TERNARY EXPERIMENTAL EXCESS FUNCTIONS BY MEANS OF HIGH-ORDER POLYNOMIALS - ENTHALPY OF MIXING OF LIQUID PB - SN - SB ALLOYS

Calculations of ternary phase diagrams need accurate analytic representations of the excess functions of extended solutions. For experimentalists the problem is to find the mathematical mould suitable to translate the full information, without loss of data, but requiring a minimum set of experiments. The Darken quadratic formalism for ternaries is able to accurately fit the experimental partial excess functions in the area corresponding to a relatively high level of one component, for example x(i) greater-than-or-equal-to 0.33. This quadratic formalism needs only 2 x 2 binary adjustable parameters and only one ternary. The whole system is divided into three adjacent quadrilaterals, each one corresponding to one comer element, and the 5 x 3 Darken adjustable parameters are fitted by rational measurements. A small gap of the excess function can be observed at the boundary isopleths connecting the three quadrilaterals. A very simple Redlich-Kister ternary formalism of the fifth degree is able to mix together the three comers in the form of a sole polynomial representation of the excess function. The method is tested successfully for the mixing enthalpy of the ternary Pb - Sn - Sb liquid phase with an accuracy better than 100 J . mol-1 in the whole system and saving the measured partial functions.