Journal of Phase Equilibria and Diffusion最新文献

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Mass-Preserving Modeling of Diffusion in a Closed System
IF 1.5 4区 材料科学
Journal of Phase Equilibria and Diffusion Pub Date : 2025-02-01 DOI: 10.1007/s11669-025-01174-7
Dmitri V. Malakhov
{"title":"Mass-Preserving Modeling of Diffusion in a Closed System","authors":"Dmitri V. Malakhov","doi":"10.1007/s11669-025-01174-7","DOIUrl":"10.1007/s11669-025-01174-7","url":null,"abstract":"<div><p>With zero-flux boundary conditions imposed at both ends, amounts of components in a system cannot change as a result of a unidimensional diffusion in it. With appropriately chosen time steps, the Crank-Nicolson scheme can dependably track a temporal evolution of an initial discrete concentration profile, but an invariance of an area below a continuously changing concentration <i>vs.</i> position curve is not guaranteed. In this work, a heuristic yet mathematically sound technique of incorporating a \"constant integral\" requirement into the Crank-Nicolson method is proposed.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"46 1","pages":"31 - 48"},"PeriodicalIF":1.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Phase Equilibria in the Tm-Co, Tm-Fe and Tm-Co-Fe Systems
IF 1.5 4区 材料科学
Journal of Phase Equilibria and Diffusion Pub Date : 2025-01-08 DOI: 10.1007/s11669-024-01171-2
I. Fartushna, D. Kapush, I. Tikhonova, V. Kremenytskyi, M. Bulanova
{"title":"Phase Equilibria in the Tm-Co, Tm-Fe and Tm-Co-Fe Systems","authors":"I. Fartushna,&nbsp;D. Kapush,&nbsp;I. Tikhonova,&nbsp;V. Kremenytskyi,&nbsp;M. Bulanova","doi":"10.1007/s11669-024-01171-2","DOIUrl":"10.1007/s11669-024-01171-2","url":null,"abstract":"<div><p>Phase diagrams of the ternary Tm-Co-Fe and boundary binary systems Tm-Co and Tm-Fe were constructed in the entire composition ranges using differential thermal analysis, powder x-ray diffraction, microscopic examination and electron probe microanalysis. The Tm-Co phase diagram was plotted for the first time. A new binary compound Tm<sub>12</sub>Co<sub>7</sub> was found and its crystal structure was established. The Tm-Fe phase diagram was revised: all invariant temperatures were updated, and disagreements with previously reported data were resolved. The Tm-Co-Fe system was studied for the first time. The results are given in the form of liquidus and solidus projections, isothermal sections at 1200 and 1000 °C, and Scheil reaction scheme. Ternary compounds are not formed in the system. Instead, the isostructural phases of Tm-Co and Tm-Fe systems form continuous solid solutions (αCo,γFe), Tm<sub>2</sub>(Co,Fe)<sub>17</sub>, Tm(Co,Fe)<sub>3</sub>, Tm(Co,Fe)<sub>2</sub> at all studied temperatures. The Tm<sub>6</sub>Fe<sub>23</sub> phase dissolves up to 45 at.% Co. The solubility of Fe in Tm-Co compounds is much lower. Five three-phase regions are present on the solidus projection, which form from one eutectic and four transition (U) type invariant reactions. The boundaries of the primary crystallization regions of phases, types and coordinates of invariant and monovariant equilibria are determined. Isothermal sections differ from the solidus projection by: (i) the presence of wide areas of melt, resulting in the absence of Tm<sub>3</sub>Co and Tm<sub>12</sub>Co<sub>7</sub> compounds and (ii) the absence of TmCo<sub>5</sub> compound. As a result, there are two three-phase regions at 1200 and 1000 °C.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"46 1","pages":"100 - 118"},"PeriodicalIF":1.5,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Experimental Investigation of Phase Equilibria in the Y-Co-Cu Ternary System
IF 1.5 4区 材料科学
Journal of Phase Equilibria and Diffusion Pub Date : 2024-12-28 DOI: 10.1007/s11669-024-01170-3
S. Y. Yang, X. Liu, Q. R. Yao, J. Wang, G. H. Rao, H. Y. Zhou
{"title":"Experimental Investigation of Phase Equilibria in the Y-Co-Cu Ternary System","authors":"S. Y. Yang,&nbsp;X. Liu,&nbsp;Q. R. Yao,&nbsp;J. Wang,&nbsp;G. H. Rao,&nbsp;H. Y. Zhou","doi":"10.1007/s11669-024-01170-3","DOIUrl":"10.1007/s11669-024-01170-3","url":null,"abstract":"<div><p>The phase equilibria of the Y-Co-Cu ternary system were investigated experimentally by scanning electron microscopy with energy dispersive spectroscopy and X-ray diffraction. The experimental results did not indicate any ternary intermetallic compounds and revealed that the YCo<sub>5</sub> and YCu<sub>6</sub> binary intermetallic compounds form the continuous solid solution phase Y(Co, Cu)<sub>5</sub> because of having the same space groups. According to the measured phase compositions at 873 K, the solid solubilities of Co in fcc(Cu), YCu<sub>4</sub>, Y<sub>2</sub>Cu<sub>7</sub> and YCu<sub>2</sub> are 8.6, 1.7, 44.0 and 8.6 at.%, respectively, while those of Cu in fcc(Co), Y<sub>2</sub>Co<sub>17</sub>, Y<sub>2</sub>Co<sub>7</sub>, YCo<sub>3</sub>, YCo<sub>2</sub>, Y<sub>2</sub>Co<sub>3</sub>, Y<sub>6</sub>Co<sub>7</sub>, Y<sub>4</sub>Co<sub>3</sub>, Y<sub>8</sub>Co<sub>5</sub> and Y<sub>3</sub>Co were determined to be 15.8, 6.4, 8.1, 13.5, 7.9, 1.2, 1.4, 3.9, 7.6 and 10.6 at.%, respectively. Furthermore, at 1073 K the solid solubilities of Co in fcc(Cu), YCu<sub>4</sub>, Y<sub>2</sub>Cu<sub>7</sub> and YCu<sub>2</sub> were measured to be 3.9, 2.5, 40.0 and 10.8 at.%, respectively, while those of Cu in fcc(Co), Y<sub>2</sub>Co<sub>17</sub>, Y<sub>2</sub>Co<sub>7</sub>, YCo<sub>3</sub>, YCo<sub>2</sub>, Y<sub>2</sub>Co<sub>3</sub> and YCo were determined to be 13.6, 9.4, 7.4, 13.7, 10.3, 2.3 and 31.4 at.%, respectively. Two isothermal sections of the Y-Co-Cu ternary system at 1073 K and 873 K were established finally.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"46 1","pages":"133 - 150"},"PeriodicalIF":1.5,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Special Issue in Memory of Mats Hillert 纪念马茨·希勒特特刊
IF 1.5 4区 材料科学
Journal of Phase Equilibria and Diffusion Pub Date : 2024-12-17 DOI: 10.1007/s11669-024-01168-x
John Ågren, Qing Chen, Greta Lindwall, Malin Selleby, Wei Xiong, Ursula R. Kattner
{"title":"Special Issue in Memory of Mats Hillert","authors":"John Ågren,&nbsp;Qing Chen,&nbsp;Greta Lindwall,&nbsp;Malin Selleby,&nbsp;Wei Xiong,&nbsp;Ursula R. Kattner","doi":"10.1007/s11669-024-01168-x","DOIUrl":"10.1007/s11669-024-01168-x","url":null,"abstract":"","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 6","pages":"929 - 933"},"PeriodicalIF":1.5,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Legacy of “The Regular Solution Model for Stoichiometric Phases and Ionic Melts” “化学计量相和离子熔体的规则溶液模型”的遗产
IF 1.5 4区 材料科学
Journal of Phase Equilibria and Diffusion Pub Date : 2024-12-14 DOI: 10.1007/s11669-024-01163-2
Bo Sundman, Nathalie Dupin, Marcel H. F. Sluiter, Suzana G. Fries, Christine Guéneau, Bengt Hallstedt, Ursula R. Kattner, Malin Selleby
{"title":"The Legacy of “The Regular Solution Model for Stoichiometric Phases and Ionic Melts”","authors":"Bo Sundman,&nbsp;Nathalie Dupin,&nbsp;Marcel H. F. Sluiter,&nbsp;Suzana G. Fries,&nbsp;Christine Guéneau,&nbsp;Bengt Hallstedt,&nbsp;Ursula R. Kattner,&nbsp;Malin Selleby","doi":"10.1007/s11669-024-01163-2","DOIUrl":"10.1007/s11669-024-01163-2","url":null,"abstract":"<div><p>In 1970, Hillert and Staffansson published a paper entitled “The Regular Solution Model for Stoichiometric Phases and Ionic Melts”. It was the beginning of the sublattice model that has been a key component in the development of Computational Thermodynamics. This formalism, now often called the Compound Energy Formalism (CEF), has been used to describe a great variety of phases driven by the need for accurate descriptions of thermodynamic phase stability in a wide range of materials involving many elements. The purpose of this paper is to describe the formalism, the physical meaning of its various parameters and the way they can be assessed using experimental and theoretical data. Furthermore, new developments derived from the CEF, such as the Effective Bond Energy Formalism, and other ideas for further development are presented.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 6","pages":"934 - 964"},"PeriodicalIF":1.5,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Thermodynamic Assessment of the Mg–La–Nd System
IF 1.5 4区 材料科学
Journal of Phase Equilibria and Diffusion Pub Date : 2024-12-04 DOI: 10.1007/s11669-024-01169-w
Tao Luo, Kai Zhu, Hongwei Xiong, Weisen Zheng, Jingya Wang, Xiao-Gang Lu
{"title":"Thermodynamic Assessment of the Mg–La–Nd System","authors":"Tao Luo,&nbsp;Kai Zhu,&nbsp;Hongwei Xiong,&nbsp;Weisen Zheng,&nbsp;Jingya Wang,&nbsp;Xiao-Gang Lu","doi":"10.1007/s11669-024-01169-w","DOIUrl":"10.1007/s11669-024-01169-w","url":null,"abstract":"<div><p>Ternary Mg–La–Nd and constituent binary Mg–La and Mg–Nd systems were assessed after a critical review of the experimental data and <i>ab initio</i> data using the CALPHAD method. The enthalpies of formation of the end-member compounds of the Mg(La, Nd) and Mg<sub>3</sub>(La, Nd) phases were obtained by <i>ab initio</i> calculations and then used to determine their model parameters. The binary Mg–La system was revised to maintain the consistency of the thermodynamic models, whereas the binary Mg–Nd system was reassessed to describe the homogeneity ranges of the hcp, dhcp, and Mg<sub>3</sub>Nd phases. Moreover, the metastable Mg<sub>12</sub>Nd phase was modeled to reproduce the phase constituents of the as-cast Mg–Nd alloys. Based on the updated binary descriptions, the ternary Mg–La–Nd system was assessed according to recent experimental data. Through a comprehensive comparison between the calculated and experimental phase equilibria and thermochemical property data, a reasonable agreement was achieved for the binary and ternary systems.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"46 1","pages":"60 - 75"},"PeriodicalIF":1.5,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
CALPHAD-Type Reassessment of Cu-Si and Full Assessment of the Al-Cu-Si Systems Cu-Si的calphad型再评估和Al-Cu-Si体系的全面评估
IF 1.5 4区 材料科学
Journal of Phase Equilibria and Diffusion Pub Date : 2024-12-02 DOI: 10.1007/s11669-024-01160-5
Ales Kroupa, Ondrej Zobac, Adela Zemanova, Klaus W. Richter
{"title":"CALPHAD-Type Reassessment of Cu-Si and Full Assessment of the Al-Cu-Si Systems","authors":"Ales Kroupa,&nbsp;Ondrej Zobac,&nbsp;Adela Zemanova,&nbsp;Klaus W. Richter","doi":"10.1007/s11669-024-01160-5","DOIUrl":"10.1007/s11669-024-01160-5","url":null,"abstract":"<div><p>The theoretical assessment of the Al-Cu-Si was carried out in this work based on recent experimental studies (Riani et al. in Intermetallics, 17:154-164, 2009; He et al. in CALPHAD, 33:200-210, 2009. http://dx.doi.org/10.1016/j.calphad.2008.07.015; Ponweiser N and Richter KW in J. of Alloys and Compd, 512:252-263, 2012; Hallstedt et al. in CALPHAD, 53:25-38, 2016; Zobac et al in J Mater Sci, 55:5322-15333, 2020). The reassessment of the Cu-Si system was also carried out in the scope of this work, as experimental data indicates reasonable solubility of Al in all intermetallic phases in the Cu-Si binary system, and the stoichiometric models used in previous assessments of the Cu-Si binary system are not fully suitable for the extension into the ternary system. Excellent agreement was reached for the reassessment of the Cu-Si system with previous works, and new original results were obtained during the assessment of the ternary system. The high solubility of Si in the β(bcc) phase at high temperatures was modelled to explain experimental inconsistencies in the Cu-rich corner between 600 and 800 °C, and this assumption was confirmed experimentally. All main features of the experimental Al-Cu-Si phase diagram were reproduced well by theoretical modelling.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 6","pages":"1206 - 1243"},"PeriodicalIF":1.5,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11669-024-01160-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
From Zero Kelvin Upwards: Thermodynamic Modeling of the Mn-Ni System with Third Generation Calphad Models 从零开尔文开始:第三代calphhad模型的Mn-Ni系统热力学建模
IF 1.5 4区 材料科学
Journal of Phase Equilibria and Diffusion Pub Date : 2024-11-29 DOI: 10.1007/s11669-024-01165-0
Liangyan Hao, Sedigheh Bigdeli, Wei Xiong
{"title":"From Zero Kelvin Upwards: Thermodynamic Modeling of the Mn-Ni System with Third Generation Calphad Models","authors":"Liangyan Hao,&nbsp;Sedigheh Bigdeli,&nbsp;Wei Xiong","doi":"10.1007/s11669-024-01165-0","DOIUrl":"10.1007/s11669-024-01165-0","url":null,"abstract":"<div><p>Accurate thermodynamic prediction at low temperatures presents a significant challenge in solid state physics and materials science. To address this, the third generation Calphad (CALculation of PHAse Diagrams) models are being developed, which enable a physics-based prediction of thermodynamic properties down to zero kelvin. Furthermore, the Inden-Hillert-Xiong (IHX) model, an improved Calphad magnetic model, has been proposed to enhance the modeling accuracy of magnetic transition temperatures and magnetic moments across the entire composition range. The previous assessments of the Mn-Ni system based on the second generation Calphad encountered limitations in reproducing the magnetic properties for the (<i>γ</i>Mn,Ni) phase, particularly due to the contrasting ferromagnetic behavior on the Ni-rich side and the antiferromagnetic behavior on the Mn-rich side. In this work, the Mn-Ni system was reoptimized on the basis of third generation unary descriptions and Calphad models. To represent the structural characteristics, both the ordered fcc and bcc phases were described by the four-sublattice model for the first time. The obtained thermodynamic parameters result in satisfactory predictions of the phase diagram and thermochemical properties for the Mn-Ni system.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 6","pages":"1182 - 1193"},"PeriodicalIF":1.5,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Third Generation Calphad for Key Elements 第三代卡尔帕德关键元件
IF 1.5 4区 材料科学
Journal of Phase Equilibria and Diffusion Pub Date : 2024-11-26 DOI: 10.1007/s11669-024-01166-z
Zhangting He, Qing Chen, Malin Selleby
{"title":"Third Generation Calphad for Key Elements","authors":"Zhangting He,&nbsp;Qing Chen,&nbsp;Malin Selleby","doi":"10.1007/s11669-024-01166-z","DOIUrl":"10.1007/s11669-024-01166-z","url":null,"abstract":"<div><p>This paper presents an overview of the models we used so far for the 3rd generation Calphad descriptions of the elements. It covers both stable and metastable solid phases, as well as the liquid phase. The “evolution\" of thermodynamic descriptions of the key elements Al, C, Cr, Co, Fe, Ga, Ni, and W is discussed in detail and new assessments are conducted when deemed necessary. To support future work, we provide practical guidelines, including suggested starting values for optimising various parameters. Comprehensive thermodynamic descriptions of the elements are also included to facilitate further modelling efforts.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 6","pages":"1163 - 1181"},"PeriodicalIF":1.5,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Critical Assessment of Phase Equilibria in the Al-Co-Ta and Al-Ni-Ta Systems Al-Co-Ta和Al-Ni-Ta体系相平衡的临界评价
IF 1.5 4区 材料科学
Journal of Phase Equilibria and Diffusion Pub Date : 2024-11-15 DOI: 10.1007/s11669-024-01161-4
L. Fenocchio, S. Gambaro, G. Cacciamani
{"title":"Critical Assessment of Phase Equilibria in the Al-Co-Ta and Al-Ni-Ta Systems","authors":"L. Fenocchio,&nbsp;S. Gambaro,&nbsp;G. Cacciamani","doi":"10.1007/s11669-024-01161-4","DOIUrl":"10.1007/s11669-024-01161-4","url":null,"abstract":"<div><p>Despite the importance of Al and Ta as alloying elements for Co- and Ni-base alloys, there has been limited research on the phase equilibria in the Al-Co-Ta and Al-Ni-Ta systems. Additionally, the available data are sparse and sometimes inconsistent due to the peculiar experimental challenges of these systems. Based on that, a comprehensive and critical evaluation of their phase equilibria is useful in view of further experimental and computational studies. Within this framework, the Al-Co-Ta and Al-Ni-Ta ternary systems and the respective binary subsystems are here critically assessed. All available literature investigations are analyzed and as a result, a set of self-consistent diagrams and tables are presented, reporting crystal structure data, liquidus projections, isothermal sections, etc.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 6","pages":"986 - 1010"},"PeriodicalIF":1.5,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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