As I understand it, a given CALPHAD database is essentially just a set of equations that model the Gibbs free energy of each phase within a given alloy system (set of elements). Typically, the main way ThermoCalc, or any other CALPHAD implementation, works is that the user inputs the thermodynamic conditions (e.g. elements and their fractions and temperature), ThermoCalc then numerically solves for the convex hull defined by the database equations mentioned above, and then returns the equilibrium phases and phase fractions.
This usually works well. However, sometimes you may only be interested in materials with a certain phase, or combination of phases (e.g. only BCC and FCC in equilibrium, or a single phase region of only HCP, etc.). In this case the method described above is very annoying because you essentially have to guess and check different compositions until you find one with the desired phases. This can be very slow, so I want to know if there is a way to use CALPHAD in the reverse way.
Specifically, my question is: if you had access to the database equations for a given alloy system, could you analytically solve (and thus solve quickly) for the conditions (i.e. temperatures and compositions) that would produce the phase combination that you desire? Bonus points if you can point me to a paper where this was demonstrated!
I am aware that getting access to these equations is not feasible for most databases because the equations are essentially the intellectual property, and database creators would be stupid to give that out to users. However, I just want to know if this is theoretically possible, because I am developing algorithms to approximate a phase region of interest using the guess and check method, but I want to know if my algos are actually necessary.