If a model for activity-composition relationships applies right across a binary system, then the Gibbs-Duhem equation provides a straightforward formulation for the activity coefficient of one endmember, given the formulation for the other endmember. The algebraic convenience of this may blind us to the improbability of devising models that might apply right across a system, given the obvious complexity of the energetics in even simple minerals. A model that has more realistic objectives is Darken’s quadratic formalism. In this model the compositional range is divided into two terminal regions, connected by a transitional central region. In each of the terminal regions the solution behaves as a regular solution between an actual and a fictive endmember. The interaction energies in the two regions are usually very different. Whereas the subregular model involves the linear dependence of the interaction energy with composition, the quadratic formalism involves a constant interaction energy in each of the terminal regions, with the interaction energy changing only within the central region. In contrast to the subregular model, the quadratic formalism provides consistent descriptions of volume-composition relationships for binary mineral solid solutions. The inapplicability of the subregular model invalidates its use in expressing activity-composition relationships. Adoption of the quadratic formalism has important implications for geothermometry and geobarometry.