I primarily use Thermo-Calc so I will use that to describe my problem but I am interested to hear general CALPHAD insight as well.
Using Thermo-Calc I can quickly get an idea of the phase regions present (isothermally) by running a phase diagram calculation for a ternary. What appeals to me most about this is how fast the calculation is (as opposed to having to run ~5000 single eq calcs to get an idea of the phase regions). I have a vague understanding that behind the scenes Thermo-Calc is zeroing on each of the phase boundaries and so only has to do a limited number of calculations. In Thermo-Calc and TC-Python it only seems possible to do this for binary and ternary systems (e.g., using "with_phase_diagram_calculation()" in TC-Python it seems to only let me specify "with_first_axis" and "with_second_axis"). I guess they don't have this implemented because you can't easily visualize quaternaries, etc., but I am interested in still extracting the data relating to the phase regions/boundaries. So, my question is how can I extract this phase data using TC-Python for an arbitrary system of elements?
A secondary question I would be interested to hear an answer to is how exactly Thermo-Calc (or other CALPHAD implementations) calculate the phase region/boundary information so quickly.