Pub Date : 2026-01-21DOI: 10.1016/j.calphad.2026.102920
Haojie Li , Guanglong Xu , Fuwen Chen , Zhuo Wang , Jiheng Fang , Yuwen Cui , Aimin Zhang
We present a new Machine Learning (ML) scheme to build equilibrium phase boundaries of precious alloy systems via combining efficient sampling of the derivatives of thermochemistry properties and active learning iterations. We have taken full advantage of the domain-specific knowledge on thermodynamics of phase diagram that the thermochemistry properties of the system, such as chemical potential of the system and activity of particular component, etc., continuously changes with chemical compositions in a single-phase equilibrium region, however, the derivatives of the above thermochemistry properties with respect to chemical composition undergo abrupt changes at phase boundaries composition. We have employed the continuity of the thermochemistry derivatives as data features, reformulated them into restructured labels as inputs, utilized Support Vector Classification (SVC) as the optimal algorithm, and finally shaped a tentative ML model to estimate the phase boundaries on phase diagrams. The ML model has been optimized through parameter tuning based on Bayesian posterior distribution and active learning iterations. The uncertainties have been evaluated via confidential scores against the test dataset. The accuracy and the efficiency of the proposed ML method have been validated by reconstructing the Temperature-Composition (T-x) isopleth phase diagram of Pd-Pt binary and the compositional isothermal sections of Au-Ag-Ge ternary systems. The outstanding performance of the predictions underscores the effectiveness of integrating thermodynamic knowledge with ML techniques. It opens up a new way to determine phase boundaries directly based on the measurements of thermochemistry properties.
{"title":"Estimating phase boundaries using sampling and machine learning of derivatives of thermochemistry properties","authors":"Haojie Li , Guanglong Xu , Fuwen Chen , Zhuo Wang , Jiheng Fang , Yuwen Cui , Aimin Zhang","doi":"10.1016/j.calphad.2026.102920","DOIUrl":"10.1016/j.calphad.2026.102920","url":null,"abstract":"<div><div>We present a new Machine Learning (ML) scheme to build equilibrium phase boundaries of precious alloy systems via combining efficient sampling of the derivatives of thermochemistry properties and active learning iterations. We have taken full advantage of the domain-specific knowledge on thermodynamics of phase diagram that the thermochemistry properties of the system, such as chemical potential of the system and activity of particular component, etc., continuously changes with chemical compositions in a single-phase equilibrium region, however, the derivatives of the above thermochemistry properties with respect to chemical composition undergo abrupt changes at phase boundaries composition. We have employed the continuity of the thermochemistry derivatives as data features, reformulated them into restructured labels as inputs, utilized Support Vector Classification (SVC) as the optimal algorithm, and finally shaped a tentative ML model to estimate the phase boundaries on phase diagrams. The ML model has been optimized through parameter tuning based on Bayesian posterior distribution and active learning iterations. The uncertainties have been evaluated via confidential scores against the test dataset. The accuracy and the efficiency of the proposed ML method have been validated by reconstructing the Temperature-Composition (T-<em>x</em>) isopleth phase diagram of Pd-Pt binary and the compositional isothermal sections of Au-Ag-Ge ternary systems. The outstanding performance of the predictions underscores the effectiveness of integrating thermodynamic knowledge with ML techniques. It opens up a new way to determine phase boundaries directly based on the measurements of thermochemistry properties.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"92 ","pages":"Article 102920"},"PeriodicalIF":1.9,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034274","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 Mg-Sn-Y alloys have shown significant potential in the development of magnesium alloys with high strength and ductility at elevated temperatures. In this work, thermodynamic re-assessment of the Mg-Sn-Y system was performed within the framework of the CALPHAD method, incorporating new thermochemical and phase equilibrium data. The updated thermodynamic model includes improved phase descriptions for the Sn3Y5 and MgSnY phases, as well as the inclusion of a new ternary phase, MgSn2Y. Phase relations at 673 K were revisited at key points using long-term equilibrated alloys. First principles calculations based on density functional theory were used to estimate the formation enthalpies of stable and metastable end-member configurations of the phases MgSnY, MgSn2Y, and Sn3Y5. Phonon calculations based on the quasi-harmonic approximation were employed to estimate the finite-temperature thermodynamic properties, such as the heat capacity, of the ternary phases MgSnY and MgSn2Y. The estimated thermochemical and phase constitution information from the present study was combined with experimental data from the literature to obtain a self-consistent set of Gibbs energy parameters for the Mg-Sn-Y system. The Scheil solidification sequence obtained from the assessed database was compared with the experimentally verified cast alloys from the literature. The current thermodynamic model will facilitate the design of new lightweight, creep-resistant magnesium alloys for elevated temperature applications.
{"title":"Thermodynamic reassessment of Mg-Sn-Y system assisted by the first-principles calculations and key experiments","authors":"Rohit Shandley , Soumya Sridar , Appala Naidu Gandi , K.R. Ravi","doi":"10.1016/j.calphad.2026.102921","DOIUrl":"10.1016/j.calphad.2026.102921","url":null,"abstract":"<div><div>The Mg-Sn-Y alloys have shown significant potential in the development of magnesium alloys with high strength and ductility at elevated temperatures. In this work, thermodynamic re-assessment of the Mg-Sn-Y system was performed within the framework of the CALPHAD method, incorporating new thermochemical and phase equilibrium data. The updated thermodynamic model includes improved phase descriptions for the Sn<sub>3</sub>Y<sub>5</sub> and MgSnY phases, as well as the inclusion of a new ternary phase, MgSn<sub>2</sub>Y. Phase relations at 673 K were revisited at key points using long-term equilibrated alloys. First principles calculations based on density functional theory were used to estimate the formation enthalpies of stable and metastable end-member configurations of the phases MgSnY, MgSn<sub>2</sub>Y, and Sn<sub>3</sub>Y<sub>5</sub>. Phonon calculations based on the quasi-harmonic approximation were employed to estimate the finite-temperature thermodynamic properties, such as the heat capacity, of the ternary phases MgSnY and MgSn<sub>2</sub>Y. The estimated thermochemical and phase constitution information from the present study was combined with experimental data from the literature to obtain a self-consistent set of Gibbs energy parameters for the Mg-Sn-Y system. The Scheil solidification sequence obtained from the assessed database was compared with the experimentally verified cast alloys from the literature. The current thermodynamic model will facilitate the design of new lightweight, creep-resistant magnesium alloys for elevated temperature applications.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"92 ","pages":"Article 102921"},"PeriodicalIF":1.9,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145973245","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 : 2026-01-14DOI: 10.1016/j.calphad.2026.102918
Jingjing Zhou , Kun Yang , Weimin Chen , Qianxin Long
In the present work, eleven diffusion couples in the bcc single-phase region of Ti-rich Ti-Cr-Mo system were fabricated and measured after annealing at 1273 K, 1373 K and 1473 K for 25 h, 18 h and 7 h, respectively. Subsequently, novel diffusion models were employed within the pragmatic numerical inverse method to determine the atomic mobility interaction parameters. And then, the interdiffusion coefficients obtained by using Matano-Kirkaldy method and the experimentally measured composition profiles were used by comparing with the present interdiffusion coefficients and the model-predicted composition profiles, respectively, which further verified the validation of the present results. This work demonstrates that the pragmatic numerical inverse method combined with novel diffusion models is very effective for developing diffusion databank of multicomponent alloys.
{"title":"Interdiffusion coefficients and atomic mobilities of Ti-rich Ti-Cr-Mo system","authors":"Jingjing Zhou , Kun Yang , Weimin Chen , Qianxin Long","doi":"10.1016/j.calphad.2026.102918","DOIUrl":"10.1016/j.calphad.2026.102918","url":null,"abstract":"<div><div>In the present work, eleven diffusion couples in the bcc single-phase region of Ti-rich Ti-Cr-Mo system were fabricated and measured after annealing at 1273 K, 1373 K and 1473 K for 25 h, 18 h and 7 h, respectively. Subsequently, novel diffusion models were employed within the pragmatic numerical inverse method to determine the atomic mobility interaction parameters. And then, the interdiffusion coefficients obtained by using Matano-Kirkaldy method and the experimentally measured composition profiles were used by comparing with the present interdiffusion coefficients and the model-predicted composition profiles, respectively, which further verified the validation of the present results. This work demonstrates that the pragmatic numerical inverse method combined with novel diffusion models is very effective for developing diffusion databank of multicomponent alloys.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"92 ","pages":"Article 102918"},"PeriodicalIF":1.9,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145973092","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 : 2026-01-12DOI: 10.1016/j.calphad.2026.102919
Sang-Ho Oh, Byeong-Joo Lee
A thermodynamic assessment was conducted for the Al-Mo-Nb-Ti quaternary alloy system to enable the efficient design of refractory materials for high-temperature applications. A thermodynamic description of the Al-Mo-Nb ternary system was newly developed based on experimental isothermal sections and a liquidus projection. In combination with the thermodynamic descriptions of the Al-Mo-Ti and Al-Nb-Ti systems available in the literature, a self-consistent thermodynamic database of the Al-Mo-Nb-Ti quaternary system was constructed. The developed thermodynamic description reproduces the experimentally observed phase constitution and provides a reliable basis for future alloy design.
{"title":"Thermodynamic assessment of the Al-Mo-Nb ternary system for efficient design of Al-Mo-Nb-Ti alloys","authors":"Sang-Ho Oh, Byeong-Joo Lee","doi":"10.1016/j.calphad.2026.102919","DOIUrl":"10.1016/j.calphad.2026.102919","url":null,"abstract":"<div><div>A thermodynamic assessment was conducted for the Al-Mo-Nb-Ti quaternary alloy system to enable the efficient design of refractory materials for high-temperature applications. A thermodynamic description of the Al-Mo-Nb ternary system was newly developed based on experimental isothermal sections and a liquidus projection. In combination with the thermodynamic descriptions of the Al-Mo-Ti and Al-Nb-Ti systems available in the literature, a self-consistent thermodynamic database of the Al-Mo-Nb-Ti quaternary system was constructed. The developed thermodynamic description reproduces the experimentally observed phase constitution and provides a reliable basis for future alloy design.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"92 ","pages":"Article 102919"},"PeriodicalIF":1.9,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145973246","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 : 2026-01-08DOI: 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":"2026-01-08","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 : 2026-01-07DOI: 10.1016/j.calphad.2025.102914
Xin Wan, Wenxuan Dai, Hongyang Pan, Zhipeng Pi, Fan Zhang
Thermodynamic modeling of the Sm2O3-SiO2, Yb2O3-SiO2, and Lu2O3-SiO2 is part of a broader effort of developing thermodynamic databases for rare earth silicates systems, providing critical insights for designing environmental barrier coatings (EBCs) for gas turbine engines. This study aims to derive a set of self-consistent thermodynamic parameters for Sm2O3-SiO2, Yb2O3-SiO2, and Lu2O3-SiO2 systems. The ionic two-sublattice model was adopted to describe the liquid phase, and all binary phases were treated as stoichiometric compounds given their negligible solubility. The CALPHAD (CALculation of PHAse Diagram) method was employed to carry out thermodynamic optimization on these binary systems, with the aid of existing experimental phase diagram data and thermodynamic properties. By comprehensively comparing experimental results with our calculations, it can be found that the calculated phase diagrams and thermodynamic properties align well with existing experimental data. This confirms the reasonableness of our thermodynamic descriptions, which can further provide a reliable foundation for thermodynamic calculations in higher-order systems based on RE2O3-SiO2 systems.
{"title":"Thermodynamic modeling of phase diagrams in Sm2O3-SiO2, Yb2O3-SiO2 and Lu2O3-SiO2 systems","authors":"Xin Wan, Wenxuan Dai, Hongyang Pan, Zhipeng Pi, Fan Zhang","doi":"10.1016/j.calphad.2025.102914","DOIUrl":"10.1016/j.calphad.2025.102914","url":null,"abstract":"<div><div>Thermodynamic modeling of the Sm<sub>2</sub>O<sub>3</sub>-SiO<sub>2</sub>, Yb<sub>2</sub>O<sub>3</sub>-SiO<sub>2</sub>, and Lu<sub>2</sub>O<sub>3</sub>-SiO<sub>2</sub> is part of a broader effort of developing thermodynamic databases for rare earth silicates systems, providing critical insights for designing environmental barrier coatings (EBCs) for gas turbine engines. This study aims to derive a set of self-consistent thermodynamic parameters for Sm<sub>2</sub>O<sub>3</sub>-SiO<sub>2</sub>, Yb<sub>2</sub>O<sub>3</sub>-SiO<sub>2</sub>, and Lu<sub>2</sub>O<sub>3</sub>-SiO<sub>2</sub> systems. The ionic two-sublattice model was adopted to describe the liquid phase, and all binary phases were treated as stoichiometric compounds given their negligible solubility. The CALPHAD (CALculation of PHAse Diagram) method was employed to carry out thermodynamic optimization on these binary systems, with the aid of existing experimental phase diagram data and thermodynamic properties. By comprehensively comparing experimental results with our calculations, it can be found that the calculated phase diagrams and thermodynamic properties align well with existing experimental data. This confirms the reasonableness of our thermodynamic descriptions, which can further provide a reliable foundation for thermodynamic calculations in higher-order systems based on RE<sub>2</sub>O<sub>3</sub>-SiO<sub>2</sub> systems.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"92 ","pages":"Article 102914"},"PeriodicalIF":1.9,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145921634","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 : 2025-12-31DOI: 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":"2025-12-31","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 : 2025-12-29DOI: 10.1016/j.calphad.2025.102913
Zhe Yuan , Fali Liu , Hongyu Zhang , Yueyan Tian , Kaige Wang , Chenbo Li , Libin Liu , Ligang Zhang
The Ti–Zr–Si ternary system was experimentally investigated in the Ti–Zr-rich corner at 1073 K and 1273 K using scanning electron microscopy (SEM), X-ray diffraction (XRD), and electron probe microanalysis (EPMA). The existence of the ternary compound TiZrSi was confirmed. Meanwhile, the solid solubilities of Ti and Zr in Ti5Si3, Ti3Si, TiZrSi, Zr2Si and Zr3Si were also determined. A thermodynamic description of the Ti–Zr–Si system was established by combining the experimental data obtained in this work and from the literature, together with first-principles calculations of formation enthalpies reported previously. Four isothermal sections and one isopleth in the Ti–Zr-rich corner of the Ti–Zr–Si system were calculated, and the calculated results show good agreement with the experimental data.
{"title":"Experimental investigation and thermodynamic assessment of the ternary Ti–Zr–Si system","authors":"Zhe Yuan , Fali Liu , Hongyu Zhang , Yueyan Tian , Kaige Wang , Chenbo Li , Libin Liu , Ligang Zhang","doi":"10.1016/j.calphad.2025.102913","DOIUrl":"10.1016/j.calphad.2025.102913","url":null,"abstract":"<div><div>The Ti–Zr–Si ternary system was experimentally investigated in the Ti–Zr-rich corner at 1073 K and 1273 K using scanning electron microscopy (SEM), X-ray diffraction (XRD), and electron probe microanalysis (EPMA). The existence of the ternary compound TiZrSi was confirmed. Meanwhile, the solid solubilities of Ti and Zr in Ti<sub>5</sub>Si<sub>3</sub>, Ti<sub>3</sub>Si, TiZrSi, Zr<sub>2</sub>Si and Zr<sub>3</sub>Si were also determined. A thermodynamic description of the Ti–Zr–Si system was established by combining the experimental data obtained in this work and from the literature, together with first-principles calculations of formation enthalpies reported previously. Four isothermal sections and one isopleth in the Ti–Zr-rich corner of the Ti–Zr–Si system were calculated, and 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":"92 ","pages":"Article 102913"},"PeriodicalIF":1.9,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880601","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 : 2025-12-29DOI: 10.1016/j.calphad.2025.102912
Miao Liu , Rucheng Wang , Hang Su , Xinyue Li , Liwen Hu , Xuewei Lv , Yuntao Xin
High-purity Fe2VO4 samples were synthesized using a hydrothermal method, and their thermodynamic properties were systematically investigated through a combination of experimental measurements and theoretical calculations. The heat capacity of Fe2VO4 was determined by low-temperature calorimetry and drop calorimetry. Additionally, density functional theory (DFT) calculations highlighted a significant contribution of magnetic entropy to the overall heat capacity, leading to values that exceed the classical Dulong-Petit limit. Thermodynamic analyses clarified the preferential formation of Ca2V2O7 and Ca3V2O8 during vanadium oxidation roasting, and indicated that increasing oxygen pressure and alkali activity facilitates the dissolution of Fe2VO4. These results provide essential thermodynamic data that can guide the synthesis and metallurgical processing of Fe2VO4 for practical applications.
{"title":"Thermodynamic properties of spinel-structured Fe2VO4 and their implications for application processes","authors":"Miao Liu , Rucheng Wang , Hang Su , Xinyue Li , Liwen Hu , Xuewei Lv , Yuntao Xin","doi":"10.1016/j.calphad.2025.102912","DOIUrl":"10.1016/j.calphad.2025.102912","url":null,"abstract":"<div><div>High-purity Fe<sub>2</sub>VO<sub>4</sub> samples were synthesized using a hydrothermal method, and their thermodynamic properties were systematically investigated through a combination of experimental measurements and theoretical calculations. The heat capacity of Fe<sub>2</sub>VO<sub>4</sub> was determined by low-temperature calorimetry and drop calorimetry. Additionally, density functional theory (DFT) calculations highlighted a significant contribution of magnetic entropy to the overall heat capacity, leading to values that exceed the classical Dulong-Petit limit. Thermodynamic analyses clarified the preferential formation of Ca<sub>2</sub>V<sub>2</sub>O<sub>7</sub> and Ca<sub>3</sub>V<sub>2</sub>O<sub>8</sub> during vanadium oxidation roasting, and indicated that increasing oxygen pressure and alkali activity facilitates the dissolution of Fe<sub>2</sub>VO<sub>4</sub>. These results provide essential thermodynamic data that can guide the synthesis and metallurgical processing of Fe<sub>2</sub>VO<sub>4</sub> for practical applications.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"92 ","pages":"Article 102912"},"PeriodicalIF":1.9,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880746","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 : 2025-12-16DOI: 10.1016/j.calphad.2025.102909
Cong Zhang , Minsi Liao , Xi Li , Chong Chen , Shizhong Wei
The Fe-Al-Si alloy system is a material with excellent thermal management and thermoelectric properties, making it an ideal choice for automobile engine manufacturing materials and electronic packaging applications. In this work, the thermal conductivity of the Fe-Al-Si system was evaluated by means of the CALPHAD (CALculation of PHAse Diagrams) method. The thermal conductivity of the part related to elemental interactions in solid solutions was modeled using Redlich-Kister interaction parameters. In the case of alloys within a two-phase region, an interface thermal resistance parameter was incorporated into the model to address the impact of interfaces on heat transfer. The parameters of binary and ternary systems were evaluated to guarantee a high degree of consistency between the model and experimental results. This study is beneficial for forecasting the thermal conductivity of the Fe-Al-Si alloy system in industrial manufacturing and supplies necessary thermophysical properties for microstructure and processing simulations.
{"title":"Thermal conductivity modeling of the Si-rich region of Fe-Al-Si system by the CALPHAD method","authors":"Cong Zhang , Minsi Liao , Xi Li , Chong Chen , Shizhong Wei","doi":"10.1016/j.calphad.2025.102909","DOIUrl":"10.1016/j.calphad.2025.102909","url":null,"abstract":"<div><div>The Fe-Al-Si alloy system is a material with excellent thermal management and thermoelectric properties, making it an ideal choice for automobile engine manufacturing materials and electronic packaging applications. In this work, the thermal conductivity of the Fe-Al-Si system was evaluated by means of the CALPHAD (CALculation of PHAse Diagrams) method. The thermal conductivity of the part related to elemental interactions in solid solutions was modeled using Redlich-Kister interaction parameters. In the case of alloys within a two-phase region, an interface thermal resistance parameter was incorporated into the model to address the impact of interfaces on heat transfer. The parameters of binary and ternary systems were evaluated to guarantee a high degree of consistency between the model and experimental results. This study is beneficial for forecasting the thermal conductivity of the Fe-Al-Si alloy system in industrial manufacturing and supplies necessary thermophysical properties for microstructure and processing simulations.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":"92 ","pages":"Article 102909"},"PeriodicalIF":1.9,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145788120","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号