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Phase-field Analysis Of Nucleation Phenomena Ph. D. Thesis

Crystalline materials play an essential role in our everyday life. Most of them are polycrystalline, ie, composed of a large number of crystallites, whose size, shape and composition distributions determine their properties and failure

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  PHASE-FIELD ANALYSIS OFNUCLEATION PHENOMENA Ph.D. thesis Gyula T´OTH Supervisors: Prof. L´aszl´o Gr´an´asy Research Institute for Solid State Physics and Optics, Budapest, HungaryBrunel Centre for Advanced Solidification TechnologyBrunel University, London, United Kingdom Prof. J´anos Kert´esz Budapest University of Technology and EconomicsDepartment of Theoretical Physics, Budapest, Hungary Budapest2011  ´ Edesap´ amnak. K¨osz¨onetnyilv´an´ıt´as Mindenekel˝ott k¨osz¨onetemet fejezem ki t´emavezet˝omnek, Dr. Gr´an´asy L´aszl´onak bel´em vetett bizalm´a´ert, t¨urelm´e´ert, a munk´am sor´an ny´ujtott ir´anymutat´as´a´ert, ´es a dolgozat elk´esz´ıt´es´eben ny´ujtott seg´ıts´eg´e´ert. K¨osz¨onet illeti feles´egemet ´es sz¨uleimet kitart´asuk´ert ´est´amogat´asuk´ert, akiknek ´aldozatk´eszs´ege ´es munk´aja n´elk ¨ul ez a dolgozat nem j¨ohetett volnal´etre. K¨osz¨onetemet fejezem ki tov´abb´a az MTA Szil´ardtestfizikai ´es Optikai Kutat´oint´ezet K´ıs´erleti Szil´ardtestfizika Oszt´aly´anak, ezen bel¨ul k¨ozvetlen munkat´arsaimnak, a R¨ontgen-diffrakci´os Csoportnak. K¨ul¨on k¨osz¨onet illeti a doktori munka alatt ny´ujtott¨onzetlen seg´ıt-s´eg´e´ert Dr. Pusztai Tam´ast, a hasznos konzult´aci´ok´ert Dr. Oszl´anyi G´abort, Dr. Tegze Mikl´ost, Dr. Tegze Gy¨orgy¨ot ´es Dr. K¨ornyei L´aszl´ot, ´es k¨osz¨onet illeti dr. Faigel Gyula pro-fesszort meg´ert˝o seg´ıts´eg´e´ert. Munk´amat az OTKA-K-62588 p´aly´azat, valamint az ESA PECS 98058 sz´am´u szerz˝od´es keretei k ¨oz¨ott v´egeztem.  Contents 1 Introduction62 Theoretical methods applied15 2.1 Classical Nucleation Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.1.1 Self-Consistent Classical Theory. . . . . . . . . . . . . . . . . . . . . . 162.2 Diffuse Interface Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Phase-Field Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.3.1 The phase-field model and the equations of motion. . . . . . . . . . . 202.3.2 Application to the hard-sphere system. . . . . . . . . . . . . . . . . . 242.3.3 Application to binary systems. . . . . . . . . . . . . . . . . . . . . . . 262.3.4 Multiphase generalization of the phase-field theory. . . . . . . . . . . 29 3 Fixing the model parameters32 3.1 Hard-sphere system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2 Ag-Cu eutectic system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.3 Fe-Ni system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4 Results38 4.1 Hard-sphere system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.1.1 Order parameter profiles. . . . . . . . . . . . . . . . . . . . . . . . . . 384.1.2 Nucleation barrier height. . . . . . . . . . . . . . . . . . . . . . . . . . 404.1.3 Error of the input parameters. . . . . . . . . . . . . . . . . . . . . . . 414.2 Ag-Cu eutectic system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2.1 Phase diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2.2 Transitions in the one-phase liquid region. . . . . . . . . . . . . . . . . 464.2.3 Nucleation in the metastable liquid immiscibility region. . . . . . . . . 594