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Mass-Preserving Modeling of Diffusion in a Closed System
IF 1.5 4区 材料科学 Q4 CHEMISTRY, PHYSICAL Pub Date : 2025-02-01 DOI: 10.1007/s11669-025-01174-7
Dmitri V. Malakhov

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 vs. 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.

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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 Q4 CHEMISTRY, PHYSICAL Pub Date : 2025-01-08 DOI: 10.1007/s11669-024-01171-2
I. Fartushna, D. Kapush, I. Tikhonova, V. Kremenytskyi, M. Bulanova

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 Tm12Co7 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), Tm2(Co,Fe)17, Tm(Co,Fe)3, Tm(Co,Fe)2 at all studied temperatures. The Tm6Fe23 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 Tm3Co and Tm12Co7 compounds and (ii) the absence of TmCo5 compound. As a result, there are two three-phase regions at 1200 and 1000 °C.

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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 Q4 CHEMISTRY, PHYSICAL 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

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 YCo5 and YCu6 binary intermetallic compounds form the continuous solid solution phase Y(Co, Cu)5 because of having the same space groups. According to the measured phase compositions at 873 K, the solid solubilities of Co in fcc(Cu), YCu4, Y2Cu7 and YCu2 are 8.6, 1.7, 44.0 and 8.6 at.%, respectively, while those of Cu in fcc(Co), Y2Co17, Y2Co7, YCo3, YCo2, Y2Co3, Y6Co7, Y4Co3, Y8Co5 and Y3Co 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), YCu4, Y2Cu7 and YCu2 were measured to be 3.9, 2.5, 40.0 and 10.8 at.%, respectively, while those of Cu in fcc(Co), Y2Co17, Y2Co7, YCo3, YCo2, Y2Co3 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.

{"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 Q4 CHEMISTRY, PHYSICAL 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
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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 Q4 CHEMISTRY, PHYSICAL 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

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.

1970年,Hillert和Staffansson发表了一篇题为“化学计量相和离子熔体的规则溶液模型”的论文。这是子晶格模型的开始,它已成为计算热力学发展的关键组成部分。这种形式,现在通常被称为复合能量形式(CEF),已经被用来描述各种各样的相,这是由于需要准确描述涉及许多元素的广泛材料的热力学相稳定性。本文的目的是描述其形式,其各种参数的物理意义,以及如何使用实验和理论数据来评估它们。此外,本文还介绍了基于CEF的新发展,如有效键能形式,以及其他进一步发展的想法。
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引用次数: 0
Thermodynamic Assessment of the Mg–La–Nd System
IF 1.5 4区 材料科学 Q4 CHEMISTRY, PHYSICAL 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

Ternary Mg–La–Nd and constituent binary Mg–La and Mg–Nd systems were assessed after a critical review of the experimental data and ab initio data using the CALPHAD method. The enthalpies of formation of the end-member compounds of the Mg(La, Nd) and Mg3(La, Nd) phases were obtained by ab initio 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 Mg3Nd phases. Moreover, the metastable Mg12Nd 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.

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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 Q4 CHEMISTRY, PHYSICAL Pub Date : 2024-12-02 DOI: 10.1007/s11669-024-01160-5
Ales Kroupa, Ondrej Zobac, Adela Zemanova, Klaus W. Richter

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.

本文基于最近的实验研究对Al-Cu-Si进行了理论评估(Riani et al. in intermetallic, 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和Richter KW .合金与复合材料,2012;Hallstedt et al. in CALPHAD, 53:25-38, 2016;[J] .地球科学进展(英文版),2016(5):532 - 533。对Cu-Si体系的重新评估也在本工作的范围内进行,因为实验数据表明,在Cu-Si二元体系中,Al在所有金属间相中都具有合理的溶解度,并且以前对Cu-Si二元体系进行评估时使用的化学计量模型并不完全适合扩展到三元体系。对Cu-Si体系的重新评价与前人的工作达成了很好的一致性,并在对三元体系的评价中获得了新的原创性结果。模拟了Si在高温下在β(bcc)相中的高溶解度,以解释600 ~ 800℃富cu角的实验不一致,并通过实验证实了这一假设。理论模型较好地再现了实验Al-Cu-Si相图的所有主要特征。
{"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 Q4 CHEMISTRY, PHYSICAL Pub Date : 2024-11-29 DOI: 10.1007/s11669-024-01165-0
Liangyan Hao, Sedigheh Bigdeli, Wei Xiong

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 (γMn,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.

低温下准确的热力学预测是固体物理和材料科学中的一个重大挑战。为了解决这个问题,第三代calphhad(相图计算)模型正在开发中,它可以基于物理预测热力学性质,温度降至零开尔文。此外,为了提高整个成分范围内磁转变温度和磁矩的建模精度,提出了改进的calphhad磁模型Inden-Hillert-Xiong (IHX)模型。先前基于第二代calphl的Mn-Ni体系的评估在再现(γMn,Ni)相的磁性方面遇到了限制,特别是由于富镍侧的铁磁行为和富锰侧的反铁磁行为的对比。在第三代一元描述和calphhad模型的基础上,对Mn-Ni体系进行了重新优化。为了描述结构特征,首次用四亚晶格模型描述了有序fcc相和bcc相。所得的热力学参数对Mn-Ni体系的相图和热化学性质的预测结果令人满意。
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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 Q4 CHEMISTRY, PHYSICAL Pub Date : 2024-11-26 DOI: 10.1007/s11669-024-01166-z
Zhangting He, Qing Chen, Malin Selleby

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.

本文概述了迄今为止我们用于第三代calphhad元素描述的模型。它既包括稳定的和亚稳定的固相,也包括液相。详细讨论了关键元素Al, C, Cr, Co, Fe, Ga, Ni和W的热力学描述的“演变”,并在必要时进行了新的评估。为了支持未来的工作,我们提供了实用的指导方针,包括优化各种参数的建议起始值。还包括对元素的全面热力学描述,以促进进一步的建模工作。
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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 Q4 CHEMISTRY, PHYSICAL Pub Date : 2024-11-15 DOI: 10.1007/s11669-024-01161-4
L. Fenocchio, S. Gambaro, G. Cacciamani

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.

尽管Al和Ta作为Co基和ni基合金的合金元素很重要,但对Al-Co-Ta和Al- ni -Ta体系相平衡的研究还很有限。此外,由于这些系统的特殊实验挑战,可用的数据是稀疏的,有时不一致。在此基础上,对它们的相平衡进行全面和批判性的评价,对进一步的实验和计算研究是有用的。在这个框架内,Al-Co-Ta和Al-Ni-Ta三元体系和各自的二元子系统在这里进行了严格的评估。分析了所有可用的文献调查结果,并提出了一套自一致的图表和表格,报告了晶体结构数据,液相线投影,等温切片等。
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引用次数: 0
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Journal of Phase Equilibria and Diffusion
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