Interfaces in Crystalline Materials

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  • Edition: Reprint
  • Format: Paperback
  • Copyright: 2007-03-01
  • Publisher: Oxford University Press

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The study of interfaces within and between materials is a central field which is relevant to almost all aspects of materials science. For example, interfaces play a role in many of the mechanical and electrical properties of materials, phase transformations, and microstructure ofmaterials.This book is intended to serve as a graduate text consisting of four inter-related parts spanning the structure, thermodynamics, kinetics, and properties of interfaces in crystalline materials. Throughout the book emphasis is placed on the conceptual foundations of the subject through theexposition of simple models and descriptions of key experimental observations. In this way the reader is gradually taken to the forefront of the subject. The first four chapters deal with structural aspects of interfaces - interfacial geometry, dislocation models, interatomic forces, and atomicstructure. There are three chapters dealing with thermodynamic aspects of interfaces; the thermodynamics of interfaces; interfacial phases and phase transitions, and segregation of solute atoms. The kinetics of interfaces are covered in three chapters concerned with diffusion, conservative motion,and non-conservative motion. Finally there are two chapters which cover the electrical and mechanical properties of interfaces.This book is a unique introduction to the field of interfaces in crystalline materials spanning the subject in a coherent and pedagogical style.

Table of Contents

List of symbolsp. xxvii
Glossaryp. xxix
Interfacial Structure
The geometry of interfacesp. 3
Introductionp. 3
All the group theory we needp. 4
The relationship between two crystalsp. 5
Crystals and latticesp. 5
Vector and coordinate transformationsp. 6
Descriptions of lattice rotationsp. 8
Vector and matrix representationsp. 8
The Frank-Rodrigues mapp. 10
Fundamental zonesp. 12
Quaternionsp. 17
Geometrical specification of an interfacep. 20
Macroscopic and microscopic geometrical degrees of freedomp. 20
Macroscopic geometrical degrees of freedom of an arbitrary interfacep. 21
Grain boundaries in cubic materialsp. 21
The median lattice and the mean boundary planep. 21
Tilt and twist componentsp. 23
Symmetric and asymmetric tilt boundariesp. 24
Bicrystallographyp. 25
Introductionp. 25
Outline of crystallographic methodologyp. 26
Introduction to Seitz symbolsp. 30
Symmetry of dichromatic patternsp. 30
Symmetry of dichromatic complexesp. 38
Symmetry of ideal bicrystalsp. 40
Symmetry of real bicrystalsp. 41
Two examplesp. 42
Lattice matched polar-non-polar epitaxial interfacesp. 42
Lattice matched metal-silicide silicon interfacesp. 45
Classification of isolated interfacial line defectsp. 46
General formulationp. 48
Interfacial dislocationsp. 51
DSC dislocationsp. 51
Supplementary displacement dislocationsp. 52
Relaxation displacement dislocationsp. 55
Non-holosymmetric crystals and interfacial defectsp. 56
Interfacial disclinations and dispirationsp. 58
The morphologies of embedded crystalsp. 58
Quasiperiodicity and incommensurate interfacesp. 62
Referencesp. 68
Dislocation models for interfacesp. 70
Introductionp. 70
Classification of interfacial dislocationsp. 74
The Frank-Bilby equationp. 86
Comments on the Frank-Bilby equation and the dislocation content of an interfacep. 92
Frank's formulap. 95
The O-latticep. 96
The geometry of discrete dislocation arrays in interfacesp. 101
The general interfacep. 101
Application to a grain boundary with arbitrary geometrical parametersp. 104
Grain boundaries containing one and two sets of dislocationsp. 105
Epitaxial interfacesp. 108
Local dislocation interactionsp. 110
Two examplesp. 111
Pt-NiO interfacesp. 111
A1-A1[subscript 3] Ni eutectic interfacesp. 113
Elastic fields of interfacesp. 115
Introductionp. 115
Stress and distortion fields of grain boundaries in isotropic elasticityp. 116
Grain boundary energiesp. 120
Stress fields of heterophase interfaces in isotropic elasticityp. 125
Dislocation arrays at interfaces in anisotropic elasticityp. 129
Isotropic elastic analysis of epitaxial interfacesp. 129
Stress fields of precipitates and non-planar interfacesp. 131
Degree of localization of the cores of interfacial dislocationsp. 132
Introductionp. 132
Lattice theories of dislocation arraysp. 133
Introductionp. 133
Peierls-Nabarro model for an isolated edge dislocationp. 135
Peierls-Nabarro model for a symmetrical tilt boundaryp. 136
The van der Merwe model for a symmetrical tilt boundaryp. 138
Atomistic models using computer simulation and interatomic forcesp. 139
Experimental observations of arrays of interfacial dislocationsp. 139
Mainly room-temperature observationsp. 139
High-temperature observationsp. 146
Referencesp. 147
Models of interatomic forces at interfacesp. 149
Introductionp. 149
Density functional theoryp. 152
The variational principle and the Kohn-Sham equationsp. 152
The Harris-Foulkes energy functionalp. 158
Valence and core electrons: pseudopotentialsp. 160
The force theorem and Hellmann-Feynman forcesp. 163
Cohesion and pair potentials in sp-bonded metalsp. 165
Effective medium theoryp. 174
The embedded atom methodp. 177
Tight binding modelsp. 181
Introductionp. 181
The diatomic moleculep. 181
Bands, bonds, and Green functionsp. 185
Moments of the spectral density matrixp. 196
The tight binding bond (TBB) modelp. 202
The second moment approximationp. 207
Beyond the second moment approximationp. 210
Temperature dependence of atomic interactionsp. 211
Ionic bondingp. 224
Interatomic forces at heterophase interfacesp. 229
Referencesp. 236
Models and experimental observations of atomic structurep. 240
Introduction: classification of interfacesp. 240
Diffuse interfacesp. 241
Heterophase interfaces in systems with a miscibility gapp. 243
Antiphase domain boundaries in systems with long-range orderp. 247
Displacive transformation interfaces in systems near a mechanical instabilityp. 249
Sharp homophase interfaces: large-angle grain boundariesp. 252
Large-angle grain boundaries in metalsp. 253
The significance of the rigid body displacement parallel to the boundary planep. 253
The significance of the expansion normal to the boundary planep. 259
Testing the analytic modelp. 264
The significance of individual atomic relaxationp. 265
Discussion: singular, vicinal, and general interfacesp. 272
Methods of computer simulationp. 277
The polyhedral unit modelp. 284
The structural unit modelp. 286
Three-dimensional grain boundary structuresp. 305
The influence of temperaturep. 311
Grain boundaries in ionic crystalsp. 318
Grain boundaries in covalent crystalsp. 324
Sharp heterophase interfacesp. 327
Introductionp. 327
Metal-metal interfacesp. 330
Metal-insulator interfacesp. 332
Metal-semiconductor interfacesp. 338
Referencesp. 341
Interfacial Thermodynamics
Thermodynamics of interfacesp. 349
Introductionp. 349
The interface free energyp. 349
Additional interface thermodynamic quantities and relationships between themp. 353
Introduction of the interface stress and strain variablesp. 359
Introduction of the geometric thermodynamic variablesp. 366
Dependence of [sigma] on the interface inclinationp. 367
The Wulff plotp. 367
Equilibrium shape (Wulff form) of embedded second-phase particlep. 369
Faceting of initially flat interfacep. 372
The capillarity vector, [xi]p. 375
Capillary pressure associated with smoothly curved interfacep. 378
Equilibrium lattice solubility at a smoothly curved heterophase interfacep. 379
Equilibrium solubility at embedded second-phase particlep. 381
Equilibrium interface configurations at interface junction linesp. 382
Further thermodynamic relationships involving changes in interface inclinationp. 383
Dependence of [sigma] on the crystal misorientationp. 384
Dependence of [sigma] on simultaneous variations of the interface inclination and crystal misorientationp. 386
Chemical potentials and diffusion potentials, M[subscript i], in non-uniform systems containing interfacesp. 387
Introductionp. 387
Analysis of system at equilibrium; introduction of the diffusion potential, M[subscript i]p. 387
Incoherent interfacep. 389
Coherent interfacep. 392
Summaryp. 392
Diffusional transport in non-equilibrium systemsp. 393
Referencesp. 394
Interface phases and phase transitionsp. 396
Introductionp. 396
Interface phase equilibriap. 397
Interface phase transitionsp. 400
Non-congruent phase transitionsp. 400
Faceting of initially flat interfacesp. 400
Faceting of embedded particle interfacesp. 401
Interface dissociationp. 402
Congruent phase transitionsp. 404
Various transitions induced by changes in temperature, composition, or crystal misorientationp. 405
Interface wetting by a solid phasep. 409
Interface wetting by a liquid phase in alloy systemsp. 410
Grain boundary melting in a one-component systemp. 410
Referencesp. 412
Segregation of solute atoms to interfacesp. 414
Introductionp. 414
Overview of some of the main features of interface segregation in metalsp. 414
Physical models for the interaction between solute atoms and interfacesp. 424
Introductionp. 424
Elastic interaction modelsp. 426
Size accommodation modelp. 426
Hydrostatic pressure (P[Delta]V) and elastic inhomogeneity modelsp. 427
Further elastic modelsp. 430
Atomistic models at 0 Kp. 430
Electronic interaction modelsp. 433
Statistical mechanical models of segregationp. 435
Introductionp. 435
Regular solution modelp. 436
Mean field modelsp. 438
McLean isothermp. 442
Fowler-Guggenheim isothermp. 443
Multiple segregation site modelsp. 443
Beyond mean field modelsp. 447
Some additional modelsp. 449
Atomistic models at a finite temperaturep. 450
Interface segregation in ionic solidsp. 457
Referencesp. 462
Interfacial Kinetics
Diffusion at interfacesp. 467
Introductionp. 467
Fast diffusion along interfaces of species which are substitutional in the crystal latticep. 468
Slab model and regimes of diffusion behaviourp. 468
Mathematical analysis of the diffusant distribution in the type A, B, and C regimesp. 472
Experimental observationsp. 474
Some major results for diffusion along interfacesp. 475
Effects of interface structurep. 481
Mechanisms for fast grain boundary diffusionp. 486
Equilibrium point defects in the grain boundary corep. 487
'Ring', vacancy, interstitialcy, and interstitial mechanismsp. 492
Models for grain boundary self-diffusivities via the different mechanismsp. 495
Vacancy mechanismp. 498
Interstitialcy mechanismp. 498
Interstitial mechanismp. 499
General characteristics of the models for boundary self-diffusionp. 499
On the question of the mechanism (or mechanisms) of fast grain boundary diffusionp. 502
Metalsp. 502
Ionic materialsp. 506
Covalent materialsp. 508
Diffusion along interfaces of solute species which are interstitial in the crystal latticep. 509
Slow diffusion across interfaces in fast ion conductorsp. 513
Diffusion-induced grain boundary motion (DIGM)p. 514
Referencesp. 518
Conservative motion of interfacesp. 522
Introductionp. 522
'Conservative' versus 'non-conservative' motion of interfacesp. 522
Driving pressures for conservative motionp. 523
Basic mechanisms: correlated versus uncorrelated processesp. 525
Impediments to interface motionp. 525
Mechanisms and models for sharp interfacesp. 526
Glissile motion of interfacial dislocationsp. 526
Small-angle grain boundariesp. 526
Large-angle grain boundariesp. 531
Heterophase interfacesp. 536
Glide and climb of interfacial dislocationsp. 540
Small-angle grain boundariesp. 540
Large-angle grain boundariesp. 543
Heterophase interfacesp. 549
Shuffling motion of pure stepsp. 550
Uncorrelated atom shuffling and/or diffusional transportp. 555
Uncorrelated atom shufflingp. 557
Uncorrelated diffusional transportp. 558
Solute atom dragp. 560
Experimental observations of non-glissile (thermally activated) grain boundary motion in metalsp. 563
General large-angle grain boundariesp. 563
Singular (or vicinal) large-angle grain boundariesp. 566
Solute atom drag effectsp. 569
Small-angle grain boundariesp. 572
Mechanisms and models for diffuse interfacesp. 573
Propagation of non-linear elastic wave (or, alternatively, coherency dislocations)p. 574
Self-diffusionp. 574
Equations of interface motionp. 577
Motion when v = v(n)p. 577
Motion of curved interfaces under capillary pressurep. 580
More general conservative motionp. 582
Impediments to interface motion due to pinningp. 583
Pinning effects due to embedded particlesp. 583
Pinning at stationary particles at low temperaturesp. 583
Thermally activated unpinningp. 587
Diffusive motion of pinned particles along with the interfacep. 587
Pinning at free surface groovesp. 590
Referencesp. 594
Non-conservative motion of interfaces: interfaces as sources/sinks for diffusional fluxes of atomsp. 598
Introductionp. 598
General aspects of interfaces as sources/sinksp. 599
'Diffusion-controlled', 'interface-controlled', and 'mixed' kineticsp. 599
Dissipation of energy during source/sink actionp. 603
The maximum energy available to drive the source/sink actionp. 604
Grain boundaries as sources/sinks for fluxes of atomsp. 606
Introductionp. 606
Small-angle grain boundariesp. 606
Modelsp. 606
Experimental observationsp. 613
Large-angle grain boundariesp. 614
Models for singular or vicinal grain boundariesp. 614
Models for general grain boundariesp. 617
Experimental observationsp. 618
Sharp heterophase interfaces as sources/sinks for fluxes of atomsp. 621
Modelsp. 621
Singular or vicinal heterophase interfacesp. 621
General heterophase interfacesp. 624
Experimental observationsp. 624
Growth, coarsening, shape-equilibration, and shrinkage of small precipitate particlesp. 624
Growth of phases in the form of flat parallel layersp. 634
Annealing of supersaturated vacanciesp. 640
Diffusional accommodation of boundary sliding at second phase particlesp. 642
Diffuse heterophase interfaces as sources/sinks for solute atomsp. 644
On the question of interface stability during source/sink actionp. 647
Referencesp. 651
Interfacial Properties
Electronic properties of interfacesp. 657
Introductionp. 657
Metal-semiconductor interfacesp. 660
Introductionp. 660
The Schottky modelp. 660
The Bardeen modelp. 663
Metal-induced gap states (MIGS)p. 664
The defect modelp. 668
The development of the Schottky barrier as a function of metal coveragep. 669
Schottky barriers on Sip. 671
Discussion of models for Schottky barriersp. 673
Inhomogeneous Schottky barriersp. 673
Semiconductor heterojunctionsp. 674
Introductionp. 674
The band offsetsp. 676
Grain boundaries in metalsp. 684
Grain boundaries in semiconductorsp. 689
Grain boundaries in high temperature superconductorsp. 695
Referencesp. 700
Mechanical properties of interfacesp. 704
Introductionp. 704
Compatibility stresses in bicrystals and polycrystalsp. 704
Compatibility stresses caused by applied elastic stressp. 704
Compatibility stresses caused by plastic strainingp. 709
Compatibility stresses caused by heating/coolingp. 710
Elastic interactions between dislocations and interfacesp. 711
Interfaces as sinks, or traps, for lattice dislocationsp. 714
Introductionp. 714
Small-angle grain boundariesp. 716
Large-angle grain boundaries and heterophase boundariesp. 721
Singular boundariesp. 721
General boundariesp. 726
On the global equilibration of impinged lattice dislocationsp. 729
Interfaces as sources of both interfacial and lattice dislocationsp. 730
Interfaces as sources of interfacial dislocationsp. 731
Interfaces as sources of lattice dislocationsp. 732
Singular interfacesp. 733
General interfacesp. 734
Interfaces as barriers to the glide of lattice dislocations (slip)p. 737
Grain boundariesp. 737
Heterophase interfacesp. 740
Effects of interfaces on the plastic deformation of bicrystals and polycrystals at low temperaturesp. 740
Homophase bicrystals and polycrystalsp. 741
Heterophase bicrystals and polycrystalsp. 744
Role of interfaces in the plastic deformation of bicrystals and polycrystals at high temperaturesp. 744
Interface slidingp. 745
Sliding at an ideally planar grain boundaryp. 745
Sliding at a non-planar grain boundary by means of elastic accommodationp. 748
Sliding at a non-planar grain boundary by means of diffusional accommodationp. 750
Sliding at a non-planar grain boundary by means of plastic flow accommodation in the latticep. 752
Experimental observations of sliding at interfacesp. 753
Creep of polycrystalsp. 758
Creep of homophase polycrystals controlled by diffusional transportp. 759
Creep of homophase polycrystals controlled by boundary slidingp. 763
Creep of homophase polycrystals controlled by movement of lattice dislocationsp. 766
Further aspects of the creep of polycrystalsp. 767
Fracture at homophase interfacesp. 768
Overview of the different types of fracture observed experimentally in homophase polycrystalsp. 768
Propagation of cleavage cracksp. 772
Crack propagation in a single crystalp. 772
Crack propagation along a grain boundaryp. 779
Crack propagation in homophase polycrystalsp. 781
Growth and coalescence of cavities at grain boundaries at low temperatures by plastic flow due to dislocation glidep. 785
Growth and coalescence of cavities at grain boundaries at high temperatures by diffusion, power-law creep, and boundary slidingp. 786
Initiation of cavitiesp. 786
Growth of cavitiesp. 789
Coalescence of cavities and complete intergranular fracturep. 794
Fracture at heterophase interfacesp. 794
Referencesp. 798
Indexp. 805
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