{"title":"Catastrophe theory and thermodynamic instability to predict congruent melting temperature of crystals","authors":"","doi":"10.1016/j.calphad.2024.102761","DOIUrl":"10.1016/j.calphad.2024.102761","url":null,"abstract":"<div><div>Melting temperature (<em>T</em><sub>m</sub>) is a crucial physical property of solids and plays an important role in the characterization of materials. Therefore, the capacity to predict <em>T</em><sub>m</sub> is a relevant issue for solid state sciences. This investigation aims i) to provide a theoretical basis for the link between catastrophe theory and thermodynamic instability; ii) to estimate <em>T</em><sub>m</sub> through the notion of “degenerate critical temperature” (<em>T</em><sub>d</sub>), related to (<em>P</em><sub>d</sub>,<em>V</em><sub>d</sub>,<em>T</em><sub>d</sub>), where <em>K</em><sub><em>T</em></sub> → 0 and the Gibbs function shows a <em>non</em>-Morse behaviour; iii) to compare predictions of (<em>P</em><sub>m</sub>,<em>T</em><sub>m</sub>) with observations for three crystalline pure substances that undergo congruent melting and exhibit different bonding and stability ranges: NaCl (halite), SiO<sub>2,st</sub> (stishovite), and MgSiO<sub>3</sub> (perovskite). The <em>P</em>-<em>T locus</em> of <em>K</em><sub><em>T</em></sub> = 0 associated with melting is identified using the maximum values of <em>T</em><sub>d</sub> and Δ<em>H</em>/Δ<em>V</em> at a given pressure. We observed an average absolute discrepancy ranging between 0.2 % (halite) and 5.8 % (stishovite), and an agreement between theoretical and experimental <em>T</em>(<em>P</em>)<sub>melting</sub>-points from better than 1 to approximately 14 %.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142577460","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}
{"title":"A new model for precipitation kinetics considering diffusion within the precipitates","authors":"","doi":"10.1016/j.calphad.2024.102764","DOIUrl":"10.1016/j.calphad.2024.102764","url":null,"abstract":"<div><div>Quantitative modelling of precipitation kinetics can play an important role in a computational materials design framework. For many material systems, e.g., the Fe-Cu system, the precipitates (rich in Cu at equilibrium) nucleate at a composition far away from the equilibrium. This in turn affects the precipitation kinetics, and the capability to model the compositional evolution of the Cu precipitates is therefore important. In the present work we propose a new approach implemented in a Langer-Schwartz-Kampmann-Wagner precipitation modelling framework where the concentration profile inside the precipitates is defined with an explicit function and the diffusive fluxes in both precipitates and matrix are solved concurrently to compute the growth rate of the precipitates. The new model is evaluated with respect to results from atom probe tomography for Cu precipitation in a 15–5 PH stainless steel. A parameter study of the effect of diffusion coefficients and interfacial energies is conducted, and it is concluded that the new model is capable of describing the experimentally determined evolution of the Cu precipitate volume fraction, mean radius, number density and composition.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142571725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Critical assessment of the Si-P system: P solubility in the Si-rich region and refining by phosphorus distillation","authors":"","doi":"10.1016/j.calphad.2024.102758","DOIUrl":"10.1016/j.calphad.2024.102758","url":null,"abstract":"<div><div>The P-Si system has been studied due to its poisonous importance in silicon electronic devices for photovoltaic applications. Thermodynamic and phase diagram data of the Si-P system available in literature are critically evaluated for further optimization of thermodynamic properties in order to improve the thermodynamic description of this system, especially in the Si-rich region. After revising the solubility data of P in solid Si in the Si-rich region its upper limit is now evaluated at 1w% P (mole fraction X<sub>P</sub> ≈ 0.0095). With this controversial solubility limit resolved, current modelling of the liquid and solid phases is described more accurately. Distillation capacity of phosphorus by vaporization is then assessed for liquid and solid silicon on the basis of the determination of the infinite dilution activity coefficient of phosphorus in silicon - the Henry's coefficient - as well as numerous gaseous species existing in the Si-P binary system. The lack of original calorimetric data is highlighted in view to a further more reliable description of the complete Si-P system.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535656","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}
{"title":"Study on the γ + γ′ microstructure characterization of the Co–V–Zr system based on CALPHAD method","authors":"","doi":"10.1016/j.calphad.2024.102762","DOIUrl":"10.1016/j.calphad.2024.102762","url":null,"abstract":"<div><div>The γ + γ′ microstructure in novel Co-based superalloys is often obtained by means of alloying method. Therefore, this study focuses on exploring the evolution of the γ + γ′ microstructure through the addition of Zr using CALculation of PHAse Diagram (CALPHAD) method. The heat capacity of τ was experimentally determined by the sapphire method, and the enthalpy of formation of τ at 0 K was calculated using Density Functional Theory (DFT). The thermodynamic parameters were derived based on experimental results from phase equilibrium data and first-principles calculations using CALPHAD method. According to the thermodynamic analyses, the alloy Co80.0V18.5Zr1.5 (at. %) was homogenized at 1473 K for 10 h and aged at 1173 K for different time, the ordered L1<sub>2</sub>-γ′ precipitates coarsened and dissolved after 2 h, and transformed into needle-like D0<sub>19</sub>-Co<sub>3</sub>V after 67 h of aging, which indicated that the γ′ phase was not in a thermodynamically stable state in the Co–V–Zr system. If the stable γ′ phase is obtained, additional alloying elements is necessary to be added.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535655","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}
{"title":"Assessment of thermal conductivity for FCC Al-X (X=Zn, Mg) and Al-Zn-Mg alloys: Experiments and modeling","authors":"","doi":"10.1016/j.calphad.2024.102763","DOIUrl":"10.1016/j.calphad.2024.102763","url":null,"abstract":"<div><div>Thermal conductivity is one of the critical thermophysical properties for Al alloys. However, in comparison with mechanical properties, fewer studies focused on investigating thermal conductivity for Al alloys such as Al-Zn-Mg and its sub-systems. This study aims to combine experiments and modeling to assess thermal conductivity of FCC Al-Zn, Al-Mg and Al-Zn-Mg alloys. FCC Al-Zn, Al-Mg and Al-Zn-Mg alloys were first designed by CALPHAD (Calculation of PHAse Diagram) method. The alloy samples were prepared using the vacuum induction melting furnace, and their compositions and structures were validated via ICP (Inductively Coupled Plasma), XRD (X-ray diffraction) and SEM (Scanning Electron Microscope). Subsequently, LFA (Laser Flash Analysis) was applied to measure thermal conductivity of the presently prepared samples at 298, 348, 398, 448 and 498 K. Moreover, a novel model incorporated in CALTPP (CALculation of ThermoPhysical Properties) software was implemented for evaluating thermal conductivity of FCC Al-Zn, Al-Mg and Al-Zn-Mg alloys from 298 K to 498 K. All the deviations between the model-evaluated thermal conductivity and measured ones are within ±10 %, indicating that the present calculations are reliable. Furthermore, this work used this developed model to predict composition-dependent and temperature-dependent thermal conductivity for FCC Al-Zn, Al-Mg and Al-Zn-Mg alloys. The present work provides an effective way to investigate thermal conductivity for single-phase solid solutions combining experiments and modeling.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535657","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}
{"title":"Re-investigation the phase equilibria and thermodynamic assessment of the Nd-Sn binary system","authors":"","doi":"10.1016/j.calphad.2024.102757","DOIUrl":"10.1016/j.calphad.2024.102757","url":null,"abstract":"<div><div>The Nd-Sn phase diagram has been investigated within the range of 20–80 at.% Sn using X-ray diffraction (XRD), scanning electron microscope equipped with energy dispersive spectrometer (SEM-EDS), and differential scanning calorimetric (DSC). In addition to the nine known compounds, Nd<sub>5</sub>Sn<sub>3</sub>, Nd<sub>5</sub>Sn<sub>4</sub>, Nd<sub>11</sub>Sn<sub>10</sub>, NdSn, Nd<sub>3</sub>Sn<sub>5</sub>, NdSn<sub>2</sub>, Nd<sub>3</sub>Sn<sub>7</sub>, Nd<sub>2</sub>Sn<sub>5</sub> and NdSn<sub>3</sub>, two reported compounds, Nd<sub>3</sub>Sn and Nd<sub>2</sub>Sn<sub>3,</sub> as well as two new compounds Nd<sub>2</sub>Sn and Nd<sub>4</sub>Sn<sub>5</sub>, have been detected. The formation of Nd<sub>2</sub>Sn, Nd<sub>4</sub>Sn<sub>5</sub> and Nd<sub>2</sub>Sn<sub>3</sub> has been determined as follows: Nd<sub>2</sub>Sn forms by peritectoid reaction Nd<sub>3</sub>Sn + Nd<sub>5</sub>Sn<sub>3</sub> → Nd<sub>2</sub>Sn at 1134 °C; Nd<sub>4</sub>Sn<sub>5</sub> and Nd<sub>2</sub>Sn<sub>3</sub> form by peritectic reaction at 1168 °C and 1146 °C, respectively. Nd<sub>3</sub>Sn and Nd<sub>3</sub>Sn<sub>5</sub> are only stable at high temperatures, Nd<sub>3</sub>Sn forms by a peritectic reaction at 1163 °C and decomposes at 1114 °C, and Nd<sub>3</sub>Sn<sub>5</sub> is formed via a peritectic reaction at 1153 °C and decomposes at 1136 °C. Additionally, five invariant reaction temperature have been updated. The Nd-Sn system was modeled using the Calphad approach, incorporating new experimental data along with all other available experimental information. A comprehensive thermodynamic description of the Nd-Sn system has been obtained, and extensive comparisons between calculated and experimental data indicating that almost all adopted experimental and theoretical data are satisfactorily matched.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535654","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}
{"title":"Thermodynamic properties of neodymium silicates at high temperature (298.15–1273K) and thermodynamic reassessment of the Nd2O3-SiO2 system","authors":"","doi":"10.1016/j.calphad.2024.102760","DOIUrl":"10.1016/j.calphad.2024.102760","url":null,"abstract":"<div><div>Solid oxide fuel cells (SOFCs) have garnered significant interest due to their potential as alternative electrical power generation systems that offer low pollutant emissions and high energy conversion efficiency. Neodymium silicates have emerged as promising electrolyte materials owing to their high ionic conductivity. To enhance our understanding of their performance in SOFC applications, it is essential to investigate the thermodynamic properties of neodymium silicates. In this study, we measured the heat capacities of the prepared samples over the temperature range of 673–1273 K using a multi-high temperature calorimeter (MHTC) 96 line. The temperature dependence of heat capacities for Nd<sub>2</sub>SiO<sub>5</sub>, Nd<sub>14</sub>Si<sub>9</sub>O<sub>39</sub>, and Nd<sub>2</sub>Si<sub>2</sub>O<sub>7</sub> were modeled as functions: Cp<sub>(Nd2SiO5)</sub> = 194.7 + 0.028 T–4,714,800 T<sup>−2</sup> – 239.75 T<sup>−0.5</sup> + 491568400 T<sup>−3</sup> (J·mol<sup>−1</sup>·K<sup>−1</sup>) (298.15 - 1400K), Cp<sub>(Nd14Si9O39)</sub> =1527.1 + 0.22 T − 40097000 T<sup>−2</sup> – 2150.3 T<sup>−0.5</sup> + 4424200000 T<sup>−3</sup> (J·mol<sup>−1</sup>·K<sup>−1</sup>) (298.15 - 1400K), Cp<sub>(Nd2Si2O7)</sub> =276 + 0.032 T − 8261400 T<sup>−2</sup> – 480 T<sup>−0.5</sup> + 983136800 T<sup>−3</sup> (J mol<sup>−1</sup> K<sup>−1</sup>) (298.15–1400K), and then used for computing changes in entropy and Gibbs free energy. The Nd<sub>2</sub>O<sub>3</sub>-SiO<sub>2</sub> system was reassessed based on the phase diagram experimental data and measured heat capacities in this work.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535653","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}
{"title":"Pressure effect on ternary phase diagrams: Bi-Sb-Pb as a case study","authors":"","doi":"10.1016/j.calphad.2024.102759","DOIUrl":"10.1016/j.calphad.2024.102759","url":null,"abstract":"<div><div>Pressure can affect phase diagrams significantly, as previously demonstrated on several binary systems. However, the effect of pressure on ternary phase diagrams is mostly unexplored. In this study, a thermodynamic model of a ternary phase diagram under high pressure is formulated and applied to calculate the Bi-Sb-Pb system. The model employs binary interaction parameters and elemental thermodynamic functions to which the effect of pressure on the binary interaction parameters and elemental properties are added. The complete ternary Bi-Sb-Pb phase diagram was calculated up to a pressure of 2 GPa at selected temperatures as a case study, as this system involves three different types of binary phase diagrams: isomorphous, eutectic, and peritectic. The results show how pressure affects the stability of solid phases, leading to changes in the three-phase triangles and the four-phase equilibrium quadrilateral. This study provides insights into the pressure-dependent behavior of ternary systems and contributes to the thermodynamic understanding of ternary phase diagrams under high-pressure conditions.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442392","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}
{"title":"Thermodynamic study on the phase diagram of the Hg-Ca and Hg-Sr binary systems for dental amalgam restoration application","authors":"","doi":"10.1016/j.calphad.2024.102755","DOIUrl":"10.1016/j.calphad.2024.102755","url":null,"abstract":"<div><div>Dental amalgam, known for its biocompatibility and ductility, is widely used in restorative materials. In dental crown restorations, studying the interactions between amalgam fillings and crown tissues, particularly the roles of calcium (Ca) and strontium (Sr), is essential for improving function stability and biocompatibility. This study conducts critical literature evaluation and thermodynamic optimization of binary systems involving mercury (Hg) with Ca and Sr, focusing specifically on their suitability for dental amalgam restoration. Using first-principles calculations (FPC), the enthalpies of formation for compounds within the Hg-Ca and Hg-Sr binary systems were calculated in this work. Thermodynamic modeling of the liquid solution employed the modified quasichemical model in the pair approximation (MQM), uncovering significant short-range ordering. Conversely, solid phases were modeled using the compound energy formalism (CEF). The incorporation of FPC proves to be a valuable and effective method, providing essential insights to complement the calculation of phase diagrams (CALPHAD) modeling approach. Ultimately, this research significantly enhances our understanding of the thermodynamic characteristics of Hg-X alloys, with notable implications for their potential application in dental amalgam restoration.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142432031","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}
{"title":"Experimental investigation and thermodynamic description of the Ni-Mo-Y ternary system","authors":"","doi":"10.1016/j.calphad.2024.102739","DOIUrl":"10.1016/j.calphad.2024.102739","url":null,"abstract":"<div><div>Nickel-based superalloys are extensively utilized in aerospace engines, marine gas turbines, and other environments with severe operating conditions. The phase relations of the Ni-Mo-Y ternary system were experimentally studied across the entire composition range at 800 °C and 1000 °C using scanning electron microscopy (SEM) coupled with energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD). Thirteen three-phase regions were confirmed at 800 °C, and eleven three-phase regions were observed at 1000 °C. No ternary compound was observed at these temperatures. In addition, the experimental results indicate that molybdenum (Mo) has almost no solubility in the binary compounds found in the Ni-Y binary system. Furthermore, the primary solidification phases and the solidification process of typical alloys were investigated, and three different primary solidification phases were found. Based on the experimental results, thermodynamic calculations for the Ni-Mo-Y system were performed through the CALPHAD technique. The experimental results agree well with the calculated, a set of self-consistent thermodynamic parameters for the Ni-Mo-Y ternary system was obtained in the present work.</div></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357593","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}