Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Acknowledgements -- Notes on Units, Scales and Conventions -- Part one Thinking About the Material World -- ONE Idealizing Material Response -- 1.1 A Material World -- 1.1.1 Materials: A Databook Perspective -- 1.1.2 The Structure-Properties Paradigm -- 1.1.3 Controlling Structure: The World of Heat and Beat -- 1.2 Modeling of Materials -- 1.2.1 The Case for Modeling -- 1.2.2 Modeling Defined: Contrasting Perspectives -- 1.2.3 Case Studies in Modeling -- 1.2.4 Modeling and the Computer: Numerical Analysis vs Simulation -- 1.3 Further Reading -- TWO Continuum Mechanics Revisited -- 2.1 Continuum Mechanics as an Effective Theory -- 2.2 Kinematics: The Geometry of Deformation -- 2.2.1 Deformation Mappings and Strain -- 2.2.2 Geometry of Rigid Deformation -- 2.2.3 Geometry of Slip and Twinning -- 2.2.4 Geometry of Structural Transformations -- 2.3 Forces and Balance Laws -- 2.3.1 Forces Within Continua: Stress Tensors -- 2.3.2 Equations of Continuum Dynamics -- 2.3.3 Configurational Forces and the Dynamics of Defects -- 2.4 Continuum Descriptions of Deformation and Failure -- 2.4.1 Constitutive Modeling -- 2.4.2 Linear Elastic Response of Materials -- 2.4.3 Plastic Response of Crystals and Polycrystals -- 2.4.4 Continuum Picture of Fracture -- 2.5 Boundary Value Problems and Modeling -- 2.5.1 Principle of Minimum Potential Energy and Reciprocal Theorem -- 2.5.2 Elastic Green Function -- 2.5.3 Method of Eigenstrains -- 2.5.4 Numerical Solutions: Finite Element Method -- 2.6 Difficulties with the Continuum Approach -- 2.7 Further Reading -- 2.8 Problems -- THREE Quantum and Statistical Mechanics Revisited -- 3.1 Background -- 3.2 Quantum Mechanics -- 3.2.1 Background and Formalism -- 3.2.2 Catalog of Important Solutions -- 3.2.3 Finite Elements and Schrödinger.

3.2.4 Quantum Corrals: A Finite Element Analysis -- 3.2.5 Metals and the Electron Gas -- 3.2.6 Quantum Mechanics of Bonding -- 3.3 Statistical Mechanics -- 3.3.1 Background -- 3.3.2 Entropy of Mixing -- 3.3.3 The Canonical Distribution -- 3.3.4 Information Theoretic Approach to Statistical Mechanics -- 3.3.5 Statistical Mechanics Models for Materials -- 3.3.6 Bounds and Inequalities: The Bogoliubov Inequality -- 3.3.7 Correlation Functions: The Kinematics of Order -- 3.3.8 Computational Statistical Mechanics -- 3.4 Further Reading -- 3.5 Problems -- Part two Energetics of Crystalline Solids -- FOUR Energetic Description of Cohesion in Solids -- 4.1 The Role of the Total Energy in Modeling Materials -- 4.2 Conceptual Backdrop for Characterizing the Total Energy -- 4.2.1 Atomistic and Continuum Descriptions Contrasted -- 4.2.2 The Many-Particle Hamiltonian and Degree of Freedom Reduction -- 4.3 Pair Potentials -- 4.3.1 Generic Pair Potentials -- 4.3.2 Free Electron Pair Potentials -- 4.4 Potentials with Environmental and Angular Dependence -- 4.4.1 Diagnostics for Evaluating Potentials -- 4.4.2 Pair Functionals -- 4.4.3 Angular Forces: A First Look -- 4.5 Tight-Binding Calculations of the Total Energy -- 4.5.1 The Tight-Binding Method -- 4.5.2 An Aside on Periodic Solids: k-space Methods -- 4.5.3 Real Space Tight-Binding Methods -- 4.6 First-Principles Calculations of the Total Energy -- 4.6.1 Managing the Many-Particle Hamiltonian -- 4.6.2 Total Energies in the Local Density Approximation -- 4.7 Choosing a Description of the Total Energy: Challenges and Conundrums -- 4.8 Further Reading -- 4.9 Problems -- FIVE Thermal and Elastic Properties of Crystals -- 5.1 Thermal and Elastic Material Response -- 5.2 Mechanics of the Harmonic Solid -- 5.2.1 Total Energy of the Thermally Fluctuating Solid -- 5.2.2 Atomic Motion and Normal Modes -- 5.2.3 Phonons.

5.2.4 Buckminsterfullerene and Nanotubes: A Case Study in Vibration -- 5.3 Thermodynamics of Solids -- 5.3.1 Harmonic Approximation -- 5.3.2 Beyond the Harmonic Approximation -- 5.4 Modeling the Elastic Properties of Materials -- 5.4.1 Linear Elastic Moduli -- 5.4.2 Nonlinear Elastic Material Response: Cauchy-Born Elasticity -- 5.5 Further Reading -- 5.6 Problems -- SIX Structural Energies and Phase Diagrams -- 6.1 Structures in Solids -- 6.2 Atomic-Level Geometry in Materials -- 6.3 Structural energies of solids -- 6.3.1 Pair Potentials and Structural Stability -- 6.3.2 Structural Stability in Transition Metals -- 6.3.3 Structural Stability Reconsidered: The Case of Elemental Si -- 6.4 Elemental Phase Diagrams -- 6.4.1 Free Energy of the Crystalline Solid -- 6.4.2 Free Energy of the Liquid -- 6.4.3 Putting It All Together -- 6.4.4 An Einstein Model for Structural Change -- 6.4.5 A Case Study in Elemental Mg -- 6.5 Alloy Phase Diagrams -- 6.5.1 Constructing the Effective Energy: Cluster Expansions -- 6.5.2 Statistical Mechanics for the Effective Hamiltonian -- 6.5.3 The Effective Hamiltonian Revisited: Relaxations and Vibrations -- 6.5.4 The Alloy Free Energy -- 6.5.5 Case Study: Oxygen Ordering in High TC Superconductors -- 6.6 Summary -- 6.7 Further Reading -- 6.8 Problems -- Part three Geometric Structures in Solids: Defects and Microstructures -- SEVEN Point Defects in Solids -- 7.1 Point Defects and Material Response -- 7.1.1 Material Properties Related to Point Disorder -- 7.2 Diffusion -- 7.2.1 Effective Theories of Diffusion -- 7.3 Geometries and Energies of Point Defects -- 7.3.1 Crystallographic Preliminaries -- 7.3.2 A Continuum Perspective on Point Defects -- 7.3.3 Microscopic Theories of Point Defects -- 7.3.4 Point Defects in Si: A Case Study -- 7.4 Point Defect Motions -- 7.4.1 Material Parameters for Mass Transport.

7.4.2 Diffusion via Transition State Theory -- 7.4.3 Diffusion via Molecular Dynamics -- 7.4.4 A Case Study in Diffusion: Interstitials in Si -- 7.5 Defect Clustering -- 7.6 Further Reading -- 7.7 Problems -- EIGHT Line Defects in Solids -- 8.1 Permanent Deformation of Materials -- 8.1.1 Yield and Hardening -- 8.1.2 Structural Consequences of Plastic Deformation -- 8.1.3 Single Crystal Slip and the Schmid Law -- 8.2 The Ideal Strength Concept and the Need for Dislocations -- 8.3 Geometry of Slip -- 8.3.1 Topological Signature of Dislocations -- 8.3.2 Crystallography of Slip -- 8.4 Elastic Models of Single Dislocations -- 8.4.1 The Screw Dislocation -- 8.4.2 The Volterra Formula -- 8.4.3 The Edge Dislocation -- 8.4.4 Mixed Dislocations -- 8.5 Interaction Energies and Forces -- 8.5.1 The Peach-Koehler Formula -- 8.5.2 Interactions and Images: Peach-Koehler Applied -- 8.5.3 The Line Tension Approximation -- 8.6 Modeling the Dislocation Core: Beyond Linearity -- 8.6.1 Dislocation Dissociation -- 8.6.2 The Peierls-Nabarro Model -- 8.6.3 Structural Details of the Dislocation Core -- 8.7 Three-Dimensional Dislocation Configurations -- 8.7.1 Dislocation Bow-Out -- 8.7.2 Kinks and Jogs -- 8.7.3 Cross Slip -- 8.7.4 Dislocation Sources -- 8.7.5 Dislocation Junctions -- 8.8 Further Reading -- 8.9 Problems -- NINE Wall Defects in Solids -- 9.1 Interfaces in Materials -- 9.1.1 Interfacial Confinement -- 9.2 Free Surfaces -- 9.2.1 Crystallography and Energetics of Ideal Surfaces -- 9.2.2 Reconstruction at Surfaces -- 9.2.3 Steps on Surfaces -- 9.3 Stacking Faults and Twins -- 9.3.1 Structure and Energetics of Stacking Faults -- 9.3.2 Planar Faults and Phase Diagrams -- 9.4 Grain Boundaries -- 9.4.1 Bicrystal Geometry -- 9.4.2 Grain Boundaries in Polycrystals -- 9.4.3 Energetic Description of Grain Boundaries -- 9.4.4 Triple Junctions of Grain Boundaries.

9.5 Diffuse Interfaces -- 9.6 Modeling Interfaces: A Retrospective -- 9.7 Further Reading -- 9.8 Problems -- TEN Microstructure and its Evolution -- 10.1 Microstructures in Materials -- 10.1.1 Microstructural Taxonomy -- 10.1.2 Microstructural Change -- 10.1.3 Models of Microstructure and its Evolution -- 10.2 Inclusions as Microstructure -- 10.2.1 Eshelby and the Elastic Inclusion -- 10.2.2 The Question of Equilibrium Shapes -- 10.2.3 Precipitate Morphologies and Interfacial Energy -- 10.2.4 Equilibrium Shapes: Elastic and Interfacial Energy -- 10.2.5 A Case Study in Inclusions: Precipitate Nucleation -- 10.2.6 Temporal Evolution of Two-Phase Microstructures -- 10.3 Microstructure in Martensites -- 10.3.1 The Experimental Situation -- 10.3.2 Geometrical and Energetic Preliminaries -- 10.3.3 Twinning and Compatibility -- 10.3.4 Fine-Phase Microstructures and Attainment -- 10.3.5 The Austenite-Martensite Free Energy Reconsidered -- 10.4 Microstructural Evolution in Polycrystals -- 10.4.1 Phenomenology of Grain Growth -- 10.4.2 Modeling Grain Growth -- 10.5 Microstructure and Materials -- 10.6 Further Reading -- 10.7 Problems -- Part four Facing the Multiscale Challenge of Real Material Behavior -- ELEVEN Points, Lines and Walls: Defect Interactions and Material Response -- 11.1 Defect Interactions and the Complexity of Real Material Behavior -- 11.2 Diffusion at Extended Defects -- 11.2.1 Background on Short-Circuit Diffusion -- 11.2.2 Diffusionat Surfaces -- 11.3 Mass Transport Assisted Deformation -- 11.3.1 Phenomenology of Creep -- 11.3.2 Nabarro-Herring and Coble Creep -- 11.4 Dislocations and Interfaces -- 11.4.1 Dislocation Models of Grain Boundaries -- 11.4.2 Dislocation Pile-Ups and Slip Transmission -- 11.5 Cracks and Dislocations -- 11.5.1 Variation on a Theme of Irwin -- 11.5.2 Dislocation Screening at a Crack Tip.

11.5.3 Dislocation Nucleation at a Crack Tip.