A convex hull algorithm for a grid minimization of Gibbs energy as initial step in equilibrium calculations in two-phase multicomponent alloys

An efficient method for computing two-phase equilibria in multicomponent alloys is proposed. It relies on a hybrid scheme using as a first step the Quick Hull algorithm with the general dimension Beneath-Beyond algorithm of Barber et al. (1996) [1] adapted for computing the convex hull of the Gibbs energy hypersurface of multicomponent two-phase alloys. First, the salient features of our method are illustrated with calculations of isothermal ferrite–austenite equilibria in Fe–C–Cr, described by the Compound Energy Formalism with two sublattices. Then, computational efficiency is investigated to suggest strategies to achieve the best compromise between efficiency and robustness. Finally, successive equilibrium calculations in a Fe–C–Cr-Mo steel over a large temperature range show the benefit of computing the convex hull before performing the conventional Newton–Raphson search.