Pub Date : 2025-03-01DOI: 10.1016/j.calphad.2025.102807
Yanzhou Ji , Yueze Tan , Long-Qing Chen
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.
{"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}
Pub Date : 2025-03-01DOI: 10.1016/j.calphad.2024.102775
Z.-K. Liu
{"title":"Corrigendum to “Thermodynamics and its prediction and CALPHAD modeling: Review, state of the art, and perspectives” [CALPHAD 82 (2023) 102580]","authors":"Z.-K. Liu","doi":"10.1016/j.calphad.2024.102775","DOIUrl":"10.1016/j.calphad.2024.102775","url":null,"abstract":"","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"88 ","pages":"Article 102775"},"PeriodicalIF":1.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143550259","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}
The Diffusion Coefficient Calculation software (DCal.app) is a free, user-friendly tool designed to investigate the atomic diffusivity and mobility of the most common alloy structures, like FCC, BCC, and HCP by pre- and post-processing the results of first-principles calculation. The software with intuitive graphical user interface (GUI) enables users to obtain tracer diffusion coefficients, interdiffusion coefficients, and mobility parameters for binary alloys. Additionally, DCal.app can generate the perfect structures of any supercell size, as well as the initial and final defect state structures for each diffusion path based on the analytical diffusion models. The software also provides a way to estimate the key factors in atomic diffusion behavior such as jump frequency, correlation factor, and vacancy concentration. This article offers a concise overview of the current version of DCal.app, including the underlying theory of atomic diffusion, the algorithm, and the various functions it incorporates. Four examples are provided to demonstrate each function in our software. The application of DCal.app optimizes resource efficiency in obtaining the kinetic properties, accelerating research in common alloys with precise mobility database.
{"title":"DCal.app: A user-friendly tool for tracer and interdiffusion coefficient in FCC/BCC/HCP alloys","authors":"Haiyu Luo, Wensheng Liu, Yunzhu Ma, Chaoping Liang","doi":"10.1016/j.calphad.2025.102811","DOIUrl":"10.1016/j.calphad.2025.102811","url":null,"abstract":"<div><div>The Diffusion Coefficient Calculation software (DCal.app) is a free, user-friendly tool designed to investigate the atomic diffusivity and mobility of the most common alloy structures, like FCC, BCC, and HCP by pre- and post-processing the results of first-principles calculation. The software with intuitive graphical user interface (GUI) enables users to obtain tracer diffusion coefficients, interdiffusion coefficients, and mobility parameters for binary alloys. Additionally, DCal.app can generate the perfect structures of any supercell size, as well as the initial and final defect state structures for each diffusion path based on the analytical diffusion models. The software also provides a way to estimate the key factors in atomic diffusion behavior such as jump frequency, correlation factor, and vacancy concentration. This article offers a concise overview of the current version of DCal.app, including the underlying theory of atomic diffusion, the algorithm, and the various functions it incorporates. Four examples are provided to demonstrate each function in our software. The application of DCal.app optimizes resource efficiency in obtaining the kinetic properties, accelerating research in common alloys with precise mobility database.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102811"},"PeriodicalIF":1.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526776","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 : 2025-02-24DOI: 10.1016/j.calphad.2025.102804
Hong Bo, Rui Cheng, Yanwei Han, Xudong Chen, Li-min Wang
As a ternary subsystem of the high-temperature bulk metallic glass system, the Co-Ni-B system was systematically studied through both experimentation and thermodynamic modeling. Using equilibrated alloys, the isothermal section at 1073 K was investigated via electron probe microanalyzer (EPMA) equipped with wavelength dispersive spectrometer (WDS) and x-ray diffraction (XRD). Differential scanning calorimetry (DSC) tests were also conducted to determine the phase transition temperatures. By combining the experimental data and first-principles calculation results from this work, the Co-Ni-B system was thermodynamically optimized with the CALculation of PHAse Diagram (CALPHAD) method. The calculated isothermal section, vertical section and liquidus projection accounted for the experimental data successfully. This study provides a foundation for establishing a multi-component thermodynamic database that includes Co-Ni-B and facilitates the design of novel high-temperature metallic glasses.
{"title":"Experimental investigation and thermodynamic modeling of the Co-Ni-B system","authors":"Hong Bo, Rui Cheng, Yanwei Han, Xudong Chen, Li-min Wang","doi":"10.1016/j.calphad.2025.102804","DOIUrl":"10.1016/j.calphad.2025.102804","url":null,"abstract":"<div><div>As a ternary subsystem of the high-temperature bulk metallic glass system, the Co-Ni-B system was systematically studied through both experimentation and thermodynamic modeling. Using equilibrated alloys, the isothermal section at 1073 K was investigated via electron probe microanalyzer (EPMA) equipped with wavelength dispersive spectrometer (WDS) and x-ray diffraction (XRD). Differential scanning calorimetry (DSC) tests were also conducted to determine the phase transition temperatures. By combining the experimental data and first-principles calculation results from this work, the Co-Ni-B system was thermodynamically optimized with the CALculation of PHAse Diagram (CALPHAD) method. The calculated isothermal section, vertical section and liquidus projection accounted for the experimental data successfully. This study provides a foundation for establishing a multi-component thermodynamic database that includes Co-Ni-B and facilitates the design of novel high-temperature metallic glasses.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"88 ","pages":"Article 102804"},"PeriodicalIF":1.9,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474458","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 : 2025-02-18DOI: 10.1016/j.calphad.2025.102808
Mingzhong Yuan, Changrong Li, Cuiping Guo, Zhenmin Du
The phase relationships of the Sc-Sb binary system were experimentally investigated using the heat-treated alloys as well as the as-cast alloys by scanning electron microscopy with energy dispersive spectrometer (SEM-EDS), powder X-ray diffraction (XRD) and differential scanning calorimetry (DSC). Four stable intermetallic phases, Sc2Sb, Sc4Sb2.52, Sc5Sb3 and ScSb, are confirmed to exist in the Sc-Sb binary system. The phases Sc5Sb3, Sc4Sb2.52 and ScSb solidify congruently while the phases Sc2Sb is formed through the peritectic transformation. There are six invariant reactions in the Sc-Sb system. The liquid compositions of the four eutectic isothermal reactions are approximately 16.3 at.% Sb at 1188 °C for L → α-Sc + Sc2Sb, 38.3 at.% Sb at 1548 °C for L → Sc5Sb3 + Sc4Sb2.52, 48.4 at.% Sb at 1442 °C for L → Sc4Sb2.52 + ScSb and 88.0 at.% Sb at 575 °C for L → ScSb + Rhom-Sb, and a peritectic isothermal reaction is about 23.2 at.% Sb at 1349 °C for L + Sc5Sb3 → Sc2Sb. The liquid composition of the metatectic isothermal reaction β-Sc → α-Sc + L is 14.39 at.% Sb at 1263 °C. The solubilities of Sb in α-Sc are 3.8, 4.8 and 5.5 at.% Sb at 1000, 1100 and 1200 °C, respectively. According to the experimental heat capacity of the Sc4Sb2.52 compound, the Gibbs energy of this compound was firstly determined from 0 to 2000 K. Based on the presently obtained experimental data and the data from literatures, the Sc-Sb system was thermodynamically described and critically assessed by means of the CALPHAD approach. A self-consistent set of thermodynamic parameters was obtained. The calculated results show good agreement with the experimental data.
{"title":"Experimental investigation and thermodynamic optimization of the Sc-Sb binary system","authors":"Mingzhong Yuan, Changrong Li, Cuiping Guo, Zhenmin Du","doi":"10.1016/j.calphad.2025.102808","DOIUrl":"10.1016/j.calphad.2025.102808","url":null,"abstract":"<div><div>The phase relationships of the Sc-Sb binary system were experimentally investigated using the heat-treated alloys as well as the as-cast alloys by scanning electron microscopy with energy dispersive spectrometer (SEM-EDS), powder X-ray diffraction (XRD) and differential scanning calorimetry (DSC). Four stable intermetallic phases, Sc<sub>2</sub>Sb, Sc<sub>4</sub>Sb<sub>2.52</sub>, Sc<sub>5</sub>Sb<sub>3</sub> and ScSb, are confirmed to exist in the Sc-Sb binary system. The phases Sc<sub>5</sub>Sb<sub>3</sub>, Sc<sub>4</sub>Sb<sub>2.52</sub> and ScSb solidify congruently while the phases Sc<sub>2</sub>Sb is formed through the peritectic transformation. There are six invariant reactions in the Sc-Sb system. The liquid compositions of the four eutectic isothermal reactions are approximately 16.3 at.% Sb at 1188 °C for L → <em>α</em>-Sc + Sc<sub>2</sub>Sb, 38.3 at.% Sb at 1548 °C for L → Sc<sub>5</sub>Sb<sub>3</sub> + Sc<sub>4</sub>Sb<sub>2.52</sub>, 48.4 at.% Sb at 1442 °C for L → Sc<sub>4</sub>Sb<sub>2.52</sub> + ScSb and 88.0 at.% Sb at 575 °C for L → ScSb + Rhom-Sb, and a peritectic isothermal reaction is about 23.2 at.% Sb at 1349 °C for L + Sc<sub>5</sub>Sb<sub>3</sub> → Sc<sub>2</sub>Sb. The liquid composition of the metatectic isothermal reaction <em>β</em>-Sc → <em>α</em>-Sc + L is 14.39 at.% Sb at 1263 °C. The solubilities of Sb in <em>α</em>-Sc are 3.8, 4.8 and 5.5 at.% Sb at 1000, 1100 and 1200 °C, respectively. According to the experimental heat capacity of the Sc<sub>4</sub>Sb<sub>2.52</sub> compound, the Gibbs energy of this compound was firstly determined from 0 to 2000 K. Based on the presently obtained experimental data and the data from literatures, the Sc-Sb system was thermodynamically described and critically assessed by means of the CALPHAD approach. A self-consistent set of thermodynamic parameters was obtained. 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":"88 ","pages":"Article 102808"},"PeriodicalIF":1.9,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429474","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 : 2025-02-09DOI: 10.1016/j.calphad.2025.102806
Junjun Wang , Bingquan Xu , Kyungjun Lee , Wei Huang , Huihui Wang , Jian Peng , Man Xu
A machine learning assisted CALPHAD framework is applied in this study to thermodynamically analyze the chemical vapor deposition (CVD) process for silicon oxynitride films. Among the various machine learning algorithms evaluated, Random Forest (RF) was identified as the optimal model due to its superior accuracy and generalization performance. The study identified that only 5 % data of the original dataset is required to effectively train the RF model. The best-trained RF model can excellently reproduce results from CALPHAD. SHAP analysis was performed to quantify the contribution of input features to the performance of machine learning model. The results revealed that NH3/N2O and NH3/SiCl4 ratios have the most significant influence on the mole fractions of SiO2 and Si2N2O, while the NH3/N2O ratio is the dominant factor affecting the mole fraction of Si3N4 in the deposit. Notably, the ML-assisted CALPHAD framework demonstrated a 20-fold increase in analysis efficiency compared to traditional CALPHAD calculations.
{"title":"Machine learning assisted CALPHAD framework for thermodynamic analysis of CVD SiOxNy thin films","authors":"Junjun Wang , Bingquan Xu , Kyungjun Lee , Wei Huang , Huihui Wang , Jian Peng , Man Xu","doi":"10.1016/j.calphad.2025.102806","DOIUrl":"10.1016/j.calphad.2025.102806","url":null,"abstract":"<div><div>A machine learning assisted CALPHAD framework is applied in this study to thermodynamically analyze the chemical vapor deposition (CVD) process for silicon oxynitride films. Among the various machine learning algorithms evaluated, Random Forest (RF) was identified as the optimal model due to its superior accuracy and generalization performance. The study identified that only 5 % data of the original dataset is required to effectively train the RF model. The best-trained RF model can excellently reproduce results from CALPHAD. SHAP analysis was performed to quantify the contribution of input features to the performance of machine learning model. The results revealed that NH<sub>3</sub>/N<sub>2</sub>O and NH<sub>3</sub>/SiCl<sub>4</sub> ratios have the most significant influence on the mole fractions of SiO<sub>2</sub> and Si<sub>2</sub>N<sub>2</sub>O, while the NH<sub>3</sub>/N<sub>2</sub>O ratio is the dominant factor affecting the mole fraction of Si<sub>3</sub>N<sub>4</sub> in the deposit. Notably, the ML-assisted CALPHAD framework demonstrated a 20-fold increase in analysis efficiency compared to traditional CALPHAD calculations.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"88 ","pages":"Article 102806"},"PeriodicalIF":1.9,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143372392","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 : 2025-02-08DOI: 10.1016/j.calphad.2025.102798
Xiaoke Wu , Ting Cheng , Jing Zhong , Shenglan Yang , Sa Ma , Na Ta , Lijun Zhang
In this work, a framework for efficient phase-field simulation of microstructure evolution is developed and demonstrated in Ni-based superalloys. Firstly, a universal schema for phase-field simulation coupling with various CALPHAD-type data/databases is postulated. Identifiers for illustrating fruitful prerequisite properties/parameters for phase-field modeling are proposed. An open exchange coupling file format is also put forward according to the data reconstruction strategy based on hash algorithm and interpolation. After that, the presently developed coupling schema is combined with the phase-field model with finite interface dissipation as well as the parallelism technique for elaborate demonstration. Various benchmark tests for the presently proposed coupling schema are carried out for validation. Finally, efficient phase-field simulation of the long-time aging process of Ni-Al alloy and the medium-scale directional solidification process of the Ni-Al-Ta ternary alloy within various preparation process parameters were performed for further validation. It is anticipated that the presently developed framework is of general validity for industrial materials in the spirit of integrated computational materials engineering.
{"title":"An efficient microstructure simulation framework by integrating phase-field model, general coupling schema and parallelism: Demo in Ni-based superalloys","authors":"Xiaoke Wu , Ting Cheng , Jing Zhong , Shenglan Yang , Sa Ma , Na Ta , Lijun Zhang","doi":"10.1016/j.calphad.2025.102798","DOIUrl":"10.1016/j.calphad.2025.102798","url":null,"abstract":"<div><div>In this work, a framework for efficient phase-field simulation of microstructure evolution is developed and demonstrated in Ni-based superalloys. Firstly, a universal schema for phase-field simulation coupling with various CALPHAD-type data/databases is postulated. Identifiers for illustrating fruitful prerequisite properties/parameters for phase-field modeling are proposed. An open exchange coupling file format is also put forward according to the data reconstruction strategy based on hash algorithm and interpolation. After that, the presently developed coupling schema is combined with the phase-field model with finite interface dissipation as well as the parallelism technique for elaborate demonstration. Various benchmark tests for the presently proposed coupling schema are carried out for validation. Finally, efficient phase-field simulation of the long-time aging process of Ni-Al alloy and the medium-scale directional solidification process of the Ni-Al-Ta ternary alloy within various preparation process parameters were performed for further validation. It is anticipated that the presently developed framework is of general validity for industrial materials in the spirit of integrated computational materials engineering.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"88 ","pages":"Article 102798"},"PeriodicalIF":1.9,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143351008","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 : 2025-01-31DOI: 10.1016/j.calphad.2025.102805
H. Bouchta , A. Bendarma , D.O. Poletaev , M.A. Boukideur , S. Kardellass , N. Selhaoui , L. Rabhi , M. Idbenali
In this work, a standard enthalpies of formation for metal compounds within the Eu-Rh system were determined using first-principles calculations within the framework of density functional theory (DFT). The system analysis was carried out by employing thermodynamic data and phase diagram information sourced from literature, and a CALPHAD-type optimization and Thermo-Calc software.
The Eu-Rh phase diagram includes four intermetallic compounds: All phases present a stoichiometry, except the which has a homogeneity range and was modeled using a two-sublattice model with substitution in each sublattice.
To describe the additional term of the Gibbs energy ( for the liquid phase and the solid solution within the Eu-Rh system, a solution model has been used. The liquid phase was characterized using the linear dependence of the Redlich-Kister model. The individual Gibbs energies include temperature-dependent contributions for all compounds. A comparative analysis shows a good agreement between the enthalpies of formation calculated in this study using the VASP method and current literature data. Finally, a set of self-consistent thermodynamic parameters for the Eu-Rh system was derived.
{"title":"Thermodynamic assessment of the Eu-Rh system by the combination of ab-initio calculations and CALPHAD approach","authors":"H. Bouchta , A. Bendarma , D.O. Poletaev , M.A. Boukideur , S. Kardellass , N. Selhaoui , L. Rabhi , M. Idbenali","doi":"10.1016/j.calphad.2025.102805","DOIUrl":"10.1016/j.calphad.2025.102805","url":null,"abstract":"<div><div>In this work, a standard enthalpies of formation for metal compounds within the Eu-Rh system were determined using first-principles calculations within the framework of density functional theory (DFT). The system analysis was carried out by employing thermodynamic data and phase diagram information sourced from literature, and a CALPHAD-type optimization and Thermo-Calc software.</div><div>The Eu-Rh phase diagram includes four intermetallic compounds: <span><math><mrow><msub><mtext>Eu</mtext><mn>9</mn></msub><mtext>Rh</mtext><mo>,</mo><msub><mtext>Eu</mtext><mn>3</mn></msub><mtext>Rh</mtext><mo>,</mo><msub><mtext>Eu</mtext><mn>5</mn></msub><mtext>Rh</mtext><mspace></mspace><mtext>and</mtext><mspace></mspace><mtext>Eu</mtext><msub><mtext>Rh</mtext><mrow><mn>2</mn><mspace></mspace><mo>.</mo><mspace></mspace></mrow></msub></mrow></math></span> All phases present a stoichiometry, except the <span><math><mrow><mtext>Eu</mtext><msub><mtext>Rh</mtext><mrow><mn>2</mn><mspace></mspace></mrow></msub><mtext>,</mtext></mrow></math></span> which has a homogeneity range and was modeled using a two-sublattice model with substitution in each sublattice.</div><div>To describe the additional term of the Gibbs energy (<span><math><mrow><mmultiscripts><mi>G</mi><mprescripts></mprescripts><none></none><mtext>ex</mtext></mmultiscripts><mo>)</mo></mrow></math></span> for the liquid phase and the solid solution within the Eu-Rh system, a solution model has been used. The liquid phase was characterized using the linear dependence of the Redlich-Kister model. The individual Gibbs energies include temperature-dependent contributions for all compounds. A comparative analysis shows a good agreement between the enthalpies of formation calculated in this study using the VASP method and current literature data. Finally, a set of self-consistent thermodynamic parameters for the Eu-Rh system was derived.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"88 ","pages":"Article 102805"},"PeriodicalIF":1.9,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180685","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 : 2025-01-30DOI: 10.1016/j.calphad.2025.102802
Ryota Nagashima, Masao Takeyama
Experimental studies were conducted to investigate the phase equilibria of the Ni-rich portion of the Ni–Cr–Mo ternary system using scanning electron microscopy and electron probe microanalysis of heat-treated alloys. Experimental isothermal sections involving L-liquid, γ-Ni, P-NiCrMo, NiMo, Ni3Mo, and Ni2(Cr, Mo)-oP6 phases were constructed at temperatures below 1573 K. Two distinct liquid phase regions with varying compositions were observed at 1573 K, indicating a phase separation of the liquid phase (L → L1 + L2). This can result in the presence of two ternary eutectic reactions: L1 → γ + P + NiMo and L2 → γ + σ + P. The Ni2Cr phase in the binary system was stabilized by substituted Cr by Mo at temperatures above 200 K. The Ni2(Cr, Mo)-oP6 single-phase region existed as an island around the composition of Ni–9Cr–24Mo (at.%) at 1073 K. The experimentally identified γ + oP6 + Ni3Mo and γ + P + oP6 regions suggest that the oP6 phase is formed by a ternary peritectoid reaction (γ + P + Ni3Mo → oP6). Based on these results, the reaction pathways related to the liquid and oP6 phases in the Ni–Cr–Mo ternary system were modified.
{"title":"Experimental phase diagram study of the Ni-rich part of the Ni–Cr–Mo ternary system","authors":"Ryota Nagashima, Masao Takeyama","doi":"10.1016/j.calphad.2025.102802","DOIUrl":"10.1016/j.calphad.2025.102802","url":null,"abstract":"<div><div>Experimental studies were conducted to investigate the phase equilibria of the Ni-rich portion of the Ni–Cr–Mo ternary system using scanning electron microscopy and electron probe microanalysis of heat-treated alloys. Experimental isothermal sections involving L-liquid, γ-Ni, P-NiCrMo, NiMo, Ni<sub>3</sub>Mo, and Ni<sub>2</sub>(Cr, Mo)-<em>oP</em>6 phases were constructed at temperatures below 1573 K. Two distinct liquid phase regions with varying compositions were observed at 1573 K, indicating a phase separation of the liquid phase (L → L<sub>1</sub> + L<sub>2</sub>). This can result in the presence of two ternary eutectic reactions: L<sub>1</sub> → γ + P + NiMo and L<sub>2</sub> → γ + σ + P. The Ni<sub>2</sub>Cr phase in the binary system was stabilized by substituted Cr by Mo at temperatures above 200 K. The Ni<sub>2</sub>(Cr, Mo)-<em>oP</em>6 single-phase region existed as an island around the composition of Ni–9Cr–24Mo (at.%) at 1073 K. The experimentally identified γ + <em>oP</em>6 + Ni<sub>3</sub>Mo and γ + P + <em>oP</em>6 regions suggest that the <em>oP</em>6 phase is formed by a ternary peritectoid reaction (γ + P + Ni<sub>3</sub>Mo → <em>oP</em>6). Based on these results, the reaction pathways related to the liquid and <em>oP</em>6 phases in the Ni–Cr–Mo ternary system were modified.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"88 ","pages":"Article 102802"},"PeriodicalIF":1.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180686","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}
Pub Date : 2025-01-29DOI: 10.1016/j.calphad.2025.102803
Kai Liang, Linna Shen, Cuiping Guo, Changrong Li, Zhenmin Du
The liquidus surface projection of the Ni–Ta–Ti system was constructed in this work. Thirty-seven as-cast alloys were characterized using scanning electron microscope equipped with energy dispersive spectrometer (SEM/EDS) and X-ray diffraction (XRD) methods to analyze the primary phases and solidification paths of alloys. Ten primary solidification regions of bcc(Ta,Ti), fcc(Ni), NiTi, NiTi2, NiTa2, Ni2Ta, Ni3Ta, Ni3Ti, μ and τ were determined. The crystal structure of the intermetallic phase τ was identified as the Ni3Sn type with space group P63/mmc. Moreover, the thermodynamic parameters of the Ni–Ta–Ti system were optimized via the CALculation of PHAse Diagram (CALPHAD) method based on the available experimental data. In this work, NiTi2, Ni3Ti, NiTa2, Ni2Ta, Ni3Ta and τ were modelled by two-sublattice model (Ni,Ta,Ti)m(Ni,Ta,Ti)n. A four-sublattice model (Ni,Ta,Ti)1(Ta,Ti)4(Ni,Ta,Ti)2(Ni,Ta,Ti)6 was adopted to describe μ. The calculated liquidus surface projection and isothermal sections with the obtained thermodynamic parameters were consistent with the experimental data.
{"title":"Experimental investigation and thermodynamic optimization of the Ni–Ta–Ti system","authors":"Kai Liang, Linna Shen, Cuiping Guo, Changrong Li, Zhenmin Du","doi":"10.1016/j.calphad.2025.102803","DOIUrl":"10.1016/j.calphad.2025.102803","url":null,"abstract":"<div><div>The liquidus surface projection of the Ni–Ta–Ti system was constructed in this work. Thirty-seven as-cast alloys were characterized using scanning electron microscope equipped with energy dispersive spectrometer (SEM/EDS) and X-ray diffraction (XRD) methods to analyze the primary phases and solidification paths of alloys. Ten primary solidification regions of bcc(Ta,Ti), fcc(Ni), NiTi, NiTi<sub>2</sub>, NiTa<sub>2</sub>, Ni<sub>2</sub>Ta, Ni<sub>3</sub>Ta, Ni<sub>3</sub>Ti, μ and τ were determined. The crystal structure of the intermetallic phase τ was identified as the Ni<sub>3</sub>Sn type with space group <em>P</em>6<sub>3</sub>/<em>mmc</em>. Moreover, the thermodynamic parameters of the Ni–Ta–Ti system were optimized via the CALculation of PHAse Diagram (CALPHAD) method based on the available experimental data. In this work, NiTi<sub>2</sub>, Ni<sub>3</sub>Ti, NiTa<sub>2</sub>, Ni<sub>2</sub>Ta, Ni<sub>3</sub>Ta and τ were modelled by two-sublattice model (Ni,Ta,Ti)<sub><em>m</em></sub>(Ni,Ta,Ti)<sub><em>n</em></sub>. A four-sublattice model (Ni,Ta,Ti)<sub>1</sub>(Ta,Ti)<sub>4</sub>(Ni,Ta,Ti)<sub>2</sub>(Ni,Ta,Ti)<sub>6</sub> was adopted to describe μ. The calculated liquidus surface projection and isothermal sections with the obtained thermodynamic parameters were consistent with the experimental data.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"88 ","pages":"Article 102803"},"PeriodicalIF":1.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181092","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}
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