{"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}
{"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}
Sinn-wen Chen , Te-Wei Lin , Hsin-Chieh Huang , Cheng-Hsi Ho , Chuan Zhang , Jun Zhu
{"title":"Phase transformation temperatures of the Sn–In–Ni–Zn quaternary system","authors":"Sinn-wen Chen , Te-Wei Lin , Hsin-Chieh Huang , Cheng-Hsi Ho , Chuan Zhang , Jun Zhu","doi":"10.1016/j.calphad.2025.102854","DOIUrl":"10.1016/j.calphad.2025.102854","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102854"},"PeriodicalIF":1.9,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144518206","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}
Amedeo Morsa , Elena Yazhenskikh , Mirko Ziegner , Egbert Wessel , Rhys Dominic Jacob , Michael Müller , Dmitry Sergeev
{"title":"Experimental study and thermodynamic assessment of the MgSO4-CaSO4 system","authors":"Amedeo Morsa , Elena Yazhenskikh , Mirko Ziegner , Egbert Wessel , Rhys Dominic Jacob , Michael Müller , Dmitry Sergeev","doi":"10.1016/j.calphad.2025.102855","DOIUrl":"10.1016/j.calphad.2025.102855","url":null,"abstract":"<div><div>This work presents a comprehensive experimental investigation into the thermal properties of the binary system MgSO<sub>4</sub>-CaSO<sub>4</sub>, alongside thermodynamic modelling of its thermodynamic properties, with a focus on enhancing its application in thermal energy storage. The phase diagram and thermodynamic properties of the pure sulphates and intermediate compounds were determined using Differential Thermal Analysis (DTA) and Differential Scanning Calorimetry (DSC). The DSC results led to the refinement of the enthalpy values for phase transitions of MgSO<sub>4</sub>, with updated values of 14.6 kJ/mol and 43.4 kJ/mol for the solid-solid and solid-liquid transitions, respectively. High-Temperature X-ray Diffraction (HTXRD) was employed to study the intermediate compounds, leading to the identification of CaMg<sub>2</sub>(SO<sub>4</sub>)<sub>3</sub>. For the first time, the melting temperature and the enthalpy of fusion for this compound were experimentally determined, yielding a value of 145.5 kJ/mol at 1213 ± 5 °C. A novel phase with the composition CaMg(SO<sub>4</sub>)<sub>2</sub> was identified using DTA, HTXRD, and Scanning Electron Microscopy (SEM). This phase exhibits a melting temperature of 1309 ± 5 °C, as determined by DTA, and demonstrates thermal stability within a high-temperature range of 1020–1308 °C. These experimental data were used to update the thermodynamic database for the system MgSO<sub>4</sub>-CaSO<sub>4</sub> for more accurate thermochemical calculations and predictions.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102855"},"PeriodicalIF":1.9,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517238","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}
Jesus A. Arias Hernandez, Elmira Moosavi-Khoonsari
{"title":"Modified polyhedron model for predicting standard enthalpy of formation and entropy of mixed oxides","authors":"Jesus A. Arias Hernandez, Elmira Moosavi-Khoonsari","doi":"10.1016/j.calphad.2025.102848","DOIUrl":"10.1016/j.calphad.2025.102848","url":null,"abstract":"<div><div>Thermodynamic modeling of oxidic systems is crucial in advancing various fields of science and technology. Polyhedron Model (PM) estimates the standard enthalpy of formation and entropy of mixed oxides via the linear summation of the thermodynamic properties of constituent polyhedra. Each polyhedron consists of a centered cation with neighboring oxygen anions; hence, the model accounts for the interaction between anions and cations. While second-order transitions have been considered in previous iterations of the model, the PM has certain shortcomings, including neglect of variations in polyhedron volume, polyhedron distortion, inter-polyhedron linkage, and second nearest-neighbor or higher-order interactions, which are not negligible. The present work introduces the Modified Polyhedron Model (MPM), which aims to incorporate these contributions through a neural network (NN) model to improve the accuracy of predictions for standard enthalpy of formation (<span><math><mrow><msubsup><mrow><mo>Δ</mo><mi>H</mi></mrow><mrow><mn>298</mn><mspace></mspace><mi>K</mi></mrow><mi>o</mi></msubsup></mrow></math></span>) and standard entropy (<span><math><mrow><msubsup><mi>S</mi><mrow><mn>298</mn><mspace></mspace><mi>K</mi></mrow><mi>o</mi></msubsup></mrow></math></span>). This is possible by using the residuals from the PM as inputs to the NN model, whose outputs are the calculated thermodynamic properties of compounds. The dataset consists of 155 compounds in the Li-Na-K-Ca-Mg-Mn-Fe-Al-Ti-Si-O system, classified by 20 polyhedra. The MPM considerably reduces the error in predicting enthalpy of formation and entropy, improving the alignment with experimental values across most analyzed compounds in comparison with the PM. These results suggest that the MPM can significantly improve the predictability of thermodynamic properties for mixed oxides.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102848"},"PeriodicalIF":1.9,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144489490","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":"Crystal structure and thermodynamic properties of post-spinel-type CaV2O4 at high temperatures (298.15–1373 K)","authors":"Dapeng Zhong , Jie Yu , Xin Jin , Guishang Pei , Wenhao Yu , Qingyun Huang , Changcai Zhou , Xuewei Lv , Wei Lv","doi":"10.1016/j.calphad.2025.102850","DOIUrl":"10.1016/j.calphad.2025.102850","url":null,"abstract":"<div><div>We conducted an analysis of the crystal structure and thermodynamic properties of CaV<sub>2</sub>O<sub>4</sub> synthesized through high-temperature solid-state calcination under elevated temperature conditions. The XRD analysis indicated that CaV<sub>2</sub>O<sub>4</sub> crystallizes in an orthorhombic structure, characterized by unit cell parameters <em>a</em> = 9.21311(10) Å, <em>b</em> = 3.008421(35) Å, <em>c</em> = 10.68206(12) Å, and <em>α</em> = <em>β</em> = <em>γ</em> = 90°. The enthalpy of formation and entropy of CaV<sub>2</sub>O<sub>4</sub> at 298.15 K are −1890.56 ± 5.84 kJ/mol J·mol<sup>−1</sup> and 129.62 ± 1.09 J·mol<sup>−1</sup> K<sup>−1</sup>, respectively. The heat capacity of CaV<sub>2</sub>O<sub>4</sub> at 573–1373 K was determined using drop calorimetry, yielding the expression <em>C</em><sub><em>p</em></sub> = 165.7748 + 3.2353 × 10<sup>−2</sup><em>T</em> - 2.64268 × 10<sup>6</sup><em>T</em><sup>−2</sup> (J·mol<sup>−1</sup>·K<sup>−1</sup>). Additional thermodynamic data for CaV<sub>2</sub>O<sub>4</sub> were derived using the <em>C</em><sub><em>p,m</em></sub> expression at elevated temperatures.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102850"},"PeriodicalIF":1.9,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331373","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}
Jin Tao , Rui Zhang , Yuhan Wang , Zewei Chen , Shitao Zhang , Caimin Huang , Qianxin Long , Zhao Lu , Like Tao , Qingrong Yao , Jiang Wang
{"title":"Experimental investigation and thermodynamic description of binary Er-Si and ternary Al-Si-Er systems","authors":"Jin Tao , Rui Zhang , Yuhan Wang , Zewei Chen , Shitao Zhang , Caimin Huang , Qianxin Long , Zhao Lu , Like Tao , Qingrong Yao , Jiang Wang","doi":"10.1016/j.calphad.2025.102839","DOIUrl":"10.1016/j.calphad.2025.102839","url":null,"abstract":"<div><div>In this study, thermodynamic optimization of the Er-Si binary system was performed using the CALPHAD method. The calculated phase diagram showed good consistency with existing experimental data. Furthermore, the phase equilibrium of the Al-Si-Er ternary system was investigated via electron probe microanalysis (EPMA) and X-ray diffraction (XRD), building on prior experimental data. Based on the experimental results obtained in this work and literature reports, the thermodynamic parameters of the Al-Si-Er ternary system were optimized. Both calculated isothermal cross section at 600 °C and the vertical cross section along Al<sub>70</sub>Si<sub>30</sub>-Al<sub>70</sub>Er<sub>30</sub> (at. %) in the ternary system are in agreement with experimental data, indicating reliability of the thermodynamic description. This work provides essential foundational data for the development of high-performance rare earth Al-Si-Er alloys.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"90 ","pages":"Article 102839"},"PeriodicalIF":1.9,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144243397","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}
Xinming Wang , Ying Ran , Zheng Peng , Guangjing Liao , Siqi Wang , Xuemei Ouyang , Yan Liu , Min Zhou , Fucheng Yin , Jingxian Hu
{"title":"Experimental determination and thermodynamic optimization of Co-Al-V ternary system","authors":"Xinming Wang , Ying Ran , Zheng Peng , Guangjing Liao , Siqi Wang , Xuemei Ouyang , Yan Liu , Min Zhou , Fucheng Yin , Jingxian Hu","doi":"10.1016/j.calphad.2025.102837","DOIUrl":"10.1016/j.calphad.2025.102837","url":null,"abstract":"<div><div>Novel Co-based superalloys, which possess superior high-temperature performance and oxidation resistance, have been extensively employed in high-temperature applications. Studying the phase relationships of Co-based alloys is crucial for their practical applications. The phase relationships in the isothermal section of the Co-Al-V ternary system at 1373 K (1100 °C) were experimentally determined by scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD). Nine three-phase regions were experimentally confirmed. On the basis of the previous data and the present experimental results, thermodynamic optimization of the Co-Al-V ternary system was conducted via the CALPHAD method. The calculated results are in good agreement with the experimental results, and a set of reasonable and self-consistent thermodynamic parameters has been obtained. These results provide a basis for the design of Co-based alloys and enrich the database of Co-based alloys.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102837"},"PeriodicalIF":1.9,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178116","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}
Jesus Alejandro Arias-Hernandez , Sun Yong Kwon , Elmira Moosavi-Khoonsari
{"title":"Application of polyhedron model to predict heat capacity of mixed oxides","authors":"Jesus Alejandro Arias-Hernandez , Sun Yong Kwon , Elmira Moosavi-Khoonsari","doi":"10.1016/j.calphad.2025.102836","DOIUrl":"10.1016/j.calphad.2025.102836","url":null,"abstract":"<div><div>The heat capacity of mixed oxides can be estimated using a linear summation of the heat capacities of their structural constituent polyhedra. This approach is particularly useful for hygroscopic and volatile oxides, where experimental data can be difficult to obtain. The present work aims to enhance the polyhedron model (PM) by incorporating contributions from second-order transitions, including magnetic and site order-disorders, into <span><math><mrow><msub><mi>C</mi><mi>p</mi></msub></mrow></math></span> and expanding it to include ZnO and PbO-containing systems in comparison to the previous version of the model. A regression analysis was performed over the new dataset consisting of the properties of 85 compounds in the system Li-Na-K-Ca-Mg-Mn-Fe-Pb-Zn-Al-Ti-Si-O to obtain optimized <span><math><mrow><msub><mi>C</mi><mi>p</mi></msub></mrow></math></span> for 20 constituent polyhedra. We validate the updated PM against experimental data, demonstrating an overall improvement between 7 and 9 % in the estimation of <span><math><mrow><msub><mi>C</mi><mi>p</mi></msub></mrow></math></span> compared to the previous version of the model. We also compare the updated model with well-established models in the literature, such as the Neumann-Kopp Rule, and ab-initio calculations. The PM shows higher precision than NKR and the linear summation nature of PM endows the model with simplicity which contrasts with ab-initio calculations. Additionally, the model has demonstrated an inherent self-correction capability relative to the original input values, as shown for K<sub>2</sub>Si<sub>4</sub>O<sub>9</sub>. The model is also applied to predict the heat capacity of 10 compounds in the Na<sub>2</sub>O-PbO-SiO<sub>2</sub> and Na<sub>2</sub>O-ZnO-SiO<sub>2</sub> systems, where experimental data are lacking.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102836"},"PeriodicalIF":1.9,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090365","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":"The SGTE collection of binary datasets","authors":"Bengt Hallstedt","doi":"10.1016/j.calphad.2025.102833","DOIUrl":"10.1016/j.calphad.2025.102833","url":null,"abstract":"<div><div>SGTE has collected (and also produced) binary assessments since the 1980's. This was documented with about 450 binary systems in five volumes of the Landolt-Börnstein series. These volumes were accompanied by a database with which the phase diagrams could be calculated, but the database itself was encrypted. It is now time to make the SGTE collection of binary datasets publicly available. The collection now contains 2773 datasets from 1238 different binary systems. By providing this collection in open form it is hoped that Calphad modelling of, in particular, ternary and higher order systems can be further promoted.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102833"},"PeriodicalIF":1.9,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937795","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}