Verfügbarkeit: The diffuse interface approach in materials science

The diffuse interface approach in materials science: thermodynamic concepts and applications of phase-field models

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Bibliographische Detailangaben
1. Verfasser:	Emmerich, Heike 1969- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin [u.a.] Springer 2003
Schriftenreihe:	Lecture notes in physics New series M, monographs ; 73
Schlagworte:	Interfaces (Physical sciences) Materials science Phasenfeldmodell
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Includes bibliographical references and index.
Beschreibung:	VIII, 178 S. Ill., graph. Darst.
ISBN:	3540004165

Internformat

MARC


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Datensatz im Suchindex

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adam_text	CONTENTS 1. INTRODUCTION .............................................. 1 1.1 STRUCTURE AND SCOPE OF THIS WORK . . . . . . . . . . . . . . . . . . . . . . . . 4 2. WHAT IS AN INTERFACE? .................................... 7 3. EQUILIBRIUM THERMODYNAMICS OF MULTIPHASE SYSTEMS: THERMODYNAMIC POTENTIALS AND PHASE DIAGRAMS .......... 19 3.1 CALCULATING PHASE DIAGRAMS FROM ENERGY FUNCTIONALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 ABSTRACTED PHASE DIAGRAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.1 CONSTRUCTING THE GIBBS FREE ENERGIES . . . . . . . . . . . . . . . 26 3.2.2 NON-CONSERVED VERSUS CONSERVED VARIABLE APPROACH . . 28 4. THERMODYNAMIC CONCEPTS OF PHASE-FIELD MODELING ....... 31 4.1 DERIVATION OF TRANSPORT EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . 32 4.1.1 CONSIDERING CONSERVED QUANTITIES ONLY . . . . . . . . . . . . . 32 4.1.2 EXTENSION TO NON-CONSERVED QUANTITIES . . . . . . . . . . . . . . 35 4.2 INTRODUCING THE PHASE-FIELD VARIABLE * . . . . . . . . . . . . . . . . . . . . 38 4.3 THERMODYNAMIC CONSISTENCY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.3.1 THE GRADIENT FLOW METHOD . . . . . . . . . . . . . . . . . . . . . . . . 47 4.3.2 ENTROPY PRODUCTION IN TERMS OF TRANSPORT VARIABLES . . 49 4.4 APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5. ASYMPTOTIC ANALYSIS ...................................... 59 5.1 A FORMAL MATHEMATICAL APPROACH TOWARDS MATCHING . . . . . . . 59 5.1.1 ILLUSTRATION OF EXTENDED DOMAINS . . . . . . . . . . . . . . . . . . . 63 5.1.2 MATCHING IN THE CONTEXT OF DIFFUSE INTERFACE MODELING 67 5.2 ASYMPTOTIC MATCHING FOR THIN FILM EPITAXIAL GROWTH . . . . . . 68 5.2.1 MOTIVATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2.2 SHARP INTERFACE FORMULATION . . . . . . . . . . . . . . . . . . . . . . . 70 5.2.3 THE DIFFUSE INTERFACE MODEL EQUATIONS AND THEIR ASYMPTOTIC ANALYSIS . . . . . . . . . . . . . . . . . . . . 72 5.3 A GENERALIZED APPROACH TOWARDS THE ASYMPTOTIC ANALYSIS OF DIFFUSE INTERFACE MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 VIII CONTENTS 5.3.1 ROLE OF THE GOVERNING THERMODYNAMIC POTENTIAL . . . . . 78 5.3.2 THE EXPANSION PROCEDURE IN DETAIL . . . . . . . . . . . . . . . . . 81 5.4 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.5 APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6. APPLICATION OF DIFFUSE INTERFACE MODELING TO HYDRODYNAMICALLY DRIVEN GROWTH ..................... 97 6.1 DIFFUSE INTERFACE MODELING FOR HYDRODYNAMICALLY INFLUENCED GROWTH . . . . . . . . . . . . . . . . . . 99 6.2 THE SELECTION PROBLEM OF DENDRITIC GROWTH REVISITED . . . . . . . 104 6.3 COMPARISON TO EXPERIMENTAL DATA . . . . . . . . . . . . . . . . . . . . . . . . 119 6.4 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.5 APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 7. APPLICATION TO EPITAXIAL GROWTH INVOLVING ELASTICITY ...... 131 7.1 ELASTIC DRIVING FORCES WITHIN THE DIFFUSE INTERFACE APPROACH . 132 7.2 COMPARING SIMULATIONS AND EXPERIMENTS . . . . . . . . . . . . . . . . . . 134 7.3 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 8. CONCLUSIONS AND PERSPECTIVES ............................. 141 APPENDIX ..................................................... 145 A. NUMERICAL ISSUES OF DIFFUSE INTERFACE MODELING ........... 145 A.1 RELATIONSHIP BETWEEN PHYSICAL VARIABLES AND NUMERICAL PARAMETERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 A.2 COMPUTATIONAL UNIVERSALITY OF PHASE FIELD MODELS . . . . . . . . . . 151 A.3 SELECTED STATE-OF-THE-ART NUMERICAL APPROACHES . . . . . . . . . . . . 154 A.3.1 2D ADAPTIVE MESH REFINEMENT COMPUTATION . . . . . . . . . 155 A.3.2 3D SIMULATIONS INCLUDING FLUID FLOW . . . . . . . . . . . . . . . 161 REFERENCES .................................................... 165 INDEX ......................................................... 175
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author	Emmerich, Heike 1969-
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spelling	Emmerich, Heike 1969- Verfasser (DE-588)115358978 aut The diffuse interface approach in materials science thermodynamic concepts and applications of phase-field models Heike Emmerich Berlin [u.a.] Springer 2003 VIII, 178 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics : New series M, monographs 73 Physics and astronomy online library Includes bibliographical references and index. Interfaces (Physical sciences) Materials science Phasenfeldmodell (DE-588)4736241-8 gnd rswk-swf Phasenfeldmodell (DE-588)4736241-8 s DE-604 Lecture notes in physics New series M, monographs ; 73 (DE-604)BV021852221 73 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010175726&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Emmerich, Heike 1969- The diffuse interface approach in materials science thermodynamic concepts and applications of phase-field models Lecture notes in physics Interfaces (Physical sciences) Materials science Phasenfeldmodell (DE-588)4736241-8 gnd
subject_GND	(DE-588)4736241-8
title	The diffuse interface approach in materials science thermodynamic concepts and applications of phase-field models
title_auth	The diffuse interface approach in materials science thermodynamic concepts and applications of phase-field models
title_exact_search	The diffuse interface approach in materials science thermodynamic concepts and applications of phase-field models
title_full	The diffuse interface approach in materials science thermodynamic concepts and applications of phase-field models Heike Emmerich
title_fullStr	The diffuse interface approach in materials science thermodynamic concepts and applications of phase-field models Heike Emmerich
title_full_unstemmed	The diffuse interface approach in materials science thermodynamic concepts and applications of phase-field models Heike Emmerich
title_short	The diffuse interface approach in materials science
title_sort	the diffuse interface approach in materials science thermodynamic concepts and applications of phase field models
title_sub	thermodynamic concepts and applications of phase-field models
topic	Interfaces (Physical sciences) Materials science Phasenfeldmodell (DE-588)4736241-8 gnd
topic_facet	Interfaces (Physical sciences) Materials science Phasenfeldmodell
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010175726&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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