{"title":"Thermodynamic modeling of Mo–Os, W–Os and Mo–Os–W systems","authors":"Baogang Liu , Yong Du , Lei Huang , Yafei Pan","doi":"10.1016/j.calphad.2025.102823","DOIUrl":"10.1016/j.calphad.2025.102823","url":null,"abstract":"<div><div>Based on critical evaluation of the literature data, the Mo–Os and W–Os binary systems have been reviewed and assessed by means of the CALPHAD technique. The substitutional solution models are adopted to describe the liquid, bcc (βMo, βW) and hcp (αOs) phases, and the compound energy models with two sublattices are to describe the σ and Mo<sub>3</sub>Os phases. The phase equilibrium data of the Mo–Os and W–Os systems are well produced by the present modeling. Using the obtained thermodynamic parameters of the sub-binary systems, the thermodynamic description has been extended to the Mo–Os–W ternary system, covering the whole composition and temperature ranges. There is no ternary compound in this system. The σ phase forms a continuous solid solution crossing the phase diagram. A set of self-consistent thermodynamic parameters for the Mo–Os–W system is systematically optimized to describe to the bcc, σ and Mo<sub>3</sub>Os phases. Comprehensive comparisons between the calculated and reported phase diagram information show that the reliable information is satisfactorily accounted for by the present modeling. The liquidus projection and reaction scheme of the Mo–Os–W system are also generated by using the present thermodynamic parameters.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102823"},"PeriodicalIF":1.9,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wei Yang , Yiwei Wang , Shuhong Liu , Peisheng Wang , Wei Zhai
{"title":"Experimental determination and thermodynamic assessment of the Dy-Fe-B system","authors":"Wei Yang , Yiwei Wang , Shuhong Liu , Peisheng Wang , Wei Zhai","doi":"10.1016/j.calphad.2025.102826","DOIUrl":"10.1016/j.calphad.2025.102826","url":null,"abstract":"<div><div>The phase equilibria of the Fe-Dy-B system on the Fe-Dy side are crucial for the development of Nd-Dy-Fe-B permanent magnets. Alloys located on the Fe-Dy side were prepared and annealed at 1073 K and 1173 K for 60 days. The annealed samples were analyzed by electron probe microanalysis (EPMA) and X-ray diffraction (XRD). In this work, three ternary compounds τ<sub>1</sub>, τ<sub>3</sub>, and τ<sub>4</sub> were identified on the Fe-Dy side at 1073 K and 1173 K. The previously reported τ<sub>2</sub> phase was not observed in the present work. Nine three-phase regions were determined in the present study and the isothermal sections of the Dy-Fe-B system on the Dy-Fe side at 1073 K and 1173 K were constructed. Based on the experimental data, thermodynamic modeling of the system was performed using the CALculation of PHAse Diagrams (CALPHAD) method. The calculated results show good agreement with the experimental data.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102826"},"PeriodicalIF":1.9,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143679057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sinn-wen Chen , Yi-An Lee , Cheng-Hsi Ho , Jun Zhu , Hsin-Chieh Huang , Te-Wei Lin , Chuan Zhang
{"title":"Phase transformation temperatures of Sn-Ag-Bi-Cu quaternary system","authors":"Sinn-wen Chen , Yi-An Lee , Cheng-Hsi Ho , Jun Zhu , Hsin-Chieh Huang , Te-Wei Lin , Chuan Zhang","doi":"10.1016/j.calphad.2025.102822","DOIUrl":"10.1016/j.calphad.2025.102822","url":null,"abstract":"<div><div>Sn-Ag-Bi-Cu and its constituent systems are important material systems, especially for electronic soldering. Although these alloys have attracted significant interest for industrial applications and have been the subject of various Calphad studies, it is surprising to find that there are significant deviations observed between the calculated and experimentally determined results regarding the phase transformation temperatures. To address this issue, Sn-Ag, Sn-Bi, Sn-Cu, Sn-Ag-Bi, Sn-Ag-Cu, Sn-Bi-Cu and Sn-Ag-Bi-Cu alloys on the Sn-rich side are prepared. Simultaneous thermal analysis and holding-quenching experimental measurements are conducted to determine their liquidus temperatures and invariant reaction temperatures. The experimentally determined results are then compared with the Calphad-calculated results and utilized to improve the thermodynamic parameters in the Calphad models. The calculated results with the revised databases are in good agreement with the experimental measurements.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102822"},"PeriodicalIF":1.9,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143679059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multicomponent cluster variation method: Application to high entropy alloys","authors":"Vikas Jindal, Shrikant Lele","doi":"10.1016/j.calphad.2025.102825","DOIUrl":"10.1016/j.calphad.2025.102825","url":null,"abstract":"<div><div>Cluster expansion, a method commonly used in computational thermodynamics, expresses the configurational properties of alloys as a sum of products of correlation functions and cluster expansion coefficients (CECs). The CECs are defined using a basis in configurational space that is not unique and changes during the extension of the generalized Ising model from binary alloys to multicomponent alloys. In contrast to the CALPHAD formulation, this change severely restricts the development and use of CEC-based databases. To address this, a new framework is introduced where lower-order CECs remain unchanged in higher-order systems. This is achieved by choosing configurational variables (and corresponding CECs) which are not dependent on a particular choice of basis as correlation functions (CFs). Such a set is provided by cluster variables (CVs), which represent the fraction of cluster configurations of various types. A carefully selected subset of independent CVs is chosen as CFs. Completeness of the basis is demonstrated by deriving expressions for all remaining CVs in terms of these new CFs for disordered bcc, fcc, and hcp structures. A set of CECs for the bcc phase of the Nb-Ti-V-Zr system has been developed using this new formulation. Optimized CECs of all binary and ternary subsystems of the Nb-Ti-V-Zr have been used in its construction. This is a crucial step towards creating a self-consistent computational thermodynamics database. The utility of the Nb-Ti-V-Zr database was demonstrated through calculations of thermodynamic quantities, SRO parameters, and phase diagrams. Additionally, a procedure is outlined to transform existing CALPHAD databases to CEC-based databases under certain assumptions.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102825"},"PeriodicalIF":1.9,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143679058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xuemei Ouyang , Quan wang , Fucheng Yin , Yuling Shi , Jingxian Hu
{"title":"Experimental investigation and thermodynamic calculation of the B-Co-Ti ternary system","authors":"Xuemei Ouyang , Quan wang , Fucheng Yin , Yuling Shi , Jingxian Hu","doi":"10.1016/j.calphad.2025.102819","DOIUrl":"10.1016/j.calphad.2025.102819","url":null,"abstract":"<div><div>The phase equilibrium of the B-Co-Ti ternary system is important for the preparation and development of Co-containing TiB<sub>2</sub>-based ceramics. To obtain the liquidus projection, 54 kinds of as-cast alloys were prepared via arc melting. The microstructures and solidification paths of the 54 kinds of alloys were analyzed by scanning electron microscopy, electron probe microanalysis, X-ray diffraction and differential scanning calorimetry. The results show that the proposed liquidus projection of the B-Co-Ti ternary system contains 15 primary precipitation regions: BCC, CoTi<sub>2</sub>, CoTi, Co<sub>2</sub>Ti, Co<sub>3</sub>Ti, αCo, TiB, Ti<sub>3</sub>B<sub>4</sub>, TiB<sub>2</sub>, (B), CoB, Co<sub>2</sub>B, Co<sub>3</sub>B, τ<sub>1</sub> and τ<sub>2</sub>. Six E-type and nine U-type ternary invariant reactions are suggested on the basis of experimental data. The thermodynamic calculation of the B-Co-Ti ternary system was carried out, and a set of self-consistent thermodynamic parameters was obtained. The calculated liquidus projection and 800 °C isothermal sections are in good agreement with the experimental data.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102819"},"PeriodicalIF":1.9,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143632063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wenhao Ma , Julian Gebauer , Andreas Klaus Czerny , Maryam Rahimi Chegeni , Isabella Gallino , Ralf Busch , Hans Jürgen Seifert
{"title":"Thermodynamic assessment of the sulfur and the nickel-sulfur systems","authors":"Wenhao Ma , Julian Gebauer , Andreas Klaus Czerny , Maryam Rahimi Chegeni , Isabella Gallino , Ralf Busch , Hans Jürgen Seifert","doi":"10.1016/j.calphad.2025.102821","DOIUrl":"10.1016/j.calphad.2025.102821","url":null,"abstract":"<div><div>The sulfur and the nickel-sulfur binary systems are important in many fields. In this work, the pure sulfur is remodeled within the framework of the third-generation database approach from 0 K to above the melting point. Likewise, a new thermodynamic dataset is developed for the nickel sulfur binary system. The new thermodynamic dataset provides a reliable description of all relevant intermetallic and non-stoichiometric phases. The supercooled liquid described using the two-state liquid model is considered more realistic. An assessment on the sulfur solubility in FCC nickel is also conducted in this work. The calculated phase diagram, thermodynamic and thermophysical data show good agreement with the literature.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102821"},"PeriodicalIF":1.9,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143632031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chengyang Ma , Shao-Yang Wang , Weisen Zheng , Jingya Wang , Huarui Cao , Xiao-Gang Lu
{"title":"Thermodynamic modeling of the Mg-Zn-Nd system and its application to solidification","authors":"Chengyang Ma , Shao-Yang Wang , Weisen Zheng , Jingya Wang , Huarui Cao , Xiao-Gang Lu","doi":"10.1016/j.calphad.2025.102820","DOIUrl":"10.1016/j.calphad.2025.102820","url":null,"abstract":"<div><div>The excellent thermal conductivity and mechanical properties of Mg-Zn-Nd alloys are closely linked to the formation of intermetallic compounds and the solubility in the αMg matrix after their formation. However, recent experimental findings on new ternary compounds highlight gaps in the understanding of the phase equilibrium relationships, which complicates design of advanced Mg-Zn-Nd alloys. To address this, all the experimental phase equilibrium data available in the literature were critically evaluated. Thermodynamic modeling of the Mg-Zn-Nd system was performed based on the selected reliable experimental data and updated binary thermodynamic descriptions. The seven ternary compounds (τ1 to τ6 and (Mg,Zn)<sub>12</sub>Nd) in the Mg-Zn-Nd system were modeled using compound energy formalism (CEF), particularly considering the consistency between their homogeneity range and crystallographic sublattices. The thermodynamic model parameters optimized in this study satisfactorily reproduced the isothermal sections, isoplethal sections, and liquidus projections. Combined with the Scheil–Gulliver model, the solidification behavior of Mg-Zn-Nd alloys was predicted. The predicted results were consistent with the experimental data, further demonstrating the reliability and practical applicability of the thermodynamic description developed in this study.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102820"},"PeriodicalIF":1.9,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143578983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"High throughput determination of diffusion coefficients and hardness using diffusion couple technique of γ-phase Fe-Ni-Cu alloys at 1000 °C","authors":"Susanta Kumar Nayak, Kaustubh N. Kulkarni","doi":"10.1016/j.calphad.2025.102809","DOIUrl":"10.1016/j.calphad.2025.102809","url":null,"abstract":"<div><div>A high-throughput method was employed for γ-phase Fe-Ni-Cu alloy system. In this study solute and intrinsic diffusivities are determined from interdiffusion coefficients, alongside determining nano-indent hardness from diffusion couple experiments. This could be an important study to obtain various diffusivities and hardness-composition relationship with minimum experiments. Analysis of inter and intrinsic diffusion coefficients, along with thermodynamic factors, revealed significant diffusional interactions among the alloy elements. In addition, it has been shown that Cu is the slowest diffusing species, and the solute diffusivities alone cannot be used as criterion for determining the kinetics of alloying elements. The diffusion interactions in inter and intrinsic diffusion need not to be similar but interdiffusion coefficients are more convenient in practical uses. A high-throughput hardness-composition relations were developed, which illustrate the applicability of diffusion couples to enable high throughput determination of various properties as functions of compositions.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102809"},"PeriodicalIF":1.9,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xinyi Zhang , Liang Zhang , Taibai Fu , Jiangxing Wang , Bo Wang , Ziqing Xie , Yuling Liu , Yong Du
{"title":"A new algorithm to optimize thermodynamic parameters: Application to the Ag-Pd and La-C systems","authors":"Xinyi Zhang , Liang Zhang , Taibai Fu , Jiangxing Wang , Bo Wang , Ziqing Xie , Yuling Liu , Yong Du","doi":"10.1016/j.calphad.2025.102810","DOIUrl":"10.1016/j.calphad.2025.102810","url":null,"abstract":"<div><div>A new algorithm for optimizing thermodynamic parameters of binary systems is introduced. Unlike traditional algorithms that are commonly single-objective and need extensive manual testing, this algorithm constructs a multi-objective optimization for different types of experimental data. Then, by using weighted sum method, the multi-objective optimization problem is transformed into a single-objective optimization, which is solved by Barzilai-Borwein method. The key advantage of this algorithm is that no restrictions on the selection of initial values are needed. Finally, this algorithm is applied to optimize the thermodynamic parameters in the Ag-Pd and La-C systems. The experimental phase diagrams and thermodynamic properties in these two systems are satisfactorily reproduced by the present calculation.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102810"},"PeriodicalIF":1.9,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143528867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Identifying independent components and internal process order parameters in nonequilibrium multicomponent nonstoichiometric compounds","authors":"Yanzhou Ji , Yueze Tan , Long-Qing Chen","doi":"10.1016/j.calphad.2025.102807","DOIUrl":"10.1016/j.calphad.2025.102807","url":null,"abstract":"<div><div>In CALPHAD-type thermodynamic databases, nonstoichiometric compounds are typically described by sublattice models where the sublattice site fractions represent the occupation probability of different atomic, ionic or defect species on different sublattices. Here, we develop a general procedure and corresponding linear algebra tools for converting the sublattice site fractions to a combination of independent component compositions and internal process order parameters describing the extent of internal atomic exchange, electronic redox and defect generation reactions. We apply them to a number of nonstoichiometric phases in thermodynamic databases and literature. The general procedure can be applied to constructing thermodynamic databases in terms of internal process order parameters for nonstoichiometric phases in multicomponent systems such as high-entropy oxides and alloys, which can be utilized to model their kinetics of nonequilibrium processes and microstructure evolution.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102807"},"PeriodicalIF":1.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}