Interfaces in Crystalline Materials

by Sutton, A. P.; Balluffi, R. W.

• ISBN13: 9780199211067
• ISBN10: 019921106X
• Edition: Reprint
• Format: Paperback
• Copyright: 2007-03-01
• Publisher: Oxford University Press

Summary

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 symbols	p. xxvii
Glossary	p. xxix
Interfacial Structure
The geometry of interfaces	p. 3
Introduction	p. 3
All the group theory we need	p. 4
The relationship between two crystals	p. 5
Crystals and lattices	p. 5
Vector and coordinate transformations	p. 6
Descriptions of lattice rotations	p. 8
Vector and matrix representations	p. 8
The Frank-Rodrigues map	p. 10
Fundamental zones	p. 12
Quaternions	p. 17
Geometrical specification of an interface	p. 20
Macroscopic and microscopic geometrical degrees of freedom	p. 20
Macroscopic geometrical degrees of freedom of an arbitrary interface	p. 21
Grain boundaries in cubic materials	p. 21
The median lattice and the mean boundary plane	p. 21
Tilt and twist components	p. 23
Symmetric and asymmetric tilt boundaries	p. 24
Bicrystallography	p. 25
Introduction	p. 25
Outline of crystallographic methodology	p. 26
Introduction to Seitz symbols	p. 30
Symmetry of dichromatic patterns	p. 30
Symmetry of dichromatic complexes	p. 38
Symmetry of ideal bicrystals	p. 40
Symmetry of real bicrystals	p. 41
Two examples	p. 42
Lattice matched polar-non-polar epitaxial interfaces	p. 42
Lattice matched metal-silicide silicon interfaces	p. 45
Classification of isolated interfacial line defects	p. 46
General formulation	p. 48
Interfacial dislocations	p. 51
DSC dislocations	p. 51
Supplementary displacement dislocations	p. 52
Relaxation displacement dislocations	p. 55
Non-holosymmetric crystals and interfacial defects	p. 56
Interfacial disclinations and dispirations	p. 58
The morphologies of embedded crystals	p. 58
Quasiperiodicity and incommensurate interfaces	p. 62
References	p. 68
Dislocation models for interfaces	p. 70
Introduction	p. 70
Classification of interfacial dislocations	p. 74
The Frank-Bilby equation	p. 86
Comments on the Frank-Bilby equation and the dislocation content of an interface	p. 92
Frank's formula	p. 95
The O-lattice	p. 96
The geometry of discrete dislocation arrays in interfaces	p. 101
The general interface	p. 101
Application to a grain boundary with arbitrary geometrical parameters	p. 104
Grain boundaries containing one and two sets of dislocations	p. 105
Epitaxial interfaces	p. 108
Local dislocation interactions	p. 110
Two examples	p. 111
Pt-NiO interfaces	p. 111
A1-A1[subscript 3] Ni eutectic interfaces	p. 113
Elastic fields of interfaces	p. 115
Introduction	p. 115
Stress and distortion fields of grain boundaries in isotropic elasticity	p. 116
Grain boundary energies	p. 120
Stress fields of heterophase interfaces in isotropic elasticity	p. 125
Dislocation arrays at interfaces in anisotropic elasticity	p. 129
Isotropic elastic analysis of epitaxial interfaces	p. 129
Stress fields of precipitates and non-planar interfaces	p. 131
Degree of localization of the cores of interfacial dislocations	p. 132
Introduction	p. 132
Lattice theories of dislocation arrays	p. 133
Introduction	p. 133
Peierls-Nabarro model for an isolated edge dislocation	p. 135
Peierls-Nabarro model for a symmetrical tilt boundary	p. 136
The van der Merwe model for a symmetrical tilt boundary	p. 138
Atomistic models using computer simulation and interatomic forces	p. 139
Experimental observations of arrays of interfacial dislocations	p. 139
Mainly room-temperature observations	p. 139
High-temperature observations	p. 146
References	p. 147
Models of interatomic forces at interfaces	p. 149
Introduction	p. 149
Density functional theory	p. 152
The variational principle and the Kohn-Sham equations	p. 152
The Harris-Foulkes energy functional	p. 158
Valence and core electrons: pseudopotentials	p. 160
The force theorem and Hellmann-Feynman forces	p. 163
Cohesion and pair potentials in sp-bonded metals	p. 165
Effective medium theory	p. 174
The embedded atom method	p. 177
Tight binding models	p. 181
Introduction	p. 181
The diatomic molecule	p. 181
Bands, bonds, and Green functions	p. 185
Moments of the spectral density matrix	p. 196
The tight binding bond (TBB) model	p. 202
The second moment approximation	p. 207
Beyond the second moment approximation	p. 210
Temperature dependence of atomic interactions	p. 211
Ionic bonding	p. 224
Interatomic forces at heterophase interfaces	p. 229
References	p. 236
Models and experimental observations of atomic structure	p. 240
Introduction: classification of interfaces	p. 240
Diffuse interfaces	p. 241
Heterophase interfaces in systems with a miscibility gap	p. 243
Antiphase domain boundaries in systems with long-range order	p. 247
Displacive transformation interfaces in systems near a mechanical instability	p. 249
Sharp homophase interfaces: large-angle grain boundaries	p. 252
Large-angle grain boundaries in metals	p. 253
The significance of the rigid body displacement parallel to the boundary plane	p. 253
The significance of the expansion normal to the boundary plane	p. 259
Testing the analytic model	p. 264
The significance of individual atomic relaxation	p. 265
Discussion: singular, vicinal, and general interfaces	p. 272
Methods of computer simulation	p. 277
The polyhedral unit model	p. 284
The structural unit model	p. 286
Three-dimensional grain boundary structures	p. 305
The influence of temperature	p. 311
Grain boundaries in ionic crystals	p. 318
Grain boundaries in covalent crystals	p. 324
Sharp heterophase interfaces	p. 327
Introduction	p. 327
Metal-metal interfaces	p. 330
Metal-insulator interfaces	p. 332
Metal-semiconductor interfaces	p. 338
References	p. 341
Interfacial Thermodynamics
Thermodynamics of interfaces	p. 349
Introduction	p. 349
The interface free energy	p. 349
Additional interface thermodynamic quantities and relationships between them	p. 353
Introduction of the interface stress and strain variables	p. 359
Introduction of the geometric thermodynamic variables	p. 366
Dependence of [sigma] on the interface inclination	p. 367
The Wulff plot	p. 367
Equilibrium shape (Wulff form) of embedded second-phase particle	p. 369
Faceting of initially flat interface	p. 372
The capillarity vector, [xi]	p. 375
Capillary pressure associated with smoothly curved interface	p. 378
Equilibrium lattice solubility at a smoothly curved heterophase interface	p. 379
Equilibrium solubility at embedded second-phase particle	p. 381
Equilibrium interface configurations at interface junction lines	p. 382
Further thermodynamic relationships involving changes in interface inclination	p. 383
Dependence of [sigma] on the crystal misorientation	p. 384
Dependence of [sigma] on simultaneous variations of the interface inclination and crystal misorientation	p. 386
Chemical potentials and diffusion potentials, M[subscript i], in non-uniform systems containing interfaces	p. 387
Introduction	p. 387
Analysis of system at equilibrium; introduction of the diffusion potential, M[subscript i]	p. 387
Incoherent interface	p. 389
Coherent interface	p. 392
Summary	p. 392
Diffusional transport in non-equilibrium systems	p. 393
References	p. 394
Interface phases and phase transitions	p. 396
Introduction	p. 396
Interface phase equilibria	p. 397
Interface phase transitions	p. 400
Non-congruent phase transitions	p. 400
Faceting of initially flat interfaces	p. 400
Faceting of embedded particle interfaces	p. 401
Interface dissociation	p. 402
Congruent phase transitions	p. 404
Various transitions induced by changes in temperature, composition, or crystal misorientation	p. 405
Interface wetting by a solid phase	p. 409
Interface wetting by a liquid phase in alloy systems	p. 410
Grain boundary melting in a one-component system	p. 410
References	p. 412
Segregation of solute atoms to interfaces	p. 414
Introduction	p. 414
Overview of some of the main features of interface segregation in metals	p. 414
Physical models for the interaction between solute atoms and interfaces	p. 424
Introduction	p. 424
Elastic interaction models	p. 426
Size accommodation model	p. 426
Hydrostatic pressure (P[Delta]V) and elastic inhomogeneity models	p. 427
Further elastic models	p. 430
Atomistic models at 0 K	p. 430
Electronic interaction models	p. 433
Statistical mechanical models of segregation	p. 435
Introduction	p. 435
Regular solution model	p. 436
Mean field models	p. 438
McLean isotherm	p. 442
Fowler-Guggenheim isotherm	p. 443
Multiple segregation site models	p. 443
Beyond mean field models	p. 447
Some additional models	p. 449
Atomistic models at a finite temperature	p. 450
Interface segregation in ionic solids	p. 457
References	p. 462
Interfacial Kinetics
Diffusion at interfaces	p. 467
Introduction	p. 467
Fast diffusion along interfaces of species which are substitutional in the crystal lattice	p. 468
Slab model and regimes of diffusion behaviour	p. 468
Mathematical analysis of the diffusant distribution in the type A, B, and C regimes	p. 472
Experimental observations	p. 474
Some major results for diffusion along interfaces	p. 475
Effects of interface structure	p. 481
Mechanisms for fast grain boundary diffusion	p. 486
Equilibrium point defects in the grain boundary core	p. 487
'Ring', vacancy, interstitialcy, and interstitial mechanisms	p. 492
Models for grain boundary self-diffusivities via the different mechanisms	p. 495
Vacancy mechanism	p. 498
Interstitialcy mechanism	p. 498
Interstitial mechanism	p. 499
General characteristics of the models for boundary self-diffusion	p. 499
On the question of the mechanism (or mechanisms) of fast grain boundary diffusion	p. 502
Metals	p. 502
Ionic materials	p. 506
Covalent materials	p. 508
Diffusion along interfaces of solute species which are interstitial in the crystal lattice	p. 509
Slow diffusion across interfaces in fast ion conductors	p. 513
Diffusion-induced grain boundary motion (DIGM)	p. 514
References	p. 518
Conservative motion of interfaces	p. 522
Introduction	p. 522
'Conservative' versus 'non-conservative' motion of interfaces	p. 522
Driving pressures for conservative motion	p. 523
Basic mechanisms: correlated versus uncorrelated processes	p. 525
Impediments to interface motion	p. 525
Mechanisms and models for sharp interfaces	p. 526
Glissile motion of interfacial dislocations	p. 526
Small-angle grain boundaries	p. 526
Large-angle grain boundaries	p. 531
Heterophase interfaces	p. 536
Glide and climb of interfacial dislocations	p. 540
Small-angle grain boundaries	p. 540
Large-angle grain boundaries	p. 543
Heterophase interfaces	p. 549
Shuffling motion of pure steps	p. 550
Uncorrelated atom shuffling and/or diffusional transport	p. 555
Uncorrelated atom shuffling	p. 557
Uncorrelated diffusional transport	p. 558
Solute atom drag	p. 560
Experimental observations of non-glissile (thermally activated) grain boundary motion in metals	p. 563
General large-angle grain boundaries	p. 563
Singular (or vicinal) large-angle grain boundaries	p. 566
Solute atom drag effects	p. 569
Small-angle grain boundaries	p. 572
Mechanisms and models for diffuse interfaces	p. 573
Propagation of non-linear elastic wave (or, alternatively, coherency dislocations)	p. 574
Self-diffusion	p. 574
Equations of interface motion	p. 577
Motion when v = v(n)	p. 577
Motion of curved interfaces under capillary pressure	p. 580
More general conservative motion	p. 582
Impediments to interface motion due to pinning	p. 583
Pinning effects due to embedded particles	p. 583
Pinning at stationary particles at low temperatures	p. 583
Thermally activated unpinning	p. 587
Diffusive motion of pinned particles along with the interface	p. 587
Pinning at free surface grooves	p. 590
References	p. 594
Non-conservative motion of interfaces: interfaces as sources/sinks for diffusional fluxes of atoms	p. 598
Introduction	p. 598
General aspects of interfaces as sources/sinks	p. 599
'Diffusion-controlled', 'interface-controlled', and 'mixed' kinetics	p. 599
Dissipation of energy during source/sink action	p. 603
The maximum energy available to drive the source/sink action	p. 604
Grain boundaries as sources/sinks for fluxes of atoms	p. 606
Introduction	p. 606
Small-angle grain boundaries	p. 606
Models	p. 606
Experimental observations	p. 613
Large-angle grain boundaries	p. 614
Models for singular or vicinal grain boundaries	p. 614
Models for general grain boundaries	p. 617
Experimental observations	p. 618
Sharp heterophase interfaces as sources/sinks for fluxes of atoms	p. 621
Models	p. 621
Singular or vicinal heterophase interfaces	p. 621
General heterophase interfaces	p. 624
Experimental observations	p. 624
Growth, coarsening, shape-equilibration, and shrinkage of small precipitate particles	p. 624
Growth of phases in the form of flat parallel layers	p. 634
Annealing of supersaturated vacancies	p. 640
Diffusional accommodation of boundary sliding at second phase particles	p. 642
Diffuse heterophase interfaces as sources/sinks for solute atoms	p. 644
On the question of interface stability during source/sink action	p. 647
References	p. 651
Interfacial Properties
Electronic properties of interfaces	p. 657
Introduction	p. 657
Metal-semiconductor interfaces	p. 660
Introduction	p. 660
The Schottky model	p. 660
The Bardeen model	p. 663
Metal-induced gap states (MIGS)	p. 664
The defect model	p. 668
The development of the Schottky barrier as a function of metal coverage	p. 669
Schottky barriers on Si	p. 671
Discussion of models for Schottky barriers	p. 673
Inhomogeneous Schottky barriers	p. 673
Semiconductor heterojunctions	p. 674
Introduction	p. 674
The band offsets	p. 676
Grain boundaries in metals	p. 684
Grain boundaries in semiconductors	p. 689
Grain boundaries in high temperature superconductors	p. 695
References	p. 700
Mechanical properties of interfaces	p. 704
Introduction	p. 704
Compatibility stresses in bicrystals and polycrystals	p. 704
Compatibility stresses caused by applied elastic stress	p. 704
Compatibility stresses caused by plastic straining	p. 709
Compatibility stresses caused by heating/cooling	p. 710
Elastic interactions between dislocations and interfaces	p. 711
Interfaces as sinks, or traps, for lattice dislocations	p. 714
Introduction	p. 714
Small-angle grain boundaries	p. 716
Large-angle grain boundaries and heterophase boundaries	p. 721
Singular boundaries	p. 721
General boundaries	p. 726
On the global equilibration of impinged lattice dislocations	p. 729
Interfaces as sources of both interfacial and lattice dislocations	p. 730
Interfaces as sources of interfacial dislocations	p. 731
Interfaces as sources of lattice dislocations	p. 732
Singular interfaces	p. 733
General interfaces	p. 734
Interfaces as barriers to the glide of lattice dislocations (slip)	p. 737
Grain boundaries	p. 737
Heterophase interfaces	p. 740
Effects of interfaces on the plastic deformation of bicrystals and polycrystals at low temperatures	p. 740
Homophase bicrystals and polycrystals	p. 741
Heterophase bicrystals and polycrystals	p. 744
Role of interfaces in the plastic deformation of bicrystals and polycrystals at high temperatures	p. 744
Interface sliding	p. 745
Sliding at an ideally planar grain boundary	p. 745
Sliding at a non-planar grain boundary by means of elastic accommodation	p. 748
Sliding at a non-planar grain boundary by means of diffusional accommodation	p. 750
Sliding at a non-planar grain boundary by means of plastic flow accommodation in the lattice	p. 752
Experimental observations of sliding at interfaces	p. 753
Creep of polycrystals	p. 758
Creep of homophase polycrystals controlled by diffusional transport	p. 759
Creep of homophase polycrystals controlled by boundary sliding	p. 763
Creep of homophase polycrystals controlled by movement of lattice dislocations	p. 766
Further aspects of the creep of polycrystals	p. 767
Fracture at homophase interfaces	p. 768
Overview of the different types of fracture observed experimentally in homophase polycrystals	p. 768
Propagation of cleavage cracks	p. 772
Crack propagation in a single crystal	p. 772
Crack propagation along a grain boundary	p. 779
Crack propagation in homophase polycrystals	p. 781
Growth and coalescence of cavities at grain boundaries at low temperatures by plastic flow due to dislocation glide	p. 785
Growth and coalescence of cavities at grain boundaries at high temperatures by diffusion, power-law creep, and boundary sliding	p. 786
Initiation of cavities	p. 786
Growth of cavities	p. 789
Coalescence of cavities and complete intergranular fracture	p. 794
Fracture at heterophase interfaces	p. 794
References	p. 798
Index	p. 805
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