Herlach · Matson Dieter M. Herlach, Douglas M. Matson All metallic materials are prepared from the liquid state as their parent phase. Solidification is therefore one of the most important phase transformation in daily human life. Solidification is the transi- tion from liquid to solid state of matter. The conditions under which material is transformed determines the physical and chemical proper- ties of the as-solidified body. The processes involved, like nucleation Solidification of and crystal growth, are governed by heat and mass transport. Convection and undercooling provide additional processing parameters to tune the solidification process and to control solid material perfor- mance from the very beginning of the production chain. To develop a predictive capability for efficient materials production Containerless the processes involved in solidification have to be understood in detail. This book provides a comprehensive overview of the solidification of metallic melts processed and undercooled in a containerless manner by drop tube, electromagnetic and electrostatic levitation, and experi- Undercooled Melts ments in reduced gravity. The experiments are accompanied by model calculations on the in- fluence of thermodynamic and hydrodynamic conditions that control selection of nucleation mechanisms and modify crystal growth deve- lopment throughout the solidification process. Undercooled Melts Solidification of Containerless Dieter Herlach is leader of the group „Undercooling of Materials“ and Senior Scientist at the Institute of Materials Physics in Space of the German Aerospace Center (DLR) in Cologne. He is full professor of physics at the Ruhr-University Bochum. Dieter Herlach has authored more than 300 scientific publications in refereed journals and organized sixteen conferences and sym- posia. He is author and editor of six books and member of the advisory board of Advanced En- gineering Materials (Wiley-VCH). He was member of the advisory board of directors of the German Physical Society and deputy chairman of the German Society of Materials Science and Engineering. Two priority programs of the German Research Foundation (DFG) and several European projects of the European Space Agency and the European Commission were coordi- nated by him. He was lead scientist for NASA Spacelab missions IML2 and MSL1 and granted as honorary professor of four Chinese Universities and Research Centers. Douglas M. Matson is Vice Chairman and Associate Professor in the Mechanical Engineering Department at Tufts University, Medford MA, USA. He is an internationally recognized expert with over fifty peer reviewed articles in thermal manufacturing, machine design, materials pro- cessing, solidification research, and microgravity experimentation. He has organized five symposi- um, is the former president of the North Alabama Chapter of the American Society for Materials (ASM) and received an Erskine Fellowship at the University of Canterbury, Christchurch, New Zealand. He has served as lead scientist for the MSL-1 Spacelab mission and currently is the NASA facility scientist for the MSL-EML project aboard the International Space Station. ISBN 978-3-527-33122-2 www.wiley-vch.de Edited by Dieter M. Herlach and Douglas M. Matson Solidification of Containerless Undercooled Melts Related Titles Barsoum, M. Krzyzanowski, M., Beynon, J. H., Farrugia, D. C. J. MAX Phases Properties of Machinable Ternary Oxide Scale Behavior in High Carbides and Nitrides Temperature Metal Processing 2013 2010 ISBN: 978-3-527-33011-9 ISBN: 978-3-527-32518-4 Bathias, C., Pineau, A. (eds.) Slezov, V. V. Fatigue of Materials and Structures Kinetics of First-order Phase E-Book Transitions 2009 ISBN: 978-0-470-39401-4 ISBN: 978-3-527-40775-0 Dubois, J.-M., Belin-Ferré, E. (eds.) Blondeau, R. (ed.) Complex Metallic Alloys Fundamentals and Applications Metallurgy and Mechanics 2011 of Welding 2008 ISBN: 978-3-527-32523-8 ISBN: 978-1-84821-038-7 Jackson, K. A. Scheel, H. J., Capper, P. (eds.) Kinetic Processes Crystal Growth, Diffusion, and Crystal Growth Technology Phase Transitions in Materials From Fundamentals and Simulation Second edition to Large-scale Production 2008 2010 ISBN: 978-3-527-31762-2 ISBN: 978-3-527-32736-2 Edited by Dieter M. Herlach and Douglas M. Matson Solidification of Containerless Undercooled Melts Wiley-VCH The Editors All books published by are carefully produced. Nevertheless, authors, editors, and Prof. Dieter M. Herlach publisher do not warrant the information contained Institut für Materialphysik im Weltraum in these books, including this book, to be free of Deutsches Zentrum für Luft- und Raumfahrt errors. Readers are advised to keep in mind that 51147 Köln statements, data, illustrations, procedural details or Germany other items may inadvertently be inaccurate. Library of Congress Card No.: applied for Prof. Douglas M. Matson Tufts University British Library Cataloguing-in-Publication Data Dept. of Mechanical Eng. A catalogue record for this book is available from the 200 College Avenue British Library. Medford, MA 02155 USA Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publica- tion in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de. We would like to thank the DLR for the material used in the cover picture. # 2012 Wiley-VCH Verlag & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, micro- film, or any other means – nor transmitted or trans- lated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Composition Thomson Digital, Noida, India Printing and Binding Markono Print Media Pte Ltd, Singapore Cover Design Adam Design, Weinheim Print ISBN: 978-3-527-33122-2 ePDF ISBN: 978-3-527-64793-4 ePub ISBN: 978-3-527-64792-7 mobi ISBN: 978-3-527-64791-0 oBook ISBN: 978-3-527-64790-3 Printed in Singapore Printed on acid-free paper V Contents Preface XV List of Contributors XIX 1 Containerless Undercooling of Drops and Droplets 1 Dieter M. Herlach 1.1 Introduction 1 1.2 Drop Tubes 3 1.2.1 Short Drop Tubes 4 1.2.2 Long Drop Tubes 5 1.3 Containerless Processing Through Levitation 8 1.3.1 Electromagnetic Levitation 9 1.3.2 Electrostatic Levitation 16 1.3.3 Electromagnetic Levitation in Reduced Gravity 23 1.4 Summary and Conclusions 26 References 27 2 Computer-Aided Experiments in Containerless Processing of Materials 31 Robert W. Hyers 2.1 Introduction 31 2.1.1 Nomenclature 32 2.2 Planning Experiments 33 2.2.1 Example: Feasible Range of Conditions to Test Theory of Coupled-Flux Nucleation 33 2.2.2 Example: The Effect of Fluid Flow on Phase Selection 37 2.3 Operating Experiments 40 2.4 Data Reduction, Analysis, Visualization, and Interpretation 41 2.4.1 Example: Noncontact Measurement of Density and Thermal Expansion 42 2.4.2 Example: Noncontact Measurement of Creep 45 2.5 Conclusion 47 References 47 VI Contents 3 Demixing of Cu–Co Alloys Showing a Metastable Miscibility Gap 51 Matthias Kolbe 3.1 Introduction 51 3.2 Mechanism of Demixing 52 3.3 Demixing Experiments in Terrestrial EML and in Low Gravity 54 3.4 Demixing Experiments in a Drop Tube 56 3.5 Spinodal Decomposition in Cu–Co Melts 62 3.6 Conclusions 64 References 66 4 Short-Range Order in Undercooled Melts 69 Dirk Holland- Moritz 4.1 Introduction 69 4.2 Experiments on the Short-Range Order of Undercooled Melts 71 4.2.1 Experimental Techniques 72 4.2.2 Structure of Monatomic Melts 73 4.2.3 Structure of Alloy Melts 77 4.3 Conclusions 83 References 84 5 Ordering and Crystal Nucleation in Undercooled Melts 87 Kenneth F. Kelton and A. Lindsay Greer 5.1 Introduction 87 5.2 Nucleation Theory–— Some Background 88 5.2.1 Classical Nucleation Theory 88 5.2.1.1 Homogeneous Steady-State Nucleation 88 5.2.1.2 Heterogeneous Nucleation 90 5.2.2 Nucleation Models that Take Account of Ordering 93 5.2.2.1 Diffuse-Interface Model 94 5.2.2.2 Density-Functional Models 95 5.3 Liquid Metal Undercooling Studies 97 5.3.1 Experimental Techniques 97 5.3.2 Selected Experimental Results 98 5.3.2.1 Maximum-Undercooling Data 98 5.3.2.2 Nucleation Rate Measurements 99 5.4 Coupling of Ordering in the Liquid to the Nucleation Barrier 101 5.4.1 Icosahedral Ordering 101 5.4.2 Coupling of Ordering and Nucleation Barrier 102 5.4.3 Ordering in the Liquid Adjacent to a Heterogeneity 106 5.5 Conclusions 107 References 108 Contents VII 6 Phase-Field Crystal Modeling of Homogeneous and Heterogeneous Crystal Nucleation 113 Gyula I. Tóth, Tamás Pusztai, György Tegze, and László Gránásy 6.1 Introduction 113 6.2 Phase-Field Crystal Models 114 6.2.1 Free Energy Functionals 115 6.2.2 Euler–Lagrange Equation and the Equation of Motion 117 6.3 Homogeneous Nucleation 118 6.3.1 Solution of the Euler–Lagrange Equation 118 6.3.2 Solution of the Equation of Motion 120 6.4 PFC Modeling of Heterogeneous NuCleation 129 6.5 Summary 134 References 135 7 Effects of Transient Heat and Mass Transfer on Competitive Nucleation and Phase Selection in Drop Tube Processing of Multicomponent Alloys 139 M. Krivilyov and Jan Fransaer 7.1 Introduction 139 7.2 Model 140 7.2.1 Equations of Time-Dependent Motion, Fluid Flow, and Heat Transfer 141 7.2.2 Equations of Nucleation Kinetics and Crystal Growth 143 7.2.3 Coupling of the Models