Phase Transitions in Materials

Contents
Preface
Notation
Part I Basic Thermodynamics and Kinetics of Phase Transformations
	1 Introduction
		1.1 What Is a Phase Transition?
		1.2 Atoms and Materials
		1.3 Pure Elements
		1.4 Alloys: Unmixing and Ordering
		1.5 What Is a Phase Transformation?
		1.6 Brief Review of Thermodynamics and Kinetics
		Problems
	2 Temperature–Composition Phase Diagrams
		2.1 Intuition and Expectations about Alloy Thermodynamics
		2.2 Free Energy Curves, Solute Conservation, and the Lever Rule
		2.3 Common Tangent Construction
		2.4 Continuous Solid Solubility Phase Diagram
		2.5 Eutectic and Peritectic Phase Diagrams
		2.6 Ternary Phase Diagrams
		2.7 Free Energy of a Solid Solution
		2.8 Unmixing Phase Diagram
		2.9 Order–Disorder Phase Diagram
		2.10 Alloy Phase Diagrams
		Problems
	3 Diffusion
		3.1 Processes of Atom Movements in Crystals
		3.2 The Diffusion Equation
		3.3 Gaussian and Error Functions in One Dimension
		3.4 Fourier Series Solutions to the Diffusion Equation
		3.5 Bessel Functions and Other Special Function Solutions
		Problems
	4 Nucleation
		4.1 Nucleation Phenomena and Terminology
		4.2 Critical Nucleus
		4.3 Heterogeneous Nucleation
		4.4 Free Energy Curves and Nucleation
		4.5 The Nucleation Rate
		4.6 Time-Dependent Nucleation
		4.7 Nucleation in Multicomponent Systems
		Problems
	5 Effects of Diffusion and Nucleation on Phase Transformations
		5.1 Nonequilibrium Processing of Materials
		5.2 Alloy Solidification with Suppressed Diffusion in the Solid
		5.3 Alloy Solidification with Suppressed Diffusion in Both Solid and Liquid
		5.4 Time, Temperature, and Transformation
		5.5 Glasses and Liquids
		5.6 Kinetics near Equilibrium
		Problems
Part II TheAtomicOriginsofThermodynamicsandKinetics
	6 Energy
		6.1 Atomic Schr ¨ odinger Equations and Formalism
		6.2 Molecular Orbital Theory of Diatomic Molecules
		6.3 Electronic Bands and the Tight-Binding Model
		6.4 Free and Nearly-Free Electrons
		6.5 Some Electronic Structures of Materials
		6.6 Elastic Constants and the Interatomic Potential
		6.7 Linear Elasticity
		6.8 Misfitting Particle
		Problems
	7 Entropy
		7.1 Counting and Entropy
		7.2 Short-Range Order and the Pair Approximation
		7.3 Materials Structures and Properties Described by Clusters
		7.4 Concept of Vibrational Entropy
		7.5 Phonon Thermodynamics
		7.6 Bond Proportion Model
		7.7 Bond-Stiffness-versus-Bond-Length Model
		Problems
	8 Pressure
		8.1 Materials under Pressure at Low Temperatures
		8.2 Thermal Pressure, a Step beyond the Harmonic Model
		8.3 Free Energies and Phase Boundaries under Pressure
		8.4 Chemical Bonding and Antibonding under Pressure
		8.5 Pressure-Driven Phase Transitions
		8.6 Activation Volume
		Problems
	9 Interactions in Microstructures and Constrained Equilibrium
		9.1 Solid-State Amorphization
		9.2 Self-Trapping
		9.3 Thermodynamics of Complex Materials
		9.4 Partitioning of Energy in Polycrystals and Single Crystals
		9.5 Coherency Strains in Chemical Unmixing
		9.6 Coupling between Unmixing Processes
		9.7 Factoring the Partition Function
		Problems
	10 Atom Movements with the Vacancy Mechanism
		10.1 Random Walk and Correlations
		10.2 Correlation Factors for Atoms and Vacancies in Alloys
		10.3 Phenomena in Alloy Diffusion
		10.4 Diffusion in a Potential Gradient
		10.5 Diffusion in a Temperature Gradient
		10.6 Nonthermodynamic Equilibrium in Driven Systems
		10.7 Vineyard’s Theory of Diffusion
		Problems
Part III TypesofPhaseTransformations
	11 ThermodynamicsandPhaseTransitionsatSurfaces
		11.1 Surface Structure
		11.2 Thermodynamic Roughening Transition
		11.3 Surface Structure and Kinetics
		11.4 Energies of Grain Boundaries and Interfaces
		11.5 Anisotropic Surface Energy
		11.6 Reactions at Surfaces
		11.7 Gas Adsorption
		Problems
	12 Melting
		12.1 Structure and Thermodynamics of Melting
		12.2 Chemical Trends of Melting
		12.3 Free Energy of a Solid
		12.4 Entropy of a Liquid
		12.5 Thermodynamic Condition for the Melting Temperature
		12.6 Glass Transition
		12.7 Two Dimensions
		Problems
	13 Solidification
		13.1 Solidification Microstructures
		13.2 Alloy Solidification with Suppressed Diffusion in the Liquid
		13.3 Constitutional Supercooling
		13.4 Cellular and Dendritic Microstructures
		13.5 Dendrite Growth with Solute Segregation
		13.6 Surface Energy
		13.7 Developments in Solidification Science
		Problems
	14 Phase Transformations with Interfaces: 1. Microstructure
		14.1 Guinier–Preston Zones and Precipitation Sequences
		14.2 Precipitation at Grain Boundaries and Defects
		14.3 The Eutectoid Transformation and Pearlite
		14.4 Heat Treatments of Steel
		14.5 The Kolmogorov–Johnson–Mehl–Avrami Growth Equation
		14.6 Coarsening
		Problems
	15 Phase Transformations with Interfaces: 2. Energetics and Kinetics
		15.1 Interface Thermodynamics and Kinetics
		15.2 Atomistic Model of Interface Motion
		15.3 Local Nonequilibrium at Fast Interfaces
		15.4 Elastic Energy and Shape of Growing Plate-Like Precipitates
		15.5 Elastic Energy and Solute Atoms
		Problems
	16 Spinodal Decomposition
		16.1 Concentration Fluctuations and the Free Energy of Solution
		16.2 A Square Gradient Term in the Free Energy
		16.3 Constrained Minimization of the Free Energy
		16.4 The Diffusion Equation
		16.5 Effects of Elastic Energy on Spinodal Decomposition
		Problems
	17 Phase Field Theory
		17.1 Spatial Distribution of Phases and Interfaces
		17.2 Order Parameters as Field Quantities
		17.3 Domain Boundary Structure
		17.4 Domain Boundary Kinetics
		Problems
	18 Method of Concentration Waves and Chemical Ordering
		18.1 Structure in Real Space and Reciprocal Space
		18.2 Symmetry and the Star
		18.3 The Free Energy in k-Space with Concentration Waves
		18.4 Symmetry Invariance of Free Energy and Landau–Lifshitz Rule for Second-Order Phase Transitions
		18.5 Thermodynamics of Ordering in the Mean Field Approximation with Long-Range Interactions
		Problems
	19 Diffusionless Transformations
		19.1 Dislocations, Mechanisms, and Twinning
		19.2 Martensite
		19.3 Landau Theory of Displacive Phase Transitions
		19.4 Crystal Instabilities and Phonons
		Problems
	20 Thermodynamics of Nanomaterials
		20.1 Energies of Atoms at Grain Boundaries in Nanocrystals
		20.2 Gibbs–Thomson Effect
		20.3 Atomic Structures of Nanocrystals
		20.4 Electron Energies in Nanomaterials
		20.5 Entropy of Nanomaterials
		20.6 Magnetic Nanoparticles
		Problems
	21 Magnetic and Electronic Phase Transitions
		21.1 Overview of Magnetic and Electronic Phase Transitions
		21.2 Exchange Interactions
		21.3 Thermodynamics of Ferromagnetism
		21.4 Spin Waves
		21.5 Thermodynamics of Antiferromagnetism
		21.6 Dzyaloshinskii–Moriya Interactions and Skyrmions
		21.7 Thermodynamics of Ionic Crystals
		21.8 Ferroelectric Transition
		21.9 Domains
		Problems
Further Reading
References
Index