The implementation of an algorithm to calculate thermodynamic equilibria for multi-component systems with non-ideal phases in a free software

Thermodynamics is a central part of materials science. Thermodynamic models provide a unique method to combine experimental data and results from first-principles calculations in databases. Equilibrium calculations based on these databases are essential to provide values of many different thermodynamic properties for software tools for simulating materials processes and to predict their final properties. It is important for such work to have a free software with access to the source code. In this paper, a well-established algorithm to calculate thermodynamic equilibria for multi-component systems using different kinds of conditions for non-ideal solution phases with different models is explained in detail, including changes of the set of stable phases during iterations. A new definition of the molar Gibbs energy and a powerful method to handle composition variables and phase amounts are presented. The technique to calculate derivatives of state variables based on the first and second derivatives of the Gibbs energy is explained. The algorithm can also be used to calculate properties outside the equilibrium state as required for the simulation of phase transitions.