how to get the phase diagram of a ternary system?

Alloy Theoretic Automated Toolkit (ATAT)
1

Hi everyone,

I am now trying to construct a ternary phase diagram. The lattice is:

1 1 1 90 90 90
0.5 0.5 0.5
0.5 -0.5 0.5
0.5 0.5 -0.5
0 0 0 A,B,C

I already got a satisfied ECIs set. However, I am stuck in the monte carlo simulation. Actually, I don’t know how does ATAT calculate free energies through thermodynamic integration. The integration process of binary system is clear for me. Could anyone explain to me how does ATAT do that integration or send me any papers or equations about this?

Thank you
Sha