PREDICTING PHASE AND CHEMICAL-EQUILIBRIUM USING THE CONVEX-HULL OF THE GIBBS FREE-ENERGY

While it is well known that the Gibbs free energy of a system is minim ized at phase and chemical equilibrium, the solution of this minimizat ion problem is not straightforward. A geometric algorithm that uses a convex hull approach to minimize the Gibbs free energy, and thereby pr edict equilibrium, is presented in this paper. The algorithm, which ca n be used to predict either phase or simultaneous phase and chemical e quilibrium, is a general method that does not have convergence problem s. Furthermore, provided the thermodynamic data for all possible phase s are included, the algorithm automatically generates both the number and types of phases present at equilibrium. The approach is illustrate d for two- and three-dimensional examples. It is shown that some previ ously published results are incorrect, and that even simple systems wh ere chemical and phase equilibria exist simultaneously can show very i nteresting and complex behaviour.