Pub Date : 2026-03-01Epub Date: 2026-01-08DOI: 10.1016/j.calphad.2026.102917
I. Fartushna, D. Kapush, O. Koval, M. Bulanova
<div><div>The binary system Lu-Fe has been completely revised, while the binary Lu-Co and ternary Lu-Co-Fe systems have been studied for the first time by differential thermal analysis, X-ray diffraction, scanning electron microscopy and electron probe microanalysis techniques. The existence of four intermediate phases in the Lu-Fe system has been confirmed: Lu<sub>2</sub>Fe<sub>17</sub>, Lu<sub>6</sub>Fe<sub>23</sub>, LuFe<sub>3</sub> and LuFe<sub>2</sub>. All these phases are line compounds. Lu<sub>2</sub>Fe<sub>17</sub> and LuFe<sub>2</sub> melt congruently at 1370 and 1470 °C, respectively, while Lu<sub>6</sub>Fe<sub>23</sub> and LuFe<sub>3</sub> form by peritectic reactions at 1410 and 1440 °C, respectively. There are also three eutectic reactions in the Lu-Fe system. Six intermetallic phases are observed in the Lu-Co system: Lu<sub>3</sub>Co, Lu<sub>12</sub>Co<sub>7</sub>, Lu<sub>4</sub>Co<sub>3</sub>, LuCo<sub>2</sub>, LuCo<sub>3</sub>, and Lu<sub>2</sub>Co<sub>17</sub>. All these phases are line compounds. Lu<sub>12</sub>Co<sub>7</sub> was found by us for the first time. Its crystal structure was determined as the monoclinic Ho<sub>12</sub>Co<sub>7</sub>-type structure (<em>mP</em>38-<em>P</em>2<sub>1</sub>/<em>c</em>) with the lattice parameters <em>a = 8.2038(2), b = 11.0970(3), c = 10.8692(2) Å, β = 124.071(2).</em> It is thus isotypic to the other R<sub>12</sub>Co<sub>7</sub> binaries (R = Tb-Tm). The previously reported phase Lu<sub>2</sub>Co<sub>7</sub> was not detected. The compounds Lu<sub>12</sub>Co<sub>7</sub>, LuCo<sub>2</sub>, LuCo<sub>3</sub> and Lu<sub>2</sub>Co<sub>17</sub> melt congruently at 897, 1430, 1435, and 1355 °C, respectively. Lu<sub>3</sub>Co is formed by peritectic reaction at 975 °C; Lu<sub>4</sub>Co<sub>3</sub> is formed in solid state at 690 °C by peritectoid reaction LuCo<sub>2</sub> + Lu<sub>12</sub>Co<sub>7</sub> ⇄ Lu<sub>4</sub>Co<sub>3</sub>. In addition, five eutectic reactions have been well determined in the Lu-Co system. The complete liquidus and solidus projections, as well as the melting diagram of the Lu-Co-Fe system were constructed. Three continuous solid solutions Lu<sub>2</sub>(Co,Fe)<sub>17</sub>, Lu(Co,Fe)<sub>3</sub> and Lu(Co,Fe)<sub>2</sub> were found to exist at the solidus temperatures. The solubility of Co in Lu<sub>6</sub>Fe<sub>23</sub> is 47.3 at.%, while the solubility of Fe in Lu<sub>12</sub>Co<sub>7</sub> and Lu<sub>3</sub>Co is just 3.4 and 5.7 at.%, respectively. The solubility of Lu in the (αCo,γFe) phase is negligible. No ternary compounds were detected. Nine primary crystallization regions exist on the liquidus surface. These are: (δFe), (αCo,γFe), (Lu), Lu<sub>2</sub>(Co,Fe)<sub>17</sub>, Lu(Co,Fe)<sub>3</sub>, Lu(Co,Fe)<sub>2</sub>, Lu<sub>6</sub>Fe<sub>23</sub>, Lu<sub>12</sub>Co<sub>7</sub> and Lu<sub>3</sub>Co. The solidus projection shows three three-phase regions, (Lu) + Lu(Co,Fe)<sub>2</sub> + Lu<sub>3</sub>Co, Lu<sub>3</sub>Co + Lu(Co,Fe)<sub>2</sub> + Lu<sub>12</su
{"title":"An experimental investigation of the Lu-Fe, Lu-Co and Lu-Co-Fe phase diagrams","authors":"I. Fartushna, D. Kapush, O. Koval, M. Bulanova","doi":"10.1016/j.calphad.2026.102917","DOIUrl":"10.1016/j.calphad.2026.102917","url":null,"abstract":"<div><div>The binary system Lu-Fe has been completely revised, while the binary Lu-Co and ternary Lu-Co-Fe systems have been studied for the first time by differential thermal analysis, X-ray diffraction, scanning electron microscopy and electron probe microanalysis techniques. The existence of four intermediate phases in the Lu-Fe system has been confirmed: Lu<sub>2</sub>Fe<sub>17</sub>, Lu<sub>6</sub>Fe<sub>23</sub>, LuFe<sub>3</sub> and LuFe<sub>2</sub>. All these phases are line compounds. Lu<sub>2</sub>Fe<sub>17</sub> and LuFe<sub>2</sub> melt congruently at 1370 and 1470 °C, respectively, while Lu<sub>6</sub>Fe<sub>23</sub> and LuFe<sub>3</sub> form by peritectic reactions at 1410 and 1440 °C, respectively. There are also three eutectic reactions in the Lu-Fe system. Six intermetallic phases are observed in the Lu-Co system: Lu<sub>3</sub>Co, Lu<sub>12</sub>Co<sub>7</sub>, Lu<sub>4</sub>Co<sub>3</sub>, LuCo<sub>2</sub>, LuCo<sub>3</sub>, and Lu<sub>2</sub>Co<sub>17</sub>. All these phases are line compounds. Lu<sub>12</sub>Co<sub>7</sub> was found by us for the first time. Its crystal structure was determined as the monoclinic Ho<sub>12</sub>Co<sub>7</sub>-type structure (<em>mP</em>38-<em>P</em>2<sub>1</sub>/<em>c</em>) with the lattice parameters <em>a = 8.2038(2), b = 11.0970(3), c = 10.8692(2) Å, β = 124.071(2).</em> It is thus isotypic to the other R<sub>12</sub>Co<sub>7</sub> binaries (R = Tb-Tm). The previously reported phase Lu<sub>2</sub>Co<sub>7</sub> was not detected. The compounds Lu<sub>12</sub>Co<sub>7</sub>, LuCo<sub>2</sub>, LuCo<sub>3</sub> and Lu<sub>2</sub>Co<sub>17</sub> melt congruently at 897, 1430, 1435, and 1355 °C, respectively. Lu<sub>3</sub>Co is formed by peritectic reaction at 975 °C; Lu<sub>4</sub>Co<sub>3</sub> is formed in solid state at 690 °C by peritectoid reaction LuCo<sub>2</sub> + Lu<sub>12</sub>Co<sub>7</sub> ⇄ Lu<sub>4</sub>Co<sub>3</sub>. In addition, five eutectic reactions have been well determined in the Lu-Co system. The complete liquidus and solidus projections, as well as the melting diagram of the Lu-Co-Fe system were constructed. Three continuous solid solutions Lu<sub>2</sub>(Co,Fe)<sub>17</sub>, Lu(Co,Fe)<sub>3</sub> and Lu(Co,Fe)<sub>2</sub> were found to exist at the solidus temperatures. The solubility of Co in Lu<sub>6</sub>Fe<sub>23</sub> is 47.3 at.%, while the solubility of Fe in Lu<sub>12</sub>Co<sub>7</sub> and Lu<sub>3</sub>Co is just 3.4 and 5.7 at.%, respectively. The solubility of Lu in the (αCo,γFe) phase is negligible. No ternary compounds were detected. Nine primary crystallization regions exist on the liquidus surface. These are: (δFe), (αCo,γFe), (Lu), Lu<sub>2</sub>(Co,Fe)<sub>17</sub>, Lu(Co,Fe)<sub>3</sub>, Lu(Co,Fe)<sub>2</sub>, Lu<sub>6</sub>Fe<sub>23</sub>, Lu<sub>12</sub>Co<sub>7</sub> and Lu<sub>3</sub>Co. The solidus projection shows three three-phase regions, (Lu) + Lu(Co,Fe)<sub>2</sub> + Lu<sub>3</sub>Co, Lu<sub>3</sub>Co + Lu(Co,Fe)<sub>2</sub> + Lu<sub>12</su","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"92 ","pages":"Article 102917"},"PeriodicalIF":1.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145921452","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 : 2026-03-01Epub Date: 2025-12-13DOI: 10.1016/j.calphad.2025.102911
Yuanlu Zhou , Chenyang Zhou , Jiaxin Cui , Weibin Xie , Huiming Chen , Hang Wang
The microstructural and compositional analyses were carried out for 30 ternary equilibrated alloys to investigate the Al–Co–Ti phase equilibria at 1173 K. 14 three-phase equilibrium regions with 3 ternary compounds were confirmed at this temperature in the Al–Co–Ti system. Subsequently, the thermodynamic modeling of this system was conducted via the CALculation of PHAse Diagram (CALPHAD) method based on the experimental data from this study and the literature. The substitutional model was utilized for assessing the disordered solution phases Liquid, A1 (Al and γCo), A2 (βTi) and A3 (αCo and αTi). Both A1-L12 and A2-B2 order-disorder transitions were modeled simultaneously utilizing a single Gibbs energy function. The binary intermetallic phases Co2Ti(h), Co2Ti(c) and CoTi2 were described as (Al,Co,Ti)2(Al,Co,Ti)1, (Al,Co,Ti)2(Al,Co,Ti)1 and Co1(Al,Ti)2, while the others with the limited ternary solubility were treated as binary compounds. The ternary intermetallic phases τ1, τ2 and τ3 were modeled in the form of Al0.66Co0.05Ti0.29, (Al,Ti)16Ti6(Co,Ti)7 and (Al,Ti)1Co2(Al,Co,Ti)1. A set of self-consistent thermodynamic parameters for this system has been provided, and the majority of the experimental data can be reproduced well with the parameters.
{"title":"Experimental phase equilibria and thermodynamic modeling of the Al–Co–Ti ternary system","authors":"Yuanlu Zhou , Chenyang Zhou , Jiaxin Cui , Weibin Xie , Huiming Chen , Hang Wang","doi":"10.1016/j.calphad.2025.102911","DOIUrl":"10.1016/j.calphad.2025.102911","url":null,"abstract":"<div><div>The microstructural and compositional analyses were carried out for 30 ternary equilibrated alloys to investigate the Al–Co–Ti phase equilibria at 1173 K. 14 three-phase equilibrium regions with 3 ternary compounds were confirmed at this temperature in the Al–Co–Ti system. Subsequently, the thermodynamic modeling of this system was conducted via the CALculation of PHAse Diagram (CALPHAD) method based on the experimental data from this study and the literature. The substitutional model was utilized for assessing the disordered solution phases Liquid, A1 (Al and γCo), A2 (βTi) and A3 (αCo and αTi). Both A1-L1<sub>2</sub> and A2-B2 order-disorder transitions were modeled simultaneously utilizing a single Gibbs energy function. The binary intermetallic phases Co<sub>2</sub>Ti(h), Co<sub>2</sub>Ti(c) and CoTi<sub>2</sub> were described as (Al,Co,Ti)<sub>2</sub>(Al,Co,Ti)<sub>1</sub>, (Al,Co,Ti)<sub>2</sub>(Al,Co,Ti)<sub>1</sub> and Co<sub>1</sub>(Al,Ti)<sub>2</sub>, while the others with the limited ternary solubility were treated as binary compounds. The ternary intermetallic phases τ<sub>1</sub>, τ<sub>2</sub> and τ<sub>3</sub> were modeled in the form of Al<sub>0.66</sub>Co<sub>0.05</sub>Ti<sub>0.29</sub>, (Al,Ti)<sub>16</sub>Ti<sub>6</sub>(Co,Ti)<sub>7</sub> and (Al,Ti)<sub>1</sub>Co<sub>2</sub>(Al,Co,Ti)<sub>1</sub>. A set of self-consistent thermodynamic parameters for this system has been provided, and the majority of the experimental data can be reproduced well with the parameters.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"92 ","pages":"Article 102911"},"PeriodicalIF":1.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145735889","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 : 2026-03-01Epub Date: 2026-02-12DOI: 10.1016/j.calphad.2026.102925
Jiaxing Sun , Daomin Ye , Lingbing Meng , Zhenmin Du
The diffusion coefficient is crucial to control microstructure evolution; hence, an atomic mobility database for fcc phase is indispensable for the design of novel Co-based superalloys. Eleven diffusion couples of fcc phase in Co-rich Co–Fe–Ti alloys were prepared and annealed at 1473 K for 18 h (hours) and 1373 K for 48 h in this study. The interdiffusion coefficients of Co–Fe–Ti system were determined by means of the experimental concentration profiles using the Whittle-Green method in combination with electron probe microanalysis (EPMA). Subsequently, the atomic mobility parameters of fcc phase in Co–Fe–Ti system were systematically evaluated using 12 models within the framework of CALPHAD method, in which Model-11 was identified as the most reliable solution. The accuracy and reliability of the optimized parameters were further validated by comparing the experimental interdiffusion coefficients, concentration profiles, and diffusion paths with the corresponding calculated results.
{"title":"Diffusivities and atomic mobilities of fcc phase in Co-rich Co–Fe–Ti system: Experimental study and CALPHAD assessment","authors":"Jiaxing Sun , Daomin Ye , Lingbing Meng , Zhenmin Du","doi":"10.1016/j.calphad.2026.102925","DOIUrl":"10.1016/j.calphad.2026.102925","url":null,"abstract":"<div><div>The diffusion coefficient is crucial to control microstructure evolution; hence, an atomic mobility database for fcc phase is indispensable for the design of novel Co-based superalloys. Eleven diffusion couples of fcc phase in Co-rich Co–Fe–Ti alloys were prepared and annealed at 1473 K for 18 h (hours) and 1373 K for 48 h in this study. The interdiffusion coefficients of Co–Fe–Ti system were determined by means of the experimental concentration profiles using the Whittle-Green method in combination with electron probe microanalysis (EPMA). Subsequently, the atomic mobility parameters of fcc phase in Co–Fe–Ti system were systematically evaluated using 12 models within the framework of CALPHAD method, in which Model-11 was identified as the most reliable solution. The accuracy and reliability of the optimized parameters were further validated by comparing the experimental interdiffusion coefficients, concentration profiles, and diffusion paths with the corresponding calculated results.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"92 ","pages":"Article 102925"},"PeriodicalIF":1.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146184653","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 : 2026-03-01Epub Date: 2025-12-31DOI: 10.1016/j.calphad.2025.102915
Jiacheng Mei , Chengliang Qiu , Shuhong Liu, Yong Du
Phase equilibria of the Nd-Fe-Sm system were investigated by combining experiments with thermodynamic calculations. Using electron probe microanalysis and X-ray powder diffraction analysis, the isothermal sections at 673 and 873 K were investigated, and revealed similar phase equilibria, except for a minor difference in the solid solubility of the binary compounds. No ternary compounds were identified. There are three three-phase regions and four two-phase regions at 673 K and three three-phase regions and five two-phase regions at 873 K experimentally observed in this work. Due to the comparable atomic radii and electronegativities of Nd and Sm, the continuous solid solution Fe17(Nd,Sm)2 was formed between Fe17Sm2 and Fe17Nd2. The solubility of Nd in Fe2Sm and Fe3Sm, along with that of Sm in Fe17Nd5, was determined to be 14.09 at.%, 2.98 at.% and 12.30 at.% at 673 K, and 15.91 at.%, 3.90 at.% and 12.04 at.% 873 K, respectively. Thermodynamic optimization of the Nd-Sm and Nd-Fe-Sm systems were performed using the CALPHAD method based on the experimental data obtained from this work and literature. Based on the obtained thermodynamic parameters, the calculated isothermal sections, vertical sections and liquidus projection as well as the solidification path of the Nd-Fe-Sm alloys are in reasonable agreement with the experimental observation, indicating a self-consistent set of thermodynamic parameters of the system was presently obtained.
{"title":"Experimental and thermodynamic investigation of the Nd-Fe-Sm system","authors":"Jiacheng Mei , Chengliang Qiu , Shuhong Liu, Yong Du","doi":"10.1016/j.calphad.2025.102915","DOIUrl":"10.1016/j.calphad.2025.102915","url":null,"abstract":"<div><div>Phase equilibria of the Nd-Fe-Sm system were investigated by combining experiments with thermodynamic calculations. Using electron probe microanalysis and X-ray powder diffraction analysis, the isothermal sections at 673 and 873 K were investigated, and revealed similar phase equilibria, except for a minor difference in the solid solubility of the binary compounds. No ternary compounds were identified. There are three three-phase regions and four two-phase regions at 673 K and three three-phase regions and five two-phase regions at 873 K experimentally observed in this work. Due to the comparable atomic radii and electronegativities of Nd and Sm, the continuous solid solution Fe<sub>17</sub>(Nd,Sm)<sub>2</sub> was formed between Fe<sub>17</sub>Sm<sub>2</sub> and Fe<sub>17</sub>Nd<sub>2</sub>. The solubility of Nd in Fe<sub>2</sub>Sm and Fe<sub>3</sub>Sm, along with that of Sm in Fe<sub>17</sub>Nd<sub>5</sub>, was determined to be 14.09 at.%, 2.98 at.% and 12.30 at.% at 673 K, and 15.91 at.%, 3.90 at.% and 12.04 at.% 873 K, respectively. Thermodynamic optimization of the Nd-Sm and Nd-Fe-Sm systems were performed using the CALPHAD method based on the experimental data obtained from this work and literature. Based on the obtained thermodynamic parameters, the calculated isothermal sections, vertical sections and liquidus projection as well as the solidification path of the Nd-Fe-Sm alloys are in reasonable agreement with the experimental observation, indicating a self-consistent set of thermodynamic parameters of the system was presently obtained.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"92 ","pages":"Article 102915"},"PeriodicalIF":1.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880600","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 : 2025-12-01Epub Date: 2025-09-27DOI: 10.1016/j.calphad.2025.102872
Tobias Spitaler, Lorenz Romaner
The binary Ti-W system is reassessed with uncertainty quantification using the open source software ESPEI (Extensible, Self-optimizing Phase Equilibria Infrastructure). Mixing energy data at 0 K from ab-initio are used to supplement the phase diagram data measured at 1373 K and above. For the parameter optimization, Bayesian Inference with Markov Chain Monte Carlo is used as implemented in ESPEI, which allows for an inherent uncertainty quantification of the model parameters and a propagation of the uncertainty to the phase diagram, mixing enthalpy, and the position of invariant points. The new phase diagram shows a higher solubility of Ti in BCC_A2 W at low temperatures compared to older phase diagrams obtained from phase diagram data only.
{"title":"Assessed uncertainty in the Ti-W phase diagram combining experimental and ab-initio data","authors":"Tobias Spitaler, Lorenz Romaner","doi":"10.1016/j.calphad.2025.102872","DOIUrl":"10.1016/j.calphad.2025.102872","url":null,"abstract":"<div><div>The binary Ti-W system is reassessed with uncertainty quantification using the open source software ESPEI (Extensible, Self-optimizing Phase Equilibria Infrastructure). Mixing energy data at 0<!--> <!-->K from ab-initio are used to supplement the phase diagram data measured at 1373<!--> <!-->K and above. For the parameter optimization, Bayesian Inference with Markov Chain Monte Carlo is used as implemented in ESPEI, which allows for an inherent uncertainty quantification of the model parameters and a propagation of the uncertainty to the phase diagram, mixing enthalpy, and the position of invariant points. The new phase diagram shows a higher solubility of Ti in BCC_A2 W at low temperatures compared to older phase diagrams obtained from phase diagram data only.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"91 ","pages":"Article 102872"},"PeriodicalIF":1.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155691","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 development of advanced thermodynamic descriptions for pure elements is essential for accurate modelling of multicomponent systems. The third-generation Calphad descriptions incorporate physical effects such as electronic, vibrational and anharmonic contributions. In this study, we have developed a third-generation Calphad description for pure niobium (Nb). Thermodynamic properties of key phases — bcc, fcc, hcp and liquid — are presented for pure Nb. The vibrational contribution to the heat capacity of the solid phases has been modelled with the Einstein model, and the liquid phase has been modelled with the two-state model. In addition, the modelling of unstable phases has been extensively analysed. The traditional Calphad approach is evaluated and compared with the ab initio approach, which has a stronger theoretical basis. The 0 K energies of the unstable phases, fcc and hcp, have been selected from ab initio calculations using the inflection–detection method. Good agreement has been achieved with the selected experimental and ab initio data.
{"title":"A third-generation Calphad description of pure Nb","authors":"Felicia Larsson , Lorenzo Fenocchio , Qing Chen , Gabriele Cacciamani , Malin Selleby","doi":"10.1016/j.calphad.2025.102894","DOIUrl":"10.1016/j.calphad.2025.102894","url":null,"abstract":"<div><div>The development of advanced thermodynamic descriptions for pure elements is essential for accurate modelling of multicomponent systems. The third-generation Calphad descriptions incorporate physical effects such as electronic, vibrational and anharmonic contributions. In this study, we have developed a third-generation Calphad description for pure niobium (Nb). Thermodynamic properties of key phases — bcc, fcc, hcp and liquid — are presented for pure Nb. The vibrational contribution to the heat capacity of the solid phases has been modelled with the Einstein model, and the liquid phase has been modelled with the two-state model. In addition, the modelling of unstable phases has been extensively analysed. The traditional Calphad approach is evaluated and compared with the ab initio approach, which has a stronger theoretical basis. The 0 K energies of the unstable phases, fcc and hcp, have been selected from ab initio calculations using the inflection–detection method. Good agreement has been achieved with the selected experimental and ab initio data.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"91 ","pages":"Article 102894"},"PeriodicalIF":1.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145568519","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 : 2025-12-01Epub Date: 2025-09-13DOI: 10.1016/j.calphad.2025.102881
Daiman Zhu , Xiaohan Liu , Nele Moelans
A thermodynamic description of the Al-Cd-Mg ternary system has been developed using the CALPHAD (CALculation of PHAse Diagrams) approach, based on critical assessment of the three constituent binary systems: Al-Cd, Al-Mg, and Cd-Mg, and considering available experimental data and information on phase equilibria, crystallography, and constitutional information from literature. The solution phases, liquid, Hcp_A3 and Fcc_A1, are modeled using the Redlich-Kister formalism. Ternary solubilities of the binary phases Al3Mg2, Al12Mg17, Al30Mg23 and of the binary ordered phases, Cd3Mg, CdMg and CdMg3, are included. Comparisons between calculated results and experimental data for the liquidus projection and two isothermal sections demonstrate good agreement, confirming that the proposed thermodynamic model reliably reproduces the phase equilibria of the Al-Cd-Mg system. A consistent set of thermodynamic parameters has thus been obtained for application in computation assisted Al-Cd-Mg alloy design.
{"title":"Thermodynamic description of aluminum -cadmium-magnesium system","authors":"Daiman Zhu , Xiaohan Liu , Nele Moelans","doi":"10.1016/j.calphad.2025.102881","DOIUrl":"10.1016/j.calphad.2025.102881","url":null,"abstract":"<div><div>A thermodynamic description of the Al-Cd-Mg ternary system has been developed using the CALPHAD (CALculation of PHAse Diagrams) approach, based on critical assessment of the three constituent binary systems: Al-Cd, Al-Mg, and Cd-Mg, and considering available experimental data and information on phase equilibria, crystallography, and constitutional information from literature. The solution phases, liquid, Hcp_A3 and Fcc_A1, are modeled using the Redlich-Kister formalism. Ternary solubilities of the binary phases Al<sub>3</sub>Mg<sub>2</sub>, Al<sub>12</sub>Mg<sub>17</sub>, Al<sub>30</sub>Mg<sub>23</sub> and of the binary ordered phases, Cd<sub>3</sub>Mg, CdMg and CdMg<sub>3</sub>, are included. Comparisons between calculated results and experimental data for the liquidus projection and two isothermal sections demonstrate good agreement, confirming that the proposed thermodynamic model reliably reproduces the phase equilibria of the Al-Cd-Mg system. A consistent set of thermodynamic parameters has thus been obtained for application in computation assisted Al-Cd-Mg alloy design.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"91 ","pages":"Article 102881"},"PeriodicalIF":1.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046915","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 : 2025-12-01Epub Date: 2025-10-27DOI: 10.1016/j.calphad.2025.102891
Z.Q. Wang , C.B. Li , L.D. Ye , J.F. Wu , Z.X. Deng , K.G. Wang , L.B. Liu , L.G. Zhang
Due to the volatile nature of Mn during smelting, the refractory metal of Zr, and the greatest practical significance of the Al-rich corner in the Al-Zr-Mn system, this work determined the Al-rich corner isothermal sections of the Al-Zr-Mn system at 673 K and 873 K using the equilibrium alloy method. The maximum solid solubility of Zr in Al8Mn5 was established. A new ternary compound Al9Zr3Mn was experimentally identified and designated as the τ phase. Based on the available experimental data, a thermodynamic optimization was conducted on the Al-Zr-Mn ternary system: the Al8Mn5 compound was described using the sublattice model of (Al, Zr)12(Mn)5(Al, Zr, Mn)9. This work ultimately established a new thermodynamic database for the Al-Zr-Mn system that exhibits high consistency with the experimental data.
{"title":"Experimental investigation and thermodynamic assessment of the Al-Zr-Mn system","authors":"Z.Q. Wang , C.B. Li , L.D. Ye , J.F. Wu , Z.X. Deng , K.G. Wang , L.B. Liu , L.G. Zhang","doi":"10.1016/j.calphad.2025.102891","DOIUrl":"10.1016/j.calphad.2025.102891","url":null,"abstract":"<div><div>Due to the volatile nature of Mn during smelting, the refractory metal of Zr, and the greatest practical significance of the Al-rich corner in the Al-Zr-Mn system, this work determined the Al-rich corner isothermal sections of the Al-Zr-Mn system at 673 K and 873 K using the equilibrium alloy method. The maximum solid solubility of Zr in Al<sub>8</sub>Mn<sub>5</sub> was established. A new ternary compound Al<sub>9</sub>Zr<sub>3</sub>Mn was experimentally identified and designated as the τ phase. Based on the available experimental data, a thermodynamic optimization was conducted on the Al-Zr-Mn ternary system: the Al<sub>8</sub>Mn<sub>5</sub> compound was described using the sublattice model of (Al, Zr)<sub>12</sub>(Mn)<sub>5</sub>(Al, Zr, Mn)<sub>9</sub>. This work ultimately established a new thermodynamic database for the Al-Zr-Mn system that exhibits high consistency with the experimental data.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"91 ","pages":"Article 102891"},"PeriodicalIF":1.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145412539","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 : 2025-12-01Epub Date: 2025-11-08DOI: 10.1016/j.calphad.2025.102893
Weiyin Huang , Wei Yang , Xiaozhong Huang , Zhi Li , Xinming Wang , Peisheng Wang , Shuhong Liu , Yong Du
Phase equilibria of the Fe-Dy-Y system are essential for developing Dy/Y substituted Nd-Fe-B permanent magnets. In this work, the isothermal phase diagrams at 973 K and 773 K of the system were investigated by electron probe microanalysis (EPMA) and X-ray diffraction (XRD). Given the exceptionally slow diffusion kinetics of rare earth elements, achieving thermodynamic equilibrium necessitated prolonged annealing times of up to 130 days at 773 K, as confirmed by microstructural evolution studies. Key findings include the absence of ternary compounds and the formation of continuous solid solutions across the Dy-Y join for all binary intermetallic phases, except the Fe17RE2 phase. The liquidus and solidus of selected alloys were analyzed by differential scanning calorimetry (DSC). The CALPHAD assessment of the Fe-Dy-Y system was performed, which is consistent with the experimental data.
{"title":"Experimental determination and thermodynamic assessment of the Fe-Dy-Y system","authors":"Weiyin Huang , Wei Yang , Xiaozhong Huang , Zhi Li , Xinming Wang , Peisheng Wang , Shuhong Liu , Yong Du","doi":"10.1016/j.calphad.2025.102893","DOIUrl":"10.1016/j.calphad.2025.102893","url":null,"abstract":"<div><div>Phase equilibria of the Fe-Dy-Y system are essential for developing Dy/Y substituted Nd-Fe-B permanent magnets. In this work, the isothermal phase diagrams at 973 K and 773 K of the system were investigated by electron probe microanalysis (EPMA) and X-ray diffraction (XRD). Given the exceptionally slow diffusion kinetics of rare earth elements, achieving thermodynamic equilibrium necessitated prolonged annealing times of up to 130 days at 773 K, as confirmed by microstructural evolution studies. Key findings include the absence of ternary compounds and the formation of continuous solid solutions across the Dy-Y join for all binary intermetallic phases, except the Fe<sub>17</sub>RE<sub>2</sub> phase. The liquidus and solidus of selected alloys were analyzed by differential scanning calorimetry (DSC). The CALPHAD assessment of the Fe-Dy-Y system was performed, which is consistent with the experimental data.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"91 ","pages":"Article 102893"},"PeriodicalIF":1.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145462610","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 : 2025-12-01Epub Date: 2025-09-15DOI: 10.1016/j.calphad.2025.102869
Hantong Chen , Qi-Jun Hong , Alexandra Navrotsky , Axel van de Walle
The CALPHAD (CALculation of PHAse Diagram) framework relies heavily on the availability of a well-defined free energy for all possible phases, including metastable and even mechanically unstable phases. However, for phases that exhibit mechanical instability, the determination of the free energy represents a challenge, both experimentally and computationally. This situation hinders the seamless integration of experimental and ab initio thermodynamic data. A newly developed method, named “inflection-detection”, provides a practical computational solution to this problem with a sound theoretical basis. Extending upon existing energy calculations at absolute zero, we provide further evidence of this method’s effectiveness by computing the temperature-dependent free energy references for 22 elemental structures involving mechanically unstable phases and showing that they are reasonably consistent with the (often wide) range of values determined in earlier experimental assessments. This suggests the feasibility of a reliable computation-based reference free energy standard for mechanically unstable pure elements.
{"title":"A computational free energy reference for mechanically unstable phases","authors":"Hantong Chen , Qi-Jun Hong , Alexandra Navrotsky , Axel van de Walle","doi":"10.1016/j.calphad.2025.102869","DOIUrl":"10.1016/j.calphad.2025.102869","url":null,"abstract":"<div><div>The CALPHAD (CALculation of PHAse Diagram) framework relies heavily on the availability of a well-defined free energy for all possible phases, including metastable and even mechanically unstable phases. However, for phases that exhibit mechanical instability, the determination of the free energy represents a challenge, both experimentally and computationally. This situation hinders the seamless integration of experimental and ab initio thermodynamic data. A newly developed method, named “inflection-detection”, provides a practical computational solution to this problem with a sound theoretical basis. Extending upon existing energy calculations at absolute zero, we provide further evidence of this method’s effectiveness by computing the temperature-dependent free energy references for 22 elemental structures involving mechanically unstable phases and showing that they are reasonably consistent with the (often wide) range of values determined in earlier experimental assessments. This suggests the feasibility of a reliable computation-based reference free energy standard for mechanically unstable pure elements.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"91 ","pages":"Article 102869"},"PeriodicalIF":1.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145060883","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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