{"title":"热力学-用于理解晶体生长-","authors":"Tatau Nishinaga","doi":"10.1016/j.pcrysgrow.2016.04.001","DOIUrl":null,"url":null,"abstract":"<div><p>To understand what entropy is, thermodynamical entropy was derived from Boltzmann's entropy formula. After defining the Helmholtz and the Gibbs free energies, we calculated the formation Gibbs free energies of an equilibrium and a non-equilibrium nucleus following Toschev's approach taking a water droplet as an example. It is demonstrated that the Gibbs free energy for the formation of a cluster takes the maximum as the cluster radius is increased. The cluster at this maximum is called critical nucleus.</p><p>Thermodynamics is also a useful tool to obtain the rate of crystal growth in a vapor phase. The partial pressures of all gaseous species are calculated by solving equations given by the law of mass action and the initial conditions. The mathematical formulas to give the growth rates in a closed tube and in a gas flow system are derived.</p></div>","PeriodicalId":409,"journal":{"name":"Progress in Crystal Growth and Characterization of Materials","volume":"62 2","pages":"Pages 43-57"},"PeriodicalIF":4.5000,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.pcrysgrow.2016.04.001","citationCount":"3","resultStr":"{\"title\":\"Thermodynamics -for understanding crystal growth-\",\"authors\":\"Tatau Nishinaga\",\"doi\":\"10.1016/j.pcrysgrow.2016.04.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>To understand what entropy is, thermodynamical entropy was derived from Boltzmann's entropy formula. After defining the Helmholtz and the Gibbs free energies, we calculated the formation Gibbs free energies of an equilibrium and a non-equilibrium nucleus following Toschev's approach taking a water droplet as an example. It is demonstrated that the Gibbs free energy for the formation of a cluster takes the maximum as the cluster radius is increased. The cluster at this maximum is called critical nucleus.</p><p>Thermodynamics is also a useful tool to obtain the rate of crystal growth in a vapor phase. The partial pressures of all gaseous species are calculated by solving equations given by the law of mass action and the initial conditions. The mathematical formulas to give the growth rates in a closed tube and in a gas flow system are derived.</p></div>\",\"PeriodicalId\":409,\"journal\":{\"name\":\"Progress in Crystal Growth and Characterization of Materials\",\"volume\":\"62 2\",\"pages\":\"Pages 43-57\"},\"PeriodicalIF\":4.5000,\"publicationDate\":\"2016-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.pcrysgrow.2016.04.001\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Progress in Crystal Growth and Characterization of Materials\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S096089741630002X\",\"RegionNum\":2,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CRYSTALLOGRAPHY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Progress in Crystal Growth and Characterization of Materials","FirstCategoryId":"88","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S096089741630002X","RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CRYSTALLOGRAPHY","Score":null,"Total":0}
To understand what entropy is, thermodynamical entropy was derived from Boltzmann's entropy formula. After defining the Helmholtz and the Gibbs free energies, we calculated the formation Gibbs free energies of an equilibrium and a non-equilibrium nucleus following Toschev's approach taking a water droplet as an example. It is demonstrated that the Gibbs free energy for the formation of a cluster takes the maximum as the cluster radius is increased. The cluster at this maximum is called critical nucleus.
Thermodynamics is also a useful tool to obtain the rate of crystal growth in a vapor phase. The partial pressures of all gaseous species are calculated by solving equations given by the law of mass action and the initial conditions. The mathematical formulas to give the growth rates in a closed tube and in a gas flow system are derived.
期刊介绍：
Materials especially crystalline materials provide the foundation of our modern technologically driven world. The domination of materials is achieved through detailed scientific research.
Advances in the techniques of growing and assessing ever more perfect crystals of a wide range of materials lie at the roots of much of today''s advanced technology. The evolution and development of crystalline materials involves research by dedicated scientists in academia as well as industry involving a broad field of disciplines including biology, chemistry, physics, material sciences and engineering. Crucially important applications in information technology, photonics, energy storage and harvesting, environmental protection, medicine and food production require a deep understanding of and control of crystal growth. This can involve suitable growth methods and material characterization from the bulk down to the nano-scale.
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