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The aim of this paper is to investigate the contribution of the mixing enthalpy to the stability of the faced-centered cubic (fcc) phase of the Co–Cr–Fe–Mn–Ni system. For this purpose, systematic first principles calculations on Special Quasirandom Structures (SQS) were performed in a comprehensive manner on the fcc solution in every 5 2 = 10 binary, 5 3 = 10 ternary, 5 4 = 5 quaternary and the quinary systems. The magnetic contributions have been considered carefully i.e. including non-collinear spin polarization. An analysis of the different system order interactions to the enthalpy of mixing is detailed. This concludes that, at equiatomic composition, there is no special "cocktail" effect with an increase of components and that the thermodynamic properties can be well anticipated from the lower order systems, essentially binary and ternary systems. [ABSTRACT FROM AUTHOR]

The phase diagram and thermodynamic data of the H–Nb system are evaluated and re-assessed to improve the description of this system. This system is modeled up to a few MPa. Only the gas phase and the solid phases are considered in the present study. Since only a few data were available for the H–Nb–Zr ternary system, a new set of experimental data has been obtained in the present work. For the first time, the solubility of niobium into the ε-ZrH 2 phase is found. In addition, Density Functional Theory calculations and the Special Quasirandom Structures method are used to determine the formation enthalpies of all the compounds and the mixing enthalpies in the different phases, respectively. Finally, the literature data as well as our experimental and calculated data are used for the Calphad modeling of the H–Nb–Zr system. [ABSTRACT FROM AUTHOR]

Abstract This work reports the Calphad modelling of the Cr–Nb–Sn–Zr quaternary system. In a previous paper, the thermodynamic modelling of the Cr–Nb–Sn system was presented. Since no experimental data were available for the Cr–Sn–Zr ternary system, new experimental data are provided, within this study, on the isothermal section at 900 °C. A ternary C 14 phase has been identified on the Sn-poor side of the phase diagram. In addition to these experimental data, Density Functional Theory (DFT) calculations are carried out in order to determine formation enthalpies of the stable and metastable compounds. At last, the Special Quasirandom Structures (SQS) method is jointly used with DFT calculations in order to estimate the mixing enthalpies of the A 2 and A 3 binary solid solutions. Finally, these experimental and calculated data in addition to those from the literature, are used as input data for the Calphad modelling of the Cr–Zr, Nb–Zr and Sn–Zr binary systems and the Cr–Nb–Zr, Cr–Sn–Zr and Nb–Sn–Zr ternary systems. A complete database for the Cr–Nb–Sn–Zr quaternary system is provided. [ABSTRACT FROM AUTHOR]

The Cr-Nb-Sn system has been studied experimentally, by first principles calculation and finally modeled with the Calphad method. The experimental study has been carried out on the Cr-Sn binary system to determine the solubility of Sn in the A 2 (Cr) solid solution, but also in the Cr-Nb-Sn ternary system in order to determine phase equilibria of the isothermal section at 800 °C and 1100 °C. Besides, the formation enthalpies of all the ordered configurations of the C 15 and A 15 phases and the stoichiometric Nb 6 Sn 5 and NbSn 2 phases have been calculated using the Density Functional Theory (DFT). The mixing enthalpies of the A 2 binary solid solutions have been estimated using the Special Quasirandom Structures (SQS). All these new experimental and calculated data have been taken into account for a new thermodynamic assessment of the three binary and the ternary systems. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the Calphad modelling of the Cr–Fe–Nb–Sn–Zr quinary system. In previous papers, the thermodynamic modelling of the Cr–Nb–Sn–Zr quaternary system, the Fe–Sn–Zr and Fe–Nb–Zr ternary systems as well as the Fe–Nb binary system were carried out. Since no experimental data were available for the Cr–Fe–Sn and Fe–Nb–Sn ternary systems, new partial isothermal sections have been measured at 1073K and 973K, respectively. In addition to these experimental data, Density Functional Theory (DFT) calculations are performed in order to determine formation enthalpies of the stable and metastable ordered compounds. At last, the Special Quasirandom Structures (SQS) method is used together with DFT calculations in order to calculate the mixing enthalpy of the A 2 (bcc) binary solid solution. Finally, these experimental and calculated data are jointly used with those from the literature as input data for the Calphad modelling of the Cr–Fe binary system as well as the Cr–Fe–Nb, Cr–Fe–Sn, Cr–Fe–Zr and Fe–Nb–Sn ternary systems. The ternary systems are then combined into a quinary database for which application examples are provided. [ABSTRACT FROM AUTHOR]

We present an ab-initio -based effective interaction model (EIM) for the study of magnetism, thermodynamics, and their interplay in body-centered cubic Fe-Co alloys, with Co content from 0 to 70%. The model includes explicitly both spin and chemical variables. For the former, a Heisenberg formalism is adopted. But, the spin magnitude of each Fe atom varies according to its local chemical environment, following a simple rule determined by density functional theory (DFT) calculations. The proposed model is able to describe precisely the ground-state magneto-energetic landscape of both chemically ordered and disordered Fe-Co systems, as given by DFT and experiments. In combination with on-lattice Monte Carlo simulations, it enables an accurate prediction at finite temperatures. In particular, the Curie point and the chemical order–disorder (B2-A2) transition temperature are accurately predicted, for all the concentrations considered. A strong dependency of the chemical transition temperature on the magnetic configuration is evidenced and analyzed. We also suggest a more important effect of magnetic rather than vibrational entropy on the chemical transition. However, this transition is not affected by a commonly accessible external magnetic field. [ABSTRACT FROM AUTHOR]

The Fe–Sn–Zr system has been studied by first principles calculation and modelled with the Calphad method using the literature and new experimental data. The work includes a revision of Fe–Sn and Fe–Zr systems. Our experimental study has confirmed that the W 5 Si 3 phase (stoichiometry Zr 5 Sn 2,3 Fe 0,7) is stable at 1350 °C but also down to 1000 °C. Moreover, the crystal structure of the X " phase has been determined. The formation enthalpies of all the ordered configurations of the C 15, C 16, C 36, E 1a phases and the stoichiometric Fe 5 Sn 3 , Fe 3 Sn 2 , FeSn, FeSn 2, Fe 23 Zr 6 , FeSn 2 Zr 6 (θ), Fe 36.36 Sn 36.36 Zr 27.27 (N) et Fe 14.39 Sn 43.47 Zr 39.13 (X ″) compounds have been calculated using the Density Functional Theory (DFT). The mixing enthalpies of the A 1, A 2 and A 3 binary solid solutions have been calculated using the Special Quasirandom Structures (SQS) and DFT calculation. From these new experimental and calculated data, new thermodynamic assessments are proposed for Fe–Sn, Fe–Zr and Fe–Sn–Zr systems. • New experiments are provided for Fe–Sn–Zr system. • The structure of X″ phase has been determined. • a complete Calphad description of Fe–Sn–Zr system is given for the first time. • New thermodynamic assessments are provided for Fe–Sn and Fe–Zr systems. [ABSTRACT FROM AUTHOR]

Among the ferromagnetic binary alloys, body centered cubic (bcc) Fe-Co is the one showing the highest magnetization. It is known experimentally that ordered Fe-Co structures show a larger magnetization than the random solid solutions with the same Co content. In this work, based on density functional theory (DFT) studies, we aim at a quantitative prediction of this feature, and point out the role of the orbital magnetic moments. Then, we introduce a DFT-based analytical model correlating local magnetic moments and chemical compositions for Co concentrations ranging from 0 to 70 at.%. It is also extended to predict the global magnetization of both ordered and disordered structures at given concentration and chemical short range orders. The latter model is particularly useful for interpreting experimental data. Based on these models, we note that the local magnetic moment of a Fe atom is mainly dictated by the Co concentration in its first two neighbor shells. The detailed local arrangement of the Co atoms has a minor effect. These simple models can fully reproduce the difference in magnetization between the ordered and disordered Fe-Co alloys between 30% and 70% Co, in good agreement with experimental data. Finally, we show that a similar model can be established for another bcc binary Fe alloy, the Fe-Ni, also presenting ferromagnetic interactions between atoms. [ABSTRACT FROM AUTHOR]