Site occupancies in a chemically complex σ-phase from the high-entropy Cr–Mn–Fe–Co–Ni system

Site occupancies in a single-phase σ-intermetallic compound of composition Cr 46 Mn 15.2 Fe 16.3 Co 17 Ni 5.5 (in at.%) were studied. To the best of the authors' knowledge, such a complex analysis with 5 elements occupying 5 different sites has never been tackled before and is addressed here using cutting edge X-ray diffraction techniques, absorption spectroscopy and simulations. Resonant powder diffraction data were collected at the K-edges of each of the five elements and the site occupancies were refined by a joint Rietveld analysis. Dispersion coefficients were retrieved independently from tabulated values, Kramers-Kronig relations and reference samples. Additional Extended X-ray Absorption Fine Structure (EXAFS) measurements were used to confirm the site occupancies and bond lengths. The site occupancies were independently obtained by a thermodynamic approach based on the enthalpies of formation of the 5 5 = 3125 configurations generated by the ordered distribution of the five components on the five sublattices, derived from a machine learning approach based on a DFT database. Overall, the calculations and experiments are in excellent agreement and reveal that the σ phase can accommodate a considerable degree of disorder, which consequences for thermodynamic modelling are discussed. The configurational entropy (S) of the σ phase represents 84% of that of a fully disordered alloy with the same composition, which is much larger than that expected for a fully ordered intermetallic phase (S = 0). The corresponding entropic stabilization is one of the reasons for the fact that the σ phase is one of the most important intermetallic that precipitates in high-entropy alloys and many engineering materials.