Journal of Phase Equilibria and Diffusion最新文献

{"title":"Phase Equilibria of the Zn-Cu-Cr Ternary System at 450 and 600 °C","authors":"Xinyu Chen,&nbsp;Manxiu Zhao,&nbsp;Zhi Li,&nbsp;Wendao Li","doi":"10.1007/s11669-026-01259-x","DOIUrl":"10.1007/s11669-026-01259-x","url":null,"abstract":"<div><p>The phase equilibria of the Zn-Cu-Cr ternary system at 450 and 600 °C were studied using equilibrium alloy method. The phase constitution of the alloys were analyzed by means of the scanning electron microscope equipped with energy dispersive x-ray spectroscopy (SEM-EDS), and x-ray diffraction (XRD). The results show that five three-phase regions exist in the isothermal section at 450 °C, and four three-phase regions exist in the isothermal section at 600 °C. No new ternary compound was found in the system. The (Cr) phase is found in equilibrium with all phases. At 450 °C the solubility of Cu in CrZn₁₇ is 0.69 at.%, and the maximum solubility of Cr in CuZn₄ (ε), Cu₅Zn₈ (γ), and CuZn (β′) is 1.15, 0.6, and 0.43 at.%, respectively. At 600 °C the maximum solubility of Cr in CuZn₃ (δ), Cu₅Zn₈ (γ), and CuZn (β) is up to 1.95, 1.03, and 7.8 at.%, respectively.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"47 3","pages":"289 - 300"},"PeriodicalIF":1.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental Investigation of Solidification and Isothermal Section at 1000 °C in the Fe-Al-Ti-C System","authors":"I. Fartushna,&nbsp;A. Samelyuk,&nbsp;V. Kravchuk,&nbsp;D. Kapush,&nbsp;M. Bulanova","doi":"10.1007/s11669-026-01255-1","DOIUrl":"10.1007/s11669-026-01255-1","url":null,"abstract":"<div><p>Phase equilibria in the Fe-rich corner of the quaternary Fe-Al-Ti-C system upon solidification and at 1000 °C were studied using differential thermal analysis (DTA), powder x-ray diffraction (XRD), microscopic examination and electron probe microanalysis (EPMA). The partial liquidus and solidus projections and the isothermal section at 1000 °C were constructed. The results are presented on the Fe-25Al-Ti-C composition triangle, where the corner Fe-25Al corresponds to the disordered (<i>α</i>Fe) solid solution or its ordered derivatives FeAl or Fe₃Al, depending on the temperature. The boundaries of the primary crystallization regions of the phases, types and coordinates of mono- and bivariant equilibria are determined. The liquidus surface in the studied region is characterized by the regions of primary crystallization of the (<i>α</i>Fe), Fe₂Ti, Fe₃AlC (<i>κ</i>-carbide), TiC and graphite (C) phases. The solidus surface and isothermal section at 1000 °C are defined by the co-existence of the TiC phase with all phases of the system forming two three-phase regions, which form by transition (U) type four-phase reactions.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"47 3","pages":"228 - 238"},"PeriodicalIF":1.7,"publicationDate":"2026-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148237208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental Study and Thermodynamic Calculation of Phase Equilibria in the Ce-Co-Cu Ternary System","authors":"R. C. Zhang,&nbsp;F. L. Dai,&nbsp;X. Liu,&nbsp;H. Y. Zhang,&nbsp;Q. R. Yao,&nbsp;J. Wang","doi":"10.1007/s11669-026-01260-4","DOIUrl":"10.1007/s11669-026-01260-4","url":null,"abstract":"<div><p>Experimental investigation of the phase equilibria in the Ce-Co-Cu ternary system was conducted via the equilibrated alloy technique, utilizing x-ray diffraction (XRD) and scanning electron microscopy coupled with energy dispersive spectroscopy (SEM-EDS). Ten binary intermetallic compounds, CeCo₂, CeCo₃, Ce₂Co₇, Ce₅Co₁₉, CeCo₅, Ce₂Co₁₇, CeCu₂, CeCu₄, CeCu₅, and CeCu₆, were confirmed, and no ternary intermetallic compounds were detected. It was found that the continuous solid solution phase Ce(Co, Cu)₅ was formed between the CeCo₅ and CeCu₅ binary intermetallic compounds due to having the same crystal structure. The solid solubilities of Cu in CeCo₂, CeCo₃, Ce₂Co₇, Ce₅Co₁₉, and Ce₂Co₁₇ as well as that of Co in CeCu₂, CeCu₄, and CeCu₆ were measured. Furthermore, a thermodynamic assessment of the Ce-Co-Cu ternary system was performed via the calculation of phase diagrams (CALPHAD) approach, incorporating both the experimental data obtained in this study and available literature results. The calculated isothermal sections exhibit good agreement with the experimental observations. Consequently, a set of self-consistent thermodynamic parameters has been acquired, providing a solid foundation for developing a thermodynamic database for Sm-Co-based permanent magnets containing abundant rare-earth and transition metals.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"47 3","pages":"321 - 339"},"PeriodicalIF":1.7,"publicationDate":"2026-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148237258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermodynamic Properties of Binaries (Cu-Ni, Ni-Pt, Cu-Pt) and Ternary (Cu-Ni-Pt) Solid Alloys Predicted Using the Molecular Interaction Volume Model (MIVM)","authors":"Mithilesh Kumar Jha,&nbsp;Vinaya Kumar Jha,&nbsp;Ganesh Kumar Shrestha,&nbsp;Sanjay Kumar Sah,&nbsp;Indu Shekhar Jha,&nbsp;Ishwar Koirala","doi":"10.1007/s11669-026-01256-0","DOIUrl":"10.1007/s11669-026-01256-0","url":null,"abstract":"<div><p>The activities of the constituent metals in the binary solid alloys Cu-Ni at 973 K, Ni-Pt at 1625 K, and Cu-Pt at 1350 K, as well as their excess Gibbs energy and the activities of Cu in the ternary solid alloys Cu-Ni-Pt at 1000 K for three cross-sections, i.e., for different ratios of nickel to platinum, <i>X</i>_Ni:<i>X</i>_Pt = 2:1, 1:1, and 1:2, have been computed using the statistical thermodynamic model based on the free volume concept, i.e., the molecular interaction volume model (MIVM). The predicted values have been compared with the available experimental data and analyzed for the binary solid solutions. In addition, the excess Gibbs energy of mixing (Δ<i>G</i>^XS) of the ternary Cu-Ni-Pt alloys for all three cross-sections has been calculated using the same model. The agreement between the theoretical and experimental results for the binary solid alloys is found to be satisfactory, confirming the suitability of the model in predicting thermodynamic properties and interaction behavior in ternary and multicomponent metallic solid solutions.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"47 3","pages":"265 - 277"},"PeriodicalIF":1.7,"publicationDate":"2026-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148237107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of GNP Reinforcement on Phase Stability and Microstructure of AlCoCrFeNi HEA Composites: A Data-Driven Approach","authors":"Renju C. Daniel,&nbsp;Mohammed Mudassir,&nbsp;C. N. Shyam Kumar,&nbsp;R. Anand Sekhar","doi":"10.1007/s11669-026-01253-3","DOIUrl":"10.1007/s11669-026-01253-3","url":null,"abstract":"<div><p>This study introduces an integrated design and optimization framework for AlCoCrFeNi-based composites reinforced with graphene nanoplatelets (GNPs), combining machine learning-driven predictive modelling with experimental validation to achieve uniform reinforcement distribution across a predefined microstructure. A comprehensive dataset was constructed incorporating ten elements (Al, Co, Cr, Fe, Ni, Cu, Mn, Ti, V, Mo) with carbon additions, where carbon specifically represents various reinforcement phases, including graphene nanoplatelets, enabling diverse carbon-based reinforcement strategies. A comparative analysis of five machine learning models was performed using six thermodynamic descriptors: valence electron concentration (VEC), atomic size difference (δ), electronegativity difference (Δχ), mixing enthalpy (ΔH_mix), mixing entropy (ΔS_mix) and Gibbs energy of mixing (ΔG_mix) for the 750-sample dataset. Both random forest (RF) and extreme gradient boosting (XGBoost) demonstrated superior predictive accuracy (test accuracy: 0.94927; receiver-operating characteristic curve - area under the curve (ROC-AUC): 0.99446-0.99627; 10-fold cross-validation: 0.83315-0.85184), consistently identifying ΔH_mix as the most critical feature influencing phase stability. X-ray diffraction confirmed dual-phase (FCC + BCC) structures in all samples, with BCC phase volume fraction increasing from 77.25% (base high entropy alloy (HEA)) to 85.198% (2 wt.% GNP), indicating GNP-induced BCC stabilization. Peak shifts and broadening suggested lattice strain from carbon dissolution and thermal mismatch. Energy-dispersive x-ray spectroscopy (EDS) mapping revealed uniform GNP dispersion and aluminium segregation, aiding BCC stability. Zener pinning analysis demonstrated increased pinning pressure and grain size reduction from 55 μm to 50 μm. GNP reinforcement enhances phase control and microstructural stability in HEA composites, making them promising candidates for structural applications.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"47 3","pages":"206 - 227"},"PeriodicalIF":1.7,"publicationDate":"2026-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148237348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Hyperbolic Free-Energy Framework for Neural Dynamics: Thermodynamic Principles Underlying Brain State Transitions and Cognitive Behaviors","authors":"En Yang","doi":"10.1007/s11669-026-01252-4","DOIUrl":"10.1007/s11669-026-01252-4","url":null,"abstract":"<div><p>The brain is a dissipative, far-from-equilibrium system that continuously consumes energy to sustain structured neural activity while producing entropy. How system-level interactions among energy, entropy, structure, and physiological constraints give rise to cognition through distributed computation remains a central challenge in neuroscience. Existing free-energy frameworks have provided valuable conceptual insights, yet many remain largely metaphorical and lack explicit biological grounding, limiting the specificity and falsifiability of their predictions. Here, we propose a biologically grounded, thermodynamically inspired framework in which brain dynamics emerge from a continual balance between stability and flexibility, formalized as minimizing a Gibbs-free-energy-like function (ΔG = ΔH − TΔS). Stable neural configurations correspond to low-enthalpy, ordered states that support reliable function, whereas flexible configurations correspond to higher-entropy states that enable adaptive behavior. We further propose that neural population dynamics can be described as evolving on a hyperbolic statistical landscape shaped by metabolic, biophysical, anatomical, and bodily constraints. Neural activity samples this landscape, and experience gradually reshapes it over time. Metastable brain states occupy local free-energy minima, with transitions governed by Boltzmann-like probabilities. Learning sculpts the landscape via synaptic optimization and pruning, reducing entropy and stabilizing task-relevant dynamics. Importantly, this framework accounts for adaptive reallocation of neural resources under physiological stress, whereby higher-order cognitive functions may be transiently constrained to prioritize survival-essential processes, thereby predicting that cognitive function can remain rescuable in some cases despite structural damage. Together, this quantitative thermodynamic and geometric framework provides a unified foundation for understanding cognition as an emergent, system-level property of whole-brain dynamics.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"47 Focus:","pages":"394 - 402"},"PeriodicalIF":2.0,"publicationDate":"2026-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148903322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quaternionic Orientational Order and Defect-Driven Transitions Between Crystalline and Glassy Solids","authors":"Caroline Gorham Holden,&nbsp;Ahmed Farag Ali","doi":"10.1007/s11669-026-01249-z","DOIUrl":"10.1007/s11669-026-01249-z","url":null,"abstract":"<div><p>This paper develops a unified phenomenological description of solidification by using a quaternionic orientational order parameter to represent local atomic rotations in undercooled liquids. The novelty of the work is that the same topological language is used to describe both crystallization and glass formation. In the crystalline pathway, quantized misorientation defects bind, order, and support long-range orientational and translational coherence. In the glassy pathway, those defects proliferate and remain frustrated, producing a rigid but non-periodic solid. The competition is organized by a non-thermal tuning parameter <i>g = U/J</i> that balances orientational stiffness <i>J</i> against localization <i>U</i>, in close analogy with duality ideas known from Josephson-junction arrays. Within this framework, geometrical frustration explains persistent defect skeletons in topologically close-packed phases and the opposite temperature dependences of thermal conductivity in crystals and glasses are linked to the presence or loss of coherent heat-carrying vibrational modes. The paper is intended as a materials-oriented topological phenomenology that complements, rather than replaces, atomistic and first-principles approaches.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"47 Focus:","pages":"372 - 382"},"PeriodicalIF":2.0,"publicationDate":"2026-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11669-026-01249-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148903314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction: On Gibbs Equilibrium and Hillert Nonequilibrium Thermodynamics","authors":"Zi-Kui Liu","doi":"10.1007/s11669-026-01244-4","DOIUrl":"10.1007/s11669-026-01244-4","url":null,"abstract":"","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"47 3","pages":"341 - 341"},"PeriodicalIF":1.7,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction: Revisiting the First, Second and Combined Laws of Thermodynamics","authors":"Zi-Kui Liu","doi":"10.1007/s11669-026-01245-3","DOIUrl":"10.1007/s11669-026-01245-3","url":null,"abstract":"","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"47 3","pages":"340 - 340"},"PeriodicalIF":1.7,"publicationDate":"2026-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11669-026-01245-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148237200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Journal of Phase Equilibria and Diffusion Editor’s Choice Awards for 2025","authors":"Ursula Kattner","doi":"10.1007/s11669-026-01239-1","DOIUrl":"10.1007/s11669-026-01239-1","url":null,"abstract":"","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"47 2","pages":"111 - 112"},"PeriodicalIF":1.7,"publicationDate":"2026-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147828426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}