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Metals
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Thermodynamic Assessment of Alloy Systems
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Thermodynamic Assessment of Alloy Systems

A special issue of Metals (ISSN 2075-4701). This special issue belongs to the section "Computation and Simulation on Metals".

Deadline for manuscript submissions: 25 May 2025 | Viewed by 6208

Special Issue Editors

Prof. Dr. Weibin Zhang

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Guest Editor
Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China
Interests: phase diagram; CALPHAD approach; hard materials
Prof. Dr. Yuan Yuan

E-Mail Website
Guest Editor
National Engineering Research Center for Magnesium Alloys, College of Materials Science and Engineering, Chongqing University, Chongqing 400000, China
Interests: phase diagram; CALPHAD approach; light alloys
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Knowledge surrounding phase diagrams and phase equilibria plays a crucial role in the development, manufacture, and processing of materials. The measurement of phase diagrams is generally time consuming and expensive, with the establishment of complex phase diagrams of real multicomponent and multiphase materials for practical applications proving difficult. The CALPHAD (calculation of phase diagram) approach provides a strategy for the development of highly reliable thermodynamic databases for the assessment of binary and ternary subsystems, which in turn allows for the prediction of phase diagrams and thermodynamic properties for multicomponent systems corresponding to real materials. In the last few decades, numerous scientists have dedicated their time to assessing various kinds of systems, establishing series of thermodynamic databases, and providing guidance for various complex materials, such as steels, superalloys, Al alloys, Mg alloys, cemented carbides, etc. Moreover, outputs from thermodynamic calculations serve as inputs for diffusion, phase-field, and other multiscale simulations. Until now, CALPHAD databases have been well established; however, they require continuous revision. With the development of novel materials and processes, there is a constantly increasing demand for accurate thermodynamic databases in the academic and engineering communities. Therefore, more systems should be assessed or reassessed based on novel theoretical and experimental data to improve these databases.

This Special Issue aims to present the results of scientific and experimental investigations concerning, for example, phase equilibria and diagrams, theoretical calculations of thermodynamic properties, thermodynamic assessments of metals and alloys, as well as applications of thermodynamic calculations.

Prof. Dr. Weibin Zhang
Prof. Dr. Yuan Yuan
Guest Editors

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Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Metals is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • metals and alloys
  • phase equilibria
  • phase diagram
  • thermodynamic assessment
  • CALPHAD

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Published Papers (5 papers)

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Research

23 pages, 8405 KiB  
Article
The Concept of the Estimation of Phase Diagrams (An Optimised Set of Simplified Equations to Estimate Equilibrium Liquidus and Solidus Temperatures, Partition Ratios, and Liquidus Slopes for Quick Access to Equilibrium Data in Solidification Software) Part I: Binary Equilibrium Phase Diagrams
by Gergely Kőrösy, András Roósz and Tamás Mende
Metals 2024, 14(11), 1266; https://doi.org/10.3390/met14111266 - 7 Nov 2024
Viewed by 483
Abstract
This paper presents equations derived from thermodynamic equations for calculating the liquidus and solidus temperatures, the liquidus slope, and the partition ratio for solidification simulations. The constants of these equations can be easily determined from measurement data obtained by digitalisation from known diagrams [...] Read more.
This paper presents equations derived from thermodynamic equations for calculating the liquidus and solidus temperatures, the liquidus slope, and the partition ratio for solidification simulations. The constants of these equations can be easily determined from measurement data obtained by digitalisation from known diagrams or can be calculated using a CALPHAD-based software. ESTPHAD has a hierarchical system; the developed functions of the binary systems are used in the calculation of the functions of the ternary systems, the functions of the ternary systems in the calculation of the function of quaternary systems, and so on. The developed method is demonstrated by processing the liquidus and solidus of Si–Ge isomorphous and Al–Mg and Al–Si eutectic equilibrium phase diagrams. The use of this method for calculating the functions of ternary systems will be shown in Part II. The advantages of this method are that the equations are simple, can be determined very quickly, and can be built into the simulation software very easily. The most significant advantage is that the calculation time is shorter by some order of magnitude than that of a CALPHAD-type calculation. Full article
(This article belongs to the Special Issue Thermodynamic Assessment of Alloy Systems)
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15 pages, 10818 KiB  
Article
Experimental Investigation of Phase Equilibria in the Ti-Cr-V System at 1000–1200 °C
by Shiyu Fu, Jingjing Wang and Xiao-Gang Lu
Metals 2024, 14(5), 498; https://doi.org/10.3390/met14050498 - 25 Apr 2024
Viewed by 1448
Abstract
Ti-Cr-V-based alloys have been utilized across various domains, including aerospace structural and functional materials and hydrogen storage materials. Investigating the phase relations in the Ti-Cr-V system is significant in supporting the material design for these applications. In the present work, the isothermal sections [...] Read more.
Ti-Cr-V-based alloys have been utilized across various domains, including aerospace structural and functional materials and hydrogen storage materials. Investigating the phase relations in the Ti-Cr-V system is significant in supporting the material design for these applications. In the present work, the isothermal sections at 1000, 1100, and 1200 °C for the Ti-Cr-V system were precisely determined through a systematic investigation using scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), and X-ray diffraction (XRD). The phase region of Cr2Ti was entirely elucidated for the first time. As the temperature decreased from 1200 to 1000 °C, the V solubility range of Cr2Ti increased from 5.3 wt.% to 10.0 wt.%, while the Ti solubility range essentially remained constant at approximately 31.0–33.9 wt.%. In addition, it was suggested that the stable structure of Cr2Ti was C36 at 1200 °C and C15 at 1000 and 1100 °C. The present work will support thermodynamic re-assessment research. Full article
(This article belongs to the Special Issue Thermodynamic Assessment of Alloy Systems)
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23 pages, 2916 KiB  
Article
Estimation of Activity and Molar Excess Gibbs Energy of Binary Liquid Alloys Pb-Sn, Al-Sn and In-Zn from the Partial Radial Distribution Function Simulated by Ab Initio Molecular Dynamics
by Tianao Zhang, Xiumin Chen, Yi Lu, Jiulong Hang and Dongping Tao
Metals 2024, 14(1), 102; https://doi.org/10.3390/met14010102 - 15 Jan 2024
Viewed by 1174
Abstract
For the present, it is difficult to obtain thermodynamic data for binary liquid alloys by experimental measurements. In this study, the molecular dynamics processes of the binary liquid alloys Pb50-Sn50, Al50-Sn50, and In50-Zn50 were simulated by using the ab initio molecular dynamics (AIMD) [...] Read more.
For the present, it is difficult to obtain thermodynamic data for binary liquid alloys by experimental measurements. In this study, the molecular dynamics processes of the binary liquid alloys Pb50-Sn50, Al50-Sn50, and In50-Zn50 were simulated by using the ab initio molecular dynamics (AIMD) principle, and their partial radial distribution functions (PRDF) were obtained at different simulation steps. Combined with the relevant binary parameters of the Molecular Interaction Volume Model (MIVM), Regular Solution Model (RSM), Wilson Model, and Non-Random Two-Liquid (NRTL) models. The integral terms containing the PRDF were computed using the graphical integration method to obtain the parameters of these models, thus estimating their activity and molar excess Gibbs energy. The total average relative deviations (ARD) of the activity and molar excess Gibbs energy estimates of the four models for the binary liquid alloys Pb50-Sn50, Al50-Sn50, and In50-Zn50 at full concentration when the PRDF is obtained by the symmetry method are MIVM: 21.59% and 59.35%; RSM: 21.63% and 60.27%; Wilson: 24.27% and 86.7%; NRTL: 23.9% and 83.24%. When the PRDF is obtained by the asymmetric method: MIVM: 22.86% and 68.08%; RSM: 32.84% and 68.66%; Wilson: 25.14% and 82.75%; NRTL: 24.49% and 85.74%. This indicates that the estimation performance of the MIVM model is superior to the other three models, and the symmetric method performs better than the asymmetric method. The present study also derives and verifies the feasibility of Sommer’s equation for estimating the molar excess Gibbs energy and activity of binary liquid alloy systems in the Miedema model by using different equations of enthalpy of mixing versus excess entropy given by Tanaka, Ding, and Sommer. The total ARD of Tanaka, Ding, and Sommer’s relational equations in the Miedema model for estimating the activities and molar excess Gibbs energies of the binary liquid alloys Pb-Sn, Al-Sn, and In-Zn are 3.07% and 8.92%, 6.09% and 17.1%, and 4.1% and 14.77%. The results indicate that the estimation performance of the Miedema model is superior to the other four models. Full article
(This article belongs to the Special Issue Thermodynamic Assessment of Alloy Systems)
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18 pages, 4119 KiB  
Article
Estimation of Activity and Molar Excess Gibbs Energy of Binary Liquid Alloys Al-Cu, Al-Ni, and Al-Fe from the Partial Radial Distribution Function Simulated by Ab Initio Molecular Dynamics
by Yi Lu, Xiumin Chen, Tianao Zhang, Jiulong Hang and Dongping Tao
Metals 2023, 13(12), 2011; https://doi.org/10.3390/met13122011 - 14 Dec 2023
Viewed by 1172
Abstract
To accurately and conveniently obtain the thermodynamic data of binary liquid alloys, a new method is proposed in this study. It combines ab initio molecular dynamics (AIMD) simulation with a thermodynamic model to estimate the activity and molar excess Gibbs energy of binary [...] Read more.
To accurately and conveniently obtain the thermodynamic data of binary liquid alloys, a new method is proposed in this study. It combines ab initio molecular dynamics (AIMD) simulation with a thermodynamic model to estimate the activity and molar excess Gibbs energy of binary liquid alloys. Additionally, two methods of grouping the partial radial distribution function (PRDF) of 5000 steps obtained by simulation are proposed for the first time. The PRDF of Al50Cu50, Al50Ni50, and Al50Fe50 is obtained by AIMD simulation. These PRDF are combined with four thermodynamic models to estimate the activity and molar excess Gibbs energy. Furthermore, the estimation results of the four models are compared with those of the Miedema model. The results show that when the first peak of the PRDF is obtained by the symmetric method, the average relative deviation (ARD) of the activity and molar excess Gibbs energy of the four models are, respectively: 28% and 32% for Molecular Interaction Volume Model (MIVM); 162% and 38% for Regular Solution Model (RSM); 508% and 65% for Wilson model; 562% and 67% for Non-Random Two-Liquid (NRTL). When the first peak of PRDF is obtained by non-symmetric method, the average ARD of the activity and molar excess Gibbs energy of the four models are, respectively: 64% and 20% for MIVM; 115% and 26% for RSM; 661% and 70% for Wilson; 727% and 72% for NRTL. In addition, the average ARD of the activity and molar excess Gibbs energy of the Miedema model are 113% and 33%. These data indicate that the estimation performance of the MIVM model is superior to the other four models, and the symmetric method performs better than the non-symmetric method. The grouping treatment of PRDF data effectively improves estimation performance. Full article
(This article belongs to the Special Issue Thermodynamic Assessment of Alloy Systems)
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15 pages, 3262 KiB  
Article
Effects of Alloying Elements on the Dissolution and Precipitation Behaviour of Fe in Mg-Al Alloy Melts
by Shiyu Jiang, Li Yang, Yuan Yuan, Ligang Zhang, Jun Wang, Tao Chen, Aitao Tang, Lifeng Ma and Fusheng Pan
Metals 2023, 13(8), 1466; https://doi.org/10.3390/met13081466 - 15 Aug 2023
Viewed by 1310
Abstract
It is necessary to strictly control the iron (Fe) impurity in Mg-Al alloys to guarantee good corrosion resistance and mechanical properties. In this work, the effects of alloying elements and temperatures on the solubilities of Fe in the Mg-Al-based alloy melts (Mg-rich liquid [...] Read more.
It is necessary to strictly control the iron (Fe) impurity in Mg-Al alloys to guarantee good corrosion resistance and mechanical properties. In this work, the effects of alloying elements and temperatures on the solubilities of Fe in the Mg-Al-based alloy melts (Mg-rich liquid phases) at 963–1033 K were studied by combining the in situ sampling method for the high precision solution values and the multiple regression numerical analysis method for the feature analysis. The solubilities of Fe in Mg-xAl (x = 1 and 3 wt.%) alloy melts could be significantly reduced by adding the yttrium (Y) or manganese (Mn) elements. However, the solubilities of Fe in Mg alloy melts were not in a monotonous relationship with the contents of the alloying elements in the Mg alloys. For the addition of Mn or Y, the lowest solubilities of Fe presented in the Mg-rich liquid phases were for the Mg-xAl alloys with the addition of 2 wt.% Mn or 1 wt.% Y, respectively. Additionally, the Fe-containing precipitations in the related systems were analysed and the Fe was mainly combined with Mn or Y and precipitated, which contributed to the removal of Fe from the Mg melt. The present study provides fundamental thermodynamic information regarding Mg-Al-Fe based systems and the design principle for the removal of Fe in Mg alloys. Full article
(This article belongs to the Special Issue Thermodynamic Assessment of Alloy Systems)
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