Solidification and Crystallization Processing in Metals and Alloys

Hasse Fredriksson KTH, Royal Institute of Technology, Stockholm, Sweden

Ulla Åkerlind University of Stockholm, Sweden

Solidification or crystallization occurs when atoms are transformed from the disordered liquid state to the more ordered solid state, and is fundamental to metals processing. Conceived as a companion volume to the earlier works, Materials Processing during Casting (2006) and Physics of Functional Materials (2008), this book analyzes solidification and crystallization processes in depth.

Starting from the thermodynamic point of view, it gives a complete description, taking into account kinetics and mass transfer, down to the final structure. Importantly, the book shows the relationship between the theory and the experimental results. Topics covered include:

• Fundamentals of thermodynamics
• Properties of interfaces
• Nucleation
• Crystal growth - in vapours, liquids and melts
• Heat transport during solidification processes
• Solidification structures - faceted, dendritic, eutectic and peritectic
• Metallic glasses and amorphous alloy melts

Solidification and Crystallization Processing in Metals and Alloys features many solved examples in the text, and exercises (with answers) for students. Intended for Masters and PhD students as well as researchers in Materials Science, Engineering, Chemistry and Metallurgy, it is also a valuable resource for engineers in industry.

Preface ix

1 Thermodynamic Concepts and Relationships 1

1.1 Introduction 2

1.2 Thermodynamic Concepts and Relationships 2

1.3 Thermodynamics of Single-Component Systems 10

1.4 Thermodynamics of Multiple-Component Systems 16

1.5 Thermodynamics of Alloys 21

1.6 Thermodynamics of Ideal Binary Solutions 25

1.7 Thermodynamics of Non-Ideal Binary Solutions 26

1.8 Experimental Determination of Thermodynamic Quantities of Binary Alloys 34

Summary 36

Further Reading 41

2 Thermodynamic Analysis of Solidification Processes in Metals and Alloys 42

2.1 Introduction 42

2.2 Thermodynamics of Pure Metals 43

2.3 Thermodynamics of Binary Alloys 44

2.4 Equilibrium Between Phases in Binary Solutions. Phase Diagrams of Binary Alloys 50

2.5 Driving Force of Solidification in Binary Alloys 76

2.6 Thermodynamics of Ternary Alloys 78

2.7 Thermodynamics of Vacancies in Pure Metals and Alloys 83

Summary 90

Exercises 94

References 98

Further Reading 98

3 Properties of Interfaces 99

3.1 Introduction 99

3.2 Classical Theory of Interface Energy and Surface Tension 100

3.3 Thermodynamics of Interphases 114

3.4 Structures of Interfaces 123

3.5 Equilibrium Shapes of Crystals 145

Summary 155

Exercises 161

References 165

4 Nucleation 166

4.1 Introduction 166

4.2 Homogeneous Nucleation 167

4.3 Heterogeneous Nucleation. Inoculation 179

4.4 Nucleation of Bubbles 190

4.5 Crystal Multiplication 193

Summary 194

Exercises 197

References 200

5 Crystal Growth in Vapours 201

5.1 Introduction 202

5.2 Crystal Morphologies 202

5.3 Chemical Vapour Deposition 203

5.4 Crystal Growth 206

5.5 Normal Crystal Growth of Rough Surfaces in Vapours 210

5.6 Layer Crystal Growth of Smooth Surfaces in Vapours 214

5.7 Influence of Impurities on Crystal Growth in Vapours 238

5.8 Epitaxial Growth 244

5.9 Whisker Growth 249

5.10 Mechanical Restrictions on Thin Films 251

Summary 256

Exercises 263

References 266

6 Crystal Growth in Liquids and Melts 267

6.1 Introduction 268

6.2 Structures of Crystals and Melts 268

6.3 Growth Methods 275

6.4 Crystal Growth 278

6.5 Volume Changes and Relaxation Processes during Anelastic Crystal Growth in Metal Melts 279

6.6 Normal Crystal Growth in Pure Metal Melts 289

6.7 Layer Crystal Growth of Smooth Surfaces in Liquids 297

6.8 Normal Crystal Growth in Binary Alloys 310

6.9 Diffusion-Controlled Growth of Planar Crystals in Binary Alloys 318

6.10 Diffusion-Controlled Growth of Spherical Crystals in Alloys 324

6.11 Impingement 338

6.12 Precipitation of Pores 340

Summary 343

Exercises 355

References 360

7 Heat Transport during Solidification Processes. Thermal Analysis 361

7.1 Introduction 362

7.2 Basic Concepts and Laws of Heat Transport 362

7.3 Convection 366

7.4 Theory of Heat Transport at Unidirectional Solidification 378

7.5 Production of Single Crystals by Unidirectional Solidification 385

7.6 Thermal Analysis 395

7.7 Variable Heat of Fusion of Metals and Alloys 408

7.8 Variable Heat Capacitivity of Metals and Alloys 416

Summary 422

Exercises 429

References 432

8 Crystal Growth Controlled by Heat and Mass Transport 433

8.1 Introduction 433

8.2 Heat and Mass Transports in Alloys during Unidirectional Solidification 434

8.3 Zone Refining 443

8.4 Single Crystal Production by Czochralski Technique 450

8.5 Cellular Growth. Constitutional Undercooling. Interface Stability 454

Summary 465

Exercises 469

References 474

9 Faceted and Dendritic Solidification Structures 475

9.1 Introduction 476

9.2 Formation of Faceted Crystals 476

9.3 Growth of Faceted Crystals in Pure Metal Melts 476

9.4 Growth of Faceted Crystals in Alloy Melts 485

9.5 Growth of Dendrite Crystals 503

9.6 Development of Dendrites 529

9.7 Transitions between Structure Types in Alloys 565

Summary 573

Exercises 580

References 585

10 Eutectic Solidification Structures 587

10.1 Introduction 588

10.2 Classification of Eutectic Structures 588

10.3 Normal Eutectic Growth 589

10.4 Degenerate and Coupled Eutectic Growth 620

10.5 Structures of Ternary Alloys 635

10.6 Solidification of Fe-C Eutectics 646

10.7 Solidification of Al-Si Eutectics 658

10.8 Transition between Normal Lamellar and Rod Eutectic Growth 665

Summary 669

Exercises 675

References 680

11 Peritectic Solidification Structures 681

11.1 Introduction 681

11.2 Peritectic Reactions and Transformations 682

11.3 Peritectic Reactions and Transformations in Iron-Base Alloys 693

11.4 Metastable Reactions in Iron-Base Alloys 702

11.5 Metatectic Reactions and Transformations 704

11.6 Microsegregation in Iron-Base Alloys 708

11.7 Transitions between Peritectic and Eutectic Reactions in Iron-Base Alloys 716

Summary 719

Exercises 724

References 727

12 Metallic Glasses and Amorphous Alloy Melts 729

12.1 Introduction 730

12.2 Basic Concepts and Definitions 731

12.3 Production of Metallic Glasses 735

12.4 Experimental Methods for Structure Determination of Metallic Glasses and Amorphous Alloy Melts 741

12.5 Structures of Metallic Glasses 744

12.6 Comparison of the Structures of Metallic Glasses and Amorphous Alloy Melts. Rough Models of Metallic Glasses and Amorphous Alloy Melts 753

12.7 Casting of Metallic Glasses. Crystallization Processes in Amorphous Alloy Melts 759

12.8 Classification of Metallic Glasses 763

12.9 Properties and Applications of Metallic Glasses 764

Summary 771

Exercises 775

References 779

Answers to Exercises 781

Index 803

Hasse Fredriksson, KTH, Sweden.

Ulla ?kerlind, University of Stockholm, Sweden.