Thermodynamic assessment of Sn–Cu–Ce system

Phase relations of Sn–Cu–Ce system are important in understanding metallurgical role of Ce in Sn–Cu based lead-free solder alloys. Thermodynamic assessment of Sn–Cu–Ce ternary system has been done based on experimental data about phase equilibria and thermodynamic properties by using the CALPHAD approach combined with first-principle calculations of formation enthalpy of key compounds. The solution phases (liquid, Fcc_A1, Bcc_A2 and Bct_A5) were treated as substitutional, of which the excess Gibbs energies were modeled by the Redlich–Kister polynomial. Considering its crystal structure and solid solubility range, intermetallic compound Ce11Sn10 was described with a three-sublattice model (Ce)0.429(Sn)0.429(Ce,Cu,Sn)0.142. Other binary and ternary intermetallic compounds were described as stoichiometric phases because of their limited homogeneity ranges. During optimization, Ce–Sn binary system was first assessed; then phase relations in Sn–Cu–Ce ternary system were modeled by combining with the optimized Ce–Cu and Cu–Sn binary systems in literatures. A set of thermodynamic parameters for all known phases were obtained, which can reproduce most experimental data. The Scheil model was used to simulate the process of non-equilibrium solidification for a series of alloys.