A Convex Hull Algorithm for Minimization of Gibbs Energy in Two-Phase Multicomponent Alloys
We have adapted the Quickhull algorithm with the general dimension Beneath-Beyondalgorithm  for computing the convex hull of the Gibbs energy hypersurface of multicomponenttwo-phase alloys. We illustrate the salient features of our method with calculations of isothermalferrite-austenite equilibria in Fe-C-Cr. Finally, successive equilibrium calculations in a Fe-C-Cr-Mosteel over a large temperature range show the beneﬁt of computing the convex hull before performingthe conventional Newton-Raphson search.
Yves Bréchet, Emmanuel Clouet, Alexis Deschamps, Alphonse Finel and Frédéric Soisson
N. Perevoshchikova et al., "A Convex Hull Algorithm for Minimization of Gibbs Energy in Two-Phase Multicomponent Alloys", Solid State Phenomena, Vols. 172-174, pp. 1214-1219, 2011