Solidification of Containerless Undercooled Melts Wiley-VCH the Editors All Books Published by Are Carefully Produced

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 transition from liquid to solid state of matter. The conditions under which material is transformed determines the physical and chemical properties 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 performance 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 influence of thermodynamic and hydrodynamic conditions that control selection of nucleation mechanisms and modify crystal growth development 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 symposia. 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 processing, 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.

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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 publication 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

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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 and Experiment Data 144 7.3 Effect of Transient Heat and Mass Transfer on Nucleation and Crystal Growth 145 7.3.1 Transients in the Internal Flow 145 7.3.2 Heat Transfer, Cooling Rates, and Temperature Distribution 146 7.4 Competitive Nucleation and Phase Selection in Nd–Fe–B Droplets 148 7.4.1 Calculation of the Temperature–Time Proﬁles 148 7.4.2 Critical Undercooling as a Function of the Drop Size 151 7.4.3 Delay Time as a Function of the Convection Intensity 152 7.5 Summary 153 Appendix 7.A: Extended Model of Nonstationary Heterogeneous Nucleation 154 References 157

8 Containerless Solidification of Magnetic Materials Using the ISAS/JAXA 26-Meter Drop Tube 161 Shumpei Ozawa 8.1 Introduction 161 8.2 Drop Tube Process 162 8.2.1 Experimental Procedure 162 8.2.2 Undercooling Level and Cooling Rate of the Droplet during the Drop Tube Process 163 VIII Contents

8.3 Undercooling Solidification of Fe–Rare Earth (RE) Magnetostriction Alloys 165 167 8.3.1 Fe67Nd33 Alloy 168 8.3.2 Fe67Tb33 and Fe67Dy33 Alloys 170 8.3.3 Fe67Nd16.5Tb16.5 and Fe67Nd16.5Dy16.5 Alloys 8.4 Undercooling Solidification of Nd–Fe–B Magnet Alloys 173 8.4.1 Phase Selection and Microstructure Evolution of Nd–Fe–B Alloys Solidified from Undercooled Melt 174 8.4.2 Magnetic Property of the Metastable Phase 177 178 8.4.3 Mechanism of Transformation of the Nd2Fe17Bx Metastable Phase 8.5 Concluding Remarks 183 References 184

9 Nucleation and Solidification Kinetics of Metastable Phases in Undercooled Melts 187 Wolfgang Löser and Olga Shuleshova 9.1 Introduction 187 9.2 Thermodynamic Aspects and Nucleation of Metastable Phases 188 9.3 Metastable Phase Formation from Undercooled Melts in Various Alloy Systems 190 9.3.1 The Metastable Supersaturated Solid Solution Phases 190 9.3.2 The Metastable Phase Formation for Refractory Metals 192 9.3.3 The Metastable bcc Phase Formation in Fe-Based Alloys 193 9.3.4 The Metastable Phase Formation in Peritectic Systems with Ordered Intermetallic Compounds 198 9.3.5 The Metastable Phase Formation in Eutectic Systems with Ordered Intermetallic Compounds 203 9.3.6 The Formation of Metastable Quasicrystalline Phases 204 9.3.7 The Formation of Amorphous Phases 206 9.4 Summary and Conclusions 207 References 208

10 Nucleation Within the Mushy Zone 213 Douglas M. Matson 10.1 Introduction 213 10.1.1 Double Recalescence 213 10.1.2 Solidiﬁcation Path 217 10.2 Incubation Time 218 10.3 Cluster Formation 219 10.3.1 Homogeneous Nucleation of a Spherical Cluster 219 10.3.2 Heterogeneous Nucleation of a Spherical Cap on a Flat Surface 221 10.4 Transient Development of Heterogeneous Sites 224 10.4.1 Dendrite Fragmentation 225 10.4.2 Crack Formation 225 10.4.3 Dendrite Collision 227 Contents IX

10.4.4 Internal Grain Boundary Formation 229 10.4.5 Heterogeneous Nucleation Within a Crevice 230 10.5 Comparing Critical Nucleus Development Mechanisms 235 10.6 Concluding Remarks 236 References 237

11 Measurements of Crystal Growth Velocities in Undercooled Melts of Metals 239 Thomas Volkmann 11.1 Introduction 239 11.2 Experimental Methods 241 11.3 Summary and Conclusions 256 References 257

12 Containerless Crystallization of Semiconductors 261 Kazuhiko Kuribayashi 12.1 Introduction 261 12.2 Status of Research on Facetted Dendrite Growth 262 12.3 Twin-Related Lateral Growth and Twin-free Continuous Growth 264 12.3.1 Twin-Related h211i and h110i Facetted Dendrites 264 12.3.2 Twin-Free h100i Facet Dendrites 266 12.3.3 Transition from Twin-Related Facet Dendrites to Twin-Free Facet Dendrites 267 12.3.4 Rate-Determining Process for Crystallization into Undercooled Melts 268 12.4 Containerless Crystallization of Si 270 12.4.1 Experimental 270 12.4.2 Application to Drop-Tube Process 275 12.5 Summery and Conclusion 276 12.6 Appendix 12.A: LKT Model 276 12.A.1 Wilson–Frenkel Model 277 References 278

13 Measurements of Crystal Growth Dynamics in Glass-Fluxed Melts 281 Jianrong Gao, Zongning Zhang, Yikun Zhang, and Chao Yang 13.1 Introduction 281 13.2 Methods and Experimental Set-Up 282 13.2.1 Access to Large Undercoolings 282 13.2.2 In-Situ Observations 283 13.2.3 Data Processing 283 13.2.4 Experimental SetUp and Procedures 284 13.3 Growth Velocities in Pure Ni 286 13.3.1 Overview of Literature Data 286 13.3.2 Recalescence Characteristic 287 13.3.3 Dendritic Growth Velocities 289 X Contents 291 13.4 Growth Velocities in Ni3Sn2 Compound 13.4.1 Peculiarities of Intermetallic Compounds 291 13.4.2 Novel Data of Growth Velocities 291 13.5 Crystal Growth Dynamics in Ni–Sn Eutectic Alloys 293 13.5.1 Background 293 13.5.2 Recalescence Behavior and Growth Velocities 293 13.5.3 Microstructure 295 13.6 Opportunities with High Magnetic Fields 295 13.6.1 Motivation 295 13.6.2 Opportunities with High Magnetic Fields 296 13.6.3 Effects of Static Magnetic Fields on Undercooling Behavior 297 13.6.4 Measured Growth Velocities of Pure Ni 298 13.7 Summary 300 References 301

14 Influence of Convection on Dendrite Growth by the ACþDC Levitation Technique 305 Hideyuki Yasuda 14.1 Convection in a Levitated Melt 305 14.1.1 Challenges in Conventional Levitation 305 14.1.2 Influence of Convection 306 14.2 Static Levitation Using the Alternating and Static Magnetic Field (AC þ DC Levitation) 307 14.2.1 Simultaneous Imposition of AC þ DC Magnetic Fields 307 14.2.2 Setup of the AC þ DC Levitator 309 14.2.3 Dynamics of a Droplet Under AC þ DC Fields 309 14.2.4 Effect of the Static Magnetic Field on Flow Velocity 312 14.3 Effect of Convection on Nucleation and Solidification 313 14.3.1 Nucleation Undercooling 313 14.3.2 Solidification Structure 314 14.3.3 Growth Velocity of Dendrite 317 References 319

15 Modeling the Fluid Dynamics and Dendritic Solidification in EM-Levitated Alloy Melts 321 Valdis Bojarevics, Andrew Kao, and Koulis Pericleous 15.1 Introduction 321 15.2 Mathematical Models for Levitation Thermoﬂuid Dynamics 322 15.2.1 Thermoﬂuid Equations 326 15.2.2 Simulations of Droplet Levitation 327 15.2.3 DC Field Stabilization 330 15.2.4 Levitating Large Masses 332 15.2.5 Impurity Separation 335 15.3 Thermoelectric Magnetohydrodynamics in Levitated Droplets 336 15.3.1 Thermoelectricity 337 Contents XI

15.3.2 Solidification by the Enthalpy Method 338 15.3.3 TEMHD in Dendritic Solidification 339 15.3.4 Solidification of an Externally Cooled Droplet 345 15.4 Concluding Remarks 346 References 346

16 Forced Flow Effect on Dendritic Growth Kinetics in a Binary Nonisothermal System 349 P.K. Galenko, S. Binder, and G.J. Ehlen 16.1 Introduction 349 16.2 Convective Flow in Droplets Processed in Electromagnetic Levitation 350 16.3 The Model Equations 351 16.4 Predictions of the Model 355 16.4.1 Dendrite Growth in a Pure (One-Component) System 355 16.4.2 Dendrite Growth in a Binary Stagnant System 356 16.5 Quantitative Evaluations 356 16.5.1 Modiﬁed Ivantsov Function 356 16.5.2 Dendrite Growth Velocity and Tip Radius 357 16.6 Summary and Conclusions 360 References 361

17 Atomistic Simulations of Solute Trapping and Solute Drag 363 J.J. Hoyt, M. Asta and A. Karma 17.1 Introduction 363 17.2 Models of Solute Trapping 364 17.3 Solute Drag 367 17.4 MD Simulations 368 17.4.1 The LJ System 369 17.4.2 The Ni–Cu System 371 17.5 Implications for Dendrite Growth 376 References 379

18 Particle-Based Computer Simulation of Crystal Nucleation and Growth Kinetics in Undercooled Melts 381 Roberto E. Rozas, Philipp Kuhn, and Jürgen Horbach 18.1 Introduction 381 18.2 Solid–Liquid Interfaces in Nickel 383 18.3 Homogeneous Nucleation in Nickel 389 18.4 Crystal Growth 393 18.5 Conclusions 398 References 399 XII Contents

19 Solidification Modeling: From Electromagnetic Levitation to Atomization Processing 403 Ch.-A. Gandin, D. Tourret, T. Volkmann, D.M. Herlach, A. Ilbagi, and H. Henein 19.1 Introduction 403 19.2 Electromagnetic Levitation 404 19.3 Impulse Atomization 405 19.4 Modeling 406 19.4.1 General Assumptions 407 19.4.2 Mass Conservations 407 19.4.3 Speciﬁc Surfaces 408 19.4.4 Diffusion Lengths 409 19.4.5 Nucleation 410 19.4.6 Heat Balance 410 19.4.7 Thermodynamics Data 410 19.4.8 Growth Kinetics 411 19.4.9 Numerical Solution 412 19.5 EML Sample 413 19.6 IA Particles 418 19.6.1 Regime of Distinct Successive Growth 419 19.6.2 Regime of Shortcut of the Primary Growth 421 19.7 Conclusion 422 References 423

20 Properties of p-Si-Ge Thermoelectrical Material Solidified from Undercooled Melt Levitated by Simultaneous Imposition of Static and Alternating Magnetic Fields 425 Takeshi Okutani, Tsuyoshi Hamada, Yuko Inatomi, and Hideaki Nagai 20.1 Introduction 425 20.2 Simultaneous Imposition of Static and Alternating Magnetic Fields 427 20.3 Experimental 429 20.3.1 Si–Ge Alloy Preparation 429

20.3.2 Synthesis of Si0.8Ge0.2 with 1 at% B by Electromagnetic Levitation with Simultaneous Imposition of Static and Alternating Magnetic Fields 429 20.3.3 Evaluation 431 20.4 Results and Discussion 432 20.4.1 Temperature and Solidiﬁcation Behavior 432 20.4.2 Crystalline Orientation of Solidiﬁed Product from Undercooled Melt by EML with SMF 436

20.4.3 Microstructure and Si and Ge Distributions of Si0.8Ge0.2-1at% B Solidiﬁed from Undercooled Melts by EML with SMF 439 ﬁ 20.4.4 Thermoelectrical Properties of Si0.8Ge0.2-1at% B Solidi ed from Undercooled Melts by EML with SMF 442 Contents XIII

20.4.4.1 Thermal Conductivity 442 20.4.4.2 Electrical Conductivity 443 20.4.4.3 Seebeck Coefﬁcient 446 20.4.4.4 Figure of Merit 446 20.5 Summary and Conclusions 448 References 448

21 Quantitative Analysis of Alloy Structures Solidified Under Limited Diffusion Conditions 451 Hani Henein, Arash Ilbagi, and Charles-André Gandin 21.1 The Need for an Instrumented Drop Tube 451 21.2 Description of IA 454 21.3 Powder Characteristics 455 21.4 Quantiﬁcation of Microstructure 459 21.4.1 Secondary Dendrite Arm Spacing 459 21.4.2 X-Ray Microtomography 461 21.4.3 Neutron Diffraction 467 21.5 Modeling 469 21.5.1 Cooling Rate 469 21.5.2 Eutectic Undercooling 473 21.5.3 Peritectic Systems 477 References 480

22 Coupled Growth Structures in Univariant and Invariant Eutectic Solidification 483 Ralph E. Napolitano 22.1 Introduction 483 22.2 Historical Perspective and Background 484 22.3 Basic Theory of Eutectic Solidification 490 22.4 Eutectic Solidification Theory for Ternary Systems 493 22.5 Solidification Paths and Competitive Growth Considerations 496 22.6 Recent Developments, Emerging Issues, and Critical Research Needs 499 References 504

23 Solidification of Peritectic Alloys 509 Krishanu Biswas and Sumanta Samal 23.1 Introduction 509 23.2 Peritectic Equilibrium and Transformation 510 23.3 Peritectic Reactions in the Ternary System 512 23.4 Nucleation Studies 514 23.4.1 Solidiﬁcation of Peritectic Alloys at Low Undercooling 515 23.4.2 Solidiﬁcation of Peritectic Alloys at High Undercooling 518 23.5 Growth 522 23.5.1 Peritectic Reaction 524 XIV Contents

23.5.2 Peritectic Transformation 526 23.5.3 Direct Solidiﬁcation of the Peritectic Phase 528 23.5.4 Peritectic Reaction in Ternary Systems 529 23.5.5 Peritectic Solidiﬁcation Under Reduced Gravity Conditions 536 23.6 Conclusions 539 References 539

Index 543 jXV

Preface

Metallic materials are prepared from the liquid state as their parent phase. The conditions under which the liquid solidifies determine the physical and chemical properties of the as-solidified material. In most cases time and energy consuming post-solidification treatment of the material is mandatory to obtain the final product with its desired properties and design performance. Therefore, efforts are directed towards virtual material design with computer assisted modelling. This can shorten the entire production chain - ranging from casting the shaped solid from the melt to the final tuning of the product in order to save costs during the production process. The goal is to fabricate novel materials with improved properties for specific applications. To date, metal production is the largest industry worldwide. In the European Union there are 417 700 enterprises with 5.1 Million employees. They correspond to 3.9% of the entire workforce and produce 244.4 billion EUR added value each year (European business – Facts and figures Eurostat 2007). Therefore, even small improvements in production efficiency for the metal industry may lead to large economic gains. Computational materials science from the liquid state requires thermo-physical parameters measured with high accuracy and detailed knowledge of the physical mechanisms involved in the solidification process. In particular, these are crystal nucleation and crystal growth. Both of these processes are driven by an undercooling of the liquid below its equilibrium melting temperature to develop conditions where a driving force for the advancement of a solidification front is created. This gives access to non-equilibrium solidification pathways which can form metastable solids which may differ in their physical and chemical properties from their stable counter- parts. Detailed modelling of solidification, both near equilibrium and far away from thermodynamic equilibrium, requires that the solidification process must be investigated in every detail. In order to achieve the state of an undercooled melt, it is advantageous to remove heterogeneous nucleation sites which otherwise limit the undercoolability. The most efficient way to realize such conditions is containerless processing of melts. In such, the most dominant heterogeneous nucleation process, involving interaction with container walls, is completely avoided. Nowadays, electromagnetic and electrostatic levitation techniques have been developed for containerless undercooling and XVIj Preface

solidification of molten metals and alloys. A freely suspended drop gives the extra benefit to directly observe the solidification process by combining the levitation technique with proper diagnostic means. For instance, short range ordering as precursor of crystal nucleation has been investigated by using synchrotron radiation and neutron diffraction on containerless undercooled melts. Additionally, primary phase selection processes for rapid solidification of metastable phases has been observed in situ by energy dispersive X-ray radiation using synchrotron radiation of high intensity. Rapid growth of dendrites is observed on levitation undercooled melts by using video camera techniques characterized by high spatial and temporal resolution. The application of containerless processing on Earth is limited since large levitation forces are needed to compensate for the gravitational force acting on the samples. The large levitation forces cause undesirable effects like externally induced stirring of the liquid or deformation of the liquid sample from sphere-like geometry. These are overcome when utilizing the special environment of reduced gravity. Here, the forces to compensate for g-jitter, the small random accelerations associated with spacecraft operation, are about three orders of magnitude less than levitation forces on Earth. Based upon such consideration a facility for containerless electro-magnetic processing in space called TEMPUS (Tiegelfreies Elektro-Magnetisches Prozessieren Unter Schwerelosigkeit) has been developed by DLR, the German Space Agency. It was constructed by the German aerospace industry and tested during several parabolic flight campaigns to demonstrate technical functionality. In a cooperation between DLR Space Agency and the US National Aeronautics and Space Administration (NASA), TEMPUS had its maiden flight under real space conditions on board the shuttle Columbia during the NASA Spacelab mission International Microgravity Laboratory IML 2 in 1994. The German – USA cooperation was handled on the principle no exchange of funds meaning that the facility was provided by DLR and flight opportunity was offered by NASA. The total experiment time during the 14 days mission was shared between US and German investigator teams. The mission was successful not only by demonstrating technical functionality of TEMPUS in Space but also obtaining interesting scientific results including high accuracy measurements of thermophysical properties and investigations of gravity related phenomena in solidification of undercooled metals and alloys. Later on, TEMPUS was flown again on Columbia during NASA spacelab missions Microgravity Space Laboratory 1 (MSL-1) and Microgravity Space Laboratory 1 reflight (MSL-1R) in 1997. A broad spectrum of science return from the TEMPUS spacelab missions are published in Materials and Fluids Under Microgravity, Lecture Notes in Physics, eds.: L. Ratke, H. Walter, B. Feuerbacher (1995) and Solidification 1999, Proceedings of symposia at the TMS Fall Meeting 1998, eds.: W. H. Hofmeister, J. R. Rogers, N.B. Singh, S. P. Marsh, P. W. Vorhees (1999). At present, an advanced Electro-Magnetic Levitator (EML) facility is under development by a common effort between the DLR Space Agency and the European Space Agency ESA. The EML is constructed by ASTRIUM and is scheduled for accom- modation on board the International Space Station ISS in 2013. Meanwhile, several international investigator teams of scientists from the member states of ESA, USA Preface jXVII and Japan are preparing experiments dedicated to be performed in Space using the EML multi-user facility on the ISS. In parallel to the experimental work, modelling and theoretical evaluation of solidification processes are planned. In particular, understanding the importance of gravity-driven phenomena like changes in heat and mass transport by forced convection is a central part of these solidification investigations. These developments both on the experimental and on the theoretical side stimulated the editors of the present book to collect the state of solidification research as far as it is directly correlates to solidification of containerless undercooled melts. These attempts were supported by our colleagues who contributed to the scientific content of the present book. We appreciate their efforts and cooperation in delivering high quality articles to this book. Most of the authors of the book are members of an international Topical Team on Containerless Undercooling and Solidification of Melts (SOL-EML) sponsored by the European Space Agency. We thank ESA for this support and for their vision to bring together experts in this field from all over the world - with membership coming from Europe, North America, Japan and also from China and India. In these latter countries, enormous efforts are undertaken at present to set up a materials science programme in space. In particular, German partners and colleagues benefitted from priority programmes focused on solidification research on undercooled melts in the Earth laboratory, which were financed by the German Research Foundation DFG. This support is greatly appreciated as well. Last but not least the editors are very grateful to Dr. Martin Graf from WILEY– VCH for pleasant and efficient cooperation during the entire course of preparing and editing the present book. Dieter Herlach and Douglas Matson

XIX

List of Contributors

Mark Asta Valdis Bojarevics University of California University of Greenwich Department of Materials Science and School of Computing and Mathematical Engineering Sciences 210 Hearst Memorial Mining Building, Old Royal Naval College Room 384 Park Row Berkeley, CA 94720 London SE10 9LS USA UK

Sven Binder Georg Ehlen Institut für Materialphysik im Weltraum Institut für Materialphysik im Weltraum Deutsches Zentrum für Luft- und Deutsches Zentrum für Luft- und Raumfahrt Raumfahrt Linder Höhe Linder Höhe 51147 Köln 51147 Köln Germany Germany

Krishanu Biswas and Indian Institute of Technology Department of Materials Science and Institut für Festkörperphysik Engineering Ruhr-Universität Bochum Faculty Building, Room 407 Universitätsstraße 150 Kanpur 208016 44780 Bochum India Germany

Jan Fransaer University of Leuven Department of Metallurgy and Materials Engineering (MTM) Kasteelpark Arenberg 44 - box 2450 3001 Heverlee Belgium XX List of Contributors

Peter K. Galenko Alain Lindsay Gree Institut für Materialphysik im Weltraum University of Cambridge Deutsches Zentrum für Luft- und Department of Materials Science and Raumfahrt Metallurgy Linder Höhe Pembroke Street 51147 Köln Cambridge CB2 3QZ Germany UK

and Tsuyoshi Hamada Yokohama National University Institut für Festkörperphysik Graduate School of Environment and Ruhr-Universität Bochum Information Sciences Universitätsstraße 150 79-7 Tokiwadai 44780 Bochum Hodogaya-ku Germany Yokohama 240-8501 Japan Charles-André Gandin MINES ParisTech Hani Henein CEMEF UMR 7635, CNRS University of Alberta 06904 Sophia Antipolis Department of Chemical and Materials France Engineering 7th Floor, Electrical & Computer Jianrong Gao Engineering Research Facility (ECERF) Northeastern University 91017-116 Street Key Laboratory of Electromagnetic Edmonton, Alberta T6G 2V4 Processing of Materials Canada P.O. Box 314 3-11 Wenhua Road Dieter M. Herlach Shenyang 110004 Institut für Materialphysik im Weltraum China Deutsches Zentrum für Luft- und Raumfahrt László Gránásy Linder Höhe BCAST 51147 Köln Brunel University Germany Uxbridge Middlesex UB8 3PH Dirk Holland-Moritz UK Institut für Materialphysik im Weltraum Deutsches Zentrum für Luft- und and Raumfahrt (DLR) Linder Höhe Research Institute for Solid State 51170 Köln Physics and Optics Germany P.O. Box 49 1525 Budapest Hungary List of Contributors XXI

Jürgen Horbach Yuko Inatomi Institut für Materialphysik im Weltraum Institute of Space and Astronautical Deutsches Zentrum für Luft- und Science, JAXA Raumfahrt (DLR) 3-1-1 Yoshinodai, Sagamihara Linder Höhe Chuo-ku 51170 Köln Kanagawa 229-8510 Germany Japan and Andrew Kao University of Greenwich Heinrich Heine-Universität Düsseldorf School of Computing and Mathematical Institut für Theoretische Physik der Sciences Weichen Materie Old Royal Naval College Universitätsstraß e 1 Park Row 40225 Düsseldorf London SE10 9LS Germany UK Alain Karma Jeff J. Hoyt Northeastern University McMaster University Department of Physics Department of Materials Science and 360 Huntington Ave Engineering Boston, MA 02115 1280 Main Street USA Hamilton, Ontario L8S4LS Canada Kenneth F. Kelton Washington University in St. Louis Robert W. Hyers Department of Physics University of Massachusetts One Brookings Drive Mechanical and Industrial Engineering St. Louis, MO 63130-4899 160 Governors Drive USA Amherst, MA 01003-2210 USA Matthias Kolbe Institut für Materialphysik im Weltraum Arash L. Ilbagi Deutsches Zentrum für Luft- und University of Alberta Raumfahrt (DLR) Department of Chemical and Materials Linder Höhe Engineering Department 51147 Köln 7th Floor, Electrical & Computer Germany Engineering Research Facility (ECERF) 91017-116 Street Mikhael Krivilyov Edmonton, Alberta T6G 2V4 Udmurt State University Canada Department of Physics Laboratory of Condensed Matter Physics Universitetskaya 1 426034 Izhevsk Russia XXII List of Contributors

Philipp Kuhn Takeshi Okutani Institut für Materialphysik im Weltraum Yokohama National University Deutsches Zentrum für Luft- und Graduate School of Environment and Raumfahrt (DLR) Information Sciences Linder Höhe 79-7 Tokiwadai 51170 Köln Hodogaya-ku Germany Yokohama 240-8501 Japan Kazuhiko Kuribayashi Japan Aerospace Exploration Agency Shumpei Ozawa The Institute of Space & Astronautical Tokyo Metropolitan University Science Department of Aerospace Engineering 3-1-1 Yoshinodai, Sagamihara Hino-shi Chuo-ku Tokyo 1901-065 Kanagawa 229-8510 Japan Japan Koulis Pericleous Wolfgang Löser University of Greenwich Leibniz-Institut für Festkörper und School of Computing and Mathematical Werkstoffforschung, IFW Sciences Helmholtzstraße 20 Old Royal Naval College 01069 Dresden Park Row Germany London SE10 9LS UK Douglas M. Matson Tufts University Tamás Pusztai Department of Mechanical Engineering Research Institute for Solid State 200 College Avenue Physics and Optics Medford, MA 02155 P.O. Box 49 USA 1525 Budapest Hungary Hideaki Nagai National Institute of Advanced Roberto E. Rozas Industrial Science and Technology Institut für Materialphysik im Weltraum AIST Tsukuba Central 5 Deutsches Zentrum für Luft- und Tsukuba, Ibaraki 305-8565 Raumfahrt (DLR) Japan Linder Höhe 51170 Köln Ralph E. Napolitano Germany Iowa State University Division of Materials Science and Engineering 3273 Gilman Hall Ames, IA 50011-2300 USA List of Contributors XXIII and and

Heinrich Heine-Universität Düsseldorf Institut für Materialphysik im Weltraum Institut für Theoretische Physik der Deutsches Zentrum für Luft- und Weichen Materie Raumfahrt Universitätsstraß e 1 Linder Höhe 40225 Düsseldorf 51147 Köln Germany Germany

Sumanta Samal Thomas Volkmann Indian Institute of Technology Institut für Materialphysik im Weltraum Department of Materials Science and Deutsches Zentrum für Luft- und Engineering Faculty Building Raumfahrt Kanpur 208016 Linder Höhe India 51147 Köln Germany Olga Shuleshova Leibniz-Institut für Festkörper- und Chao Yang werkstoffforschung, IFW Northeastern University Helmholtzstr. 20 Key Laboratory of Electromagnetic 01069 Dresden Processing of Materials Germany P.O. Box 314 3-11 Wenhua Road György Tegze Shenyang 110004 Institute for Solid State China Physics and Optics Wigner Research Centre for Physics Hideyuki Yasuda P.O. Box 49 Osaka University 1525 Budapest Graduate School of Engineering Hungary Department of Adaptive Machine Systems Gyula I. Tóth Suita Institute for Solid State Osaka 565-0871 Physics and Optics Japan Wigner Research Centre for Physics P.O. Box 49 1525 Budapest Hungary

Damien Tourret MINES ParisTech CEMEF UMR 7635, CNRS 06904 Sophia Antipolis France XXIV List of Contributors

Yikun Zhang Zongning Zhang Northeastern University Northeastern University Key Laboratory of Electromagnetic Key Laboratory of Electromagnetic Processing of Materials Processing of Materials P.O. Box 314 P.O. Box 314 3-11 Wenhua Road 3-11 Wenhua Road Shenyang 110004 Shenyang 110004 China China j1

1 Containerless Undercooling of Drops and Droplets Dieter M. Herlach

1.1 Introduction

Containerless processing of droplets has a long traditional experience. In his work Discorsi e Dimostrazioni Matematiche intorno a due nuove scienze published in 1639, Galileo Galilei describes experiments in which materials of different specific mass density were dropped down to ground from the leaning tower of Pisa to demonstrate that bodies of different mass fall with same velocity if friction in the air is neglected. In 1799, it was reported that a drop tower was used to produce lead shots by containerless solidification of liquid droplets during free fall. Liquid lead was pressed through a sieve at the top of the drop shaft to produce droplets of unique size, which solidified during free fall. The conditions of reduced gravity during free fall favored an ideal sphere-like geometry of the droplets upon solidification. If a droplet is containerless solidified, often the liquid cools down below the equilibrium melting temperature prior to solidification. By using containerless processing methods, large undercoolings can be achieved since heterogeneous nucleation on container walls is completely avoided that is otherwise initiating crystallization of the melt. Nowadays, a great variety of techniques are applied for containerless undercooling. One distinguishes between drop tubes for containerless solidification of a spray of droplets, drop towers to process individual drops during free fall, and levitation techniques. Small drop tubes are quite suitable to study the statistics of phase and microstructure formation of particles on size less than 1 mm. The droplets are solidifying during free fall inside the drop tube. Thus, drop tubes are in house facilities to study solidification under reduced gravity conditions. For instance phase selection diagrams can be constructed such that they are describing the formation of competing phases in dependence of the droplet size, or the cooling rate since the droplet size directly correlates to the cooling rate [1]. Large drop tubes in height up to 150 m enable solidification of individual drops in size up to several millimeters. They are used to study the glass-forming ability of metallic alloys [2]. The temperature profile of drops falling under ultrahigh-vacuum conditions is recorded

Solidiﬁcation of Containerless Undercooled Melts, First Edition. Edited by D.M. Herlach and D.M. Matson Ó 2012 Wiley-VCH Verlag GmbH & Co, KGaA. Published 2012 by Wiley-VCH Verlag GmbH & Co. KGaA. 2j 1 Containerless Undercooling of Drops and Droplets

by a set of photodiodes arranged along the dropt tube. In such a way phase selection of refractory alloy systems is studied as a function of undercooling [3]. Drop towers and drop shafts are differing from drop tubes in such that experiment facilities are falling and samples can be studied under reduced gravity conditions for a period of 4.5 s at a falling distance of 150 m (drop tower in Bremen) and 9 s at falling distance of 500 m (drop shaft in Hokkaido), respectively. In all drop tubes and drop towers, it is difficult if not at all impossible to perform in situ diagnostics of solidification of metallic drops. Levitation techniques offer the great potential not only to containerless undercool and solidify drops in size up to 10 mm but they can also be combined with proper diagnostic means and allow for even stimulate solidification of freely suspended drops externally at various undercooling levels. A simple quasilevitation technique was frequently used to undercool a liquid metal or alloy by embedding it into a denucleation agent. In such a way, contact to the solid container is avoided, and in most cases the melt fluxing agent removes heterogeneous motes on the surface of the molten drop [4]. However, this technique is limited by the need to avoid chemical reactions between fluxing agent and liquid metal. Electromagnetic levitation was developed for containerless undercooling and solidification of metallic systems. The eddy currents induced by an alternating, inhomogeneous electromagnetic field create a secondary field that is opposite to the primary one. Thus, the eddy currents will create a repulsive force. If a properly designed coil is used and the coil current is adjusted, the repulsive force compensates the gravitational force and the sample is electromagnetically levitated. The eddy currents induced by alternating electromagnetic field cause at the same time heating the sample. Coupling of levitation and heating gives the advantage that no extra heating source is required, however, leads to the disadvantage that temperature control is only possible in a range at elevated temperature since levitations needs a minimum power absorption to guarantee a freely suspended drop [5]. This boundary condition is circumvented by applying electrostatic levitation. Here, a sample in diameter of 2–3 mm is electrically charged up and levitated in a strong electrostatic field. In most cases a laser is used to heat the sample [6]. Whereas the electromagnetic levitation is a self-stabilizing method, the electrostatic levitation needs a sophisticated sample positioning and a real-time electrostatic field control, since the sample is always in an unstable position (Earnshow theorem). Other methods like aerodynamic and acoustic levitation are frequently used for organic substances and oxides. They are not favorable techniques to undercool high melting metals. On the one side, a liquid metal changes at high temperatures the local levitation conditions, and more seriously, some residual amounts of oxygen in the environmental processing gas leads to the formation of metal oxides at the surface of the metallic drop. Sine metal oxides are in most cases thermodynamically more stable than the parent metal, they act as heterogeneous nucleation sites and limit the accessible undercooling range. Therefore, these techniques are not further dealt with in the present book. The special environment of reduced gravity during parabolic flight and in Space offers the great advantage that the forces to compensate disturbing accelerations are by orders of magnitude smaller than the force needed to compensate the gravitational 1.2 Drop Tubes j3 force on Earth. Moreover, in case of electromagnetic processing the stirring of the melt due to the eddy currents are much reduced. The German Space Agency Deutsche Agentur fur€ Raumfahrtangelegenheiten DARA, now Deutsches Zentrum fur€ Luft- und Raumfahrt – Raumfahrtagentur (DLR Space Agency) – has developed an electromagnetic levitator for the use in reduced gravity. It applies a new technical concept such that two different frequency generators operating at different frequen- cies power a coil for positioning by a quadrupole field and, separately from that, a coil that produces a dipole field for efficient heating [7]. This concept was mandatory to develop a levitator for the usage in Space since it increased the efficiency in energy consumption of high-frequency generators for levitation from 1 to 2% (conventional high-frequency generators) to more than 30%. This device, called TEMPUS (German acronym for containerless processing in reduced gravity, Tiegelfreies Electro- Magnetisches Prozessieren Unter Schwerelosigkeit) was successfully tested in the realistic environment in Space by three NASA Spacelab missions, IML2 (1994), MSL1, and MSL1R (1997). At the same time very interesting results were obtained in measuring thermophysical properties of liquid metals and alloys even in the metastable regime of the undercooled melt, and in investigating phase selection and dendrite growth in reduced gravity [8]. Basing upon the success of TEMPUS, DLR, and ESA are currently developing in a common effort, an electromagnetic levitator (EML) as a multiuser facility on board the International Space Station (ISS). Thanks to the national agencies and the European Space Agency (ESA), several international researcher teams are preparing experiments using the EML on board the ISS. These experiments are divided into four different classes: (i) solidification, (ii) measurements of surface tension and viscosity, (iii) measurements of thermodynamic properties, and (iv) measurements of the mass density and thermal expansion. In the present book we concentrate on solidification comprising both experimental research in drop tubes and levitation devices on Earth and some specific experiments in Space. These experimental works are escorted by theoretical works as mesoscopic modeling of dendrite growth and atomistic modeling of attachment kinetics of atoms from liquid to solid. In the present chapter, facilities for containerless solidification of undercooled melts are introduced. Their technical concepts are described and some exemplary results are demonstrated as obtained from experiments using the various devices.

1.2 Drop Tubes

The drop tube technique is employed to cool and solidify small molten droplets, which fall containerlessly down a tube that can be evacuated and backfilled with processing gases such as He, Ar, or others. It is convenient to distinguish between two categories of tubes – short and long – which reflect the type of the experiment that can be performed. In short drop tubes, a liquid jet of material is produced that disperses into many small droplets. In long drop tubes, individual drops in size of a few millimetres are undercooled and solidified during free fall. 4j 1 Containerless Undercooling of Drops and Droplets

1.2.1 Short Drop Tubes

Sample material in mass of several grams is melted in a crucible, which contains a small bore at its lower side. By using Ar gas at overpressure, the liquid metal is pressed through the bore of the crucible. A thin liquid jet of a metal is formed and it disperses into small droplets (Rayleigh instability of a thin liquid jet). The small droplets undercool and solidify during the free fall containerlessly in reduced gravity. This technique is employed to study undercooling and nucleation phenomena [9–11], to investigate the evolution of grain-refined microstructures [12, 13], and to produce metastable crystalline materials and metallic glasses [9–11, 14, 15]. Figure 1.1 illustrates the experimental setup of a drop tube in length of 14 m (free fall time 1.4 s) at the German Aerospace Center (DLR) in Cologne [16]. The drop tube is made of stainless steel components all of which are compatible with the requirements of ultrahigh vacuum (UHV) technique. The drop tube is evacuated before each experiment to a pressure of approximately 10 7 mbar and, subse- fi – quently, back lled with high purity He or He H2 gasofhighthermalconductivity. The processing gas is purified as it passes a chemical oxygen absorption system and a liquid nitrogen cold trap. The sample material in a crucible of, for example, fused silica, is melted inductively. After all the material is liquid, its temperature is measured by a two-color pyrometer and subsequently forced by Ar pressure of 2 bars through the small bore. The droplets solidified during free fall through the drop tube they are collected at the bottom of the drop tube and are sorted by meshes in different size groups ranging from 50 to 1000 mm diameter. Since the droplet diameter scales with the cooling rate at which the droplets cool down, drop tubes are quite suitable to study statistical processes of phase selection and their temperature–time–transformation behavior. Figure 1.2 shows the volume fractions of the various phases formed in drop tube

processed Al88Mn12 alloy as a function of droplet diameter [1]. Quasicrystalline phases of ﬁvefold symmetry were discovered as a new class of solid-state matter in

between of crystalline and amorphous solids in melt spun ribbons of Al88Mn12 alloy [18]. Depending on the preparation conditions, an icosahedral I-phase with quasiperiodicity in three dimensions, a decagonal T-phase with quasiperiodicity in two dimensions, and periodicity in the third dimension and different crystalline phases are solidiﬁed in this alloy. The drop tube experiments reveal that the I-phase is formed far from equilibrium in the smallest droplets at highest cooling rate. At

medium droplet size, T-phase and supersaturated Alss solid solution are found. The mass fraction of Alss phase increases with droplet size (decreasing cooling rate) on the expense of T-phase. At largest droplet size of drops in the order of about 1 mm in

diameter, also the equilibrium intermetallic phase Al6Mn is crystallized. Calculations of nucleation–kinetics plots reproduce the experimentally observed phase-selection

behavior of drop tube processed Al88Mn12 alloy [19]. Drop tube experiments are also used to determine the formation of different phases selected kinetically by the cooling rate. Temperature–time–transformation (TTT)