mechanism in this paper. The results show that the quantity of clusters depends mainly on the temperature and the concentration of the melt. It increases gradually with the decrease of temperature or with the increase of xNi in liquid (Zr80Al20)1–xNix alloys; the quantity of Zr2Ni clusters reaches its maximum of 0.061 mole at xNi = 0.336. In (Zr80Al20)1–xNix liquid alloy the existence of clusters causes the falling of the Gibbs energy. The Gibbs energy drops about 4000 J/mol at xNi = 0.35 if the effect of cluster of Zr2Ni is considered or about 8000 J/mol at xNi = 0.40 if both of clusters of Zr2Ni and ZrNi are taken into account.