Site occupation reversal in the Fe-Cr sigma phase

New Structural Insight into Interface-Controlled α–σ Phase Transformation in Fe-Cr Alloys

Synchrotron Laue microdiffraction scanning is used for the ex situ study of the body-centered, cubic-to-tetragonal phase transformation that occurs in equiatomic polycrystalline Fe-Cr alloys at temperatures between 550 and 800 °C. Grain orientation and grain strains were scanned with a micron step resolution after annealing at 700 °C for 12 h. Further microstructural details on the early stage of the transformation, and more particularly on the cubic-to-tetragonal phase interface, were achieved. Only the α and ordered σ phases were detected. The crystallographic relationships at the interface between the two phases did not follow the predicted rules; this result is discussed in relation to the measured microstrains.

Effect of mixed partial occupation of metal sites on the phase stability of γ-Cr23-xFe x C6 (x = 0-3) carbides

The effect of mixed partial occupation of metal sites on the phase stability of the γ-Cr_23−xFe_xC₆ (x = 0–3) carbides is explored as function of composition and temperature. Ab initio calculations combined with statistical thermodynamics approaches reveal that the site occupation of the carbides may be incorrectly predicted when only the commonly used approach of full sublattice occupation is considered. We found that the γ-M₂₃C₆ structure can be understood as a familiar sodium chloride structure with positively charged rhombic dodecahedron (M^(4a) M₁₂^(48h)) and negatively charged cubo-octahedron (M₈^(32f) C₆^(24e)) super-ion clusters, together with interstitial metal atoms at the 8c sites. The stability of the partially occupied phase can be easily rationalized on the basis of a super-ion analysis of the carbide phase. This new understanding of γ-M₂₃C₆ carbides may facilitate further development of high-chromium heat-resistant steels.

Anharmonicity, mechanical instability, and thermodynamic properties of the Cr-Re σ-phase

Using density-functional theory in combination with the direct force method and molecular dynamics we investigate the vibrational properties of a binary Cr-Re σ-phase. In the harmonic approximation, we have computed phonon dispersion curves and density of states, evidencing structural and chemical effects. We found that the σ-phase is mechanically unstable in some configurations, for example, when all crystallographic sites are occupied by Re atoms. By using a molecular-dynamics-based method, we have analysed the anharmonicity in the system and found negligible effects (~0.5 kJ/mol) on the Helmholtz energy of the binary Cr-Re σ-phase up to 2000 K (~0.8T(m)). Finally, we show that the vibrational contribution has significant consequences on the disordering of the σ-phase at high temperature.

Tight-binding simulation of transition-metal alloys

In order to perform atomistic simulations of steel, it is necessary to have a detailed understanding of the complex interatomic interactions in transition metals and their alloys. The tight-binding approximation provides a computationally efficient, yet accurate, method to investigate such interactions. In the present work, an orthogonal tight-binding model for Fe, Mn and Cr, with the explicit inclusion of magnetism, has been parameterized from ab initio density-functional calculations.

Atomic, Electronic, and Magnetic Structure of Iron-Based Sigma-Phases

A combination of ab initio total energy calculations with Calphad approach is applied to model the site occupancy and thermodynamic properties of the Fe-Cr, Co-Cr, Fe-V, and Fe-Mo binary sigma-phases as a function of composition and temperature. For each binary sigma-phase the parameters of the model are the ab initio calculated total energies of so-called end-member compounds, which represent all the 25=32 variants of complete occupancy of each of the five crystallographically inequivalent sites by one or the other alloy component. The paramagnetic state of the sigma-phases has been taken into account within the disordered local moment approach. The Fe and Co atoms are found to retain high spin moments when they occupy high-coordination-number sites in the structure. Using our model we were able to reproduce the experimentally observed site occupancy in the FeCr sigma-phase. The calculated site occupancies in the Co-Cr, Fe-V, and Fe-Mo sigma-phases are also presented and discussed.

First principles calculations of the σ and χ phases in the Mo-Re and W-Re systems

The total energies of all the ordered configurations of the σ and χ phases have been calculated by using first principles methodology in both Mo-Re and W-Re systems. These two complex structures possess 5 and 4 inequivalent sites generating 32 and 16 different ordered configurations, respectively, for a binary A-B system. The converged total energies of all the fully relaxed structures have been used to compute the occupancy of the inequivalent sites as a function of composition and temperature by using the Bragg-Williams approximation in the complete composition range. It is shown that the configurational entropy stabilizes the σ and χ phases in the Mo-Re and W-Re systems. The results evidence the preference of Re for lower coordination number site occupancy and are in very good agreement with the experimental measurements. Tentative ab initio phase diagrams have also been drawn.

Electronic structure of a σ-FeCr compound

The electronic structure of a σ-FeCr compound in a paramagnetic state was calculated for the first time in terms of isomer shifts and quadrupole splittings. The former were calculated using the charge self-consistent Korringa-Kohn-Rostoker (KKR) Green's function technique, while the latter were estimated from an extended point charge model. The calculated quantities combined with recently measured site occupancies were successfully used to analyze a Mössbauer spectrum recorded at room temperature using only five fitting parameters namely background, total intensity, linewidth, IS0 (necessary to adjust the refined spectrum to the used Mössbauer source) and the QS proportionality factor. Theoretically determined changes of the isomer shift for the σ-FeCr sample were found to be in line with the corresponding ones measured on a α-FeCr sample.