{"title":"Holzapfel解析表达式在CALPHAD数据库中近似Debye热容函数中的应用","authors":"Eli Brosh","doi":"10.1007/s11669-025-01201-7","DOIUrl":null,"url":null,"abstract":"<div><p>The Debye model for the heat capacity of solids is highly successful in modeling a wide variety of materials. Yet, it is not used in currently-developed CALPHAD (Calculation of Phase Diagrams) thermodynamic databases, just because it requires numerical integration and thus is inconvenient in implementation. Holzapfel et al. developed a simple closed-form approximation of the Debye model. The present work demonstrates the utility of Holzapfel’s expression for use in CALPHAD thermodynamic databases and software, with examples of modeling the Gibbs energy of the metallic elements Al and W. Advantages over previous work in CALPHAD modeling are pointed out.</p></div>","PeriodicalId":657,"journal":{"name":"Journal of Phase Equilibria and Diffusion","volume":"46 4","pages":"357 - 365"},"PeriodicalIF":1.7000,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Application of Holzapfel’s Analytic Expression for Approximating the Debye Heat Capacity Function in CALPHAD Databases\",\"authors\":\"Eli Brosh\",\"doi\":\"10.1007/s11669-025-01201-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The Debye model for the heat capacity of solids is highly successful in modeling a wide variety of materials. Yet, it is not used in currently-developed CALPHAD (Calculation of Phase Diagrams) thermodynamic databases, just because it requires numerical integration and thus is inconvenient in implementation. Holzapfel et al. developed a simple closed-form approximation of the Debye model. The present work demonstrates the utility of Holzapfel’s expression for use in CALPHAD thermodynamic databases and software, with examples of modeling the Gibbs energy of the metallic elements Al and W. Advantages over previous work in CALPHAD modeling are pointed out.</p></div>\",\"PeriodicalId\":657,\"journal\":{\"name\":\"Journal of Phase Equilibria and Diffusion\",\"volume\":\"46 4\",\"pages\":\"357 - 365\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Phase Equilibria and Diffusion\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11669-025-01201-7\",\"RegionNum\":4,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"CHEMISTRY, PHYSICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Phase Equilibria and Diffusion","FirstCategoryId":"88","ListUrlMain":"https://link.springer.com/article/10.1007/s11669-025-01201-7","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
Application of Holzapfel’s Analytic Expression for Approximating the Debye Heat Capacity Function in CALPHAD Databases
The Debye model for the heat capacity of solids is highly successful in modeling a wide variety of materials. Yet, it is not used in currently-developed CALPHAD (Calculation of Phase Diagrams) thermodynamic databases, just because it requires numerical integration and thus is inconvenient in implementation. Holzapfel et al. developed a simple closed-form approximation of the Debye model. The present work demonstrates the utility of Holzapfel’s expression for use in CALPHAD thermodynamic databases and software, with examples of modeling the Gibbs energy of the metallic elements Al and W. Advantages over previous work in CALPHAD modeling are pointed out.
期刊介绍:
The most trusted journal for phase equilibria and thermodynamic research, ASM International''s Journal of Phase Equilibria and Diffusion features critical phase diagram evaluations on scientifically and industrially important alloy systems, authored by international experts.
The Journal of Phase Equilibria and Diffusion is critically reviewed and contains basic and applied research results, a survey of current literature and other pertinent articles. The journal covers the significance of diagrams as well as new research techniques, equipment, data evaluation, nomenclature, presentation and other aspects of phase diagram preparation and use.
Content includes information on phenomena such as kinetic control of equilibrium, coherency effects, impurity effects, and thermodynamic and crystallographic characteristics. The journal updates systems previously published in the Bulletin of Alloy Phase Diagrams as new data are discovered.