Analysis of a three-component model phase diagram by catastrophe theory

We analyze the thermodynamical potential of a lattice-gas model with three components and five parameters using the methods of the catastrophe theory. We find the highest singularity, which has codimension five, and establish its transversality. Hence the corresponding seven-degree Landau potential, the canonical form wigwam or A₆, constitutes the adequate starting point to study the overall phase diagram of this model. We also consider a singularity of lower codimension, which we relate to the phenomenon of critical azeotropy.