{"title":"Catastrophe theory and thermodynamic instability to predict congruent melting temperature of crystals","authors":"Marcello Merli , Costanza Bonadiman , Alessandro Pavese","doi":"10.1016/j.calphad.2024.102761","DOIUrl":null,"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":"87 ","pages":"Article 102761"},"PeriodicalIF":1.9000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","FirstCategoryId":"88","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0364591624001032","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Melting temperature (Tm) is a crucial physical property of solids and plays an important role in the characterization of materials. Therefore, the capacity to predict Tm 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 Tm through the notion of “degenerate critical temperature” (Td), related to (Pd,Vd,Td), where KT → 0 and the Gibbs function shows a non-Morse behaviour; iii) to compare predictions of (Pm,Tm) with observations for three crystalline pure substances that undergo congruent melting and exhibit different bonding and stability ranges: NaCl (halite), SiO2,st (stishovite), and MgSiO3 (perovskite). The P-T locus of KT = 0 associated with melting is identified using the maximum values of Td and ΔH/ΔV 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 T(P)melting-points from better than 1 to approximately 14 %.
期刊介绍:
The design of industrial processes requires reliable thermodynamic data. CALPHAD (Computer Coupling of Phase Diagrams and Thermochemistry) aims to promote computational thermodynamics through development of models to represent thermodynamic properties for various phases which permit prediction of properties of multicomponent systems from those of binary and ternary subsystems, critical assessment of data and their incorporation into self-consistent databases, development of software to optimize and derive thermodynamic parameters and the development and use of databanks for calculations to improve understanding of various industrial and technological processes. This work is disseminated through the CALPHAD journal and its annual conference.