A geometric model correctly reproducing both the regular term and the configurational entropy of a ternary solution

The historically first geometrical method pioneered by Bonnier and Caboz to evaluate the Gibbs energy of a ternary solution from the Gibbs energies of binary solutions correctly reproduces the configurational entropy, but not the regular term. In contrast, the constructs suggested by Toop, Kohler, Colinet and Muggianu result in the correct zero-order interaction parameter, but underestimate the configurational entropy. It is demonstrated that it is always possible to select compositions of the binary solutions reproducing both the regular term and the ideal entropy of mixing. A consistent method of finding these compositions is developed.