Weiguang Yang, Georg Hasemann, Mustafa Carrion Saldaña, Bronislava Gorr, Ruth Schwaiger, Manja Krüger
{"title":"Phase Equilibria in the V-Rich Region of the V-Si-B System at 1400 °C","authors":"Weiguang Yang, Georg Hasemann, Mustafa Carrion Saldaña, Bronislava Gorr, Ruth Schwaiger, Manja Krüger","doi":"10.1007/s11669-025-01177-4","DOIUrl":"10.1007/s11669-025-01177-4","url":null,"abstract":"<div><p>The phase equilibria in the V-rich region of the V-Si-B system, including the V<sub>8</sub>SiB<sub>4</sub> phase, have been experimentally investigated. Eleven alloys with key compositions were produced by arc-melting or levitation-melting. The samples were then annealed at 1400 °C for 100/200/300 h under high vacuum condition. The as-cast and heat-treated alloys were investigated by scanning electron microscopy, electron backscatter diffraction, energy-dispersive x-ray spectroscopy and x-ray diffraction. The isothermal section at 1400 °C of the V-rich V-Si-B system was determined and compared with the one at 1600 °C. The determined isothermal section can be applied to the design of V-Si-B alloys.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"46 1","pages":"151 - 169"},"PeriodicalIF":1.5,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11669-025-01177-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638133","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}
V. M. Silveira, N. Chaia, K. E. Borowski, A. S. Ramos, E. C. Ramos, C. A. Nunes, G. C. Coelho
{"title":"Interdiffusion in the Al-V System in the 800-1000 °C Temperature Range","authors":"V. M. Silveira, N. Chaia, K. E. Borowski, A. S. Ramos, E. C. Ramos, C. A. Nunes, G. C. Coelho","doi":"10.1007/s11669-025-01179-2","DOIUrl":"10.1007/s11669-025-01179-2","url":null,"abstract":"<div><p>Vanadium and its alloys have potential for application as fuel cladding in new fast breeder reactors cooled by sodium. Diffusion aluminide coatings could be a solution of choice in providing protection against high-temperature corrosion by liquid sodium or residual oxygen for these materials. In this work, multilayered coatings were formed on V and V-44Al substrates by halide activated pack cementation, using CrCl<sub>3</sub> as transport agent and pure aluminum (high activity) as master alloy. Two types of diffusion couples, V/Al and V-44Al/Al, were investigated in order to determine the growth kinetics of the aluminide compounds in the 800-1000 °C temperature range. The growth of the saturated V<sub>ss</sub> as well as of the VAl<sub>3</sub> and V<sub>5</sub>Al<sub>8</sub> layers was controlled exclusively by solid state diffusion following a parabolic law, allowing the determination of the parabolic growth constants. Wagner’s analysis was adopted to calculate the integrated interdiffusion coefficients, resulting in values ranging approximately from 10<sup>−10</sup> to 10<sup>−12</sup> cm<sup>2</sup>/s for temperatures between 800 and 1000 °C. In general, VAl<sub>3</sub> has the highest <span>({widetilde{text{D}}}_{text{int}})</span> values in relation to those of the other two layers, considering the nominal temperatures (except for 1000 °C).</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"46 1","pages":"204 - 214"},"PeriodicalIF":1.5,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638520","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":"Mass-Preserving Modeling of Diffusion in a Closed System","authors":"Dmitri V. Malakhov","doi":"10.1007/s11669-025-01174-7","DOIUrl":"10.1007/s11669-025-01174-7","url":null,"abstract":"<div><p>With zero-flux boundary conditions imposed at both ends, amounts of components in a system cannot change as a result of a unidimensional diffusion in it. With appropriately chosen time steps, the Crank-Nicolson scheme can dependably track a temporal evolution of an initial discrete concentration profile, but an invariance of an area below a continuously changing concentration <i>vs.</i> position curve is not guaranteed. In this work, a heuristic yet mathematically sound technique of incorporating a \"constant integral\" requirement into the Crank-Nicolson method is proposed.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"46 1","pages":"31 - 48"},"PeriodicalIF":1.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638209","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}
I. Fartushna, D. Kapush, I. Tikhonova, V. Kremenytskyi, M. Bulanova
{"title":"Phase Equilibria in the Tm-Co, Tm-Fe and Tm-Co-Fe Systems","authors":"I. Fartushna, D. Kapush, I. Tikhonova, V. Kremenytskyi, M. Bulanova","doi":"10.1007/s11669-024-01171-2","DOIUrl":"10.1007/s11669-024-01171-2","url":null,"abstract":"<div><p>Phase diagrams of the ternary Tm-Co-Fe and boundary binary systems Tm-Co and Tm-Fe were constructed in the entire composition ranges using differential thermal analysis, powder x-ray diffraction, microscopic examination and electron probe microanalysis. The Tm-Co phase diagram was plotted for the first time. A new binary compound Tm<sub>12</sub>Co<sub>7</sub> was found and its crystal structure was established. The Tm-Fe phase diagram was revised: all invariant temperatures were updated, and disagreements with previously reported data were resolved. The Tm-Co-Fe system was studied for the first time. The results are given in the form of liquidus and solidus projections, isothermal sections at 1200 and 1000 °C, and Scheil reaction scheme. Ternary compounds are not formed in the system. Instead, the isostructural phases of Tm-Co and Tm-Fe systems form continuous solid solutions (αCo,γFe), Tm<sub>2</sub>(Co,Fe)<sub>17</sub>, Tm(Co,Fe)<sub>3</sub>, Tm(Co,Fe)<sub>2</sub> at all studied temperatures. The Tm<sub>6</sub>Fe<sub>23</sub> phase dissolves up to 45 at.% Co. The solubility of Fe in Tm-Co compounds is much lower. Five three-phase regions are present on the solidus projection, which form from one eutectic and four transition (U) type invariant reactions. The boundaries of the primary crystallization regions of phases, types and coordinates of invariant and monovariant equilibria are determined. Isothermal sections differ from the solidus projection by: (i) the presence of wide areas of melt, resulting in the absence of Tm<sub>3</sub>Co and Tm<sub>12</sub>Co<sub>7</sub> compounds and (ii) the absence of TmCo<sub>5</sub> compound. As a result, there are two three-phase regions at 1200 and 1000 °C.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"46 1","pages":"100 - 118"},"PeriodicalIF":1.5,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638523","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}
S. Y. Yang, X. Liu, Q. R. Yao, J. Wang, G. H. Rao, H. Y. Zhou
{"title":"Experimental Investigation of Phase Equilibria in the Y-Co-Cu Ternary System","authors":"S. Y. Yang, X. Liu, Q. R. Yao, J. Wang, G. H. Rao, H. Y. Zhou","doi":"10.1007/s11669-024-01170-3","DOIUrl":"10.1007/s11669-024-01170-3","url":null,"abstract":"<div><p>The phase equilibria of the Y-Co-Cu ternary system were investigated experimentally by scanning electron microscopy with energy dispersive spectroscopy and X-ray diffraction. The experimental results did not indicate any ternary intermetallic compounds and revealed that the YCo<sub>5</sub> and YCu<sub>6</sub> binary intermetallic compounds form the continuous solid solution phase Y(Co, Cu)<sub>5</sub> because of having the same space groups. According to the measured phase compositions at 873 K, the solid solubilities of Co in fcc(Cu), YCu<sub>4</sub>, Y<sub>2</sub>Cu<sub>7</sub> and YCu<sub>2</sub> are 8.6, 1.7, 44.0 and 8.6 at.%, respectively, while those of Cu in fcc(Co), Y<sub>2</sub>Co<sub>17</sub>, Y<sub>2</sub>Co<sub>7</sub>, YCo<sub>3</sub>, YCo<sub>2</sub>, Y<sub>2</sub>Co<sub>3</sub>, Y<sub>6</sub>Co<sub>7</sub>, Y<sub>4</sub>Co<sub>3</sub>, Y<sub>8</sub>Co<sub>5</sub> and Y<sub>3</sub>Co were determined to be 15.8, 6.4, 8.1, 13.5, 7.9, 1.2, 1.4, 3.9, 7.6 and 10.6 at.%, respectively. Furthermore, at 1073 K the solid solubilities of Co in fcc(Cu), YCu<sub>4</sub>, Y<sub>2</sub>Cu<sub>7</sub> and YCu<sub>2</sub> were measured to be 3.9, 2.5, 40.0 and 10.8 at.%, respectively, while those of Cu in fcc(Co), Y<sub>2</sub>Co<sub>17</sub>, Y<sub>2</sub>Co<sub>7</sub>, YCo<sub>3</sub>, YCo<sub>2</sub>, Y<sub>2</sub>Co<sub>3</sub> and YCo were determined to be 13.6, 9.4, 7.4, 13.7, 10.3, 2.3 and 31.4 at.%, respectively. Two isothermal sections of the Y-Co-Cu ternary system at 1073 K and 873 K were established finally.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"46 1","pages":"133 - 150"},"PeriodicalIF":1.5,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638500","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}
John Ågren, Qing Chen, Greta Lindwall, Malin Selleby, Wei Xiong, Ursula R. Kattner
{"title":"Special Issue in Memory of Mats Hillert","authors":"John Ågren, Qing Chen, Greta Lindwall, Malin Selleby, Wei Xiong, Ursula R. Kattner","doi":"10.1007/s11669-024-01168-x","DOIUrl":"10.1007/s11669-024-01168-x","url":null,"abstract":"","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 6","pages":"929 - 933"},"PeriodicalIF":1.5,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870393","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}
Bo Sundman, Nathalie Dupin, Marcel H. F. Sluiter, Suzana G. Fries, Christine Guéneau, Bengt Hallstedt, Ursula R. Kattner, Malin Selleby
{"title":"The Legacy of “The Regular Solution Model for Stoichiometric Phases and Ionic Melts”","authors":"Bo Sundman, Nathalie Dupin, Marcel H. F. Sluiter, Suzana G. Fries, Christine Guéneau, Bengt Hallstedt, Ursula R. Kattner, Malin Selleby","doi":"10.1007/s11669-024-01163-2","DOIUrl":"10.1007/s11669-024-01163-2","url":null,"abstract":"<div><p>In 1970, Hillert and Staffansson published a paper entitled “The Regular Solution Model for Stoichiometric Phases and Ionic Melts”. It was the beginning of the sublattice model that has been a key component in the development of Computational Thermodynamics. This formalism, now often called the Compound Energy Formalism (CEF), has been used to describe a great variety of phases driven by the need for accurate descriptions of thermodynamic phase stability in a wide range of materials involving many elements. The purpose of this paper is to describe the formalism, the physical meaning of its various parameters and the way they can be assessed using experimental and theoretical data. Furthermore, new developments derived from the CEF, such as the Effective Bond Energy Formalism, and other ideas for further development are presented.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 6","pages":"934 - 964"},"PeriodicalIF":1.5,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870308","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}
Tao Luo, Kai Zhu, Hongwei Xiong, Weisen Zheng, Jingya Wang, Xiao-Gang Lu
{"title":"Thermodynamic Assessment of the Mg–La–Nd System","authors":"Tao Luo, Kai Zhu, Hongwei Xiong, Weisen Zheng, Jingya Wang, Xiao-Gang Lu","doi":"10.1007/s11669-024-01169-w","DOIUrl":"10.1007/s11669-024-01169-w","url":null,"abstract":"<div><p>Ternary Mg–La–Nd and constituent binary Mg–La and Mg–Nd systems were assessed after a critical review of the experimental data and <i>ab initio</i> data using the CALPHAD method. The enthalpies of formation of the end-member compounds of the Mg(La, Nd) and Mg<sub>3</sub>(La, Nd) phases were obtained by <i>ab initio</i> calculations and then used to determine their model parameters. The binary Mg–La system was revised to maintain the consistency of the thermodynamic models, whereas the binary Mg–Nd system was reassessed to describe the homogeneity ranges of the hcp, dhcp, and Mg<sub>3</sub>Nd phases. Moreover, the metastable Mg<sub>12</sub>Nd phase was modeled to reproduce the phase constituents of the as-cast Mg–Nd alloys. Based on the updated binary descriptions, the ternary Mg–La–Nd system was assessed according to recent experimental data. Through a comprehensive comparison between the calculated and experimental phase equilibria and thermochemical property data, a reasonable agreement was achieved for the binary and ternary systems.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"46 1","pages":"60 - 75"},"PeriodicalIF":1.5,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638273","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}
Ales Kroupa, Ondrej Zobac, Adela Zemanova, Klaus W. Richter
{"title":"CALPHAD-Type Reassessment of Cu-Si and Full Assessment of the Al-Cu-Si Systems","authors":"Ales Kroupa, Ondrej Zobac, Adela Zemanova, Klaus W. Richter","doi":"10.1007/s11669-024-01160-5","DOIUrl":"10.1007/s11669-024-01160-5","url":null,"abstract":"<div><p>The theoretical assessment of the Al-Cu-Si was carried out in this work based on recent experimental studies (Riani et al. in Intermetallics, 17:154-164, 2009; He et al. in CALPHAD, 33:200-210, 2009. http://dx.doi.org/10.1016/j.calphad.2008.07.015; Ponweiser N and Richter KW in J. of Alloys and Compd, 512:252-263, 2012; Hallstedt et al. in CALPHAD, 53:25-38, 2016; Zobac et al in J Mater Sci, 55:5322-15333, 2020). The reassessment of the Cu-Si system was also carried out in the scope of this work, as experimental data indicates reasonable solubility of Al in all intermetallic phases in the Cu-Si binary system, and the stoichiometric models used in previous assessments of the Cu-Si binary system are not fully suitable for the extension into the ternary system. Excellent agreement was reached for the reassessment of the Cu-Si system with previous works, and new original results were obtained during the assessment of the ternary system. The high solubility of Si in the β(bcc) phase at high temperatures was modelled to explain experimental inconsistencies in the Cu-rich corner between 600 and 800 °C, and this assumption was confirmed experimentally. All main features of the experimental Al-Cu-Si phase diagram were reproduced well by theoretical modelling.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 6","pages":"1206 - 1243"},"PeriodicalIF":1.5,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11669-024-01160-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870319","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}