The U-Pu-Zr alloy is a widely used metallic fuel in advanced fast reactor systems due to its superior thermal and neutronic performance. Accurate thermodynamic parameters and a reliable kinetic database are essential to predict the diffusion behavior of a U-Pu-Zr alloy across various compositions and temperature ranges. This study presents a comprehensive thermodynamic assessment of the U-Pu-Zr ternary system, by optimizing ternary thermodynamic parameters to improve agreement with experimental liquidus and solidus data. Additionally, the atomic mobility parameters for the bcc U-Pu-Zr alloys were evaluated based on the available experimental diffusion data and thermodynamic parameters. The results demonstrate that the assessed thermodynamic and atomic mobility parameters accurately reproduce experimental phase diagram data and diffusion coefficients, with an emphasis on composition profiles and diffusion paths, confirms the reliability of the atomic mobility developed in this work. These results provide a robust foundation for modeling diffusion-controlled transformations in U-Pu-Zr metallic fuels and contribute to their further optimization and application in nuclear reactor systems.
Diffusion kinetics of silver (Ag) in nuclear grade graphites, IG-110 and ZXF-5Q were investigated from 500 to 900 °C by the thin film diffusion technique. Dynamic secondary ion mass spectroscopy was utilized for depth profiling of concentrations and diffusion coefficients were calculated utilizing solutions to Fick’s second law. Ag was found to diffuse through the bulk of both graphite grades with diffusivities on the order of 10−20 to 10−22 m2/s. For IG-110 graphite, temperature-dependence of Ag diffusion coefficients yielded activation energy and pre-exponential factor of 66.7 kJ/mol and 2.11 x 10−17 m2/s, respectively. For ZXF-5Q graphite, activation energy and pre-exponential factor were determined to be 66.6 kJ/mol and 2.04 x 10−17 m2/s, respectively. These diffusion coefficients were very consistent despite the difference grain size, porosity and filler presence for the two types of graphite.
The phase equilibria of the Dy-Fe-B ternary system at 873 and 1073 K were investigated experimentally in this work using the equilibrated alloy method combined with scanning electron microscopy (SEM) with energy dispersive spectroscopy (EDS) and X-ray powder diffraction (XRD). The experimental analysis identified five stable ternary intermetallic compounds, namely Dy2Fe14B (τ1) with the Nd2Fe14B-type structure and space group P42/mnm, DyFe4B4 (τ3) with the Nd1+εFe4B4-type structure and space group Pccn, Dy5Fe2B6 (τ4) with the Pr5−xCo2+xB6-type structure and space group R 3 m, Dy3FeB7 (τ5) with the Y3ReB7-type structure and space group Cmcm, and DyFeB4 (τ6) with the YCrB4-type structure and space group Pbam, at 873 and 1073 K. It is noteworthy that DyFe2B2 (τ2) reported previously in the literature was not found in the present analyses of the measured equilibrated alloys. Finally, based on the experimentally determined results, two isothermal sections of the Dy-Fe-B ternary system at 873 and 1073 K were constructed, providing key experimental data and a theoretical basis for the thermodynamic calculation of this ternary system and the design of high-performance and low-cost Nd-Dy-Fe-B permanent magnets.
Vapor–liquid equilibria and impurity separation behavior in Pb-Zn, Pb-Bi and Pb-Ag binary systems were investigated using CALPHAD-based activity calculations combined with Gibbs-energy minimization equilibrium simulations performed in HSC Chemistry software. Separation coefficients of Zn, Bi, and Ag were evaluated as a function of temperature and composition to quantify the relative volatility of impurity elements with respect to lead. The results reveal three distinct thermodynamic regimes. The Pb-Zn system exhibits strong positive deviations from ideality and extremely high separation coefficients (βZn ≫ 1), indicating a very high selective volatility of Zn relative to Pb. The Pb-Bi system shows near-ideal solution characteristics with separation coefficients approaching, but remaining below unity (βBi ≈ 0.56-0.93), indicating limited separation efficiency. In contrast, the Pb-Ag system is characterized by very low separation coefficients (βAg ≪ 1), reflecting the thermodynamic stability of Ag in the condensed phase and its negligible tendency to evaporate relative to Pb. Equilibrium composition diagrams demonstrate the combined influence of temperature and total pressure on phase redistribution. Both increasing temperature and decreasing pressure promote vapor-phase enrichment of impurities; however, these conditions simultaneously enhance lead volatilization, thereby reducing separation selectivity under single-stage equilibrium conditions. The theoretical predictions are consistent with experimental data reported in the literature, where efficient impurity removal was achieved through two-stage high-low temperature vacuum distillation of crude lead. The present study provides a quantitative thermodynamic framework for evaluating the feasibility and limitations of vacuum refining of lead alloys.
In first-principles-based calculations of thermodynamic quantities "thermodynamic consistency" has not been guaranteed when applying disparate approximation methods to diverse phases such as, compounds, solid solutions, or liquids, constituting alloy phase diagrams. In this study, we performed tailored calculations for each phase in the Cu-Ni-Si system and verified consistency using phase equilibrium calculations and likelihood analysis. The resulting phase diagrams generally reproduced experimental ones, despite extreme sensitivity to minute free energy differences. Furthermore, likelihood analysis quantitatively demonstrated that free energy residuals fall within a narrow 1-2 kJ/mol range. This indicates that a high degree of thermodynamic consistency is preserved across all phases. Therefore, we newly define the computational process encompassing the first-principles uncertainty revealed by this likelihood analysis as the “theoretical phase diagram calculation method.” By applying this method to the binaries and ternary of the Cu-Ni-Si system, we demonstrated its capability to reproduce experimental phase diagrams with high precision.
