Journal of Phase Equilibria and Diffusion最新文献

The thermodynamic assessment of the Nd-Tl binary system was performed using the CALPHAD approach, supported by ab initio calculations based on density functional theory (WIEN2k). The enthalpies of formation of six stable intermetallic compounds (Nd₃Tl, Nd₂Tl, Nd₅Tl₃, NdTl, Nd₃Tl₅, and NdTl₃) were evaluated and used to constrain the Gibbs energy models. The optimized description reproduces the available experimental phase boundaries, invariant reactions, and the measured calorimetric data for NdTl₃ within experimental uncertainty. Calculated lattice parameters are consistent with literature values, with deviations below 0.1 Å. The phase diagram is well reproduced, including the congruent melting of NdTl and NdTl₃ and the peritectic equilibria of Nd₃Tl, Nd₂Tl, and Nd₅Tl₃. Minor discrepancies remain in the Tl-rich region, attributed to the narrow stability range of NdTl₃. The present work provides the first consistent thermodynamic description of the Nd-Tl system, suitable for database development and future applications in rare-earth alloys.

Phase equilibria in the ZrNi–Ni–TiNi subsystem were comprehensively investigated using scanning electron microscopy (SEM), electron probe microanalysis (EPMA), X-ray diffraction (XRD), and differential thermal analysis (DTA). Both liquidus and solidus projections were constructed, and invariant equilibria involving the melt were identified and summarized. The study revealed three eutectic, two peritectic, and six transition-type invariant reactions. The formation of the ternary compound τ₃ with a BaPb₃-type crystal structure was confirmed. This phase forms via the peritectic invariant reaction L + TiNi₃ + Zr₂Ni₇ ⇄ τ₃ at approximately 1180 °C, nucleates on TiNi₃ grains, and results in non-equilibrium processes. The liquidus projection contains primary crystallization fields of 11 phases, while the solidus projection comprises 11 three-phase regions formed through three eutectic, two peritectic, and six transition-type reactions. A metastable compound with about 65 at.% Ni and widely varying Ti/Zr relative amounts was observed, which promotes amorphization of eutectic melts. These results refine the description of phase equilibria in the ZrNi–Ni–TiNi subsystem and provide a reliable basis for thermodynamic modeling of multicomponent Ti–Zr–Ni alloys.

Understanding and predicting the thermodynamic behavior, as well as their mutual interaction, of refractory metal constituents of High-Entropy Borides (HEBs) are essential for designing the compositions of such ceramics with enhanced oxidation-resistant capabilities. In this context, advanced CALPHAD models may provide fundamental thermodynamic descriptions, including the accurate representation of metastable solid and liquid phases, which are crucial for investigating high-temperature oxidation mechanisms and phase stability of HEBs. In this work, the third-generation CALPHAD approach is extended to elemental Hf, incorporating a complete thermodynamic description of its metastable FCC phase, in addition to the stable HCP and BCC structures, and of the liquid phase, including its behavior in the metastable region below the melting point. The Hf–Nb and Hf–Zr binary systems are also re-assessed based on the updated thermodynamic model of Hf. Then, taking advantage of these binary assessments, predictions on the Hf–Nb–Zr ternary phase diagram, for which no prior CALPHAD studies exist, are presented. This investigation represents a step toward the development of a robust, thermodynamics-based tool for modeling oxidation mechanisms and guiding the compositional design of highly resistant HEBs.

In this study, we numerically solved the diffusion equation with a concentration-dependent diffusion coefficient. When intrinsic diffusivity depends on the power of concentration, the solution to the diffusion equation was analytically derived in previous studies by Pelton and Etsell (Acta Metall 20: 1269–1274, 1972) and Blanc (J Appl Phys 45: 1948–1950, 1974). We confirmed that analytical methods for solving the diffusion equation are limited to intrinsic diffusion cases where diffusion processes are uncoupled, and we extended the method to thermodynamically coupled interdiffusion cases. The interdiffusion solutions were obtained numerically using a two-step iterative procedure, consisting of an inner step that determines the initial slope of the solution via the shooting method and an outer step that verifies the satisfaction of mass conservation. To validate our extended methodology, solution plots and penetration distances were compared with those reported in previous studies. We analyzed the characteristics of solutions to the diffusion equation where the diffusion coefficient is given as a chemical diffusivity. In particular, we examined the second derivative of the concentration profile under varying the diffusivity. The results show that increased curvature in the diffusion coefficient leads to increased curvature in the concentration profile. This improved our understanding of the nature of diffusion equation solutions in multicomponent systems.

C1990HP is a kind of commercial Cu alloy containing 3.5 wt.% Ti. It has unique mechanical and physical properties. Thus, C1990HP is regarded as a highly promising lead-frame material in electronic packaging. Sn is a base element used for lead-free solders. The knowledge of the Cu-Sn-Ti phase equilibrium plays a crucial role in understanding the interfacial reactions between C1990HP and Sn-based solders, however the phase equilibria information of this system is still lacking. The isothermal section of the Cu-Sn-Ti ternary system at 450 °C was experimentally determined. The phase equilibrium results confirmed the existence of two kinds of ternary compounds τ₁-CuSnTi and τ₂-CuSn₃Ti₅, which are only stable within a narrow composition range. No additional ternary compounds were found. Moreover, the Sn₃Ti₅ and Sn₅Ti₆ binary phases have considerable solubility of Cu. Meanwhile, the isothermal section was found to contain 17 three-phase regions, 33 two-phase regions and 17 single-phase regions.

The precipitation behavior of Cu-rich phases remains a fundamental challenge in optimizing the properties of Cu-containing alloys. The size, morphology, and distribution of these precipitates directly determine the strength and toughness of such alloys; coarse precipitates severely reduce toughness and cause premature service failure. Thus, understanding and regulating Cu precipitation is critical for fabricating high-performance Cu-bearing alloys. Current research mainly uses transmission electron microscopy and atom probe tomography for characterization, but their long cycles and limited spatiotemporal resolution hinder a comprehensive understanding of precipitation dynamics and underlying micro-mechanisms. The phase-field method—based on thermodynamic free energy—enables the dynamic modeling of the full evolution process of Cu-rich precipitate (nucleation, growth, coarsening), integrates multi-physics effects, visualizes behavior, and links it to composition/temperature. In recent years, this method has been widely used to reveal Cu-rich precipitation rules (including binary/multi-component transformation kinetics). Adding multi-physics energy terms has improved simulation accuracy and expanded applicability. Key mechanisms became quantitative equations, enabling predictive models for grain boundary precipitation and complex structures in multi-component alloys. This paper reviews the phase-field method’s application to Cu-rich precipitation, highlights its advantages in decoding micro-mechanisms and guiding alloy design, notes inherent limitations of existing models, and concludes by emphasizing that the phase-field method has exerted a transformative impact on this research field, bridging the gap between experimental observations and theoretical predictions of Cu-rich precipitation. Addressing its unresolved challenges—such as constructing non-equilibrium multi-field coupled models and establishing bidirectional cross-scale simulation frameworks—will drive the development of next-generation high-performance Cu-containing alloys.

Phase identification and analysis of 29 annealed ternary alloys enabled the creation of an isothermal section of the Zr-Fe-Bi phase diagram at 400 °C. Scanning electron microscopy (SEM), x-ray energy dispersive spectroscopy (EDS), x-ray diffraction (XRD) studies were used for the research. The above-mentioned studies confirmed the presence of the Zr₆FeBi₂ (τ₁) phase, led to the identification of two novel ternary compounds: Zr₅Fe₂Bi (τ₂) and Zr₂Fe₃Bi (τ₃), and establishment of the phase equilibria between them. The crystal structures of these intermetallic compounds are presented. The ranges of solid solutions associated with binary compounds were also determined.