The thermodynamics of critical points in multicomponent systems, more generally systems with more than two independent variables (including binary fluid mixtures, the helium $\lambda$ transition, order-disorder transitions in alloys, and antiferromagnetism) are discussed from a unified geometrical point of view, in analogy with one-component (liquid-vapor and simple-ferromagnetic) systems. It is shown that, from a few simple postulates, the qualitative behavior near the critical point of quantities such as compressibilities, susceptibilities, and heat capacities, with different choices of the variables held fixed, can be easily predicted. A number of seemingly exceptional cases (such as critical azeotropy), which arise when critical or coexistence surfaces bear an "accidental" geometrical relationship with the thermodynamic coordinate axes, are explained in terms of the same postulates. The predicted results are compared with several theoretical models and experimental data for a variety of systems.

• Received 27 March 1970

DOI:https://doi.org/10.1103/PhysRevA.2.1047