Journal of Phase Equilibria and Diffusion最新文献

Diffusion in the ordered V₃Au and disordered face-centred cubic solid-solution Au(V)_ss phases in the binary V-Au system is studied. Interdiffusion coefficients increase with increase in the Au content in Au(V)_ss due to increased pre-exponential factor and reduced migration barrier. Since the thermodynamic factor decreases with increasing Au content in Au(V)_ss, interdiffusion may likely be kinetically-driven. Integrated diffusion coefficients of V₃Au were determined with an activation energy of 87 ± 19 kJ/mol, indicating the possible dominance of grain boundary diffusion.

A comprehensive thermodynamic assessment of the Ni-Ti-Zr ternary system has been conducted using the CALPHAD (CALculation of PHAse Diagrams) methodology. Thermodynamic models for the constituent binary systems—Ni-Ti and Ni-Zr—were critically evaluated and refined based on recent experimental data and literature assessments. These models, along with an established description for the Ti-Zr system, were extrapolated to the ternary domain, where further optimization was performed using newly available experimental phase equilibria, isothermal sections, and invariant reactions. The resulting thermodynamic description captures the main features of the Ni-Ti-Zr phase diagram, including the liquidus and solidus projections, as well as the isothermal sections and isopleths. This model offers a useful basis for exploring and developing Ni-Ti-Zr-based materials, such as shape memory alloys, metallic glasses, and high-temperature structural alloys.

Establishing a reliable atomic mobility database is crucial for accurately describing the solidification processes and conducting kinetic simulations of rare earth and transition-metal (RE-TM) alloy systems. However, experimental diffusion data in these systems are sparse, fragmented, and often inconsistent due to the high chemical reactivity of rare earth elements, magnetic effects, and limited temperature windows accessible in diffusion measurements. As a result, reported self- and impurity diffusion parameters frequently exhibit significant discrepancies, which hampers their direct application in mobility modeling. In this work, a critical assessment of self and impurity diffusion parameters in RE-TM (RE = rare earth elements; TM = Fe, Co, Ni, Cu) systems is carried out. Available experimental diffusion data in bcc, fcc, and hcp phases are re-evaluated. To compensate for the lack of experimental information, previous studies based on first-principles calculations, machine-learning predictions, and semi-empirical models were also evaluated. Computational results that were inconsistent with experimental data were scrutinized and excluded when necessary. Based on the assessment of experimental data, reliable activation energies and frequency factors were obtained, providing accurate atomic mobility parameters for RE-TM systems. This study presents a comprehensive evaluation of self-diffusion and impurity diffusion in RE-TM systems and the assessed parameters provide an atomic mobility dataset that can be used to support diffusion-controlled kinetic simulations in RE-TM systems.

Mo-Co-B alloys of 14 compositions (4 for boundary binary systems and 10 for the ternary one) were prepared by arc melting in the Mo-MoB-Mo₂CoB₂-MoCoB-µ-Mo₆Co₇ region. X-ray diffraction analysis (XRD), electron probe microanalysis (SEM/EPMA), differential thermal analysis (DTA) and pyrometric measurements after Pirani and Altertum were used to determine structure and phase transformation temperatures. Based on the obtained results, a projection of the solidus surface for Mo-rich alloys of the Mo-Co-B system was constructed for the first time. It consists of five wide and one narrow isothermal planes of three-phase equilibria, separated by narrow two-phase surfaces. It was found that the incipient melting temperatures of alloys decrease with increasing Co-content from 2268 °C (the temperature of the peritectic reaction L_p + β-MoB ↔ Mo₂B in the binary Mo-B system) to 1249 °C (the melting temperature of alloys of the three-phase region µ-Mo₆Co₇ + Mo₂CoB₂ + MoCoB), passing through five isothermal plateaus at temperatures of 2005, 1422, 1408, 1388 and 1249 °C.

Magnetite concentrates from different parts of the Mesabi Range, exhibiting varying tendencies to encapsulate, were reduced using thermogravimetric analysis (TGA) and a high-temperature confocal scanning laser microscope (CSLM). Gas-phase mass-transfer conditions were intentionally varied by employing two reactors with different geometries: the TGA produced significantly slower reduction, whereas the CSLM setup yielded reduction rates up to 20 times faster under mass-transfer-controlled conditions. A preliminary mechanism is proposed to explain the transition from a porous iron product to a dense encapsulating layer. Encapsulation is interpreted as the outcome of competition between pore creation, driven by the reduction rate, and pore elimination, driven by surface diffusion. When pore formation is insufficient to counteract pore coarsening, a dense iron layer develops and restricts further reduction.

Thermodynamics is traditionally viewed as a theory of equilibrium because Gibbs formulated the combined law strictly for equilibrium systems. This historical limitation motivated the emergence of irreversible thermodynamics as a distinct field. Subsequent advances, including Kaufman’s introduction of lattice stability for quantitative treatment of nonequilibrium phases, Hillert’s integration of entropy production into the combined law, and Ågren’s development of the modern theory of atomic mobility, collectively extended Gibbs’s framework to describe real materials under evolving thermodynamic driving forces. The present author further refined Hillert’s nonequilibrium formalism by introducing partial internal energy, partial entropy, and partial volume for each component directly into the first, second, and combined laws. This refinement yields an explicit definition for the chemical potential in terms of these partial quantities, resolving subtle interdependencies among entropy, volume, and composition in open systems. Building on this foundation and Ågren’s mobility theory, the author developed and later revised the theory of cross phenomena, deriving transport equations from the first law and addressing limitations inherent in phenomenological Onsager formulations. In parallel, the author and collaborators established zentropy theory, which unifies quantum mechanics and Gibbs statistical mechanics to predict entropy and Helmholtz energy from a full ensemble of symmetry-broken configurations. This framework enables quantitative prediction of Helmholtz energy landscapes with basins, ridges, and apices across stable, metastable, and unstable states. Together, these developments establish a unified thermodynamic framework spanning equilibrium, nonequilibrium, statistical, and quantum descriptions across all-scales, and provide a thermodynamics-based artificial intelligence (AI) framework exemplified by the zentropy-enhanced neural network (ZENN), yielding physically grounded, interpretable predictions. This new AI framework also incorporates built-in safety mechanisms, including structural containment through configuration partitioning and dynamic containment via zentropy-based regulation of driving forces and system stability.

In this paper aspects of the first two papers written by Gibbs on the topic of thermodynamics are discussed. These early papers set the stage for Gibbs’ major work on thermodynamics. His use of graphical methods and geometry are reviewed and display the reasoning behind his mathematical construction of thermodynamics. This paper ends with later extensions of his work to interesting graphical plots as well as an example taken from his later work on Statistical Mechanics.

Phase equilibria and solid-state transformations in the Ni-rich region of the Ti–Zr–Ni system were investigated through a combined application of scanning electron microscopy, electron probe microanalysis, x ray diffraction, and differential thermal analysis. Comprehensive analysis enabled the construction of isothermal sections at 960 °C and 750 °C, revealing substantial differences in phase topology across this temperature interval. At 960 °C, the ternary system exhibits equilibria that differ markedly from the Zr–Ni binary: the intermetallic compounds ZrNi₃ and Zr₉Ni₁₁ remain stable due to the stabilizing effect of Ti, forming isolated phase fields that are not present in the binary diagram. The formation temperature of ZrNi₃ was established as 1000 °C, while Zr₉Ni₁₁ decomposes below 750 °C. At 750 °C, the phase relations significantly differ from those at 960 °C as a result of a sequence of solid-state reactions. The most noteworthy of these is the decomposition of the ternary compound τ₂, producing Zr₈Ni₂₁, Zr₇Ni₁₀, and TiNi₃, and fundamentally altering the topology of the isothermal section. Intermediate annealing at 900 °C provided insight into the transitional behavior between the two isothermal sections, revealing incomplete transformations and confirming the peritectoid formation of ZrNi₃ from Zr₂Ni₇, τ₃, and Zr₈Ni₂₁. The resulting reaction scheme for the ZrNi–Ni–TiNi subsystem integrates high-temperature stability, intermediate transformations, and low-temperature decomposition pathways. These findings establish a coherent thermochemical framework for the Ni-rich portion of the Ti–Zr–Ni system and provide essential reference data for thermodynamic modeling and the design of Ti–Zr–Ni intermetallic alloys.

Despite the potential of copper and silver halogen-containing argyrodites as environmentally friendly functional materials, phase equilibria in the corresponding systems remain virtually unstudied. In this study, phase equilibria in the quasi-ternary Ag₂Se-AgI-GeSe₂ system are investigated using differential thermal and X-ray phase analysis, as well as microhardness measurements. Solid-phase equilibria diagrams at 300 and 750 K, a liquidus surface projection, and several polythermal sections of the phase diagram are constructed. The primary crystallization fields of four phases, including ion-conducting solid solutions of the Ag_8−xGeSe_6−xI_x (δ-phase), were determined. The presented polythermal sections of the phase diagram clearly demonstrate the processes of phase crystallization from the melt. The relatively large primary crystallization area of the δ-phase facilitates the growth of its single crystals with various compositions by directional solution-melt crystallization over a wide range of compositions and temperatures.