General principle

MTDATA calculates the amount of different phases present at equilibrium and their composition. For this, it has to minimise the free energy of the system you defined. The free energy of the system can be written:

Gs=Na Ga + Nb Gb ...

where Ga is the molar free energy of phase a, etc. Generally, the free energy of each phase is a function of its composition, and of T, P:

Ga=Ga(T,P,xa1,xa2,..,xan)

where xa1..xan are the weight or mole fraction of each component in phase a. These free energy are calculated using different models introduced later in this page.

If we consider a system of m phases (all solutions) with n components, then, supposing that all phases will dissolve all the components, we have a system free energy which is a function of

m*n+2 variables

Working with ten elements and 5-6 phases means you ask MTDATA to find the minimum of a function of 50-60 variables. Given the fact that there are many secondary minima (corresponding to metastable phases) you understand that it is a very complex mathematical problem.