Use of immaterial constraints in Gibbs energy minimization for parametric phase diagrams and process modeling

Computation of chemical equilibria and phase diagrams for multiphase and non-ideal systems by minimizing the Gibbs free energy of a system constrained by material balance has been the leading application in computational thermodynamics. The system is divided into possible reactive species as constituents and independently conserved components. The constituents and components are interconnected by the stoichiometric conservation matrix. The mathematical reproduction of physical phenomena related to immaterial factors such as kinetic inhibition, electromagnetic, charge transport or surface phenomena require the use constraints independent of the stoichiometric conservation of elements. The constrained Gibbs free energy (CFE) technique, published in its generic form in Calphad (Koukkari & Pajarre 2006), has proven to be viable for a number of applications where additional conditioning is valid for the Gibbs energy minimisation system. The additional constraints are used to control immaterial entities with a defined physical purpose. The studies performed so far include kinetic inhibition, electromagnetic, charge transport and surface phenomena, which all require the use of constraints independent of the stoichiometric conservation of elements. In this work the CFE approach has been applied to a set of parametric or non-equilibrium phase diagram studies. Use of CFE is straightforward for the diffusionless or paraequilibrium transformations, as they are described e.g. by Hillert (2008) and shown for the composition constrained (paraequilibrium) systems already by Kozeschnik (2000). Another example of kinetic constraining is calculation of isoaffinity curves and diagrams, which are of interest for reactive separation processes in chemical engineering. This technique may also be used in process modelling for non-equilibrium systems. Finally, as an example of parametric diagrams, the chemical or phase transformations due to external magnetic fields are shortly discussed.