Structure of the critical lines for the lattice gas model

Despite its simplicity, the three-component lattice gas model (in which one component is “holes”) for compressible binary mixtures is known to have many important features of the global phase behavior in common with more realistic equations of state. In this paper the underlying structure of the critical lines in a composition-composition projection is investigated by demarking, but maintaining, all unstable segments in the diagrams. Changes in the class of phase behavior with variations of the interaction parameters are then seen to be frequently accompanied by premonitory changes in the critical lines occuring in the unstable regions. A principal transition mechanism is a “crossing point” at which two critical lines meet and exchange branches. An equation for the critical line is given in closed form and used to investigate major regions in the global phase diagram including symmetric sections and the Griffiths shield region.