Diffusion in solids fundamentals, methods, materials, diffusion-controlled processes ; with ... 27 tables

Diffusion in solids fundamentals, methods, materials, diffusion-controlled processes ; with ... 27 tables

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Bibliographische Detailangaben
1. Verfasser: Mehrer, Helmut (VerfasserIn)
Format: Buch
Sprache:English
Veröffentlicht: Berlin Springer 2007
Schriftenreihe:Springer series in solid-state sciences 155
Schlagworte:
Festkörper - Diffusion
Diffusion
Kirkendall effect
Solid state physics
Festkörper
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Datensatz im Suchindex

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adam_text Contents History and Bibliography of Diffusion .................... 1 1.1 Pioneers and Landmarks of Diffusion ..................... . 2 References ................................................. 16 1.2 Bibliography of Solid-State Diffusion ...................... 18 Part I Fundamentals of Diffusion 2 Continuum Theory of Diffusion ........................... 27 2.1 Fick s Laws in Isotropie Media ........................... 27 2.1.1 Fick s First Law .................................. 28 2.1.2 Equation of Continuity ............................ 29 2.1.3 Fick s Second Law - the Diffusion Equation ........ 30 2.2 Diffusion Equation in Various Coordinates ................. 31 2.3 Fick s Laws in Anisotropie Media ......................... 33 References ................................................. 35 3 Solutions of the Diffusion Equation ....................... 37 3.1 Steady-State Diffusion .................................. 37 3.2 Non-Steady-State Diffusion in one Dimension .............. 39 3.2.1 Thin-Film Solution ............................... 39 3.2.2 Extended Initial Distribution and Constant Surface Concentration ................ 41 3.2.3 Method of Laplace Transformation ................. 45 3.2.4 Diffusion in a Plane Sheet Separation of Variables .. 47 3.2.5 Radial Diffusion in a Cylinder ...................... 5Ü 3.2.6 Radial Diffusion in a Sphere ....................... 51 3.3 Point Source in one, two, and three Dimensions ............ 52 References ................................................. 53 4 Random Walk Theory and Atomic Jump Process ......... 55 4.1 Random Walk and Diffusion ............................. 56 4.1.1 A Simplified Model ............................... 56 4.1.2 Einstein-Smoluchowski Relation .................... 58 4.1.3 Random Walk on a Lattice ........................ 60 XII Contents 4.1.4 Correlation Factor ................................ 62 4.2 Atomic Jump Process ................................... 64 References ................................................. 66 5 Point Defects in Crystals ................................. 69 5.1 Pure Metals ........................................... 70 5.1.1 Vacancies ....................................... 70 5.1.2 Divacancies ...................................... 72 5.1.3 Determination of Vacancy Properties ............... 74 5.1.4 Sclf-Interstitials .................................. 79 5.2 Substitutional Binary Alloys ............................. 80 5.2.1 Vacancies in Dilute Alloys ......................... 81 5.2.2 Vacancies in Concentrated Alloys ................... 82 5.3 Ionic Compounds ....................................... 83 5.3.1 Frenkel Disorder ................................. 84 5.3.2 Schottky Disorder ................................ 85 5.4 Intermetallics .......................................... 86 5.5 Semiconductors ........................................ 88 References ................................................. 91 6 Diffusion Mechanisms .................................... 95 6.1 Interstitial Mechanism .................................. 95 6.2 Collective Mechanisms .................................. 97 6.3 Vacancy Mechanism .................................... 98 6.4 Divacancy Mechanism ................................... 100 6.5 Interstitialcy Mechanism ................................ 100 6.6 Interstitial-substitutional Exchange Mechanisms ............ 102 References ................................................. 103 7 Correlation in Solid-State Diffusion ....................... 105 7.1 Interstitial Mechanism .................................. 107 7.2 Interstitialcy Mechanism ................................ 107 7.3 Vacancy Mechanism of Self-diffusion ...................... 108 7.3.1 A Rule of Thumb ............................... 108 7.3.2 Vacancy-tracer Encounters ........................ 109 7.3.3 Spatial and Temporal Correlation .................. 112 7.3.4 Calculation of Correlation Factors .................. 112 7.4 Correlation Factors of Self-diffusion ....................... 115 7.5 Vacancy-mediated Solute Diffusion ....................... 116 7.5.1 Face-Centered Cubic Solvents ...................... 117 7.5.2 Body-Centered Cubic Solvents ..................... 120 7.5.3 Diamond Structure Solvents ....................... 121 7.6 Concluding Remarks .................................... 122 References ................................................. 124 Contents XIII 8 Dependence of Diffusion on Temperature and Pressure ... 127 8.1 Temperature Dependence ................................ 127 8.1.1 The Arrhenius Relation ........................... 127 8.1.2 Activation Parameters Examples ................. 130 8.2 Pressure Dependence ................................... 132 8.2.1 Activation Volumes of Self-diffusion ................. 135 8.2.2 Activation Volumes of Solute Diffusion .............. 139 8.2.3 Activation Volumes of Ionic Crystals ................ 140 8.3 Correlations between Diffusion and Bulk Properties ......... 141 8.3.1 Melting Properties and Diffusion ................... 141 8.3.2 Activation Parameters and Elastic Constants ........ 146 8.3.3 Use of Correlations ................................147 References ................................................. 147 9 Isotope Effect of Diffusion ................................ 151 9.1 Single-jump Mechanisms ................................ 151 9.2 Collective Mechanisms .................................. 155 9.3 Isotope Effect Experiments .............................. 155 References ................................................. 159 10 Interdiffusion and Kirkendall Effect ....................... 161 10.1 Interdiffusion .......................................... 161 10.1.1 Boltzmann Transformation ........................ 162 10.1.2 Boltzmann-Matano Method ........................ 163 10.1.3 Sauer-Freisc Method .............................. 166 10.2 Intrinsic Diffusion and Kirkendall Effect ................... 168 10.3 Darken Equations ...................................... 170 10.4 Darkcn-Manning Equations .............................. 172 10.5 Microstructural Stability of the Kirkendall Plane ........... 173 References ................................................. 176 11 Diffusion and External Driving Forces .................... 179 11.1 Overview .............................................. 179 11.2 Fick s Equations with Drift .............................. 181 11.3 Nernst-Einstein Relation ................................ 182 11.4 Nernst-Einstein Relation for Ionic Conductors and Haven Ratio ....................................... 184 11.5 Nernst-Planck Equation Interdiffusion in Ionic Crystals .... 186 11.6 Nernst-Planck Equation versus Darken Equation ........... 188 References ................................................. 189 12 Irreversible Thermodynamics and Diffusion ............... 191 12.1 General Remarks ....................................... 191 12.2 Phenomenological Equations of Isothermal Diffusion ........ 193 12.2.1 Tracer Self-Diffusion in Element Crystals ............ 193 XIV Contents 12.2.2 Diffusion in Binary Alloys .........................195 12.3 The Phenomenological Coefficients ........................199 12.3.1 Phenomenological Coefficients, Tracer Diffusivities, and Jump Models ................................202 12.3.2 Sum Rules - Relations between Phenomenological Coefficients ..............204 References .................................................205 Part II Experimental Methods 13 Direct Diffusion Studies ..................................209 13.1 Direct versus Indirect Methods ...........................209 13.2 The Various Diffusion Coefficients ........................212 13.2.1 Tracer Diffusion Coefficients .......................212 13.2.2 Interdiffusion and Intrinsic Diffusion Coefficients .....214 13.3 Tracer Diffusion Experiments ............................215 13.3.1 Profile Analysis by Serial Sectioning ................217 13.3.2 Residual Activity Method .........................222 13.4 Isotopically Controlled Hcterostructurcs ...................223 13.5 Secondary Ion Mass Spectrometry (SIMS) .................224 13.6 Electron Microprobe Analysis (EMPA) ....................227 13.7 Auger-Electron Spectroscopy (AES) ......................230 13.8 Ion-beam Analysis: RBS and NRA ........................231 References .................................................234 14 Mechanical Spectroscopy .................................237 14.1 General Remarks .......................................237 14.2 Anelasticity and Internal Friction .........................239 14.3 Techniques of Mechanical Spectroscopy ....................242 14.4 Examples of Diffusion-related Anelasticty ..................244 14.4.1 Snoek Effect (Snock Relaxation) ...................244 14.4.2 Zener Effect (Zener Relaxation) ....................247 14.4.3 Gorski Effect (Gorski Relaxation) ..................248 14.4.4 Mechanical Loss in Ion-conducting Glasses ...........249 14.5 Magnetic Relaxation ....................................250 References .................................................251 15 Nuclear Methods .........................................253 15.1 General Remarks .......................................253 15.2 Nuclear Magnetic Relaxation (NMR) .....................253 15.2.1 Fundamentals of NMR .............................254 15.2.2 Direct Diffusion Measurement by Field-Gradient NMR ...........................256 15.2.3 NMR Relaxation Methods .........................258 Contents XV 15.3 Mössbaiier Spectroscopy (MBS)..........................264 15.4 Quasielastic Neutron Scattering (QENS) ..................269 15.4.1 Examples of QENS studies ........................ 278 15.4.2 Advantages and Limitations of MBS and QENS ......279 References .................................................281 16 Electrical Methods .......................................285 16.1 Impedance Spectroscopy ................................285 16.2 Spreading Resistance Profiling ...........................290 References .................................................293 Part III Diffusion in Metallic Materials 17 Self-diffusion in Metals ...................................297 17.1 General Remarks .......................................297 17.2 Cubic Metals ..........................................299 17.2.1 FCC Metals - Empirical Facts .....................299 17.2.2 BCC Metals - Empirical Facts .....................301 17.2.3 Monovacancy Interpretation .......................302 17.2.4 Mono- and Divacancy Interpretation ................303 17.3 Hexagonal Close-Packed and Tetragonal Metals ............306 17.4 Metals with Phase Transitions ...........................308 References .................................................311 18 Diffusion of Interstitial Solutes in Metals .................313 18.1 -Heavy Interstitial Solutes C, N, and О ...................313 18.1.1 General Remarks .................................313 18.1.2 Experimental Methods ............................314 18.1.3 Interstitial Diffusion in Dilute Interstial Alloys .......316 18.2 Hydrogen Diffusion in Metals ............................317 18.2.1 General Remarks .................................317 18.2.2 Experimental Methods ........................... . 318 18.2.3 Examples of Hydrogen Diffusion ....................320 18.2.4 Non-Classical Isotope Effects ......................323 References .................................................324 19 Diffusion in Dilute Substitutional Alloys ..................327 19.1 Diffusion of Impurities ..................................327 19.1.1 Normal Impurity Diffusion .......................327 19.1.2 Impurity Diffusion in Al ...........................332 19.2 Impurity Diffusion in Open Metals Dissociative Mechanism .................................333 19.3 Solvite Diffusion and Solvent Diffusion in Alloys ............336 References .................................................338 XVI Contents 20 Diffusion in Binary Intermetallics .........................341 20.1 General Remarks .......................................341 20.2 Influence of Order-Disorder Transitions ....................344 20.3 B2 Intermetallics .......................................346 20.3.1 Diffusion Mechanisms in B2 Phases ..................347 20.3.2 Example B2 NiAl ................................351 20.3.3 Example B2 Fc-Al ................................353 20.4 LI 2 Intermetallics ......................................355 20.5 D03 Intermetallics ......................................357 20.6 Uniaxial Intermetallics ..................................360 20.6.1 Ll0 Intermetallics ................................360 20.6.2 Molybdenum Disilicide (C11Ď structure) .............362 20.7 Laves Phases ...........................................364 20.8 The Cu3Au Rule .......................................366 References .................................................367 21 Diffusion in Quasicrystalline Alloys .......................371 21.1 General Remarks on Quasicrystals ........................371 21.2 Diffusion Properties of Quasicrystals ......................373 21.2.1 Icosahedral Quasicrystals ..........................374 21.2.2 Decagonal Quasicrystals ...........................379 References .................................................381 Part IV Diffusion in Semiconductors 22 General Remarks on Semiconductors .....................385 22.1 Semiconductor Age and Diffusion ........................386 22.2 Specific Features of Semiconductor Diffusion ...............389 References .................................................392 23 Self-diffusion in Elemental Semiconductors ...............395 23.1 Intrinsic Point Defects and Diffusion ......................396 23.2 Germanium ............................................398 23.3 Silicon ................................................402 References .................................................406 24 Foreign-Atom Diffusion in Silicon and Germanium ........409 24.1 Solubility and Site Occupancy ...........................409 24.2 Diffusivities and Diffusion Modes .........................412 24.2.1 Interstitial Diffusion ..............................414 24.2.2 Dopant Diffusion .................................416 24.2.3 Diffusion of Hybrid Foreign Elements ...............420 24.3 Self- and Foreign Atom Diffusion - a Summary .............421 References .................................................422 Contents XVII 25 Interstitial-Substítutional Diffusion ....................... 425 25.1 Combined Dissociative and Kick-out Diffusion ..............425 25.1.1 Diffusion Limited by the Flow of Intrinsic Defects .... 427 25.1.2 Diffusion Limited by the Flow of Interstitial Solutes . . 429 25.1.3 Numerical Analysis of an Intermediate Case .........430 25.2 Kick-out Mechanism ....................................431 25.2.1 Basic Equations and two Solutions .................431 25.2.2 Examples of Kick-Out Diffusion ....................434 25.3 Dissociative Mechanism ......................... ........439 25.3.1 Basic Equations ..................................439 25.3.2 Examples of Dissociative Diffusion ..................440 References .................................................445 Part V Diffusion and Conduction in Ionic Materials 26 Ionic Crystals ............................................449 26.1 General Remarks .......................................449 26.2 Point Defects in Ionic Crystals ...........................451 26.2.1 Intrinsic Defects ..................................452 26.2.2 Extrinsic Defects .................................454 26.3 Methods for the Study of Defect and Transport Properties . . . 456 26.4 Alkali Halides ..........................................458 26.4.1 Defect Motion, Tracer Self-diffusion, and Ionic Conduction .............................458 26.4.2 Example NaCl ...................................462 26.4.3 Common Features of Alkali Halides .................467 26.5 Silver Halides AgCl and AgBr ............................468 26.5.1 Self-diffusion and Ionic Conduction .................469 26.5.2 Doping Effects ...................................471 References .................................................473 27 Fast Ion Conductors ......................................475 27.1 Fast Silver-Ion Conductors ...............................477 27.1.1 Agi and related Simple Anion Structures ............477 27.1.2 RbAg,jI5 and related Compounds ...................479 27.2 PbF2 and other Halide Ion Conductors ....................480 27.3 Stabilised Zirconia and related Oxide Ion Conductors .......481 27.4 Pcrovskite Oxide Ion Conductors .........................482 27.5 Sodium β- Alumina and related Materials ..................482 27.6 Lithium Ion Conductors .................................484 27.7 Polymer Electrolytes ....................................485 References .................................................488 XVIII Contents Part VI Diffusion in Glasses 28 The Glassy State .........................................493 28.1 What, is a Glass? .......................................493 28.2 Volume-Temperature Diagram ...........................494 28.3 Temperature-Time-Transformation Diagram ...............496 28.4 Glass Families .........................................498 References .................................................501 29 Diffusion in Metallic Glasses ..............................503 29.1 General Remarks ....................................... 503 29.2 Structural Relaxation and Diffusion ....................... 506 29.3 Diffusion Properties of Metallic Glasses ................... 509 29.4 Diffusion and Viscosity in Glass-forming Alloys ............. 517 References ................................................. 518 30 Diffusion and Ionic Conduction in Oxide Glasses .........521 30.1 General Remarks .......................................521 30.2 Experimental Methods ..................................526 30.3 Gas Permeation ........................................529 30.4 Examples of Diffusion and Ionic Conduction ...............530 References .................................................542 Part VII Diffusion along High-Diffusivity Paths and in Nanomaterials 31 High-diffusivity Paths in Metals ..........................547 31.1 General Remarks ....................................... 547 31.2 Diffusion Spectrum ..................................... 548 31.3 Empirical Rules for Grain-Boundary Diffusion .............. 549 31.4 Lattice Diffusion and Microstructural Defects .............. 551 References ................................................. 552 32 Grain-Boundary Diffusion ................................553 32.1 General Remarks .......................................553 32.2 Grain Boundaries .......................................554 32.2.1 Low- and High-Angle Grain Boundaries .............555 32.2.2 Special High-Angle Boundaries .....................557 32.3 Diffusion along an Isolated Boundary (Fisher Model) ........559 32.4 Diffusion Kinetics in Polycrystals .........................568 32.4.1 Type A Kinetics Regime ..........................568 32.4.2 Type В Kinetics Regime ..........................570 32.4.3 Type С Kinetics Regime ..........................574 Contents XIX 32.5 Grain-Boundary Diffusion and Segregation .................576 32.6 Atomic Mechanisms of Grain-Boundary Diffusion ...........579 References .................................................580 33 Dislocation Pipe Diffusion ................................583 33.1 Dislocation Pipe Model .................................584 33.2 Solutions for Mean Thin Layer Concentrations .............586 References .................................................591 34 Diffusion in Nanocrystalline Materials ....................593 34.1 General Remarks .......................................593 34.2 Synthesis of Nanocrystalline Materials ....................594 34.2.1 Powder Processing ................................594 34.2.2 Heavy Plastic Deformation ........................596 34.2.3 Chemical and Related Synthesis Methods ............598 34.2.4 Devitrification of Amorphous Precursors ............598 34.3 Diffusion in Poly- and Nanocrystals .......................599 34.3.1 Grain Size and Diffusion Regimes ..................599 34.3.2 Effective Diffusivities in Poly- and Nanocrystals ......604 34.4 Diffusion in Nanocrystalline Metals .......................606 34.4.1 General Remarks .................................606 34.4.2 Structural Relaxation and Grain Growth ............607 34.4.3 Nanomaterials with Birnodal Grain Structure ........608 34.4.4 Grain Boundary Triple Junctions ...................612 34.5 Diffusion and Ionic Conduction in Nanocrystalline Ceramics .612 References .................................................618 Index .........................................................639
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indexdate 2025-02-03T17:14:18Z
institution BVB
isbn 9783540714866
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physical XIX, 651 S. Ill., graph. Darst.
publishDate 2007
publishDateSearch 2007
publishDateSort 2007
publisher Springer
record_format marc
series Springer series in solid-state sciences
series2 Springer series in solid-state sciences
spellingShingle Mehrer, Helmut
Diffusion in solids fundamentals, methods, materials, diffusion-controlled processes ; with ... 27 tables
Springer series in solid-state sciences
Festkörper - Diffusion
Diffusion
Kirkendall effect
Solid state physics
Diffusion (DE-588)4012277-3 gnd
Festkörper (DE-588)4016918-2 gnd
subject_GND (DE-588)4012277-3
(DE-588)4016918-2
title Diffusion in solids fundamentals, methods, materials, diffusion-controlled processes ; with ... 27 tables
title_auth Diffusion in solids fundamentals, methods, materials, diffusion-controlled processes ; with ... 27 tables
title_exact_search Diffusion in solids fundamentals, methods, materials, diffusion-controlled processes ; with ... 27 tables
title_full Diffusion in solids fundamentals, methods, materials, diffusion-controlled processes ; with ... 27 tables Helmut Mehrer
title_fullStr Diffusion in solids fundamentals, methods, materials, diffusion-controlled processes ; with ... 27 tables Helmut Mehrer
title_full_unstemmed Diffusion in solids fundamentals, methods, materials, diffusion-controlled processes ; with ... 27 tables Helmut Mehrer
title_short Diffusion in solids
title_sort diffusion in solids fundamentals methods materials diffusion controlled processes with 27 tables
title_sub fundamentals, methods, materials, diffusion-controlled processes ; with ... 27 tables
topic Festkörper - Diffusion
Diffusion
Kirkendall effect
Solid state physics
Diffusion (DE-588)4012277-3 gnd
Festkörper (DE-588)4016918-2 gnd
topic_facet Festkörper - Diffusion
Diffusion
Kirkendall effect
Solid state physics
Festkörper
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