Ab initio thermodynamics of complex alloys: The case of Al- and Mn-doped ferritic steels

Understanding phase equilibria in high-entropy alloys: I. Chemical potentials in concentrated solid solutions – Atomic-scale investigation of AlCrFeMnMo

“…In our case, our assumption (initial magnetic moments on Fe atoms taken as μ(Fe) = 2.2 μ B , initial values for all the other species chosen equal to zero) was found satisfactory for steels with a high concentration of Fe (as in Ref. [10]) but it may not obviously work for AlCrFeMnMo, where the concentration of Fe is only 20%. To provide some insight into this issue, it may be useful to perform some inspection of the final magnetic moments, obtained after energy optimization of each SQS structure used in our work.…”

“…These cutoff and k-point values ensured reasonable accuracy for all total energies. All calculations were spin-polarized (collinear mode), and earlier studies [10] suggested to use zero initial magnetic moments for all species, except Fe atoms for which the usual value μ(Fe) = 2.2 μ B was specified. In all cases, the SQS optimization included atomic relaxations and supercell shape.…”

“…Keeping in mind these limitations of SQS-based approaches, it would be interesting to explore their connections with alternative routes for thermodynamic calculations on HEAs, noticeably those relying on cluster expansions, since the latter have proved efficient in providing shortand long-range order as well as compositions and chemical potentials in alloys with significant complexity [10]. To this aim, the critical issue is to elaborate a reliable energy model for the alloy in the relevant composition range, which can hardly be carried out by conventional procedures of fitting of the model on ab initio input data.…”

Understanding phase equilibria in high-entropy alloys: II. Atomic-scale study of incorporation of metallic elements in Cr carbides – Application to equilibrium with AlCrFeMnMo

“…In particular, as already mentioned for carbides and other compounds, designing an accurate CE model for a multi-element s.s. constitutes a challenge in itself, and a compromise between simplicity and efficiency should be looked for, maybe by following a route similar to that previously used in slightly simpler situations, i.e. Al-and Mn-doped ferritic steels [19]. In such systems, the main hypothesis, strongly suggested by the chemical complexity, was to make use of CEs restricted to short-ranged pairs.…”

“…A first-order Methfessel-Paxton [18] smearing scheme was used, with a smearing width of 0.2 eV. All calculations were spin-polarized (collinear mode), and earlier studies [19] suggested to use zero initial magnetic moments for all species, except (i) Fe atoms for which the usual value μ mag (Fe) = 2.2 μ B was specified, and (ii) Mn for which earlier investigations suggested to test several possibilities (−2, 0 or +2 μ B ) for the Mn initial moment [19], the lowest total energy value after relaxation being retained for each defect. In all cases, the structural optimization included full supercell relaxation, namely local atomic relaxations as well as supercell size and shape, in order to ensure zero local stress.…”