Materials Kinetics,

1. Thermodynamics vs. Kinetics
1.1 What is Equilibrium?
1.2 Thermodynamics vs. Kinetics
1.3 Spontaneous and Non-Spontaneous Processes
1.4 Microscopic Basis of Entropy
1.5 Introduction to Statistical Mechanics
1.6 First Law of Thermodynamics
1.7 Second Law of Thermodynamics
1.8 Third Law of Thermodynamics
1.9 Zeroth Law of Thermodynamics
1.10 Summary Exercises References

2. Irreversible Thermodynamics
2.1 Reversible and Irreversible Processes
2.2 Affinity
2.3 Fluxes
2.4 Entropy Production
2.5 Purely Resistive Systems
2.6 Linear Systems
2.7 Onsager Reciprosity Theorem
2.8 Thermophoresis
2.9 Thermoelectric Materials
2.10 Electromigration
2.11 Piezoelectric Materials
2.12 Thermomagnetic Materials
2.13 Galvanomagnetic Materials
2.14 Beyond Onsager’s Approach
2.15 Summary Exercises References

3. Fick’s Laws of Diffusion
3.1 Fick’s First Law
3.2 Fick’s Second Law
3.3 Driving Forces for Diffusion
3.4 Nernst-Planck Equation
3.5 Temperature Dependence of Diffusion
3.6 Interdiffusion
3.7 Kirkendall Effect
3.8 Measuring Concentration Profiles
3.9 Tracer Diffusion
3.10 Summary Exercises References

4. Analytical Solutions of the Diffusion Equation
4.1 Fick’s Second Law with Constant Diffusivity
4.2 Plane Source in One Dimension
4.3 Method of Reflection and Superposition
4.4 Solution for an Extended Source
4.5 Bounded Initial Distribution
4.6 Method of Separation of Variables
4.7 Method of Laplace Transforms
4.8 Anisotropic Diffusion
4.9 Concentration-Dependent Diffusivity
4.10 Time-Dependent Diffusivity
4.11 Diffusion in a Cylinder
4.12 Diffusion in a Sphere
4.13 Summary Exercises References

5. Multicomponent Diffusion
5.1 Introduction
5.2 Matrix Formulation of Diffusion in a Ternary System
5.3 Solution by Matrix Diagonalization
5.4 Uphill Diffusion
5.5 Examples of Multicomponent Diffusion
5.6 Summary Exercises References

6. Numerical Solutions of the Diffusion Equation
6.1 Introduction
6.2 Dimensionless Variables
6.3 Physical Interpretation of the Finite Difference Method
6.4 Finite Differences Solution
6.5 Considerations for Numerical Solutions
6.6 Software for Numerical Solutions
6.7 Summary Exercises References

7. Atomic Models for Diffusion
7.1 Introduction
7.2 Thermally Activated Atomic Jumping
7.3 Square Well Potential
7.4 Parabolic Well Potential
7.5 Generalized Formula for Particle Jump Frequency
7.6 Particle Escape Probability
7.7 Mean Squared Displacement of Particles
7.8 Einstein Diffusion Equation
7.9 Moments of a Function
7.10 Diffusion and Random Walks
7.11 Summary Exercises References

8. Diffusion in Crystals
8.1 Atomic Mechanisms for Diffusion
8.2 Diffusivity in Metals
8.3 Correlated Walks
8.4 Defects in Ionic Crystals
8.5 Schottky and Frenkel Defects
8.6 Equilibrium Constants for Defect Reactions
8.7 Diffusion in Ionic Crystals
8.8 Diffusion Along Dislocations
8.9 Summary Exercises References

9. Diffusion in Polycrystalline Materials
9.1 Defects in Polycrystalline Materials
9.2 Diffusion Mechanisms in Polycrystalline Materials
9.3 Regimes of Grain Boundary Diffusion
9.4 Diffusion Along Stationary vs. Moving Grain Boundaries
9.5 Atomic Mechanisms of Fast Grain Boundary Diffusion
9.6 Modeling of Grain Boundary Diffusion
9.7 Diffusion Along Free Surfaces
9.8 Summary Exercises References

10. Motion of Dislocations and Interfaces
10.1 Driving Forces for Dislocation Motion
10.2 Dislocation Glide and Climb
10.3 Driving Forces for Interfacial Motion
10.4 Motion of Crystal-Vapor Interfaces
10.5 Entropy-Stabilized Oxides
10.6 Crystalline Interface Motion
10.7 Summary Exercises References

11. Morphological Evolution in Polycrystalline Materials
11.1 Driving Forces for Surface Morphological Evolution
11.2 Morphological Evolution of Isotropic Surfaces
11.3 Grooving
11.4 Plateau-Rayleigh Instability
11.5 Evolution of Anisotropic Surfaces
11.6 Particle Coarsening: Ostwald Ripening
11.7 Grain Growth in Two Dimensions
11.8 Grain Growth in Three Dimensions
11.9 Diffusional Creep
11.10 Summary Exercises References

12. Sintering
12.1 Introduction
12.2 Stages of Sintering
12.3 Sintering Mechanisms
12.4 Solid-State Sintering
12.5 Liquid Phase Sintering
12.6 Spark Plasma Sintering
12.7 Cold Sintering
12.8 Summary Exercises References

13. Diffusion in Polymers and Glasses
13.1 Introduction
13.2 Stokes-Einstein Relation
13.3 Freely Jointed Chain Model of Polymers
13.4 Reptation
13.5 Polymer Chain Kinetics
13.6 Chemically Strengthened Glass by Ion Exchange
13.7 Ion-Exchanged Glass Waveguides
13.8 Anti-Microbial Glass
13.9 Proton Conducting Glasses
13.10 Summary Exercises References

14. Kinetics of Phase Separation
14.1 Thermodynamics of Mixing
14.2 Immiscibility and Spinodal Domes
14.3 Phase Separation Kinetics
14.4 Cahn-Hilliard Equation
14.5 Phase-Field Modeling
14.6 Applications of Phase-Field Modeling
14.7 Summary Exercises References

15. Nucleation and Crystallization
15.1 Kinetics of Crystallization
15.2 Classical Nucleation Theory
15.3 Homogeneous Nucleation
15.4 Heterogeneous Nucleation
15.5 Nucleation Rate
15.6 Crystal Growth Rate
15.7 Johnson-Mehl-Avrami Equation
15.8 Time-Temperature-Transformation Diagram
15.9 Glass-Ceramics
15.10 Nucleating Agents
15.11 Summary Exercises References

16. Advanced Nucleation Theories
16.1 Limitations of Classical Nucleation Theory
16.2 Statistical Mechanics of Nucleation
16.3 Diffuse Interface Theory
16.4 Applications of Diffuse Interface Theory
16.5 Density Functional Theory
16.6 Applications of Density Functional Theory
16.7 Implicit Glass Model
16.8 Toy Landscape Model
16.9 Summary Exercises References

17. Viscosity of Liquids
17.1 Introduction
17.2 Viscosity Reference Points
17.3 Viscosity Measurement Techniques
17.4 Liquid Fragility
17.5 Vogel-Fulcher-Tammann (VFT) Equation for Viscosity
17.6 Avramov-Milchev (AM) Equation for Viscosity
17.7 Adam-Gibbs Entropy Model
17.8 Mauro-Yue-Ellison-Gupta-Allan (MYEGA) Equation for Viscosity
17.9 Infinite Temperature Limit of Viscosity
17.10 Fragile-to-Strong Transition
17.11 Non-Newtonian Viscosity
17.12 Models of Non-Newtonian Viscosity
17.13 Volume Viscosity
17.14 Summary Exercises References

18. Nonequilibrium Viscosity and the Glass Transition
18.1 Introduction
18.2 The Glass Transition
18.3 Ideal Glass Transition and the Kauzmann Paradox
18.4 Thermal History Dependence of Viscosity
18.5 Modeling of Nonequilibrium Viscosity
18.6 Nonequilibrium Viscosity and Fragility
18.7 Viscosity of Medieval Cathedral Glass
18.8 Summary Exercises References

19. Topological Constraint Theory
19.1 Introduction
19.2 Constraint Counting
19.3 Rigidity Percolation Threshold
19.4 Temperature-Dependent Constraints
19.5 Calculation of Glass Transition Temperature
19.6 Calculation of Fragility Index
19.7 Composition Dependence of Viscosity
19.8 Beyond Mean-Field Theory
19.9 Summary Exercises References

20. Energy Landscapes
20.1 Potential Energy Landscapes
20.2 Enthalpy Landscapes
20.3 Landscape Kinetics
20.4 Disconnectivity Graphs
20.5 Eigenvector-Following Technique
20.6 Activation-Relaxation Technique
20.7 Nudged Elastic Band Method
20.8 ExplorerPy
20.9 Minimalist Landscape Model
20.10 Summary Exercises References

21. Broken Ergodicity
21.1 What is Ergodicity?
21.2 Deborah Number
21.3 Broken Ergodicity
21.4 Continuously Broken Ergodicity
21.5 Hierarchical Master Equation Approach
21.6 Thermodynamic Implications of Broken Ergodicity
21.7 Examples of Broken Ergodicity
21.8 Summary Exercises References

22. Master Equations
22.1 Transition State Theory
22.2 Master Equations
22.3 Degenerate Microstates
22.4 Metabasin Approach
22.5 Partitioning of the Landscape
22.5 Accessing Long Time Scales
22.6 KineticPy
22.7 Applications of the Master Equation Approach
22.8 Summary Exercises References

23. Relaxation of Glasses and Polymers
23.1 Introduction
23.2 Fictive Temperature
23.3 Tool’s Equation
23.4 Ritland Crossover Experiment
23.5 Fictive Temperature Distributions
23.6 Property Dependence of Fictive Temperature
23.7 Kinetic Interpretation of Fictive Temperature
23.8 Stretched Exponential Relaxation
23.9 Prony Series Description
23.10 Relaxation Kinetics
23.11 RelaxPy
23.12 Stress vs. Structural Relaxation
23.13 Maxwell Relation
23.14 Frequency Domain Descriptions of Relaxation
23.15 Secondary Relaxation
23.16 Summary Exercises References

24. Molecular Dynamics
24.1 Multiscale Materials Modeling
24.2 Principles of Molecular Dynamics
24.3 Interatomic Potentials
24.4 Ensembles
24.5 Integrating the Equations of Motion
24.6 Boundary Conditions and Neighbor Lists
24.7 Performing Molecular Dynamics Simulations
24.8 Thermostats
24.9 Barostats
24.10 Reactive Force Fields
24.11 Accelerated Molecular Dynamics Techniques
24.12 Tools of the Trade
24.13 Summary Exercises References

25. Monte Carlo Techniques
25.1 Introduction
25.2 Monte Carlo Integration
25.3 Monte Carlo in Statistical Mechanics
25.4 Markov Processes
25.5 The Metropolis Method
25.6 Molecular Dynamics vs. Monte Carlo
25.7 Sampling in Different Ensembles
25.8 Kinetic Monte Carlo
25.9 Applications of Kinetic Monte Carlo
25.10 Inherent Structure Density of States
25.11 Random Number Generators
25.12 Summary Exercises References

26. Ab Initio Molecular Dynamics
26.1 Introduction
26.2 The Schrödinger Equation
26.3 The Variational Principle
26.4 The Born-Oppenheimer Equation
26.5 Hartree-Fock Theory
26.6 Rayleigh-Schrödinger Perturbation Theory
26.7 The Kohn-Sham Formulation
26.8 Exchange-Correlation Energy
26.9 Pseudopotentials
26.10 Car-Parrinello Molecular Dynamics
26.11 Applications of Ab Initio Molecular Dynamics
26.12 Summary Exercises References

27. Fluctuations in Condensed Matter
27.1 What are Fluctuations?
27.2 Statistical Mechanics of Fluctuations
27.3 Fluctuations in Broken Ergodic Systems
27.4 Time Correlation Functions
27.5 Green-Kubo Relations
27.6 Dynamical Heterogeneities
27.7 Nonmonotonic Relaxation of Fluctuations
27.8 Industrial Example: Fluctuations in High Performance Display Glass
27.9 Summary Exercises References

28. Chemical Reaction Kinetics
28.1 Rate of Reactions
28.2 Order of Reactions
28.3 Equilibrium Constants
28.4 First-Order Reactions
28.5 Higher Order Reactions
28.6 Reactions in Series
28.7 Temperature Dependence of Reaction Rates
28.8 Catalysts
28.9 Heterogeneous Reactions
28.10 Solid State Transformation Kinetics
28.11 Experimental Methods
28.12 Summary Exercises References

29. Thermal Conduction
29.1 Fourier’s Law
29.2 The Heat Equation
29.3 Thermal Conductivity
29.4 Mechanisms of Thermal Conduction
29.5 Thermal Conductivity of Non-Crystalline Materials
29.6 Summary Exercises References

30. Electrical Conduction
30.1 Ohm’s Law
30.2 Electrical Resistivity and Conductivity
30.3 Electrical Conduction in Metals
30.4 Semiconductors and Insulators
30.5 Solid-State Electrolytes
30.6 Superconductors
30.7 Summary Exercises References Index