{"title":"Exploring Multicomponent Phase Space to Discover New Materials","authors":"Brian Cantor","doi":"10.1007/s11669-024-01131-w","DOIUrl":"10.1007/s11669-024-01131-w","url":null,"abstract":"<div><p>Multicomponent phase space has been shown to consist of an enormous number of materials with different compositions, the vast majority of which have never been made or investigated, with great potential, therefore, for the discovery of exciting new materials with valuable properties. At the same time, however, the enormous size of multicomponent phase space makes it far from straightforward to identify suitable strategies for exploring the plethora of potential material compositions and difficult, therefore, to be successful in discovering desirable new materials. Unfortunately, all our knowhow and understanding has been developed for materials with relatively few components in relatively limited proportions, with most of our scientific theories relying essentially on linear assumptions of component dilution and independence that no longer apply in concentrated multicomponent materials. Trial and error, controlled substitution, parameterisation, thermodynamic modelling, atomistic modelling and machine learning techniques have all been employed as methods of exploring multicomponent phase space, with varying levels of success, but ultimately none of these techniques has proved capable of delivering consistent or guaranteed results. This paper provides an overview of the different techniques that have been used to explore multicomponent phase space, indicates their main advantages and disadvantages, and describes some of their successes and failures.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 3","pages":"188 - 218"},"PeriodicalIF":1.5,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11669-024-01131-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141613832","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}
{"title":"Phase Equilibria of the Er-Al-Zr Ternary System at 500 °C","authors":"Enlang Feng, Rui Zhang, Yanbin Kang, Fangyu Gan, Qingrong Yao, Zhao Lu, Zhimao Lu, Zongning Chen, Caimin Huang, Huaiying Zhou, Liying Luo","doi":"10.1007/s11669-024-01130-x","DOIUrl":"10.1007/s11669-024-01130-x","url":null,"abstract":"<div><p>The phase equilibria of the Er-Al-Zr ternary system at 500 °C were investigated using a combination of electron probe microanalyzer and x-ray diffraction. The microstructure and diffraction peaks were analyzed to determine the phases and compositions of Er-Al-Zr ternary system. Based on the experimental results, the isothermal phase diagram of the Er-Al-Zr ternary system consists of 14 three-phase equilibrium regions, 15 two-phase equilibrium regions, and 13 stable binary compounds, but no ternary compounds were detected. The solubility of Er in the Al<sub>2</sub>Zr, Al<sub>3</sub>Zr<sub>2</sub>, AlZr, Al<sub>3</sub>Zr<sub>4,</sub> Al<sub>2</sub>Zr<sub>3</sub> is 9.9, 5.3, 9.0, 12.4, 6.7 at.%, respectively. The present work could be important for alloy design of Al-based alloys and thermodynamic analysis of the Er-Al-Zr ternary system.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 4","pages":"772 - 778"},"PeriodicalIF":1.5,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576073","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}
{"title":"The 500 °C Isothermal Section of the Al-Fe-Pr Ternary System","authors":"R. Freccero, L. Arrighi, G. Cacciamani, P. Riani","doi":"10.1007/s11669-024-01117-8","DOIUrl":"10.1007/s11669-024-01117-8","url":null,"abstract":"<div><p>Phases and equilibria involved in the isothermal section at 500 °C of the ternary Al-Fe-Pr system have been here investigated in the whole composition range by means of X-ray diffraction, optical and scanning electron microscopy, and electron probe microanalysis. Phase equilibria are characterised by the formation of two binary solid solutions, Pr<sub>2</sub>(Fe<sub>x</sub>Al<sub>1−x</sub>)<sub>17</sub> with 0.34 ≤ <i>x</i> ≤ 1.00 (<i>hR</i>57–Th<sub>2</sub>Zn<sub>17</sub>) and Pr(Fe<sub>x</sub>Al<sub>1−x</sub>)<sub>2</sub> with 0 ≤ <i>x</i> ≤ 0.20 (<i>cF</i>24–Cu<sub>2</sub>Mg), and four ternary compounds, τ<sub>1</sub>-PrFe<sub>2</sub>Al<sub>10</sub> (<i>oS</i>52-YbFe<sub>2</sub>Al<sub>10</sub>), τ<sub>2</sub>-PrFe<sub>2</sub>Al<sub>8</sub> (<i>oP</i>44-CeFe<sub>2</sub>Al<sub>8</sub>), τ<sub>3</sub>-Pr(Fe<sub>x</sub>Al<sub>1−x</sub>)<sub>12</sub> with 0.28 ≤ <i>x</i> ≤ 0.44 (<i>tI</i>26-ThMn<sub>12</sub>) and τ<sub>4</sub>-Pr<sub>6</sub>(Fe<sub>x</sub>Al<sub>1−x</sub>)<sub>14</sub> with 0.63 ≤ <i>x</i> ≤ 0.81 (<i>tI</i>80-La<sub>6</sub>Co<sub>11</sub>Ga<sub>3</sub>), which have been confirmed. The solid solubility ranges of the binary and ternary compounds have been considered and trends of their lattice parameters studied. The complete isothermal section has been obtained and the general features of the section are discussed and compared with those of other ternary systems of light R (La, Ce, Pr, Nd, Sm) with Al and Fe.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 3","pages":"596 - 611"},"PeriodicalIF":1.5,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531729","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}
Zhi Liang, Ursula Kattner, Kamal Choudharry, Francesca Tavazza, Carelyn Campbell
{"title":"Thermodynamic Assessments of Ti-Al, Ti-Fe, and Ti-Al-Fe Systems with Four-Sublattice Description of Ordered Body-Centered Cubic Phase and Density Functional Theory Data","authors":"Zhi Liang, Ursula Kattner, Kamal Choudharry, Francesca Tavazza, Carelyn Campbell","doi":"10.1007/s11669-024-01124-9","DOIUrl":"10.1007/s11669-024-01124-9","url":null,"abstract":"<div><p>A thermodynamic description of the Ti-Al-Fe system was established with reassessed Ti-Al and Ti-Fe binary systems using density function theory (DFT) data. All stable and metastable end members of BCC_B2, BCC_D0<sub>3</sub>/B32, BCC_L2<sub>1</sub>, inverse BCC_L2<sub>1</sub>, Laves C14, D0<sub>19</sub>-Ti<sub>3</sub>Al, L1<sub>0</sub>-TiAl, Ti Al<sub>2</sub>, Ti<sub>3</sub>Al<sub>5</sub>, D0<sub>22</sub>-TiAl<sub>3</sub>, τ<sub>2</sub> and τ<sub>3</sub> in the Ti-Al, Ti-Fe and Ti-Al-Fe systems were energetically defined with available experimental data and DFT calculations, reaching reasonable consistency. The ternary description was used to successfully calculate the A2-B2-L2<sub>1</sub> transformation in Fe-rich corner and A2-B2 transformation in Ti-rich corner, allowing the design of Ti-rich and Fe-rich alloys in this system.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 3","pages":"732 - 756"},"PeriodicalIF":1.5,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11669-024-01124-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501503","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}
{"title":"Measurement of Diffusion Coefficients and Assessment of Atomic Mobilities in HCP Mg-Ag-Sn Alloys","authors":"Yang Yang, Lilong Zhu, Michele V. Manuel","doi":"10.1007/s11669-024-01114-x","DOIUrl":"10.1007/s11669-024-01114-x","url":null,"abstract":"<div><p>Reliable thermodynamic and kinetic databases are essential for designing and developing novel magnesium (Mg) alloys for elevated-temperature applications in the automotive and aerospace industries. This study investigated diffusion behaviors of HCP Mg-Ag-Sn alloys by four sets of three diffusion couples annealed at 450, 500, and 550 °C, respectively. Interdiffusion and impurity diffusion coefficients at the three annealing temperatures were extracted using the forward-simulation method. The determined diffusion coefficients, combined with prior results in the literature, were then used to assess atomic mobilities for the HCP phase of the Mg-Ag-Sn system. This assessment was conducted using the DICTRA and the TCMG5 thermodynamic database within the Thermo-Calc software. Comprehensive comparisons between calculated and experimental diffusion coefficients yielded an excellent agreement. The atomic mobilities were also further validated by appropriate predictions of concentration profiles and diffusion paths observed in independent diffusion couple experiments performed at 525 °C for 18 hrs. It has been found that the addition of Sn and Ag both increase the diffusivity of Ag in HCP Mg and Sn in HCP Mg in the stable temperature range of HCP Mg, respectively. This improved understanding of the kinetics in the Mg-Ag-Sn ternary system is essential for controlling diffusion-dependent properties such as coarsening and, therefore, the mechanical properties of Mg-Ag-Sn alloys at elevated temperatures.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 3","pages":"583 - 595"},"PeriodicalIF":1.5,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11669-024-01114-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141344538","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}
{"title":"Inter-property Correlation of Al2O3-CaO-MgO-SiO2 Quaternary Slag System in Blast Furnace Ironmaking","authors":"Sujan Hazra, Devi Dutta Biswajeet, Snehanshu Pal, Supratim Sengupta, Samik Nag, Seshadri Seetharaman","doi":"10.1007/s11669-024-01123-w","DOIUrl":"10.1007/s11669-024-01123-w","url":null,"abstract":"<div><p>Exploring the correlation between the density and the thermo-physical properties of the Al<sub>2</sub>O<sub>3</sub>-CaO-MgO-SiO<sub>2</sub> quaternary slag system is a subject of great interest in the domain of high alumina slag systems. This work attempts to establish correlations between (a) molar volume/density with enthalpy of mixing and (b) molar volume/density with slag viscosity, for the quaternary slag systems. The former is targeted based on existing models to determine the slag density and enthalpy of mixing first and then to develop machine-learning models which can suitably extrapolate the enthalpy of mixing as a function of slag composition, temperature and density. The volume shrinkage and the exothermic enthalpy of mixing between the slag constituent components are correlated in the current work. The later part would involve the conjunction of two hybrid machine-learning models, one for predicting slag viscosity as a function of slag compositions and temperature, and the other which predicts slag viscosity with the incorporation of slag density. The work will facilitate the establishment of two novel quantitative relationships that could provide better insights into the blast furnace quaternary slag systems.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 3","pages":"703 - 712"},"PeriodicalIF":1.5,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11669-024-01123-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141360614","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}
O. P. Berezniuk, Y. M. Kogut, L. D. Gulay, L. V. Piskach
{"title":"Phase Equilibria in the Ag2S–Sb2S3–SnS2 System and the Novel Quaternary Chalcogenide Ag11Sb3SnS12","authors":"O. P. Berezniuk, Y. M. Kogut, L. D. Gulay, L. V. Piskach","doi":"10.1007/s11669-024-01126-7","DOIUrl":"10.1007/s11669-024-01126-7","url":null,"abstract":"<div><p>Interactions of Ag and Sb(III) and Sn(IV) sulfides were investigated by x-ray diffraction, differential thermal analysis and microstructure analysis methods. The quaternary compound Ag<sub>11</sub>Sb<sub>3</sub>SnS<sub>12</sub> was found for the first time in the Ag<sub>2</sub>S-Sb<sub>2</sub>S<sub>3</sub>-SnS<sub>2</sub> system at 500 K (227 °C) at the intersection of AgSbS<sub>2</sub>-Ag<sub>8</sub>SnS<sub>6</sub> and Ag<sub>3</sub>SbS<sub>3</sub>-Ag<sub>2</sub>SnS<sub>3</sub>. The compound melts congruently at 920 K (647 °C) and has a polymorphous transition at 646 K (373 °C). The quasi-ternary system is characterized by solid solution ranges of the binary compounds Ag<sub>2</sub>S, Sb<sub>2</sub>S<sub>3</sub>, SnS<sub>2</sub>, ternary Ag<sub>3</sub>SbS<sub>3</sub>, AgSbS<sub>2</sub>, Ag<sub>8</sub>SnS<sub>6</sub>, Ag<sub>2</sub>SnS<sub>3</sub> and quaternary compound Ag<sub>11</sub>Sb<sub>3</sub>SnS<sub>12</sub>. The separation of the composition triangle into 10 single-phase, 18 two-phase, and 9 three-phase fields was established. Seven vertical sections were investigated of which five are quasi-binary (Ag<sub>3</sub>SbS<sub>3</sub>-Ag<sub>8</sub>SnS<sub>6</sub>, Ag<sub>3</sub>SbS<sub>3</sub>-Ag<sub>2</sub>SnS<sub>3</sub>, AgSbS<sub>2</sub>-Ag<sub>8</sub>SnS<sub>6</sub>, AgSbS<sub>2</sub>-Ag<sub>2</sub>SnS<sub>3</sub>, AgSbS<sub>2</sub>-SnS<sub>2</sub>). The AgSbS<sub>2</sub>-Ag<sub>4</sub>Sn<sub>3</sub>S<sub>8</sub> and AgSbS<sub>2</sub>-Sb<sub>2</sub>SnS<sub>5</sub> sections are non-quasi-binary due to peritectic formation of Ag<sub>4</sub>Sn<sub>3</sub>S<sub>8</sub> and Sb<sub>2</sub>SnS<sub>5</sub>. The liquidus surface projection of the Ag<sub>2</sub>S-Sb<sub>2</sub>S<sub>3</sub>-SnS<sub>2</sub> system consists of 10 fields of primary crystallization of the solid solutions α-Ag<sub>2</sub>S, β-Sb<sub>2</sub>S<sub>3</sub>, γ-SnS<sub>2</sub>, δ-Ag<sub>3</sub>SbS<sub>3</sub>, ε′-AgSbS<sub>2</sub>, ζ-Ag<sub>8</sub>SnS<sub>6</sub>, η-Ag<sub>2</sub>SnS<sub>3</sub>, σ-Ag<sub>11</sub>Sb<sub>3</sub>SnS<sub>12</sub> and compounds Ag<sub>4</sub>Sn<sub>3</sub>S<sub>8</sub> and Sb<sub>2</sub>SnS<sub>5</sub>. These are separated by curves of monovariant equilibria that converge at 9 ternary invariant points (7 eutectic (E<sub>1</sub>-E<sub>7</sub>) and 2 quasi-peritectic (U<sub>1</sub>, U<sub>2</sub>)).</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 3","pages":"723 - 731"},"PeriodicalIF":1.5,"publicationDate":"2024-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141367698","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}
{"title":"Thermodynamic Description of the Gadolinium-Cadmium Phase Diagram","authors":"Hassan Azza, Mustapha Ait Boukideur, Khadija Achgar, Mohamed Idbenali, Najim Selhaoui","doi":"10.1007/s11669-024-01127-6","DOIUrl":"10.1007/s11669-024-01127-6","url":null,"abstract":"<div><p>The thermodynamic optimization of the Gd-Cd binary system was carried out with the help of CALPHAD (CALculation of PHAse Diagram) method., GdCd<sub>3</sub>, Gd<sub>13</sub>Cd<sub>58</sub> and GdCd<sub>8</sub> have been treated as stoichiometric compounds while a solution model has been used for the description of the liquid, HCP_A3 (αGd), BCC_A2 (βGd) and HCP_A3 (Cd) phases. The intermetallic compounds GdCd,α-GdCd<sub>2</sub>, β-GdCd<sub>2</sub>, Gd<sub>11</sub>Cd<sub>45</sub> and GdCd<sub>6</sub>, which have homogeneity ranges, were treated by a two-sublattice model. The calculations based on the thermodynamic modeling are in a good agreement with the phase diagram data and experimental thermodynamic values.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 3","pages":"714 - 722"},"PeriodicalIF":1.5,"publicationDate":"2024-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141367804","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}
Margarida I. Sousa Henriques, André Silva, Ladislav Havela, António Pereira Gonçalves
{"title":"On the U-Fe-C Isothermal Section at 1100 °C","authors":"Margarida I. Sousa Henriques, André Silva, Ladislav Havela, António Pereira Gonçalves","doi":"10.1007/s11669-024-01122-x","DOIUrl":"10.1007/s11669-024-01122-x","url":null,"abstract":"<div><p>The energy crisis and climate change have promoted a growing interest in non-fossil sources, such as nuclear, with uranium carbides being seen as potential fuel candidates for Generation IV nuclear reactors. However, the need of accurate thermophysical data for the fuel and its compatibility with core materials during the extreme fission conditions is still an issue. Here a study of the ternary uranium-iron-carbon system performed at 1100 °C using powder x-ray diffraction and Scanning Electron Microscopy coupled with Energy Dispersive Spectrometry is presented. The U-Fe-C isothermal section is characterized by two ternary compounds, thirteen 3-phase regions and five 2-phase regions. UFeC<sub>2</sub> and ~ U<sub>11</sub>Fe<sub>12</sub>C<sub>18</sub> were confirmed to be present at 1100 °C and crystallize in structures related to the binary uranium carbides. UFeC<sub>2</sub> crystallizes in an original structure type, a distorted variant of the UCoC<sub>2</sub> structure, with space group <i>P</i>4/<i>n</i> and <i>a</i> = 3.503(5) Å and <i>c</i> = 7.405(5) Å lattice parameters. ~ U<sub>11</sub>Fe<sub>12</sub>C<sub>18,</sub> has a crystal structure related to the Th<sub>11</sub>Ru<sub>12</sub>C<sub>18</sub> structure-type (space group <i>I</i> <span>(overline{4 })</span> <i>3m</i>) with the lattice parameter <i>a</i> ≈ 10 Å. Furthermore, an island of a α-UC<sub>2</sub>-based phase with 32U:4Fe:64C composition was found in the 1100 °C isothermal section, indicating the inclusion of Fe in the α-UC<sub>2</sub> binary compound.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"45 3","pages":"696 - 702"},"PeriodicalIF":1.5,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11669-024-01122-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256865","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}