Solidification of Containerless Undercooled Melts -- Contents -- Preface -- List of Contributors -- 1 Containerless Undercooling of Drops and Droplets -- 1.1 Introduction -- 1.2 Drop Tubes -- 1.2.1 Short Drop Tubes -- 1.2.2 Long Drop Tubes -- 1.3 Containerless Processing Through Levitation -- 1.3.1 Electromagnetic Levitation -- 1.3.2 Electrostatic Levitation -- 1.3.3 Electromagnetic Levitation in Reduced Gravity -- 1.4 Summary and Conclusions -- References -- 2 Computer-Aided Experiments in Containerless Processing of Materials -- 2.1 Introduction -- 2.1.1 Nomenclature -- 2.2 Planning Experiments -- 2.2.1 Example: Feasible Range of Conditions to Test Theory of Coupled-Flux Nucleation -- 2.2.2 Example: The Effect of Fluid Flow on Phase Selection -- 2.3 Operating Experiments -- 2.4 Data Reduction, Analysis, Visualization, and Interpretation -- 2.4.1 Example: Noncontact Measurement of Density and Thermal Expansion -- 2.4.2 Example: Noncontact Measurement of Creep -- 2.5 Conclusion -- References -- 3 Demixing of Cu-Co Alloys Showing a Metastable Miscibility Gap -- 3.1 Introduction -- 3.2 Mechanism of Demixing -- 3.3 Demixing Experiments in Terrestrial EML and in Low Gravity -- 3.4 Demixing Experiments in a Drop Tube -- 3.5 Spinodal Decomposition in Cu-Co Melts -- 3.6 Conclusions -- References -- 4 Short-Range Order in Undercooled Melts -- 4.1 Introduction -- 4.2 Experiments on the Short-Range Order of Undercooled Melts -- 4.2.1 Experimental Techniques -- 4.2.2 Structure of Monatomic Melts -- 4.2.3 Structure of Alloy Melts -- 4.3 Conclusions -- References -- 5 Ordering and Crystal Nucleation in Undercooled Melts -- 5.1 Introduction -- 5.2 Nucleation Theory--Some Background -- 5.2.1 Classical Nucleation Theory -- 5.2.1.1 Homogeneous Steady-State Nucleation -- 5.2.1.2 Heterogeneous Nucleation -- 5.2.2 Nucleation Models that Take Account of Ordering.

5.2.2.1 Diffuse-Interface Model -- 5.2.2.2 Density-Functional Models -- 5.3 Liquid Metal Undercooling Studies -- 5.3.1 Experimental Techniques -- 5.3.2 Selected Experimental Results -- 5.3.2.1 Maximum-Undercooling Data -- 5.3.2.2 Nucleation Rate Measurements -- 5.4 Coupling of Ordering in the Liquid to the Nucleation Barrier -- 5.4.1 Icosahedral Ordering -- 5.4.2 Coupling of Ordering and Nucleation Barrier -- 5.4.3 Ordering in the Liquid Adjacent to a Heterogeneity -- 5.5 Conclusions -- References -- 6 Phase-Field Crystal Modeling of Homogeneous and Heterogeneous Crystal Nucleation -- 6.1 Introduction -- 6.2 Phase-Field Crystal Models -- 6.2.1 Free Energy Functionals -- 6.2.2 Euler-Lagrange Equation and the Equation of Motion -- 6.3 Homogeneous Nucleation -- 6.3.1 Solution of the Euler-Lagrange Equation -- 6.3.2 Solution of the Equation of Motion -- 6.4 PFC Modeling of Heterogeneous NuCleation -- 6.5 Summary -- References -- 7 Effects of Transient Heat and Mass Transfer on Competitive Nucleation and Phase Selection in Drop Tube Processing of Multicomponent Alloys -- 7.1 Introduction -- 7.2 Model -- 7.2.1 Equations of Time-Dependent Motion, Fluid Flow, and Heat Transfer -- 7.2.2 Equations of Nucleation Kinetics and Crystal Growth -- 7.2.3 Coupling of the Models and Experiment Data -- 7.3 Effect of Transient Heat and Mass Transfer on Nucleation and Crystal Growth -- 7.3.1 Transients in the Internal Flow -- 7.3.2 Heat Transfer, Cooling Rates, and Temperature Distribution -- 7.4 Competitive Nucleation and Phase Selection in Nd-Fe-B Droplets -- 7.4.1 Calculation of the Temperature-Time Profiles -- 7.4.2 Critical Undercooling as a Function of the Drop Size -- 7.4.3 Delay Time as a Function of the Convection Intensity -- 7.5 Summary -- Appendix 7.A: Extended Model of Nonstationary Heterogeneous -- Nucleation -- References.

8 Containerless Solidification of Magnetic Materials Using the ISAS/JAXA 26-Meter Drop Tube -- 8.1 Introduction -- 8.2 Drop Tube Process -- 8.2.1 Experimental Procedure -- 8.2.2 Undercooling Level and Cooling Rate of the Droplet during the Drop Tube Process -- 8.3 Undercooling Solidification of Fe-Rare Earth (RE) Magnetostriction Alloys -- 8.3.1 Fe67Nd33 Alloy -- 8.3.2 Fe67Tb33 and Fe67Dy33 Alloys -- 8.3.3 Fe67Nd16.5Tb16.5 and Fe67Nd16.5Dy16.5 Alloys -- 8.4 Undercooling Solidification of Nd-Fe-B Magnet Alloys -- 8.4.1 Phase Selection and Microstructure Evolution of Nd-Fe-B Alloys Solidified from Undercooled Melt -- 8.4.2 Magnetic Property of the Metastable Phase -- 8.4.3 Mechanism of Transformation of the Nd2Fe17Bx Metastable Phase -- 8.5 Concluding Remarks -- References -- 9 Nucleation and Solidification Kinetics of Metastable Phases in Undercooled Melts -- 9.1 Introduction -- 9.2 Thermodynamic Aspects and Nucleation of Metastable Phases -- 9.3 Metastable Phase Formation from Undercooled Melts in Various Alloy Systems -- 9.3.1 The Metastable Supersaturated Solid Solution Phases -- 9.3.2 The Metastable Phase Formation for Refractory Metals -- 9.3.3 The Metastable bcc Phase Formation in Fe-Based Alloys -- 9.3.4 The Metastable Phase Formation in Peritectic Systems with Ordered Intermetallic Compounds -- 9.3.5 The Metastable Phase Formation in Eutectic Systems with Ordered Intermetallic Compounds -- 9.3.6 The Formation of Metastable Quasicrystalline Phases -- 9.3.7 The Formation of Amorphous Phases -- 9.4 Summary and Conclusions -- References -- 10 Nucleation Within the Mushy Zone -- 10.1 Introduction -- 10.1.1 Double Recalescence -- 10.1.2 Solidification Path -- 10.2 Incubation Time -- 10.3 Cluster Formation -- 10.3.1 Homogeneous Nucleation of a Spherical Cluster -- 10.3.2 Heterogeneous Nucleation of a Spherical Cap on a Flat Surface.

10.4 Transient Development of Heterogeneous Sites -- 10.4.1 Dendrite Fragmentation -- 10.4.2 Crack Formation -- 10.4.3 Dendrite Collision -- 10.4.4 Internal Grain Boundary Formation -- 10.4.5 Heterogeneous Nucleation Within a Crevice -- 10.5 Comparing Critical Nucleus Development Mechanisms -- 10.6 Concluding Remarks -- References -- 11 Measurements of Crystal Growth Velocities in Undercooled Melts of Metals -- 11.1 Introduction -- 11.2 Experimental Methods -- 11.3 Summary and Conclusions -- References -- 12 Containerless Crystallization of Semiconductors -- 12.1 Introduction -- 12.2 Status of Research on Facetted Dendrite Growth -- 12.3 Twin-Related Lateral Growth and Twin-free Continuous Growth -- 12.3.1 Twin-Related (211) and (110) Facetted Dendrites -- 12.3.2 Twin-Free (100) Facet Dendrites -- 12.3.3 Transition from Twin-Related Facet Dendrites to Twin-Free Facet Dendrites -- 12.3.4 Rate-Determining Process for Crystallization into Undercooled Melts -- 12.4 Containerless Crystallization of Si -- 12.4.1 Experimental -- 12.4.2 Application to Drop-Tube Process -- 12.5 Summery and Conclusion -- 12.6 Appendix 12.A: LKT Model -- 12.A.1 Wilson-Frenkel Model -- References -- 13 Measurements of Crystal Growth Dynamics in Glass-Fluxed Melts -- 13.1 Introduction -- 13.2 Methods and Experimental Set-Up -- 13.2.1 Access to Large Undercoolings -- 13.2.2 In-Situ Observations -- 13.2.3 Data Processing -- 13.2.4 Experimental SetUp and Procedures -- 13.3 Growth Velocities in Pure Ni -- 13.3.1 Overview of Literature Data -- 13.3.2 Recalescence Characteristic -- 13.3.3 Dendritic Growth Velocities -- 13.4 Growth Velocities in Ni3Sn2 Compound -- 13.4.1 Peculiarities of Intermetallic Compounds -- 13.4.2 Novel Data of Growth Velocities -- 13.5 Crystal Growth Dynamics in Ni-Sn Eutectic Alloys -- 13.5.1 Background -- 13.5.2 Recalescence Behavior and Growth Velocities.

13.5.3 Microstructure -- 13.6 Opportunities with High Magnetic Fields -- 13.6.1 Motivation -- 13.6.2 Opportunities with High Magnetic Fields -- 13.6.3 Effects of Static Magnetic Fields on Undercooling Behavior -- 13.6.4 Measured Growth Velocities of Pure Ni -- 13.7 Summary -- References -- 14 Influence of Convection on Dendrite Growth by the AC+DC Levitation Technique -- 14.1 Convection in a Levitated Melt -- 14.1.1 Challenges in Conventional Levitation -- 14.1.2 Influence of Convection -- 14.2 Static Levitation Using the Alternating and Static Magnetic Field (AC + DC Levitation) -- 14.2.1 Simultaneous Imposition of AC + DC Magnetic Fields -- 14.2.2 Setup of the AC + DC Levitator -- 14.2.3 Dynamics of a Droplet Under AC + DC Fields -- 14.2.4 Effect of the Static Magnetic Field on Flow Velocity -- 14.3 Effect of Convection on Nucleation and Solidification -- 14.3.1 Nucleation Undercooling -- 14.3.2 Solidification Structure -- 14.3.3 Growth Velocity of Dendrite -- References -- 15 Modeling the Fluid Dynamics and Dendritic Solidification in EM-Levitated Alloy Melts -- 15.1 Introduction -- 15.2 Mathematical Models for Levitation Thermofluid Dynamics -- 15.2.1 Thermofluid Equations -- 15.2.2 Simulations of Droplet Levitation -- 15.2.3 DC Field Stabilization -- 15.2.4 Levitating Large Masses -- 15.2.5 Impurity Separation -- 15.3 Thermoelectric Magnetohydrodynamics in Levitated Droplets -- 15.3.1 Thermoelectricity -- 15.3.2 Solidification by the Enthalpy Method -- 15.3.3 TEMHD in Dendritic Solidification -- 15.3.4 Solidification of an Externally Cooled Droplet -- 15.4 Concluding Remarks -- References -- 16 Forced Flow Effect on Dendritic Growth Kinetics in a Binary Nonisothermal System -- 16.1 Introduction -- 16.2 Convective Flow in Droplets Processed in Electromagnetic Levitation -- 16.3 The Model Equations -- 16.4 Predictions of the Model.

16.4.1 Dendrite Growth in a Pure (One-Component) System.