Pub Date : 2025-04-26DOI: 10.1016/j.calphad.2025.102832
Peisheng Wang , Hui Luo , Wei He , Honghui Xu
Accurate phase diagrams are indispensable to boost the development of novel magnesium alloys. Up to now, however, there are still tremendous uncertainties about the number of the stable ternary compounds and related phase relationships in the Mg–Zn–La system. The Mg–Zn–La phase diagram at 320 °C in the region of <50 at% La was investigated by using 45 equilibrated alloys. Ten ternary compounds (labeled as τ1 to τ10) were found and their homogeneity ranges were measured. Two of the ternary compounds, i.e. τ1 (space group Cmc21) and τ8 (space group Immm), are identified to be the reported τ1-La(Mg,Zn)11 and La3(Mg,Zn)11 in literature, respectively. The remaining eight ternary compounds (τ2 to τ7, τ9 and τ10) are newly found in the present work. The lattice parameters for five of the ternary compounds (τ1 to τ3, τ6 and τ8) were calculated with the Jade 6.5 software, based on the XRD patterns. The LaMg2 phase was found at 320 °C and could be tentatively considered as a stabilized ternary phase with the third elements. Both the τ9 and τ10, which are in phase equilibrium with the (Mg) matrix and very close to the Mg-Zn side, are expected to act as important strengthening phases in the Mg-Zn based alloys.
{"title":"Ternary compounds and phase equilibria at 320 °C of the Mg–Zn–La system in the region below 50 at%La","authors":"Peisheng Wang , Hui Luo , Wei He , Honghui Xu","doi":"10.1016/j.calphad.2025.102832","DOIUrl":"10.1016/j.calphad.2025.102832","url":null,"abstract":"<div><div>Accurate phase diagrams are indispensable to boost the development of novel magnesium alloys. Up to now, however, there are still tremendous uncertainties about the number of the stable ternary compounds and related phase relationships in the Mg–Zn–La system. The Mg–Zn–La phase diagram at 320 °C in the region of <50 at% La was investigated by using 45 equilibrated alloys. Ten ternary compounds (labeled as τ<sub>1</sub> to τ<sub>10</sub>) were found and their homogeneity ranges were measured. Two of the ternary compounds, i.e. τ<sub>1</sub> (space group Cmc2<sub>1</sub>) and τ<sub>8</sub> (space group Immm), are identified to be the reported τ<sub>1</sub>-La(Mg,Zn)<sub>11</sub> and La<sub>3</sub>(Mg,Zn)<sub>11</sub> in literature, respectively. The remaining eight ternary compounds (τ<sub>2</sub> to τ<sub>7</sub>, τ<sub>9</sub> and τ<sub>10</sub>) are newly found in the present work. The lattice parameters for five of the ternary compounds (τ<sub>1</sub> to τ<sub>3</sub>, τ<sub>6</sub> and τ<sub>8</sub>) were calculated with the Jade 6.5 software, based on the XRD patterns. The LaMg<sub>2</sub> phase was found at 320 °C and could be tentatively considered as a stabilized ternary phase with the third elements. Both the τ<sub>9</sub> and τ<sub>10</sub>, which are in phase equilibrium with the (Mg) matrix and very close to the Mg-Zn side, are expected to act as important strengthening phases in the Mg-Zn based alloys.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102832"},"PeriodicalIF":1.9,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874279","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 : 2025-04-21DOI: 10.1016/j.calphad.2025.102828
Juwei Chen , Dawei Wei , Yue Ma , Wenli Bao
The phase equilibria of the Co–Ta–W system at 1373 K and 1473 K were determined using scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), and X-ray diffraction (XRD), two isothermal sections were constructed. Four three-phase regions at 1373 K were identified and three three-phase regions at 1473 K were determined. At heat-treatment temperature of 1373 K, the solid solubility of W in λ2 and Co7Ta6 were measured to be about 23.3 at.% and 11.9 at.%, respectively, while the solubility of Ta in Co7W6 was about 13.7 at.%. And Ta-stabilized Co3W phase was stable at 1373 K. At heat-treatment temperature of 1473 K, the solid solubility of W in λ2, Co7Ta6, and CoTa2 were measured to be about 23.8 at.%, 15.7 at.%, and 3.9 at.%, respectively. No new phase was found in this work.
{"title":"Phase equilibria in the Co–Ta–W system at 1373 and 1473 K","authors":"Juwei Chen , Dawei Wei , Yue Ma , Wenli Bao","doi":"10.1016/j.calphad.2025.102828","DOIUrl":"10.1016/j.calphad.2025.102828","url":null,"abstract":"<div><div>The phase equilibria of the Co–Ta–W system at 1373 K and 1473 K were determined using scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), and X-ray diffraction (XRD), two isothermal sections were constructed. Four three-phase regions at 1373 K were identified and three three-phase regions at 1473 K were determined. At heat-treatment temperature of 1373 K, the solid solubility of W in λ<sub>2</sub> and Co<sub>7</sub>Ta<sub>6</sub> were measured to be about 23.3 at.% and 11.9 at.%, respectively, while the solubility of Ta in Co<sub>7</sub>W<sub>6</sub> was about 13.7 at.%. And Ta-stabilized Co<sub>3</sub>W phase was stable at 1373 K. At heat-treatment temperature of 1473 K, the solid solubility of W in λ<sub>2</sub>, Co<sub>7</sub>Ta<sub>6</sub>, and CoTa<sub>2</sub> were measured to be about 23.8 at.%, 15.7 at.%, and 3.9 at.%, respectively. No new phase was found in this work.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102828"},"PeriodicalIF":1.9,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855207","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 : 2025-04-17DOI: 10.1016/j.calphad.2025.102830
Chuan Zhang , Alan A. Luo , Fan Zhang
Recycling aluminum alloys provides significant economic and environmental advantages, yet the formation of Fe-containing intermetallic phases, particularly the brittle β-AlFeSi phase, in secondary (recycled) aluminum alloys presents challenges to their mechanical and corrosion properties. This study investigates the role of Cr and Mn additions in suppressing these detrimental phases in the Al-Si-Fe system based on CALPHAD modeling and experimental validation. The findings highlight the effectiveness of CALPHAD simulations in accurately predicting as-cast microstructures and sludge formation temperatures for the alloys examined in this study, as well as those reported in the literature. The addition of Cr and Mn promotes the stabilization of the α-Al15M3Si2 phase and inhibits the formation of the detrimental β-AlFeSi phase. Furthermore, virtual experiments were carried out to identify optimal compositional and thermal conditions for efficient recycling. A model relating Fe content to optimal Cr and Mn additions for industrial recycling, expressed as is proposed to guide compositional adjustments. This integrated approach, coupling experimental validation with thermodynamic modeling, highlights the effectiveness of CALPHAD in addressing the Fe impurity challenges and enhancing the sustainability of aluminum alloy recycling.
{"title":"CALPHAD-guided suppression of detrimental Fe-containing phases in secondary aluminum alloys","authors":"Chuan Zhang , Alan A. Luo , Fan Zhang","doi":"10.1016/j.calphad.2025.102830","DOIUrl":"10.1016/j.calphad.2025.102830","url":null,"abstract":"<div><div>Recycling aluminum alloys provides significant economic and environmental advantages, yet the formation of Fe-containing intermetallic phases, particularly the brittle β-AlFeSi phase, in secondary (recycled) aluminum alloys presents challenges to their mechanical and corrosion properties. This study investigates the role of Cr and Mn additions in suppressing these detrimental phases in the Al-Si-Fe system based on CALPHAD modeling and experimental validation. The findings highlight the effectiveness of CALPHAD simulations in accurately predicting as-cast microstructures and sludge formation temperatures for the alloys examined in this study, as well as those reported in the literature. The addition of Cr and Mn promotes the stabilization of the α-Al<sub>15</sub>M<sub>3</sub>Si<sub>2</sub> phase and inhibits the formation of the detrimental β-AlFeSi phase. Furthermore, virtual experiments were carried out to identify optimal compositional and thermal conditions for efficient recycling. A model relating Fe content to optimal Cr and Mn additions for industrial recycling, expressed as <span><math><mrow><mi>w</mi><mrow><mo>(</mo><mrow><mi>F</mi><mi>e</mi></mrow><mo>)</mo></mrow><mo>=</mo><msqrt><mrow><mn>0.9</mn><mo>∗</mo><msup><mrow><mi>w</mi><mrow><mo>(</mo><mrow><mi>M</mi><mi>n</mi></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>+</mo><mn>0.4</mn><mo>∗</mo><msup><mrow><mi>w</mi><mrow><mo>(</mo><mrow><mi>C</mi><mi>r</mi></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></msqrt><mo>+</mo><mn>0.4</mn></mrow></math></span> is proposed to guide compositional adjustments. This integrated approach, coupling experimental validation with thermodynamic modeling, highlights the effectiveness of CALPHAD in addressing the Fe impurity challenges and enhancing the sustainability of aluminum alloy recycling.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102830"},"PeriodicalIF":1.9,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143839096","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 : 2025-04-15DOI: 10.1016/j.calphad.2025.102829
Hongyu Zhang , Zhe Yuan , Fali Liu , Weimin Bai , Yuan Yuan , Maohua Rong , Jiang Wang , Ligang Zhang , Libin Liu
Establishing the atomic mobility database for the Ti-Fe-Mo system is essential for analyzing and simulating diffusion-controlled processes in novel low-cost biomedical titanium alloys. In this study, twelve sets of diffusion couples were prepared at annealing temperatures of 1273 K, 1323 K, and 1373 K, with annealing time of 24 h, 10 h, and 6 h, respectively. The compositional distance profiles at the diffusion couple interfaces were measured using an Electro Probe Micro-Analysis (EPMA). Numerical inverse methods were applied to calculate diffusion coefficients in a high-throughput method, complemented by the Matano-Kirkaldy approach to determine diffusion coefficients at diffusion couple intersections. The results from both methods demonstrated strong agreement. Based on accurate thermodynamic descriptions and diffusion coefficients, the kinetic parameters of the Ti-Fe-Mo sub-binary systems were re-evaluated. Using HitDIC software in conjunction with compositional distance profiles, the atomic mobility database for this system was ultimately established. Additionally, the frequency factor and activation energy, vary with composition, can be derived using the Arrhenius equation.
{"title":"Interdiffusion coefficients and atomic mobilities in the bcc phase of the Ti-Fe-Mo system","authors":"Hongyu Zhang , Zhe Yuan , Fali Liu , Weimin Bai , Yuan Yuan , Maohua Rong , Jiang Wang , Ligang Zhang , Libin Liu","doi":"10.1016/j.calphad.2025.102829","DOIUrl":"10.1016/j.calphad.2025.102829","url":null,"abstract":"<div><div>Establishing the atomic mobility database for the Ti-Fe-Mo system is essential for analyzing and simulating diffusion-controlled processes in novel low-cost biomedical titanium alloys. In this study, twelve sets of diffusion couples were prepared at annealing temperatures of 1273 K, 1323 K, and 1373 K, with annealing time of 24 h, 10 h, and 6 h, respectively. The compositional distance profiles at the diffusion couple interfaces were measured using an Electro Probe Micro-Analysis (EPMA). Numerical inverse methods were applied to calculate diffusion coefficients in a high-throughput method, complemented by the Matano-Kirkaldy approach to determine diffusion coefficients at diffusion couple intersections. The results from both methods demonstrated strong agreement. Based on accurate thermodynamic descriptions and diffusion coefficients, the kinetic parameters of the Ti-Fe-Mo sub-binary systems were re-evaluated. Using HitDIC software in conjunction with compositional distance profiles, the atomic mobility database for this system was ultimately established. Additionally, the frequency factor and activation energy, vary with composition, can be derived using the Arrhenius equation.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102829"},"PeriodicalIF":1.9,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829649","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 : 2025-04-06DOI: 10.1016/j.calphad.2025.102827
Yuwei Ning , Fali Liu , Xiaoma Tao , Guanglong Xu , Hongmei Chen , Yifang Ouyang , Yong Du
In this work, a combination of diffusion couple technique and nanoindentation were employed to investigate the diffusion behaviors and mechanical properties of Ti-Zr-Ta alloys annealed at 1373 K for 26 h. The experiments focused on Ti-rich body-centered cubic (BCC) Ti-Zr-Ta ternary alloys. Diffusion coefficients were determined using the Whittle-Green and generalized Hall methods, while nanoindentation was utilized to characterize Young's modulus and hardness of the alloys. The results indicate that the diffusion rate of Zr is considerably higher than that of Ta, and the diffusion rate of both elements exhibits a strong dependence on concentration. The mechanical testing results demonstrate a significant increase in the hardness and Young's modulus of the alloy as the Ta content increases. In contrast, the Zr content shows a relatively limited effect on hardness and Young's modulus. These results provide an essential reference for further optimization of the microstructure and mechanical properties of Ti-Zr-Ta alloys at elevated temperatures.
{"title":"Investigation of diffusivities and mechanical properties in BCC Ti rich Ti-Zr-Ta system","authors":"Yuwei Ning , Fali Liu , Xiaoma Tao , Guanglong Xu , Hongmei Chen , Yifang Ouyang , Yong Du","doi":"10.1016/j.calphad.2025.102827","DOIUrl":"10.1016/j.calphad.2025.102827","url":null,"abstract":"<div><div>In this work, a combination of diffusion couple technique and nanoindentation were employed to investigate the diffusion behaviors and mechanical properties of Ti-Zr-Ta alloys annealed at 1373 K for 26 h. The experiments focused on Ti-rich body-centered cubic (BCC) Ti-Zr-Ta ternary alloys. Diffusion coefficients were determined using the Whittle-Green and generalized Hall methods, while nanoindentation was utilized to characterize Young's modulus and hardness of the alloys. The results indicate that the diffusion rate of Zr is considerably higher than that of Ta, and the diffusion rate of both elements exhibits a strong dependence on concentration. The mechanical testing results demonstrate a significant increase in the hardness and Young's modulus of the alloy as the Ta content increases. In contrast, the Zr content shows a relatively limited effect on hardness and Young's modulus. These results provide an essential reference for further optimization of the microstructure and mechanical properties of Ti-Zr-Ta alloys at elevated temperatures.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143783489","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 : 2025-04-05DOI: 10.1016/j.calphad.2025.102824
V.P. Vassiliev , C.M. Stanley
In this work, two independent methods were used to describe the heat capacity of reference compounds with the wurtzite structure, as well as their isostructural analogs of fourth group elements in the solid state: 1) a semi-empirical method using a multiparameter function and 2) a method based on the density functional theory. In the first method, to describe a set of isostructural experimental data Cp(T) of substances in the solid state, a description of each individual phase was carried out in the first approximation, and then, after finding a set of its fitting parameters (X), a description of the entire set of data as an integral system, where the set of each individual fitting parameter was described by a polynomial equation of functions included in the multiparameter family with the best description of the set of all data. The parameters of unexplored substances were found by interpolation of the multiparameter function. The fitting parameters (X) are a function of the atomic number of the elements Si, Ge, Sn, Pb, and Fl or the half-sum of the atomic numbers of the binary phases AIIIBV: B, Al, Ga, Tl, and Nh with the element germanium having a characteristic point for the set of parameters (X) depending on the atomic number. For each substance, the parameters are found by minimizing the discrepancy between the theoretical dependence Cp(T) and the corresponding experimental data. According to the fine structure constant (α = 1/137) (or Sommerfeld constant), there are no other elements in this group. Therefore, the limiting heat capacity of the wurtzite phases is at element 114 (114Fl) and has a value of Cp = 30.5 ± 0.3 J · mol-at−1 · K−1.
The second method allows us to describe the heat capacities (Cp) for these materials using a new first-principles method based on the density functional theory. This method, called the Beyond Quasi-Harmonic method, includes all anharmonic vibrations - volume changes and phonon-phonon interactions. Our calculated values for III-V compounds with wurtzite and sphalerite structures show good agreement between the two methods.
This work also presents optimized thermodynamic properties, Gibb's energy, enthalpy and entropy of formations, as well as standard entropy and melting point of III-V nitrides, including nihonium nitride.
{"title":"Optimization of heat capacities of wurtzite phases as a single system and thermodynamic properties of nihonium nitride","authors":"V.P. Vassiliev , C.M. Stanley","doi":"10.1016/j.calphad.2025.102824","DOIUrl":"10.1016/j.calphad.2025.102824","url":null,"abstract":"<div><div>In this work, two independent methods were used to describe the heat capacity of reference compounds with the wurtzite structure, as well as their isostructural analogs of fourth group elements in the solid state: 1) a semi-empirical method using a multiparameter function and 2) a method based on the density functional theory. In the first method, to describe a set of isostructural experimental data <em>C</em><sub><em>p</em></sub><em>(T)</em> of substances in the solid state, a description of each individual phase was carried out in the first approximation, and then, after finding a set of its fitting parameters <em>(X)</em>, a description of the entire set of data as an integral system, where the set of each individual fitting parameter was described by a polynomial equation of functions included in the multiparameter family with the best description of the set of all data. The parameters of unexplored substances were found by interpolation of the multiparameter function. The fitting parameters <em>(X)</em> are a function of the atomic number of the elements Si, Ge, Sn, Pb, and Fl or the half-sum of the atomic numbers of the binary phases A<sup>III</sup>B<sup>V</sup>: B, Al, Ga, Tl, and Nh with the element germanium having a characteristic point for the set of parameters <em>(X)</em> depending on the atomic number. For each substance, the parameters are found by minimizing the discrepancy between the theoretical dependence <em>C</em><sub><em>p</em></sub><em>(T)</em> and the corresponding experimental data. According to the fine structure constant (α = 1/137) (or Sommerfeld constant), there are no other elements in this group. Therefore, the limiting heat capacity of the wurtzite phases is at element 114 (<sup>114</sup>Fl) and has a value of <em>C</em><sub><em>p</em></sub> = 30.5 ± 0.3 J · mol-at<sup>−1</sup> · K<sup>−1</sup>.</div><div>The second method allows us to describe the heat capacities (C<sub>p</sub>) for these materials using a new first-principles method based on the density functional theory. This method, called the Beyond Quasi-Harmonic method, includes all anharmonic vibrations - volume changes and phonon-phonon interactions. Our calculated values for III-V compounds with wurtzite and sphalerite structures show good agreement between the two methods.</div><div>This work also presents optimized thermodynamic properties, Gibb's energy, enthalpy and entropy of formations, as well as standard entropy and melting point of III-V nitrides, including nihonium nitride.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"89 ","pages":"Article 102824"},"PeriodicalIF":1.9,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776558","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 : 2025-03-26DOI: 10.1016/j.calphad.2025.102823
Baogang Liu , Yong Du , Lei Huang , Yafei Pan
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 Mo3Os 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 Mo3Os 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.
{"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}
Pub Date : 2025-03-24DOI: 10.1016/j.calphad.2025.102826
Wei Yang , Yiwei Wang , Shuhong Liu , Peisheng Wang , Wei Zhai
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 τ1, τ3, and τ4 were identified on the Fe-Dy side at 1073 K and 1173 K. The previously reported τ2 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.
{"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}
Pub Date : 2025-03-21DOI: 10.1016/j.calphad.2025.102822
Sinn-wen Chen , Yi-An Lee , Cheng-Hsi Ho , Jun Zhu , Hsin-Chieh Huang , Te-Wei Lin , Chuan Zhang
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.
Sn-Ag-Bi-Cu及其组成体系是重要的材料体系，尤其适用于电子焊接。尽管这些合金已经引起了工业应用的极大兴趣，并且已经成为各种calphhad研究的主题，但令人惊讶的是，在相变温度方面，计算结果和实验确定的结果之间存在显着偏差。为了解决这一问题，在富锡侧制备了Sn-Ag、Sn-Bi、Sn-Cu、Sn-Ag- bi、Sn-Ag- cu、Sn-Bi- cu和Sn-Ag- bi - cu合金。同时进行了热分析和保温淬火实验测量，确定了它们的液相温度和不变反应温度。然后将实验确定的结果与Calphad计算结果进行比较，并用于改进Calphad模型中的热力学参数。修正数据库的计算结果与实验测量结果吻合较好。
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Pub Date : 2025-03-20DOI: 10.1016/j.calphad.2025.102825
Vikas Jindal, Shrikant Lele
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.
{"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}
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