Phase stability of ternary fcc and bcc Fe-Cr-Ni alloys

The phase stability of fcc and bcc magnetic binary Fe-Cr, Fe-Ni, and Cr-Ni alloys, and ternary Fe-Cr-Ni alloys is investigated using a combination of density functional theory (DFT), cluster expansion (CE), and magnetic cluster expansion (MCE) approaches. Energies, magnetic moments, and volumes of more than 500 alloy structures have been evaluated using DFT, and the predicted most stable configurations are compared with experimental observations. Deviations from the Vegard law in fcc Fe-Cr-Ni alloys, resulting from the nonlinear variation of atomic magnetic moments as functions of alloy composition, are observed. The accuracy of the CE model is assessed against the DFT data, where for ternary Fe-Cr-Ni alloys the cross-validation error is found to be less than 12 meV/atom. A set of cluster interaction parameters is defined for each alloy, where it is used for predicting new ordered alloy structures. The fcc ${\mathrm{Fe}}_{2}\mathrm{CrNi}$ phase with ${\mathrm{Cu}}_{2}\mathrm{NiZn}$-like crystal structure is predicted to be the global ground state of ternary Fe-Cr-Ni alloys, with the lowest chemical ordering temperature of 650 K. DFT-based Monte Carlo (MC) simulations are applied to the investigation of order-disorder transitions in Fe-Cr-Ni alloys. The enthalpies of formation of ternary alloys predicted by MC simulations at 1600 K, combined with magnetic correction derived from MCE, are in excellent agreement with experimental values measured at 1565 K. The relative stability of fcc and bcc phases is assessed by comparing the free energies of alloy formation. The evaluation of the free energies involved the application of a dedicated algorithm for computing the configurational entropies of the alloys. Chemical order is analyzed, as a function of temperature and composition, in terms of the Warren-Cowley short-range order (SRO) parameters and effective chemical pairwise interactions. In addition to compositions close to binary intermetallic phases ${\mathrm{CrNi}}_{2}$, FeNi, ${\mathrm{FeNi}}_{3}$, and ${\mathrm{FeNi}}_{8}$, pronounced chemical order is found in fcc alloys near the center of the ternary alloy composition triangle. The calculated SRO parameters compare favorably with experimental data on binary and ternary alloys. Finite temperature magnetic properties of fcc Fe-Cr-Ni alloys are investigated using an MCE Hamiltonian parameterized using a DFT database of energies and magnetic moments computed for a large number of alloy configurations. MCE simulations show that the ordered ternary ${\mathrm{Fe}}_{2}\mathrm{CrNi}$ alloy phase remains magnetic up to 850--900 K due to the strong antiferromagnetic coupling between (Fe,Ni) and Cr atoms in the ternary Fe-Cr-Ni matrix.