An analytical model for calculating tie-line critical temperature in ternary immiscible alloys

An analytical model for calculating the tie-line critical temperature (TtC) in ternary immiscible alloys is proposed in this study. The results of the TtC for Al–Pb–Sn and Al–Bi–Sn alloys calculated by using the proposed model show a favorable agreement with the results obtained from the CALPHAD method and the experimental data, which verifies the correctness of the model. Based on the proposed model, the tie-line critical temperatures of several alloy systems, such as Al–In–Pb and Al–Bi–Pb, are calculated. The characteristics of the tie-lines in the ternary immiscible system are analyzed and discussed. The results indicate that ternary immiscible alloys can be divided into two types according to their characteristics of the tie-lines. For type I, the tie-line is nearly parallel to the edge binary system. For type II, there is a certain or large angle between the tie-line and the edge binary system. The relationship between the parameters for representing the tie-line equation and the critical point composition (xC) is determined by fitting the linear and secondary polynomial functions.