Predicting phase and chemical equilibrium using the convex hull of the Gibbs free energy

Abstract

While it is well known that the Gibbs free energy of a system is minimized at phase and chemical equilibrium, the solution of this minimization problem is not straightforward. A geometric algorithm that uses a convex hull approach to minimize the Gibbs free energy, and thereby predict equilibrium, is presented in this paper. The algorithm, which can be used to predict either phase or simultaneous phase and chemical equilibrium, is a general method that does not have convergence problems. Furthermore, provided the thermodynamic data for all possible phases are included, the algorithm automatically generates both the number and types of phases present at equilibrium. The approach is illustrated for two- and three-dimensional examples. It is shown that some previously published results are incorrect, and that even simple systems where chemical and phase equilibria exist simultaneously can show very interesting and complex behaviour.