Materials Kinetics

Transport and Rate Phenomena

1st Edition - November 22, 2020
Author: John C. Mauro
Language: English
Paperback ISBN:
9 7 8 - 0 - 1 2 - 8 2 3 9 0 7 - 0
eBook ISBN:
9 7 8 - 0 - 1 2 - 8 2 4 2 1 6 - 2

Materials Kinetics: Transport and Rate Phenomena provides readers with a clear understanding of how physical-chemical principles are applied to fundamental kinetic processes. The b… Read more

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Materials Kinetics: Transport and Rate Phenomena provides readers with a clear understanding of how physical-chemical principles are applied to fundamental kinetic processes. The book integrates advanced concepts with foundational knowledge and cutting-edge computational approaches, demonstrating how diffusion, morphological evolution, viscosity, relaxation and other kinetic phenomena can be applied to practical materials design problems across all classes of materials. The book starts with an overview of thermodynamics, discussing equilibrium, entropy, and irreversible processes. Subsequent chapters focus on analytical and numerical solutions of the diffusion equation, covering Fick’s laws, multicomponent diffusion, numerical solutions, atomic models, and diffusion in crystals, polymers, glasses, and polycrystalline materials.

Dislocation and interfacial motion, kinetics of phase separation, viscosity, and advanced nucleation theories are examined next, followed by detailed analyses of glass transition and relaxation behavior. The book concludes with a series of chapters covering molecular dynamics, energy landscapes, broken ergodicity, chemical reaction kinetics, thermal and electrical conductivities, Monte Carlo simulation techniques, and master equations.

Cover image
Title page
Table of Contents
Copyright
Dedication
Foreword
Preface
Acknowledgments
Chapter 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. First Law of Thermodynamics
1.6. Second Law of Thermodynamics
1.7. Third Law of Thermodynamics
1.8. Zeroth Law of Thermodynamics
1.9. Summary
Exercises
Chapter 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. Summary
Exercises
Chapter 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. Temperature Dependence of Diffusion
3.5. Interdiffusion
3.6. Measuring Concentration Profiles
3.7. Tracer Diffusion
3.8. Summary
Exercises
Chapter 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-Dependence Diffusivity
4.10. Time-Dependent Diffusivity
4.11. Diffusion in Other Coordinate Systems
4.12. Summary
Exercises
Chapter 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. Summary
Exercises
Chapter 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 Difference Solutions
6.5. Considerations for Numerical Solutions
6.6. Summary
Exercises
Chapter 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. Particle Escape Probability
7.6. Mean Squared Displacement of Particles
7.7. Einstein Diffusion Equation
7.8. Moments of a Function
7.9. Diffusion and Random Walks
7.10. Summary
Exercises
Chapter 8. Diffusion in Crystals
8.1. Atomic Mechanisms for Diffusion
8.2. Diffusion 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. Summary
Exercises
Chapter 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. Diffusion Along Dislocations
9.7. Diffusion Along Free Surfaces
9.8. Summary
Exercises
Chapter 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. Crystalline Interface Motion
10.6. Summary
Exercises
Chapter 11. Morphological Evolution in Polycrystalline Materials
11.1. Driving Forces for Surface Morphological Evolution
11.2. Morphological Evolution of Isotropic Surfaces
11.3. Evolution of Anisotropic Surfaces
11.4. Particle Coarsening
11.5. Grain Growth
11.6. Diffusional Creep
11.7. Sintering
11.8. Summary
Exercises
Chapter 12. Diffusion in Polymers and Glasses
12.1. Introduction
12.2. Stokes-Einstein Relation
12.3. Freely Jointed Chain Model of Polymers
12.4. Reptation
12.5. Chemically Strengthened Glass by Ion Exchange
12.6. Ion-Exchanged Glass Waveguides
12.7. Anti-Microbial Glass
12.8. Proton Conducting Glasses
12.9. Summary
Exercises
Chapter 13. Kinetics of Phase Separation
13.1. Thermodynamics of Mixing
13.2. Immiscibility and Spinodal Domes
13.3. Phase Separation Kinetics
13.4. Cahn-Hilliard Equation
13.5. Phase-Field Modeling
13.6. Summary
Exercises
Chapter 14. Nucleation and Crystallization
14.1. Kinetics of Crystallization
14.2. Classical Nucleation Theory
14.3. Homogeneous Nucleation
14.4. Heterogeneous Nucleation
14.5. Nucleation Rate
14.6. Crystal Growth Rate
14.7. Johnson-Mehl-Avrami Equation
14.8. Time-Temperature-Transformation Diagram
14.9. Glass-Ceramics
14.10. Summary
Exercises
Chapter 15. Advanced Nucleation Theories
15.1. Limitations of Classical Nucleation Theory
15.2. Statistical Mechanics of Nucleation
15.3. Diffuse Interface Theory
15.4. Density Functional Theory
15.5. Implicit Glass Model
15.6. Summary
Exercises
Chapter 16. Viscosity of Liquids
16.1. Introduction
16.2. Viscosity Reference Points
16.3. Viscosity Measurement Techniques
16.4. Liquid Fragility
16.5. Vogel-Fulcher-Tammann (VFT) Equation for Viscosity
16.6. Avramov-Milchev (AM) Equation for Viscosity
16.7. Adam-Gibbs Entropy Model
16.8. Mauro-Yue-Ellison-Gupta-Allan (MYEGA) Equation for Viscosity
16.9. Infinite Temperature Limit of Viscosity
16.10. Kauzmann Paradox
16.11. Fragile-to-Strong Transition
16.12. Non-Newtonian Viscosity
16.13. Volume Viscosity
16.14. Summary
Exercises
Chapter 17. Nonequilibrium Viscosity and the Glass Transition
17.1. Introduction
17.2. The Glass Transition
17.3. Thermal History Dependence of Viscosity
17.4. Modeling of Nonequilibrium Viscosity
17.5. Nonequilibrium Viscosity and Fragility
17.6. Composition Dependence of Viscosity
17.7. Viscosity of Medieval Cathedral Glass
17.8. Summary
Exercises
Chapter 18. Energy Landscapes
18.1. Potential Energy Landscapes
18.2. Enthalpy Landscapes
18.3. Landscape Kinetics
18.4. Disconnectivity Graphs
18.5. Locating Inherent Structures and Transition Points
18.6. ExplorerPy
18.7. Summary
Exercises
Chapter 19. Broken Ergodicity
19.1. What is Ergodicity?
19.2. Deborah Number
19.3. Broken Ergodicity
19.4. Continuously Broken Ergodicity
19.5. Hierarchical Master Equation Approach
19.6. Thermodynamic Implications of Broken Ergodicity
19.7. Summary
Exercises
Chapter 20. Master Equations
20.1. Transition State Theory
20.2. Master Equations
20.3. Degenerate Microstates
20.4. Metabasin Approach
20.5. Partitioning of the Landscape
20.6. Accessing Long Time Scales
20.7. KineticPy
20.8. Summary
Exercises
Chapter 21. Relaxation of Glasses and Polymers
21.1. Introduction
21.2. Fictive Temperature
21.3. Tool's Equation
21.4. Ritland Crossover Effect
21.5. Fictive Temperature Distributions
21.6. Property Dependence of Fictive Temperature
21.7. Kinetic Interpretation of Fictive Temperature
21.8. Stretched Exponential Relaxation
21.9. Prony Series Description
21.10. Relaxation Kinetics
21.11. RelaxPy
21.12. Stress vs. Structural Relaxation
21.13. Maxwell Relation
21.14. Secondary Relaxation
21.15. Summary
Exercises
Chapter 22. Molecular Dynamics
22.1. Multiscale Materials Modeling
22.2. Quantum Mechanical Techniques
22.3. Principles of Molecular Dynamics
22.4. Interatomic Potentials
22.5. Ensembles
22.6. Integrating the Equations of Motion
22.7. Performing Molecular Dynamics Simulations
22.8. Thermostats
22.9. Barostats
22.10. Reactive Force Fields
22.11. Tools of the Trade
22.12. Summary
Exercises
Chapter 23. Monte Carlo Techniques
23.1. Introduction
23.2. Monte Carlo Integration
23.3. Monte Carlo in Statistical Mechanics
23.4. Markov Processes
23.5. The Metropolis Method
23.6. Molecular Dynamics vs. Monte Carlo
23.7. Sampling in Different Ensembles
23.8. Kinetic Monte Carlo
23.9. Inherent Structure Density of States
23.10. Random Number Generators
23.11. Summary
Exercises
Chapter 24. Fluctuations in Condensed Matter
24.1. What are Fluctuations?
24.2. Statistical Mechanics of Fluctuations
24.3. Fluctuations in Broken Ergodic Systems
24.4. Time Correlation Functions
24.5. Dynamical Heterogeneities
24.6. Nonmonotonic Relaxation of Fluctuations
24.7. Industrial Example: Fluctuations in High Performance Display Glass
24.8. Summary
Exercises
Chapter 25. Chemical Reaction Kinetics
25.1. Rate of Reactions
25.2. Order of Reactions
25.3. Equilibrium Constants
25.4. First-Order Reactions
25.5. Higher Order Reactions
25.6. Reactions in Series
25.7. Temperature Dependence of Reaction Rates
25.8. Heterogeneous Reactions
25.9. Solid State Transformation Kinetics
25.10. Summary
Exercises
Chapter 26. Thermal and Electrical Conductivities
26.1. Transport Equations
26.2. Thermal Conductivity
26.3. Electrical Conductivity
26.4. Varistors and Thermistors
26.5. Summary
Exercises
Index

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