Crystals, defects and microstructures : modeling across scales / Rob Phillips.

Format:

Book

Author/Creator:

Phillips, Rob, 1960-

Language:

English

Subjects (All):

Crystals.

Crystals--Defects.

Crystal lattices.

Physical Description:

xxvi, 780 pages : illustrations ; 26 cm

Place of Publication:

Cambridge, U.K. ; New York : Cambridge University Press, 2001.

Summary:

Materials science has emerged as one of the central pillars of the modern physical sciences and engineering, and is now even beginning to claim a role in the biological sciences. A central tenet in the analysis of materials is the structure-property paradigm, which proposes a direct connection between the geometric structures within a material and its properties.

The increasing power of high-speed computation has had a major impact on theoretical materials science and has permitted the systematic examination of this connection between structure and properties. In this textbook, Rob Phillips examines the various methods that have been used in the study of crystals, defects and microstructures and that have made such computations possible. The author presents many of the key general principles used in the modeling of materials, and punctuates the text with real case studies drawn from recent research. A second key theme is the presentation of recent efforts that have been developed to treat problems involving either multiple spatial or temporal scales simultaneously.

This text is intended for graduate students and researchers in science and engineering with an interest in the theoretical constructs that have been devised to undertake the study of materials.

Contents:

Part 1 Thinking About the Material World 1

1 Idealizing Material Response 3

1.1 A Material World 3

1.1.1 Materials: A Databook Perspective 3

1.1.2 The Structure-Properties Paradigm 8

1.1.3 Controlling Structure: The World of Heat and Beat 12

1.2 Modeling of Materials 14

1.2.1 The Case for Modeling 14

1.2.2 Modeling Defined: Contrasting Perspectives 15

1.2.3 Case Studies in Modeling 18

1.2.4 Modeling and the Computer: Numerical Analysis vs Simulation 25

2 Continuum Mechanics Revisited 29

2.1 Continuum Mechanics as an Effective Theory 29

2.2 Kinematics: The Geometry of Deformation 31

2.2.1 Deformation Mappings and Strain 32

2.2.2 Geometry of Rigid Deformation 35

2.2.3 Geometry of Slip and Twinning 36

2.2.4 Geometry of Structural Transformations 37

2.3 Forces and Balance Laws 39

2.3.1 Forces Within Continua: Stress Tensors 39

2.3.2 Equations of Continuum Dynamics 41

2.3.3 Configurational Forces and the Dynamics of Defects 44

2.4 Continuum Descriptions of Deformation and Failure 51

2.4.1 Constitutive Modeling 51

2.4.2 Linear Elastic Response of Materials 51

2.4.3 Plastic Response of Crystals and Polycrystals 54

2.4.4 Continuum Picture of Fracture 60

2.5 Boundary Value Problems and Modeling 64

2.5.1 Principle of Minimum Potential Energy and Reciprocal Theorem 64

2.5.2 Elastic Green Function 66

2.5.3 Method of Eigenstrains 69

2.5.4 Numerical Solutions: Finite Element Method 72

2.6 Difficulties with the Continuum Approach 75

3 Quantum and Statistical Mechanics Revisited 81

3.2 Quantum Mechanics 82

3.2.1 Background and Formalism 82

3.2.2 Catalog of Important Solutions 87

3.2.3 Finite Elements and Schrodinger 94

3.2.4 Quantum Corrals: A Finite Element Analysis 101

3.2.5 Metals and the Electron Gas 103

3.2.6 Quantum Mechanics of Bonding 109

3.3 Statistical Mechanics 115

3.3.2 Entropy of Mixing 119

3.3.3 The Canonical Distribution 122

3.3.4 Information Theoretic Approach to Statistical Mechanics 126

3.3.5 Statistical Mechanics Models for Materials 129

3.3.6 Bounds and Inequalities: The Bogoliubov Inequality 135

3.3.7 Correlation Functions: The Kinematics of Order 137

3.3.8 Computational Statistical Mechanics 139

Part 2 Energetics of Crystalline Solids 147

4 Energetic Description of Cohesion in Solids 149

4.1 The Role of the Total Energy in Modeling Materials 149

4.2 Conceptual Backdrop for Characterizing the Total Energy 152

4.2.1 Atomistic and Continuum Descriptions Contrasted 152

4.2.2 The Many-Particle Hamiltonian and Degree of Freedom Reduction 154

4.3 Pair Potentials 156

4.3.1 Generic Pair Potentials 156

4.3.2 Free Electron Pair Potentials 158

4.4 Potentials with Environmental and Angular Dependence 164

4.4.1 Diagnostics for Evaluating Potentials 164

4.4.2 Pair Functionals 165

4.4.3 Angular Forces: A First Look 172

4.5 Tight-Binding Calculations of the Total Energy 176

4.5.1 The Tight-Binding Method 176

4.5.2 An Aside on Periodic Solids: k-space Methods 184

4.5.3 Real Space Tight-Binding Methods 189

4.6 First-Principles Calculations of the Total Energy 197

4.6.1 Managing the Many-Particle Hamiltonian 198

4.6.2 Total Energies in the Local Density Approximation 200

4.7 Choosing a Description of the Total Energy: Challenges and Conundrums 203

5 Thermal and Elastic Properties of Crystals 210

5.1 Thermal and Elastic Material Response 210

5.2 Mechanics of the Harmonic Solid 213

5.2.1 Total Energy of the Thermally Fluctuating Solid 214

5.2.2 Atomic Motion and Normal Modes 216

5.2.3 Phonons 228

5.2.4 Buckminsterfullerene and Nanotubes: A Case Study in Vibration 229

5.3 Thermodynamics of Solids 231

5.3.1 Harmonic Approximation 231

5.3.2 Beyond the Harmonic Approximation 239

5.4 Modeling the Elastic Properties of Materials 244

5.4.1 Linear Elastic Moduli 244

5.4.2 Nonlinear Elastic Material Response: Cauchy-Born Elasticity 248

6 Structural Energies and Phase Diagrams 253

6.1 Structures in Solids 253

6.2 Atomic-Level Geometry in Materials 254

6.3 Structural energies of solids 260

6.3.1 Pair Potentials and Structural Stability 261

6.3.2 Structural Stability in Transition Metals 264

6.3.3 Structural Stability Reconsidered: The Case of Elemental Si 265

6.4 Elemental Phase Diagrams 268

6.4.1 Free Energy of the Crystalline Solid 268

6.4.2 Free Energy of the Liquid 275

6.4.4 An Einstein Model for Structural Change 278

6.4.5 A Case Study in Elemental Mg 280

6.5 Alloy Phase Diagrams 282

6.5.1 Constructing the Effective Energy: Cluster Expansions 283

6.5.2 Statistical Mechanics for the Effective Hamiltonian 291

6.5.3 The Effective Hamiltonian Revisited: Relaxations and Vibrations 297

6.5.4 The Alloy Free Energy 299

6.5.5 Case Study: Oxygen Ordering in High T[subscript C] Superconductors 300

Part 3 Geometric Structures in Solids: Defects and Microstructures 309

7 Point Defects in Solids 311

7.1 Point Defects and Material Response 311

7.1.1 Material Properties Related to Point Disorder 312

7.2 Diffusion 318

7.2.1 Effective Theories of Diffusion 318

7.3 Geometries and Energies of Point Defects 326

7.3.1 Crystallographic Preliminaries 327

7.3.2 A Continuum Perspective on Point Defects 328

7.3.3 Microscopic Theories of Point Defects 332

7.3.4 Point Defects in Si: A Case Study 341

7.4 Point Defect Motions 344

7.4.1 Material Parameters for Mass Transport 345

7.4.2 Diffusion via Transition State Theory 346

7.4.3 Diffusion via Molecular Dynamics 351

7.4.4 A Case Study in Diffusion: Interstitials in Si 353

7.5 Defect Clustering 356

8 Line Defects in Solids 362

8.1 Permanent Deformation of Materials 362

8.1.1 Yield and Hardening 363

8.1.2 Structural Consequences of Plastic Deformation 365

8.1.3 Single Crystal Slip and the Schmid Law 367

8.2 The Ideal Strength Concept and the Need for Dislocations 369

8.3 Geometry of Slip 371

8.3.1 Topological Signature of Dislocations 372

8.3.2 Crystallography of Slip 375

8.4 Elastic Models of Single Dislocations 382

8.4.1 The Screw Dislocation 382

8.4.2 The Volterra Formula 388

8.4.3 The Edge Dislocation 391

8.4.4 Mixed Dislocations 392

8.5 Interaction Energies and Forces 393

8.5.1 The Peach-Koehler Formula 395

8.5.2 Interactions and Images: Peach-Koehler Applied 398

8.5.3 The Line Tension Approximation 402

8.6 Modeling the Dislocation Core: Beyond Linearity 404

8.6.1 Dislocation Dissociation 404

8.6.2 The Peierls-Nabarro Model 406

8.6.3 Structural Details of the Dislocation Core 412

8.7 Three-Dimensional Dislocation Configurations 415

8.7.1 Dislocation Bow-Out 416

8.7.2 Kinks and Jogs 418

8.7.3 Cross Slip 423

8.7.4 Dislocation Sources 426

8.7.5 Dislocation Junctions 430

9 Wall Defects in Solids 441

9.1 Interfaces in Materials 441

9.1.1 Interfacial Confinement 442

9.2 Free Surfaces 446

9.2.1 Crystallography and Energetics of Ideal Surfaces 447

9.2.2 Reconstruction at Surfaces 452

9.2.3 Steps on Surfaces 474

9.3 Stacking Faults and Twins 476

9.3.1 Structure and Energetics of Stacking Faults 477

9.3.2 Planar Faults and Phase Diagrams 484

9.4 Grain Boundaries 487

9.4.1 Bicrystal Geometry 489

9.4.2 Grain Boundaries in Polycrystals 492

9.4.3 Energetic Description of Grain Boundaries 494

9.4.4 Triple Junctions of Grain Boundaries 500

9.5 Diffuse Interfaces 501

9.6 Modeling Interfaces: A Retrospective 502

10 Microstructure and its Evolution 507

10.1 Microstructures in Materials 508

10.1.1 Microstructural Taxonomy 508

10.1.2 Microstructural Change 516

10.1.3 Models of Microstructure and its Evolution 519

10.2 Inclusions as Microstructure 520

10.2.1 Eshelby and the Elastic Inclusion 520

10.2.2 The Question of Equilibrium Shapes 527

10.2.3 Precipitate Morphologies and Interfacial Energy 528

10.2.4 Equilibrium Shapes: Elastic and Interfacial Energy 529

10.2.5 A Case Study in Inclusions: Precipitate Nucleation 537

10.2.6 Temporal Evolution of Two-Phase Microstructures 540

10.3 Microstructure in Martensites 546

10.3.1 The Experimental Situation 547

10.3.2 Geometrical and Energetic Preliminaries 551

10.3.3 Twinning and Compatibility 554

10.3.4 Fine-Phase Microstructures and Attainment 560

10.3.5 The Austenite-Martensite Free Energy Reconsidered 565

10.4 Microstructural Evolution in Polycrystals 566

10.4.1 Phenomenology of Grain Growth 567

10.4.2 Modeling Grain Growth 568

10.5 Microstructure and Materials 580

Part 4 Facing the Multiscale Challenge of Real Material Behavior 585

11 Points, Lines and Walls: Defect Interactions and Material Response 587

11.1 Defect Interactions and the Complexity of Real Material Behavior 587

11.2 Diffusion at Extended Defects 588

11.2.1 Background on Short-Circuit Diffusion 588

11.2.2 Diffusion at Surfaces 589

11.3 Mass Transport Assisted Deformation 592

11.3.1 Phenomenology of Creep 593

11.3.2 Nabarro-Herring and Coble Creep 595

11.4 Dislocations and Interfaces 599

11.4.1 Dislocation Models of Grain Boundaries 600

11.4.2 Dislocation Pile-Ups and Slip Transmission 604

11.5 Cracks and Dislocations 609

11.5.1 Variation on a Theme of Irwin 610

11.5.2 Dislocation Screening at a Crack Tip 611

11.5.3 Dislocation Nucleation at a Crack Tip 615

11.6 Dislocations and Obstacles: Strengthening 620

11.6.1 Conceptual Overview of the Motion of Dislocations Through a Field of Obstacles 622

11.6.2 The Force Between Dislocations and Glide Obstacles 625

11.6.3 The Question of Statistical Superposition 628

11.6.4 Solution Hardening 633

11.6.5 Precipitate Hardening 636

11.6.6 Dislocation-Dislocation Interactions and Work Hardening 642

12 Bridging Scales: Effective Theory Construction 649

12.1 Problems Involving Multiple Length and Time Scales 651

12.1.1 Problems with Multiple Temporal Scales: The Example of Diffusion 652

12.1.2 Problems with Multiple Spatial Scales: The Example of Plasticity 653

12.1.3 Generalities on Modeling Problems Involving Multiple Scales 655

12.2 Historic Examples of Multiscale Modeling 658

12.3 Effective Theory Construction 668

12.3.1 Degree of Freedom Selection: State Variables, Order Parameters and Configurational Coordinates 669

12.3.2 Dynamical Evolution of Relevant Variables: Gradient Flow Dynamics and Variational Principles 674

12.3.3 Inhomogeneous Systems and the Role of Locality 685

12.3.4 Models with Internal Structure 688

12.3.5 Effective Hamiltonians 697

12.4 Bridging Scales in Microstructural Evolution 701

12.4.1 Hierarchical Treatment of Diffusive Processes 701

12.4.2 From Surface Diffusion to Film Growth 709

12.4.3 Solidification Microstructures 711

12.4.4 Two-Phase Microstructures Revisited 715

12.4.5 A Retrospective on Modeling Microstructural Evolution 718

12.5 Bridging Scales in Plasticity 719

12.5.1 Mesoscopic Dislocation Dynamics 720

12.5.2 A Case Study in Dislocations and Plasticity: Nanoindentation 728

12.5.3 A Retrospective on Modeling Plasticity Using Dislocation Dynamics 731

12.6 Bridging Scales in Fracture 732

12.6.1 Atomic-Level Bond Breaking 732

12.6.2 Cohesive Surface Models 734

12.6.3 Cohesive Surface Description of Crack Tip Dislocation Nucleation 735

13 Universality and Specificity in Materials 742

13.1 Materials Observed 743

13.1.1 What is a Material: Another Look 743

13.1.2 Structural Observations 744

13.1.3 Concluding Observations on the Observations 746

13.2 How Far Have We Come? 748

13.2.1 Universality in Materials 749

13.2.2 Specificity in Materials 750

13.2.3 The Program Criticized 751

13.3 Intriguing Open Questions 752

13.4 In Which the Author Takes His Leave 754.

Notes:

Includes bibliographical references (pages 757-770) and index.

ISBN:

0521790050

0521793572

OCLC:

44669468