Liquid gallium-lead mixture spinodal, binodal, and excess thermodynamic properties

A statistical mechanical based theory is developed for incorporating the effect of the long-range forces in Ga-Pb alloy. In particular, the simplified random-phase approximation is employed in conjunction with the Grosdidier [Phys. Rev. B 72, 024207 (2005)] model for GaGa and PbPb interactions while a suitable nonadditive pair potential is introduced between unlike atoms. We present analytical expressions for the equation of state and for the concentration fluctuations S-CC(0), and then the role of the nonadditivity parameter is established by consulting the empirical critical parameters of the spinodal curve. It becomes possible to deduce the behavior of different thermodynamic functions such as Gibbs energy of mixing, excess Gibbs energy, isobaric heat capacity, and S-CC(0) in the vicinity of the liquid-liquid critical point and under extremely high pressure. The impact of temperature and pressure on segregation, and compound-forming tendencies is also investigated. Moreover, the immiscibility gap of the alloy is calculated and compared with the empirical results. The results suggest that: (i) the nonadditivity of the potential tails plays a dominant role in the determination of the spinodal curve, (ii) S-CC(0) is a very sensitive function in triggering the chemical short-range order, and (iii) the segregation or phase separation in Ga-Pb alloy is an outcome of the temperature dependence of the energy mismatch parameter. In conclusion, the present equation of state is sufficiently accurate that it provides a binodal curve, an excess Gibbs energy of mixing and isobaric heat capacity in quantitatively good agreement with the empirical results.