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 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 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 experiments 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.
Table of 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
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
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
8.3 Undercooling Solidification of Fe–Rare Earth (RE) Magnetostriction Alloys 165
8.3.1 Fe 67 Nd 33 Alloy 167
8.3.2 Fe 67 Tb 33 and Fe 67 Dy 33 Alloys 168
8.3.3 Fe 67 Nd 16.5 Tb 16.5 and Fe 67 Nd 16.5 Dy 16.5 Alloys 170
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
8.4.3 Mechanism of Transformation of the Nd 2 Fe 17 B X Metastable Phase 178
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
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
13.4 Growth Velocities in Ni 3 Sn 2 Compound 291
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
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
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 Si 0.8 Ge 0.2 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 Si 0.8 Ge 0.2 -1at% B Solidified from Undercooled Melts by EML with SMF 439
20.4.4 Thermoelectrical Properties of Si 0.8 Ge 0.2 -1at% B Solidified from Undercooled Melts by EML with SMF 442
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
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
About the Author :
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 Engineering 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 coordinated 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 symposium, 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.
