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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 $$\left( {\begin{array}{c}5\\ 2\end{array}}\right) =10$$ binary, $$\left( {\begin{array}{c}5\\ 3\end{array}}\right) =10$$ ternary, $$\left( {\begin{array}{c}5\\ 4\end{array}}\right) =5$$ 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.

International audience; 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 A2 (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 2 systems are then combined into a quinary database for which application examples are provided.

International audience; 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 W5Si3 phase (stoichiometry Zr5Sn2,3Fe0,7) 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 C15, C16, C36, E1a phases and the stoichiometric Fe5Sn3, Fe3Sn2, FeSn, FeSn2, Fe23Zr6, FeSn2Zr6 (θ), Fe36.36Sn36.36Zr27.27 (N) et Fe14.39Sn43.47Zr39.13 (X'') compounds have been calculated using the Density Functional Theory (DFT). The mixing enthalpies of the A1, A2 and A3 binary solid solutions have been calculated using the Special Quasirandom Structures (SQS) and DFT calculation. From these new experimental and calculated data, new thermodynaùic assessments are proposed for Fe-Sn, Fe-Zr and Fe-Sn-Zr systems. 2

International audience; This work reports the Calphad modelling of the Cr-Nb-Sn-Zr quaternary system. In a previous paper, the thermodynamic modelling of the CrNbSn system has been 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 DC. A ternary C14 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 phases. At last, the Special Quasirandom Structures (SQS) method is jointly used with DFT calculations in order to estimate the mixing enthalpies of the A2 and A3 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.

International audience; Les alliages de zirconium sont utilisés comme matériaux de gainage pour le combustible dans les réacteurs à eau pressurisée à 150 bars. Ces gaines sont exposées à un milieu radiatif et corrosif, et constituent la première barrière de confinement du combustible. Il est donc primordial qu’elles conservent leur intégrité pendant leur utilisation en conditions normales de fonctionnement (350°C) et/ou accidentelles (T>1000°C). Le développement d’outils permettant de prédire l’évolution des phases en fonction de la température et de la composition revêt donc un intérêt particulier.Le développement d’une base de données thermodynamique, dans le cadre de la méthode Calphad, permet de mieux appréhender le lien entre composition, microstructure et condition d’utilisation des alliages. Les différentes phases sont décrites par des fonctions thermodynamiques, cohérentes entre elles, ayant pour variables les compositions, la température, la pression, etc. A partir de la description des sous-systèmes on peut prévoir, par extrapolation, les phases stables dans des systèmes multiéléments pour des conditions données.Une première base de données thermodynamiques centrée sur les alliages de Zirconium et contenant les éléments Cr-Fe-Nb-Sn-Zr a déjà été développée*. Nous nous intéressons maintenant à l’ajout des éléments d’insertions H et O dans cette base. En effet, dans les conditions d’utilisation des gaines en réacteur, nous devons prendre en compte ces deux éléments compte tenu de leur effet sur les transformations de phases (formation d’hydrure, d’oxyde, etc.) et de leur effet sur le tenue mécanique des gaines (fragilisation de la microstructure).Notre étude porte principalement sur les sous-systèmes Zr-O-H, Zr-Nb-O, Zr-Nb-H afin de décrire, dans un premier temps, lesystème quaternaire Zr-Nb-O-H. Pour ce faire, nous avons utilisé les données expérimentales disponibles dans la littérature, nospropres données expérimentales et des calculs DFT (Density Functional Theory). Les travaux expérimentaux se sont focalisés sur les systèmes Zr-H et Zr-Nb-H. Nos calculs DFT ont porté sur des configurations ordonnées et des configurations de maille « quasialéatoires» obtenues via des calculs SQS (Special Quasirandom Structure), afin de remonter aux enthalpies de formation et aux enthalpies de mélange de différentes phases. Une description complète du système Zr-Nb-O-H sera donnée.

International audience; The phase equilibria and thermodynamic properties of the Mo-Re system are studied by combining first-principle and CALPHAD approach. The mixing enthalpies in the bcc and hcp solution phases are estimated by first-principle calculations using the special quasirandom structures. The liquid, bcc and hcp phases are described by a substitutional solution model. The intermetallic phases, sigma and chi, are described with the compound energy formalism with, respectively, 5 and 4 sublattices (SL) using the formation enthalpies of all the end-members directly from ab initio calculations. A phase diagram in agreement with the available experimental knowledge is obtained thanks to a least square procedure involving a limited number of parameters. Introducing all the elements in all the sublattices of the structure allows a proper description of the configuration of the intermetallic phases. Different simplifications of the description of the sigma phase are considered. The ideal 4SL simplification is equivalent to the full description. The 3SL and 2SL models require excess parameters in order to fit reasonably the experimental phase diagram. Among these, only the (Mo,Re)(10)(Mo,Re)(12)(Mo,Re)(8) model allows to closely approximate the low temperature thermodynamic properties of the full description.