Ternary Interaction Parameters in Calphad Solution Models

For random, diluted, multicomponent solutions, the excess chemical potentials can be expanded in power series of the composition, with coefficients that are pressure- and temperature-dependent. For a binary system, this approach is equivalent to using polynomial truncated expansions, such as the Redlich-Kister series for describing integral thermodynamic quantities. For ternary systems, an equivalent expansion of the excess chemical potentials clearly justifies the inclusion of ternary interaction parameters, which arise naturally in the form of correction terms in higher-order power expansions. To demonstrate this, we carry out truncated polynomial expansions of the excess chemical potential up to the sixth power of the composition variables.