Estimation of mixing enthalpy of the liquid Sn-Ag-Cu system at 1423 K from data on the properties of binary subsystems using geometric models of solutions

The article considers the estimation of mixing enthalpy ΔН_mix of the Sn-Ag-Cu ternary system melts at a temperature of 1423 K from the calorimetric data on the mixing enthalpy of binary subsystems Ag-Cu, Ag-Sn and Cu-Sn measured earlier. The geometric models by Toop, Kohler and Muggianu, where binary data is jointly processed in each case according to a specific mathematical procedure, were applied to the ΔН_mix assessment. The results of calculations by these models are presented by the compositional dependences of ΔН_mix of the ternary system in the form of 3D surfaces, projections of these surfaces onto the plane of the compositional triangle, as well as isotherms plotted for individual quasi-binary sections. It was found that modeling using the Kohler’s and Muggianu’s methods gives insignificantly different results, whereas the values of the mixing enthalpy of ternary compositions in the Toop’s model are noticeably more immersed into the negative (exothermic) region. As it is known from the scientific literature, the right choice of a geometric model depends on whether the ternary system under study belongs to a “symmetric” or “asymmetric” type. The shape of the available ΔН_mix isotherms of binary subsystems indicates that the Sn-Ag-Cu system is “asymmetric”. The results calculated using the Toop’s model are recognized as the most correct ones, since that model is recommended in the literature for describing “asymmetric” systems. The common limitation of all geometric models, considering only binary interparticle interactions, and the advisability of extra experimental study of three-component melts formation to reveal the possible contribution of ternary interactions to the mixing enthalpy are noted.