Set based framework for Gibbs energy minimization

A new unified approach to Gibbs energy minimization is introduced. While it has only been tested on binary and ternary systems so far, it has a built in capability of handling arbitrary multicomponent multiphase systems with any number of sublattices, miscibility gaps, order-disorder transitions, and magnetic contributions. This new unified AMPL set-based Gibbs energy description optimizes the data representation and makes it possible to subject the task of phase diagram calculation to numerous existing general purpose optimization strategies as well as custom-made solvers. The approach is tested on a variety of systems, including Co-Mo, Al-Pt and Ca-Li-Na, all known to be computationally challenging for other approaches. In most of the tested systems, the AMPL code reproduces phase diagrams obtained via Thermo-Calc. In other systems, in-depth comparison of results suggests that in prior work a sub-optimal equilibrium might have been identified as a global one, and re-evaluation of previously published diagrams and databases might be necessary.