Pub Date : 2025-07-23DOI: 10.1016/j.calphad.2025.102849
Bo Sundman , Fabio Miani , Axel van de Walle , Bengt Hallstedt , Ursula R. Kattner , Florian Tang , Taichi Abe , Reza Naraghi , Erwin Povoden-Karadeniz , Aurelie Jacob , Shuanglin Chen , Richard Otis , Kazuhisa Shobu , Malin Selleby , Alexander Pisch
The calculation of phase diagram (Calphad) method uses models that depend on assessed parameters to describe the thermodynamic properties of materials. These model parameters are assessed by researchers and students using experimental and theoretical data on binary and ternary systems that can be merged to multicomponent databases and used to calculate properties and simulate processes for a wide range of materials.
There are several different software using the Calphad method for calculations and they may use slightly different models and database formats. This paper will provide a short background on the current state of database development and proposes a new format based on the eXtensive Markup Language (XML) as a unified database format. This change is particularly important as several new models for the pure elements are currently being introduced in the Calphad databases.
{"title":"XTDB, an XML based format for Calphad databases","authors":"Bo Sundman , Fabio Miani , Axel van de Walle , Bengt Hallstedt , Ursula R. Kattner , Florian Tang , Taichi Abe , Reza Naraghi , Erwin Povoden-Karadeniz , Aurelie Jacob , Shuanglin Chen , Richard Otis , Kazuhisa Shobu , Malin Selleby , Alexander Pisch","doi":"10.1016/j.calphad.2025.102849","DOIUrl":"10.1016/j.calphad.2025.102849","url":null,"abstract":"<div><div>The calculation of phase diagram (Calphad) method uses models that depend on assessed parameters to describe the thermodynamic properties of materials. These model parameters are assessed by researchers and students using experimental and theoretical data on binary and ternary systems that can be merged to multicomponent databases and used to calculate properties and simulate processes for a wide range of materials.</div><div>There are several different software using the Calphad method for calculations and they may use slightly different models and database formats. This paper will provide a short background on the current state of database development and proposes a new format based on the eXtensive Markup Language (XML) as a unified database format. This change is particularly important as several new models for the pure elements are currently being introduced in the Calphad databases.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102849"},"PeriodicalIF":1.9,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144687100","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}
Pub Date : 2025-07-22DOI: 10.1016/j.calphad.2025.102859
M. Li, M.H. Rong, Y. Wu, P.F. Tan, J. Wang
The phase equilibria and thermodynamic properties of Au-Sn-based alloys are of great significance for designing Au-based alloys as lead-free solders to replace high-lead solders. In this work, based on the experimental data reported in the literature, thermodynamic parameters of AuSn2 and AuSn4 in the Au-Sn binary system were modified. The calculated phase diagram and thermodynamic properties of the Au-Sn binary system are in good agreement with the experimental results. Furthermore, by combining the updated calculations of the Au-Sn binary system in this work with the previous assessments of the Au-Bi, Au-Zn, Au-Ni, Sn-Bi, Sn-Zn and Sn-Ni binary systems, thermodynamic modeling of the Au-Sn-X (X = Bi, Zn, Ni) ternary systems was conducted using the CALPHAD method. The liquidus projections, isothermal sections and vertical sections of the Au-Sn-X (X = Bi, Zn, Ni) ternary systems were calculated, which are in good agreement with the reported experimental data. The reasonable thermodynamic parameters of the Au-Sn-X (X = Bi, Zn, Ni) ternary systems were obtained in this work, which would provide a good foundation for further establishing a compatible thermodynamic database of multi-component Au-Sn-based alloy systems to design novel lead-free solders.
{"title":"Thermodynamic modeling of the Au-Sn-X (X=Bi, Zn, Ni) ternary systems","authors":"M. Li, M.H. Rong, Y. Wu, P.F. Tan, J. Wang","doi":"10.1016/j.calphad.2025.102859","DOIUrl":"10.1016/j.calphad.2025.102859","url":null,"abstract":"<div><div>The phase equilibria and thermodynamic properties of Au-Sn-based alloys are of great significance for designing Au-based alloys as lead-free solders to replace high-lead solders. In this work, based on the experimental data reported in the literature, thermodynamic parameters of AuSn<sub>2</sub> and AuSn<sub>4</sub> in the Au-Sn binary system were modified. The calculated phase diagram and thermodynamic properties of the Au-Sn binary system are in good agreement with the experimental results. Furthermore, by combining the updated calculations of the Au-Sn binary system in this work with the previous assessments of the Au-Bi, Au-Zn, Au-Ni, Sn-Bi, Sn-Zn and Sn-Ni binary systems, thermodynamic modeling of the Au-Sn-X (X = Bi, Zn, Ni) ternary systems was conducted using the CALPHAD method. The liquidus projections, isothermal sections and vertical sections of the Au-Sn-X (X = Bi, Zn, Ni) ternary systems were calculated, which are in good agreement with the reported experimental data. The reasonable thermodynamic parameters of the Au-Sn-X (X = Bi, Zn, Ni) ternary systems were obtained in this work, which would provide a good foundation for further establishing a compatible thermodynamic database of multi-component Au-Sn-based alloy systems to design novel lead-free solders.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102859"},"PeriodicalIF":1.9,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680185","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}
Pub Date : 2025-07-21DOI: 10.1016/j.calphad.2025.102857
Xinming Wang , Jia Liu , Jingxian Hu , Weimin Bai , Ying Ran , Fucheng Yin , Lebin Zhao , Jinhui Tang
Ni-based superalloys have excellent high-temperature strength, oxidation resistance and creep resistance. Mo, Fe and W are important γ phase stable elements in nickel-based superalloys. The diffusion behavior of alloying elements in fcc phase Ni-Fe-X (X = Mo, W) alloys plays an important role in the microstructure evolution and material fabrication of Ni-based superalloys. In this work, the diffusion coefficients of the fcc Ni-Fe-X (X = Mo, W) system were determined by using the diffusion couple technique and the Whittle-Green method, and the atomic mobilities were evaluated based on the CALPHAD technique with the DICTRA module of the Thermo-calc software. Based on the evaluated mobility parameters, the calculation of diffusion coefficients and simulation of the diffusion processes of the diffusion couples were carried out to verify the accuracy of the parameters. The calculated diffusion coefficients and predicted composition-distance profiles and diffusion paths show good agreement with the experimental results.
{"title":"Diffusivities and atomic mobilities in the fcc phase Ni-Fe-X (X=Mo, W) system","authors":"Xinming Wang , Jia Liu , Jingxian Hu , Weimin Bai , Ying Ran , Fucheng Yin , Lebin Zhao , Jinhui Tang","doi":"10.1016/j.calphad.2025.102857","DOIUrl":"10.1016/j.calphad.2025.102857","url":null,"abstract":"<div><div>Ni-based superalloys have excellent high-temperature strength, oxidation resistance and creep resistance. Mo, Fe and W are important γ phase stable elements in nickel-based superalloys. The diffusion behavior of alloying elements in fcc phase Ni-Fe-X (X = Mo, W) alloys plays an important role in the microstructure evolution and material fabrication of Ni-based superalloys. In this work, the diffusion coefficients of the fcc Ni-Fe-X (X = Mo, W) system were determined by using the diffusion couple technique and the Whittle-Green method, and the atomic mobilities were evaluated based on the CALPHAD technique with the DICTRA module of the Thermo-calc software. Based on the evaluated mobility parameters, the calculation of diffusion coefficients and simulation of the diffusion processes of the diffusion couples were carried out to verify the accuracy of the parameters. The calculated diffusion coefficients and predicted composition-distance profiles and diffusion paths show good agreement with the experimental results.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102857"},"PeriodicalIF":1.9,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144672079","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}
This work determined the isothermal sections of the Fe-Co-W system at 1273 K and 1073 K using the equilibrated alloy method. The solubility ranges of the μ-(Fe,Co)7W6, λ-Fe2W, and Co3W compounds in the Fe-Co-W ternary system were identified. No new ternary compounds were observed. Based on existing experimental data, a thermodynamic optimization of the Fe-Co-W ternary system and related binary systems was conducted. The (A)4(A,B)2(A,B)1(A,B)6 lattice model was employed to describe the μ-(Co,Fe)7W6 compound, and the thermodynamic database of the Co-W binary system was re-assessed. A new thermodynamic database for the Fe-Co-W system was established, demonstrating high consistency with the experimental data.
{"title":"Experimental investigation and thermodynamic re-assessment of the Fe-Co-W phase diagram","authors":"C.B. Li, Z.Q. Wang, L.D. Ye, J.F. Wu, K.G. Wang, L.B. Liu, L.G. Zhang","doi":"10.1016/j.calphad.2025.102856","DOIUrl":"10.1016/j.calphad.2025.102856","url":null,"abstract":"<div><div>This work determined the isothermal sections of the Fe-Co-W system at 1273 K and 1073 K using the equilibrated alloy method. The solubility ranges of the μ-(Fe,Co)<sub>7</sub>W<sub>6</sub>, λ-Fe<sub>2</sub>W, and Co<sub>3</sub>W compounds in the Fe-Co-W ternary system were identified. No new ternary compounds were observed. Based on existing experimental data, a thermodynamic optimization of the Fe-Co-W ternary system and related binary systems was conducted. The (A)<sub>4</sub>(A,B)<sub>2</sub>(A,B)<sub>1</sub>(A,B)<sub>6</sub> lattice model was employed to describe the μ-(Co,Fe)<sub>7</sub>W<sub>6</sub> compound, and the thermodynamic database of the Co-W binary system was re-assessed. A new thermodynamic database for the Fe-Co-W system was established, demonstrating high consistency with the experimental data.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102856"},"PeriodicalIF":1.9,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655015","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}
Pub Date : 2025-07-12DOI: 10.1016/j.calphad.2025.102858
Zhaohui Long , Shan Yang , Lunjun Gong , Hong Bo , Cong Li , Haohan She , Fucheng Yin
The phase equilibria in the Si-Zr-Ag ternary system at 650 °C and 750 °C were investigated using the equilibrated alloy approach. Scanning electron microscopy equipped with energy dispersive spectroscopy (SEM-EDS) and X-ray diffraction (XRD) have been applied to characterize the phase constitution of the alloys. At 650 °C and 750 °C, Six three-phase regions have been detected. The ternary compounds τ1 and τ2 were found in the two isothermal sections. τ1 was identified as a body-centered cubic structure by transmission electron microscopy (TEM) analysis, with the lattice parameters determined as a = 0.3738 nm, α = β = γ = 90°. Based on the experimental results on phase equilibrium, the CALPHAD approach was used to develop the thermodynamic description of the Si-Zr-Ag ternary system. The calculated isothermal sections show excellent agreement with the experimental ones. Then, the liquidus projection was predicted with the obtained thermodynamic parameters.
{"title":"Experimental investigation and thermodynamic calculation of the Si-Zr-Ag ternary system","authors":"Zhaohui Long , Shan Yang , Lunjun Gong , Hong Bo , Cong Li , Haohan She , Fucheng Yin","doi":"10.1016/j.calphad.2025.102858","DOIUrl":"10.1016/j.calphad.2025.102858","url":null,"abstract":"<div><div>The phase equilibria in the Si-Zr-Ag ternary system at 650 °C and 750 °C were investigated using the equilibrated alloy approach. Scanning electron microscopy equipped with energy dispersive spectroscopy (SEM-EDS) and X-ray diffraction (XRD) have been applied to characterize the phase constitution of the alloys. At 650 °C and 750 °C, Six three-phase regions have been detected. The ternary compounds τ<sub>1</sub> and τ<sub>2</sub> were found in the two isothermal sections. τ<sub>1</sub> was identified as a body-centered cubic structure by transmission electron microscopy (TEM) analysis, with the lattice parameters determined as a = 0.3738 nm, α = β = γ = 90°. Based on the experimental results on phase equilibrium, the CALPHAD approach was used to develop the thermodynamic description of the Si-Zr-Ag ternary system. The calculated isothermal sections show excellent agreement with the experimental ones. Then, the liquidus projection was predicted with the obtained thermodynamic parameters.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102858"},"PeriodicalIF":1.9,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144611619","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}
Pub Date : 2025-07-10DOI: 10.1016/j.calphad.2025.102838
C. Frueh, C. Aras, Ö. Büyükuslu, M. to Baben
aiMP and aiOQ are databases derived from the 0 K density functional theory (DFT) calculations data stored in the Materials Project and Open Quantum Materials Database (OQMD) repositories, respectively. aiMP and aiOQ databases rely on methods to process 0 K DFT data using machine learning models trained on thousands of compounds. These models adjust formation enthalpies to improve consistency with existing CALPHAD (CALculation of PHAse Diagrams) databases and predict thermodynamic properties such as entropy and heat capacity as functions of temperature.
This work demonstrates three Materials Informatics applications of large-scale CALPHAD-compatible databases enabled by automated workflows.
First, a comparison was made between the SGTE Pure Substance database (SGPS), containing 3927 compounds, and the aiMP database, which includes overlapping entries for 1519 compounds. For these overlapping compounds, the enthalpy of formation, entropy at 298 K, and heat capacity at 298 K were analyzed. Any discrepancies exceeding the inherent error of the machine learning models were flagged. A literature survey was then conducted for compounds with larger discrepancies and erroneous data was confirmed in approximately 0.7% of the SGPS data.
Second, the aiMP database was used to estimate phase diagrams and identify potential new coating materials for SiC/SiC composites, which are under investigation as accident-tolerant fuel cladding materials.
Finally, it is shown that aiMP can serve as a starting point for both traditional and automated CALPHAD modeling. Three examples were explored Al-Ca, Mg-Si, and Ca-Li. These examples highlight the versatility of machine learning-enhanced thermodynamic databases in accelerating material discovery and improving database reliability.
aiMP和aiOQ数据库分别来源于存储在材料项目和开放量子材料数据库（OQMD）存储库中的0 K密度泛函理论（DFT）计算数据。aiMP和aiOQ数据库依赖于使用数千种化合物训练的机器学习模型来处理0 K DFT数据的方法。这些模型调整地层焓，以提高与现有CALPHAD（相图计算）数据库的一致性，并预测热力学性质，如熵和热容作为温度的函数。这项工作演示了三种材料信息学应用程序的大规模calphad兼容数据库启用自动化工作流程。首先，我们比较了包含3927种化合物的SGTE纯物质数据库（SGPS）和包含1519种化合物重叠条目的aiMP数据库。对这些重叠化合物的生成焓、298k时的熵和298k时的热容进行了分析。任何超出机器学习模型固有误差的差异都会被标记出来。然后对差异较大的化合物进行文献调查，在大约0.7%的SGPS数据中确认了错误数据。其次，aiMP数据库用于估计相图并确定潜在的SiC/SiC复合材料的新涂层材料，这些材料正在研究作为耐事故燃料包层材料。最后，表明aiMP可以作为传统和自动化CALPHAD建模的起点。以Al-Ca、Mg-Si和Ca-Li为例。这些例子突出了机器学习增强的热力学数据库在加速材料发现和提高数据库可靠性方面的多功能性。
{"title":"aiMP and aiOQ databases in FactSage: Materials informatics relying on ab initio, machine learning and CALPHAD data","authors":"C. Frueh, C. Aras, Ö. Büyükuslu, M. to Baben","doi":"10.1016/j.calphad.2025.102838","DOIUrl":"10.1016/j.calphad.2025.102838","url":null,"abstract":"<div><div>aiMP and aiOQ are databases derived from the 0 K density functional theory (DFT) calculations data stored in the Materials Project and Open Quantum Materials Database (OQMD) repositories, respectively. aiMP and aiOQ databases rely on methods to process 0 K DFT data using machine learning models trained on thousands of compounds. These models adjust formation enthalpies to improve consistency with existing CALPHAD (CALculation of PHAse Diagrams) databases and predict thermodynamic properties such as entropy and heat capacity as functions of temperature.</div><div>This work demonstrates three Materials Informatics applications of large-scale CALPHAD-compatible databases enabled by automated workflows.</div><div>First, a comparison was made between the SGTE Pure Substance database (SGPS), containing 3927 compounds, and the aiMP database, which includes overlapping entries for 1519 compounds. For these overlapping compounds, the enthalpy of formation, entropy at 298 K, and heat capacity at 298 K were analyzed. Any discrepancies exceeding the inherent error of the machine learning models were flagged. A literature survey was then conducted for compounds with larger discrepancies and erroneous data was confirmed in approximately 0.7% of the SGPS data.</div><div>Second, the aiMP database was used to estimate phase diagrams and identify potential new coating materials for SiC/SiC composites, which are under investigation as accident-tolerant fuel cladding materials.</div><div>Finally, it is shown that aiMP can serve as a starting point for both traditional and automated CALPHAD modeling. Three examples were explored Al-Ca, Mg-Si, and Ca-Li. These examples highlight the versatility of machine learning-enhanced thermodynamic databases in accelerating material discovery and improving database reliability.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102838"},"PeriodicalIF":1.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144588725","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}
Pub Date : 2025-07-09DOI: 10.1016/j.calphad.2025.102851
Weisheng Cao , Fan Zhang , Kamalnath Kadirvel , Shuanglin Chen , Eric Payton , Matthew Krug
This paper introduces PanEvolution, a modeling platform that integrates CALPHAD, microstructure modeling, and finite element method (FEM). This work represents the third generation of Pandat software, designed to simulate the microstructure evolution of metallic materials during conventional manufacturing processes. The key features of PanEvolution include: (1) direct coupling of CALPHAD with various FEM software packages. This enables FEM packages to obtain accurate input of phase information for multi-component alloys and perform simulations of microstructure evolution for technically important metallic alloys, including precipitation, recrystallization, grain growth, and coarsening, during conventional manufacturing processes such as forging and rolling. (2) an open architecture that facilitates the easy replacement and swapping of fast-acting microstructure models. This enables microstructure evolution and property models developed by academia or industry to be easily integrated into the PanEvolution platform to maximize their value in industrial applications.
{"title":"PanEvolution: Integrating CALPHAD, microstructure modeling, and finite element method","authors":"Weisheng Cao , Fan Zhang , Kamalnath Kadirvel , Shuanglin Chen , Eric Payton , Matthew Krug","doi":"10.1016/j.calphad.2025.102851","DOIUrl":"10.1016/j.calphad.2025.102851","url":null,"abstract":"<div><div>This paper introduces PanEvolution, a modeling platform that integrates CALPHAD, microstructure modeling, and finite element method (FEM). This work represents the third generation of Pandat software, designed to simulate the microstructure evolution of metallic materials during conventional manufacturing processes. The key features of PanEvolution include: (1) direct coupling of CALPHAD with various FEM software packages. This enables FEM packages to obtain accurate input of phase information for multi-component alloys and perform simulations of microstructure evolution for technically important metallic alloys, including precipitation, recrystallization, grain growth, and coarsening, during conventional manufacturing processes such as forging and rolling. (2) an open architecture that facilitates the easy replacement and swapping of fast-acting microstructure models. This enables microstructure evolution and property models developed by academia or industry to be easily integrated into the PanEvolution platform to maximize their value in industrial applications.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102851"},"PeriodicalIF":1.9,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579832","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}
The phase equilibria of the Co–Cr binary system were experimentally investigated across the whole composition range. Liquidus and solidus temperatures, measured up to 1800 °C using a differential thermal analyzer and differential scanning calorimeter, were slightly higher than those reported in the literature. The equilibrium compositions of two-phase alloys were analyzed using an electron probe microanalyzer, yielding reliable data regarding the γ(Co) + α(Cr) phase boundaries at high temperatures and ε(Co) + σ phase boundaries at low temperatures. Subsequently, a thermodynamic assessment of the Co–Cr binary system was performed using the CALPHAD technique, relying on our experimental data as well as thermodynamic property data from the literatures. The calculated Co–Cr phase diagram accurately reproduced the experimentally determined phase boundaries and thermodynamic properties, including activity, excess enthalpy, and excess Gibbs energy.
{"title":"Phase equilibria and thermodynamic assessment of the Co–Cr binary system","authors":"Kazushige Ioroi, Haruhi Kumeta, Xiao Xu, Ryosuke Kainuma, Toshihiro Omori","doi":"10.1016/j.calphad.2025.102853","DOIUrl":"10.1016/j.calphad.2025.102853","url":null,"abstract":"<div><div>The phase equilibria of the Co–Cr binary system were experimentally investigated across the whole composition range. Liquidus and solidus temperatures, measured up to 1800 °C using a differential thermal analyzer and differential scanning calorimeter, were slightly higher than those reported in the literature. The equilibrium compositions of two-phase alloys were analyzed using an electron probe microanalyzer, yielding reliable data regarding the γ(Co) + α(Cr) phase boundaries at high temperatures and ε(Co) + σ phase boundaries at low temperatures. Subsequently, a thermodynamic assessment of the Co–Cr binary system was performed using the CALPHAD technique, relying on our experimental data as well as thermodynamic property data from the literatures. The calculated Co–Cr phase diagram accurately reproduced the experimentally determined phase boundaries and thermodynamic properties, including activity, excess enthalpy, and excess Gibbs energy.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102853"},"PeriodicalIF":1.9,"publicationDate":"2025-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144570977","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}
Pub Date : 2025-07-04DOI: 10.1016/j.calphad.2025.102852
Kun Wang , Patrice Chartrand
The Modified Quasichemical Model in the Distinguishable-Pair Approximation (MQMDPA) was originally developed to describe thermodynamic properties of binary solutions with manifold short-range ordering (SRO) among atoms. This study extends the MQMDPA to multicomponent solutions through the development of an on-the-fly bond-energy formalism (OTFBEF). The OTFBEF employs interpolation functions to dynamically transform bond energy expressions from binary to ternary and higher-order multicomponent systems. By fixing the interpolation functions to specific values, the OTFBEF seamlessly reduces to traditional geometric methods, the generic method, or the hybrid Kohler-Toop loop framework, ensuring compatibility with established approaches, particularly with the widely used MQMPA. The interpolation functions can be optimized using experimental data from ternary systems or theoretically defined through integral and partial methods, providing flexibility for both prediction and calibration. The versatility and generality of the OTFBEF empower the MQMDPA to model multicomponent solutions with complex configurations effectively. Future work will focus on expanding the MQMDPA within a two-sublattice framework to address reciprocal solutions, further enhancing its applicability.
{"title":"Extension of the modified quasichemical model in the distinguishable-pair approximation to multicomponent solutions via an on-the-fly interpolation framework","authors":"Kun Wang , Patrice Chartrand","doi":"10.1016/j.calphad.2025.102852","DOIUrl":"10.1016/j.calphad.2025.102852","url":null,"abstract":"<div><div>The Modified Quasichemical Model in the Distinguishable-Pair Approximation (MQMDPA) was originally developed to describe thermodynamic properties of binary solutions with manifold short-range ordering (SRO) among atoms. This study extends the MQMDPA to multicomponent solutions through the development of an on-the-fly bond-energy formalism (OTFBEF). The OTFBEF employs interpolation functions to dynamically transform bond energy expressions from binary to ternary and higher-order multicomponent systems. By fixing the interpolation functions to specific values, the OTFBEF seamlessly reduces to traditional geometric methods, the generic method, or the hybrid Kohler-Toop loop framework, ensuring compatibility with established approaches, particularly with the widely used MQMPA. The interpolation functions can be optimized using experimental data from ternary systems or theoretically defined through integral and partial methods, providing flexibility for both prediction and calibration. The versatility and generality of the OTFBEF empower the MQMDPA to model multicomponent solutions with complex configurations effectively. Future work will focus on expanding the MQMDPA within a two-sublattice framework to address reciprocal solutions, further enhancing its applicability.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102852"},"PeriodicalIF":1.9,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144549246","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}
Pub Date : 2025-07-01DOI: 10.1016/j.calphad.2025.102854
Sinn-wen Chen , Te-Wei Lin , Hsin-Chieh Huang , Cheng-Hsi Ho , Chuan Zhang , Jun Zhu
The Sn–In–Ni–Zn system is an important material system for electronic soldering. Various alloys, such as Sn–In, Sn–Ni, Sn–Zn, and Sn–In–Zn, are frequently used in electronic products. Unexpectedly, it was found that even for these important systems, there are only limited experimental measurements of the liquidus and invariant reaction temperatures. Additionally, there are significant differences between the experimental results and those calculated using the CALPHAD method with various available databases. To tackle these issues, Sn-rich alloys including Sn–Zn, Sn–In, Sn–Ni, Sn–In–Zn, Sn–Ni–Zn, Sn–In–Ni, and Sn–In–Ni–Zn were prepared. Their liquidus temperatures were determined experimentally through thermal analysis combined with holding-quenching experiments, while invariant reaction temperatures were measured using thermal analysis with an internal marker. The uncertainties in the measurements are 3 °C for the liquidus temperatures and 1 °C for the invariant reactions. Although high-quality thermal analysis can determine phase transformation temperatures with an accuracy of up to 1 °C, reliable determination of liquidus temperatures becomes quite challenging when the heat effect is not significant. This may explain why the literature data are inconsistent. These experimental results were subsequently used to refine CALPHAD-type modeling, and phase diagram calculations with better agreement were achieved.
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