Ab initio calculations and thermodynamic modeling for the Fe–Mn–Nb system

The Fe–Nb and Mn–Nb systems have been thermodynamically investigated within the CALPHAD approach by combining available experimental data and the data from our ab initio calculations. Possible nonmagnetic (NM), ferromagnetic (FM) and antiferromagnetic (AFM) ordering for the end-members of the intermetallic compounds Laves C14 and μ were treated during ab initio calculations. It turns out that the local magnetic moment depends on the lattice site. The energetically most stable states of C14 at the stoichiometric compositions NbFe2 and NbMn2 exhibit the FM and NM ordering, respectively. The FM ordering can lower the total energies for most of the end members of μ in the Fe–Nb system. The energy of formation for the “hypothetical” end-members of μ, due to the sublattice model used for modeling the ternary solubility, was also calculated by ab initio and incorporated into the modeling of the phase. μ is predicted to be marginally stable in the Mn–Nb binary system. Compared to the conventional treatment for the end-members of C14, the introduction of physically based parameters from ab initio calculations makes the thermodynamic optimization process simpler, more effective and more reliable in the Mn–Nb binary system. The obtained thermodynamic parameters for Fe–Nb and Mn–Nb systems can describe the reliable experimental data well. The thermodynamic description for the ternary Fe–Mn–Nb system is then extrapolated for the first time from the three binary edges and the data from our ab initio calculations. Several isothermal sections, the liquidus projection and the reaction scheme have been predicted accordingly.