A globally convergent saturation state algorithm applicable to thermodynamic systems with a stable or metastable omni-component phase

A new algorithm is proposed for determining the saturation condition of a multi-component solution with respect to a thermodynamic system of phases that are in exchange equilibrium. The procedure is simple to implement, analytic in construction, and guaranteed to converge. The algorithm finds application in the computational thermodynamics of equilibrium phase relations in multi-component systems and provides a means of discriminating computed assemblages that are potentially metastable from those that are globally stable. The algorithm can be applied to any chemical system of arbitrary complexity.