Phase Transformation in Metals: Mathematics, Theory and Practice 3030491676, 9783030491673

Table of contents :
Foreword
Preface
Contents
1 Crystallography
1.1 Introduction
1.2 The Essence of Crystallography
1.3 Crystal Defects
1.4 X-Ray Crystallography
1.5 Crystal Lattice
1.6 Crystal Structures
1.7 Conventional Unit Cells and Lattice Planes
1.8 Vector Algebra in Crystallography
1.9 Rotation Matrix
1.10 Reciprocal Lattice in Crystallography
1.10.1 Primitive Lattice Vectors
1.10.2 Reciprocal Lattice Vector
1.10.3 Interplanar Spacing
1.10.4 Practical Aspects of the Reciprocal Lattice
1.11 Single-Crystal Structure
1.12 Polycrystalline Crystal Structure
1.13 Industrial Applications
1.14 Summary
1.15 Appendix 1A Fourier Transform
1.15.1 Energy Field
1.16 Appendix 1B Ewald Sphere
1.17 Problems
References
2 Surface Reconstruction
2.1 Introduction
2.2 Overlayer Lattice Planes
2.3 Two-Dimensional Bravais Lattices
2.4 Matrix and Wood Notations
2.5 Lattice Planes
2.5.1 Square Primitive Lattice
2.5.2 Overlayer Coherency
2.5.3 Hexagonal Primitive Lattice
2.6 Honeycomb and Hexagonal Lattices
2.7 Basics for Electrodeposition
2.7.1 Electrochemistry-Induced Surface Reconstruction
2.7.2 Electrochemical Cells
2.7.3 Standard Electric Potential
2.7.4 Epitaxy
2.8 Summary
2.9 Problems
References
3 Mass Transport by Diffusion
3.1 Introduction
3.2 Random Walks
3.3 Solid-State Diffusion
3.3.1 Octahedral and Tetrahedral Sites
3.4 Fick's Laws of Diffusion
3.4.1 First Law: Steady-State Diffusion
3.4.2 Second Law: Transient Diffusion
3.5 Solution to Fick's Second Law Equation
3.5.1 Method of Separation of Variables
3.5.1.1 Case 1: Bulk ConcentrationCb>0
3.5.1.2 Case 2: Bulk Concentration Cb=0
3.5.2 Amount of Diffusing Solute
3.6 Kirkendall Effect
3.7 Effects of Defects on Diffusion
3.8 Measurements of Diffusion Coefficient
3.9 Summary
3.10 Appendix 3A Second Law of Diffusion
3.10.1 Diffusion in a Rectangular Element
3.10.2 Diffusion Through a Rectangular Plane
3.10.2.1 Error Function Table
3.11 Appendix 3B Laplace Transformation
3.11.1 Introduction
3.11.2 Fick's Second Law of Diffusion and Solution
3.12 Problems
References
4 Solidification
4.1 Introduction
4.2 Foundry Sand
4.3 Thermodynamics of Phase Transformation
4.3.1 Single Phase Solutions
4.3.2 Thermodynamic Criteria for Reactions
4.4 Phase Separation
4.5 Binary Solutions
4.5.1 Internal Energy
4.5.2 Entropy of Mixing
4.5.3 Enthalpy of Mixing
4.5.4 Gibbs Energy of Mixing
4.6 Chemical Potential
4.7 The Interaction Parameter
4.8 The Gibbs–Duhem Equation
4.8.1 The Activity and Activity Coefficient Concepts
4.8.2 The Alpha Function
4.9 Degree of Undercooling
4.10 Phase Stability Criteria
4.11 Construction of Binary Phase Diagrams
4.11.1 Isomorphous Phase Diagrams
4.11.2 Eutectic Phase Diagrams
4.12 Nucleation Theory
4.12.1 Homogeneous Nucleation of Metals
4.12.2 Heterogeneous Nucleation of Metals
4.12.3 Catalyst-Induced Solidification Process
4.12.4 Nucleation Sites
4.12.5 Contact Area
4.13 Steady-State Nucleation Rate
4.14 Critical Temperature for Nuclei Formation
4.15 Solidification Methods
4.15.1 Conventional Castings
4.15.2 Single Crystals
4.15.3 Rapid Solidification
4.16 Cooling Curves and Phase Diagrams
4.17 Specific Heat
4.18 Thermal Energy Diagrams for Metals
4.19 Summary
4.20 Appendix 4A Calculation of Activities
4.20.1 Theoretical Basis of Raoult's and Henry's Laws
4.20.2 Analytical Procedure
4.21 Appendix 4B The Shape Factor
4.21.1 Spherical Cap
4.22 Problems
References
5 Planar Metal Solidification
5.1 Introduction
5.2 Melting Problem in a Half-Space Region
5.3 Solidification in Half-Space Regions
5.3.1 Heat Transfer Through Planar Surfaces
5.3.2 Solidification with Superheating
5.3.3 Solidification with Supercooling
5.4 Three-Phase Thermal Resistances
5.4.1 One-Dimensional Heat Equations
5.4.2 Latent Heat of Solidification
5.4.3 Analytical Solutions of the Heat Equations
5.5 Mold and Solid Thermal Resistances
5.5.1 Sand Mold Thermal Resistance
5.5.2 Casting Modulus and Chvorinov's Rule
5.5.3 Thermal Resistance in Solids
5.5.3.1 Moving Boundary Theory
5.5.3.2 Quasi-Static Approximation (QSA) Theory
5.5.3.3 Internal Resistance
5.6 Phase-Change Numerical Methods
5.7 Solidification Under Magnetic Fields
5.8 Summary
5.9 Appendix 5A Thermophysical Properties
5.10 Appendix 5B Separation of Variables
5.10.1 Similarity Solution
5.11 Appendix 5C Transcendental Equation
5.12 Problems
References
6 Contour Metal Solidification
6.1 Introduction
6.2 Interface Thermal Resistance
6.2.1 Stefan Dimensionless Thermal Energy Balance
6.3 Heat Transfer on Contoured Surfaces
6.3.1 Exponential Integral Function
6.4 Single-Crystal Solidification
6.4.1 Conductive–Radioactive Heat Transfer
6.4.1.1 Near-Field Temperature Distribution
6.5 Summary
6.6 Appendix 6A: Maximum Pulling Rate
6.7 Problems
References
7 Alloy Solidification I
7.1 Introduction
7.2 Binary Equilibrium Phase Diagrams
7.3 Microsegregation Models
7.3.1 Lever Rule
7.3.2 Gulliver–Scheil Model
7.4 Enthalpies of Binary Alloy Solidification
7.4.1 Latent Heat of Solidification of Binary Alloys
7.5 Single-Phase Solidification Models
7.5.1 Ideal Mold–Solid Contact Model
7.5.2 Fourier's Law of Heat Conduction Solution
7.6 Coupled Heat and Mass Transport Model
7.6.1 Dimensional Analysis
7.6.2 Dimensionless Analysis
7.6.3 Temperature Scaling
7.6.4 Solute Concentration Scaling
7.7 Coupled Heat and Solid Fraction Model
7.8 Alloy Constitutional Supercooling
7.9 Plane-Front Stability Criterion
7.10 Microstructural Design
7.11 Summary
7.12 Problems
References
8 Alloy Solidification II
8.1 Introduction
8.2 Morphology of Eutectic Solidification
8.2.1 Classification of Eutectic Structures
8.3 Dendritic Growth
8.3.1 Extended Metalstable Phase Fields
8.3.2 Invariant Eutectic Reaction
8.4 Lamellar Directional Solidification
8.4.1 Lamellar Size
8.4.2 Conservation of Mass
8.5 Tiller's Eutectic Solidification Model
8.6 Jackson–Hunt Lamellar Solidification Model
8.6.1 Decay Coefficient
8.6.2 Fourier Coefficients
8.6.3 Regular Lamellar Supercooling
8.6.4 Symmetric Boundary Groove
8.6.5 Gibbs–Thomson Coefficients
8.6.6 Extremum Condition
8.7 Free-Energy Solidification Model
8.8 Multicomponent Alloy Solidification
8.8.1 Multicomponent Eutectic Growth Model
8.9 Summary
8.10 Appendix 8A: Separation of Variables
8.10.1 Defining the Fourier Coefficients
8.11 Appendix 8B: Shape of Interfaces
8.12 Appendix 8C: Thermophysical Data
8.13 Problems
References
9 Solid-State Phase Change
9.1 Introduction
9.2 Thermally-Induced Phase Change
9.2.1 Phase-Transformation Crystallography
9.2.2 Interface Coherency
9.3 Energy of Straight Dislocations
9.4 Transformation of Austenite in Steels
9.4.1 Slow Austenitic Transformation
9.4.2 Solid-Phase Transformation Models
9.4.2.1 Ferrite Model
9.4.2.2 Ferrite–Pearlite Model
9.4.2.3 Pearlite Model
9.4.2.4 Pearlite and Cementite Model
9.4.3 Martensite Formation
9.5 Kinetics of Solid-Phase Transformation
9.6 TTT Diagram
9.7 Hardenability
9.8 TTT Diagram for Glass Formation
9.9 Thermodynamics of Transformation
9.10 Solid Transformation Thermal Resistance
9.10.1 Lumped System Analysis (LSA)
9.11 Strain-Induced Phase Transformation
9.11.1 X-Ray Diffraction Patterns
9.11.2 Volume Fraction of Martensite
9.11.3 Shape-Memory Effect
9.12 Summary
9.13 Appendix 9A: TTT Diagrams
9.14 Appendix 9B: Separation of Variables
9.15 Problems
References
10 Solidification Defects
10.1 Introduction
10.2 Riser Feeding Distance
10.2.1 Rectangular Casting
10.2.2 Designing Feeders
10.3 Morphology of Casting Defects
10.4 Mechanism of Porosity Formation
10.4.1 Bubble Absolute Pressure
10.4.2 Work Done for Bubble Formation
10.4.3 Hydrogen Gas
10.4.4 Solubility of Gases in Metallic Solutions
10.5 Melt Heat Loss
10.5.1 Gas Concentration
10.5.2 Coupled Convection and Radiation
10.5.3 Heat Flow Through Composite Cylindrical Walls
10.6 Melt Cleanliness
10.6.1 Degassing the Melt
10.6.2 Adjusting the Chemical Composition of the Melt
10.7 Thermodynamics of Metal Oxides
10.7.1 Solubility Product
10.7.2 Wagner Interaction Parameters
10.7.3 Aluminum-Oxygen Reaction in Molten Steel
10.8 Energy Diagram for Metal Oxides
10.9 Porosity-Induced Cracking
10.10 Linear-Elastic Fracture Mechanics
10.10.1 Modes of Loading
10.10.2 Stress Field for Mode I
10.10.3 Finite Specimens
10.10.4 Fracture Mechanics Criteria
10.11 Thermal Stress
10.12 Summary
10.13 Problems
References
A Metric Conversion Tables
B Solution to Problems
B.1 Chapter 1
B.2 Chapter 2
B.3 Chapter 3
B.4 Chapter 4
B.5 Chapter 5
B.6 Chapter 6
B.7 Chapter 7
B.8 Chapter 8
B.9 Chapter 9
B.10 Chapter 10
Index