Crystals, Defects and Microstructures

Modeling Across Scales

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Paperback | 2 May 2001

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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 graduate 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. 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.

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'It covers an extremely wide range of topics including good case studies of new systems such as nanotubes. It succeeds in convening modelling ideas from both a physics and materials science point of view. ... This book's distinct feature, which makes it attractive as a general reference book, is the inclusion of a lot of the author's personal opinions, and makes it stand out from most classroom or course textbooks. To support this, the style of writing is informal, easy to read, and sometimes fun.' Dr Wei Sha, Materials World '... a timely and relevant postgraduate level text covering an unusual and exciting new topic ...'. Joan Halfpenny, Chemistry in Britain 'I would recommend it to anyone wishing to get both a broad overview of the intersection of theoretical condensed matter physics with modern materials science, and some good pointers toward future research directions.' Nigel Goldenfeld, Physics Today

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Non-Fiction Science Chemistry Crystallography Mathematics Engineering & Technology Technology in General Engineering in General Mechanical Engineering & Materials Materials Science Mechanics of Solids Stress & Fracture

Preface	p. xv
Acknowledgements	p. xxi
Notes on Units, Scales and Conventions	p. xxiv
Thinking About the Material World	p. 1
Idealizing Material Response	p. 3
A Material World	p. 3
Materials: A Databook Perspective	p. 3
The Structure-Properties Paradigm	p. 8
Controlling Structure: The World of Heat and Beat	p. 12
Modeling of Materials	p. 14
The Case for Modeling	p. 14
Modeling Defined: Contrasting Perspectives	p. 15
Case Studies in Modeling	p. 18
Modeling and the Computer: Numerical Analysis vs Simulation	p. 25
Further Reading	p. 26
Continuum Mechanics Revisited	p. 29
Continuum Mechanics as an Effective Theory	p. 29
Kinematics: The Geometry of Deformation	p. 31
Deformation Mappings and Strain	p. 32
Geometry of Rigid Deformation	p. 35
Geometry of Slip and Twinning	p. 36
Geometry of Structural Transformations	p. 37
Forces and Balance Laws	p. 39
Forces Within Continua: Stress Tensors	p. 39
Equations of Continuum Dynamics	p. 41
Configurational Forces and the Dynamics of Defects	p. 44
Continuum Descriptions of Deformation and Failure	p. 51
Constitutive Modeling	p. 51
Linear Elastic Response of Materials	p. 51
Plastic Response of Crystals and Polycrystals	p. 54
Continuum Picture of Fracture	p. 60
Boundary Value Problems and Modeling	p. 64
Principle of Minimum Potential Energy and Reciprocal Theorem	p. 64
Elastic Green Function	p. 66
Method of Eigenstrains	p. 69
Numerical Solutions: Finite Element Method	p. 72
Difficulties with the Continuum Approach	p. 75
Further Reading	p. 76
Problems	p. 78
Quantum and Statistical Mechanics Revisited	p. 81
Background	p. 81
Quantum Mechanics	p. 82
Background and Formalism	p. 82
Catalog of Important Solutions	p. 87
Finite Elements and Schrodinger	p. 94
Quantum Corrals: A Finite Element Analysis	p. 101
Metals and the Electron Gas	p. 103
Quantum Mechanics of Bonding	p. 109
Statistical Mechanics	p. 115
Background	p. 115
Entropy of Mixing	p. 119
The Canonical Distribution	p. 122
Information Theoretic Approach to Statistical Mechanics	p. 126
Statistical Mechanics Models for Materials	p. 129
Bounds and Inequalities: The Bogoliubov Inequality	p. 135
Correlation Functions: The Kinematics of Order	p. 137
Computational Statistical Mechanics	p. 139
Further Reading	p. 142
Problems	p. 144
Energetics of Crystalline Solids	p. 147
Energetic Description of Cohesion in Solids	p. 149
The Role of the Total Energy in Modeling Materials	p. 149
Conceptual Backdrop for Characterizing the Total Energy	p. 152
Atomistic and Continuum Descriptions Contrasted	p. 152
The Many-Particle Hamiltonian and Degree of Freedom Reduction	p. 154
Pair Potentials	p. 156
Generic Pair Potentials	p. 156
Free Electron Pair Potentials	p. 158
Potentials with Environmental and Angular Dependence	p. 164
Diagnostics for Evaluating Potentials	p. 164
Pair Functionals	p. 165
Angular Forces: A First Look	p. 172
Tight-Binding Calculations of the Total Energy	p. 176
The Tight-Binding Method	p. 176
An Aside on Periodic Solids: k-space Methods	p. 184
Real Space Tight-Binding Methods	p. 189
First-Principles Calculations of the Total Energy	p. 197
Managing the Many-Particle Hamiltonian	p. 198
Total Energies in the Local Density Approximation	p. 200
Choosing a Description of the Total Energy: Challenges and Conundrums	p. 203
Further Reading	p. 204
Problems	p. 206
Thermal and Elastic Properties of Crystals	p. 210
Thermal and Elastic Material Response	p. 210
Mechanics of the Harmonic Solid	p. 213
Total Energy of the Thermally Fluctuating Solid	p. 214
Atomic Motion and Normal Modes	p. 216
Phonons	p. 228
Buckminsterfullerene and Nanotubes: A Case Study in Vibration	p. 229
Thermodynamics of Solids	p. 231
Harmonic Approximation	p. 231
Beyond the Harmonic Approximation	p. 239
Modeling the Elastic Properties of Materials	p. 244
Linear Elastic Moduli	p. 244
Nonlinear Elastic Material Response: Cauchy-Born Elasticity	p. 248
Further Reading	p. 250
Problems	p. 251
Structural Energies and Phase Diagrams	p. 253
Structures in Solids	p. 253
Atomic-Level Geometry in Materials	p. 254
Structural energies of solids	p. 260
Pair Potentials and Structural Stability	p. 261
Structural Stability in Transition Metals	p. 264
Structural Stability Reconsidered: The Case of Elemental Si	p. 265
Elemental Phase Diagrams	p. 268
Free Energy of the Crystalline Solid	p. 268
Free Energy of the Liquid	p. 275
Putting It All Together	p. 277
An Einstein Model for Structural Change	p. 278
A Case Study in Elemental Mg	p. 280
Alloy Phase Diagrams	p. 282
Constructing the Effective Energy: Cluster Expansions	p. 283
Statistical Mechanics for the Effective Hamiltonian	p. 291
The Effective Hamiltonian Revisited: Relaxations and Vibrations	p. 297
The Alloy Free Energy	p. 299
Case Study: Oxygen Ordering in High T[subscript C] Superconductors	p. 300
Summary	p. 304
Further Reading	p. 304
Problems	p. 305
Geometric Structures in Solids: Defects and Microstructures	p. 309
Point Defects in Solids	p. 311
Point Defects and Material Response	p. 311
Material Properties Related to Point Disorder	p. 312
Diffusion	p. 318
Effective Theories of Diffusion	p. 318
Geometries and Energies of Point Defects	p. 326
Crystallographic Preliminaries	p. 327
A Continuum Perspective on Point Defects	p. 328
Microscopic Theories of Point Defects	p. 332
Point Defects in Si: A Case Study	p. 341
Point Defect Motions	p. 344
Material Parameters for Mass Transport	p. 345
Diffusion via Transition State Theory	p. 346
Diffusion via Molecular Dynamics	p. 351
A Case Study in Diffusion: Interstitials in Si	p. 353
Defect Clustering	p. 356
Further Reading	p. 356
Problems	p. 359
Line Defects in Solids	p. 362
Permanent Deformation of Materials	p. 362
Yield and Hardening	p. 363
Structural Consequences of Plastic Deformation	p. 365
Single Crystal Slip and the Schmid Law	p. 367
The Ideal Strength Concept and the Need for Dislocations	p. 369
Geometry of Slip	p. 371
Topological Signature of Dislocations	p. 372
Crystallography of Slip	p. 375
Elastic Models of Single Dislocations	p. 382
The Screw Dislocation	p. 382
The Volterra Formula	p. 388
The Edge Dislocation	p. 391
Mixed Dislocations	p. 392
Interaction Energies and Forces	p. 393
The Peach-Koehler Formula	p. 395
Interactions and Images: Peach-Koehler Applied	p. 398
The Line Tension Approximation	p. 402
Modeling the Dislocation Core: Beyond Linearity	p. 404
Dislocation Dissociation	p. 404
The Peierls-Nabarro Model	p. 406
Structural Details of the Dislocation Core	p. 412
Three-Dimensional Dislocation Configurations	p. 415
Dislocation Bow-Out	p. 416
Kinks and Jogs	p. 418
Cross Slip	p. 423
Dislocation Sources	p. 426
Dislocation Junctions	p. 430
Further Reading	p. 435
Problems	p. 437
Wall Defects in Solids	p. 441
Interfaces in Materials	p. 441
Interfacial Confinement	p. 442
Free Surfaces	p. 446
Crystallography and Energetics of Ideal Surfaces	p. 447
Reconstruction at Surfaces	p. 452
Steps on Surfaces	p. 474
Stacking Faults and Twins	p. 476
Structure and Energetics of Stacking Faults	p. 477
Planar Faults and Phase Diagrams	p. 484
Grain Boundaries	p. 487
Bicrystal Geometry	p. 489
Grain Boundaries in Polycrystals	p. 492
Energetic Description of Grain Boundaries	p. 494
Triple Junctions of Grain Boundaries	p. 500
Diffuse Interfaces	p. 501
Modeling Interfaces: A Retrospective	p. 502
Further Reading	p. 503
Problems	p. 505
Microstructure and its Evolution	p. 507
Microstructures in Materials	p. 508
Microstructural Taxonomy	p. 508
Microstructural Change	p. 516
Models of Microstructure and its Evolution	p. 519
Inclusions as Microstructure	p. 520
Eshelby and the Elastic Inclusion	p. 520
The Question of Equilibrium Shapes	p. 527
Precipitate Morphologies and Interfacial Energy	p. 528
Equilibrium Shapes: Elastic and Interfacial Energy	p. 529
A Case Study in Inclusions: Precipitate Nucleation	p. 537
Temporal Evolution of Two-Phase Microstructures	p. 540
Microstructure in Martensites	p. 546
The Experimental Situation	p. 547
Geometrical and Energetic Preliminaries	p. 551
Twinning and Compatibility	p. 554
Fine-Phase Microstructures and Attainment	p. 560
The Austenite-Martensite Free Energy Reconsidered	p. 565
Microstructural Evolution in Polycrystals	p. 566
Phenomenology of Grain Growth	p. 567
Modeling Grain Growth	p. 568
Microstructure and Materials	p. 580
Further Reading	p. 580
Problems	p. 582
Facing the Multiscale Challenge of Real Material Behavior	p. 585
Points, Lines and Walls: Defect Interactions and Material Response	p. 587
Defect Interactions and the Complexity of Real Material Behavior	p. 587
Diffusion at Extended Defects	p. 588
Background on Short-Circuit Diffusion	p. 588
Diffusion at Surfaces	p. 589
Mass Transport Assisted Deformation	p. 592
Phenomenology of Creep	p. 593
Nabarro-Herring and Coble Creep	p. 595
Dislocations and Interfaces	p. 599
Dislocation Models of Grain Boundaries	p. 600
Dislocation Pile-Ups and Slip Transmission	p. 604
Cracks and Dislocations	p. 609
Variation on a Theme of Irwin	p. 610
Dislocation Screening at a Crack Tip	p. 611
Dislocation Nucleation at a Crack Tip	p. 615
Dislocations and Obstacles: Strengthening	p. 620
Conceptual Overview of the Motion of Dislocations Through a Field of Obstacles	p. 622
The Force Between Dislocations and Glide Obstacles	p. 625
The Question of Statistical Superposition	p. 628
Solution Hardening	p. 633
Precipitate Hardening	p. 636
Dislocation-Dislocation Interactions and Work Hardening	p. 642
Further Reading	p. 644
Problems	p. 647
Bridging Scales: Effective Theory Construction	p. 649
Problems Involving Multiple Length and Time Scales	p. 651
Problems with Multiple Temporal Scales: The Example of Diffusion	p. 652
Problems with Multiple Spatial Scales: The Example of Plasticity	p. 653
Generalities on Modeling Problems Involving Multiple Scales	p. 655
Historic Examples of Multiscale Modeling	p. 658
Effective Theory Construction	p. 668
Degree of Freedom Selection: State Variables, Order Parameters and Configurational Coordinates	p. 669
Dynamical Evolution of Relevant Variables: Gradient Flow Dynamics and Variational Principles	p. 674
Inhomogeneous Systems and the Role of Locality	p. 685
Models with Internal Structure	p. 688
Effective Hamiltonians	p. 697
Bridging Scales in Microstructural Evolution	p. 701
Hierarchical Treatment of Diffusive Processes	p. 701
From Surface Diffusion to Film Growth	p. 709
Solidification Microstructures	p. 711
Two-Phase Microstructures Revisited	p. 715
A Retrospective on Modeling Microstructural Evolution	p. 718
Bridging Scales in Plasticity	p. 719
Mesoscopic Dislocation Dynamics	p. 720
A Case Study in Dislocations and Plasticity: Nanoindentation	p. 728
A Retrospective on Modeling Plasticity Using Dislocation Dynamics	p. 731
Bridging Scales in Fracture	p. 732
Atomic-Level Bond Breaking	p. 732
Cohesive Surface Models	p. 734
Cohesive Surface Description of Crack Tip Dislocation Nucleation	p. 735
Further Reading	p. 736
Problems	p. 738
Universality and Specificity in Materials	p. 742
Materials Observed	p. 743
What is a Material: Another Look	p. 743
Structural Observations	p. 744
Concluding Observations on the Observations	p. 746
How Far Have We Come?	p. 748
Universality in Materials	p. 749
Specificity in Materials	p. 750
The Program Criticized	p. 751
Intriguing Open Questions	p. 752
In Which the Author Takes His Leave	p. 754
References	p. 757
Index	p. 771
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Crystals, Defects and Microstructures

Modeling Across Scales

At a Glance

Paperback

Industry Reviews

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How to return your order

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