Diffusion in condensed matter: methods, materials, models
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| Format: | Book |
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| Language: | English |
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Berlin [u.a.]
Springer
2005
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVI, 965 S. graph. Darst. |
| ISBN: | 3540200436 9783540200437 |
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| _version_ | 1804132961150304256 |
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| adam_text | PAUL HEITJANS * JORG KARGER
DIFFUSION IN
CONDENSED MATTER
METHODS, MATERIALS, MODELS
WITH 448 FIGURES
4Y SPRINGER
CONTENTS * IN DETAIL
PART I SOLIDS
1 DIFFUSION: INTRODUCTION AND CASE STUDIES IN METALS AND
BINARY ALLOYS
HELMUT MEHRER 3
1.1 INTRODUCTION 3
1.2 CONTINUUM DESCRIPTION OF DIFFUSION 4
1.2.1 FICK S LAWS FOR ANISOTROPIC MEDIA 4
1.2.2 FICK S SECOND LAW FOR CONSTANT DIFFUSIVITY 5
1.2.3 FICK S SECOND LAW FOR CONCENTRATION-DEPENDENT DIFFUSIVITY 6
1.3 THE VARIOUS DIFFUSION COEFFICIENTS 7
1.3.1 TRACER DIFFUSION COEFFICIENTS 7
1.3.2 CHEMICAL DIFFUSION (OR INTERDIFFUSION) COEFFICIENT 8
1.3.3 INTRINSIC DIFFUSION COEFFICIENTS 10
1.4 EXPERIMENTAL METHODS 10
1.4.1 DIRECT METHODS 11
1.4.2 INDIRECT METHODS 15
1.5 DEPENDENCE OF DIFFUSION ON THERMODYNAMIC VARIABLES 17
1.5.1 TEMPERATURE DEPENDENCE 17
1.5.2 PRESSURE DEPENDENCE 18
1.6 ATOMISTIC DESCRIPTION OF DIFFUSION 19
1.6.1 EINSTEIN-SMOLUCHOWSKI RELATION AND CORRELATION FACTOR . . 19
1.6.2 ATOMIC JUMPS AND DIFFUSION 22
1.6.3 DIFFUSION MECHANISMS 23
1.7 INTERSTITIAL DIFFUSION IN METALS 27
1.7.1 NORMAL INTERSTITIAL SOLUTES 27
1.7.2 HYDROGEN DIFFUSION 29
1.8 SELF-DIFFUSION IN METALS 31
1.8.1 FACE-CENTERED CUBIC METALS 32
1.8.2 BODY-CENTERED CUBIC METALS 34
1.9 IMPURITY DIFFUSION IN METALS 35
1.9.1 NORMAL IMPURITY DIFFUSION IN FEE METALS 36
1.9.2 SLOW DIFFUSION OF TRANSITION-METAL SOLUTES IN ALUMINIUM. 39
1.9.3 FAST SOLUTE DIFFUSION IN OPEN METALS 40
1.10 SELF-DIFFUSION IN BINARY INTERMETALLICS 42
XVI CONTENTS - IN DETAIL
1.10.1 INFLUENCE OF ORDER-DISORDER TRANSITION 43
1.10.2 COUPLED DIFFUSION IN B2 INTERMETALLICS 44
1.10.3 THE CU
3
AU RULE 47
1.11 INTERDIFFUSION IN SUBSTITUTIONAL BINARY ALLOYS 49
1.11.1 BOLTZMANN-MATANO METHOD 49
1.11.2 DARKEN S EQUATIONS 51
1.11.3 DARKEN-MANNING RELATIONS 52
1.12 MULTIPHASE DIFFUSION IN BINARY SYSTEMS 53
1.13 CONCLUSION 56
REFERENCES 60
2 THE ELEMENTARY DIFFUSION STEP IN METALS STUDIED BY THE
INTERFERENCE OF GAMMA-RAYS, X-RAYS AND NEUTRONS
GERO VOGL, BOGDAN SEPIOL 65
2.1 INTRODUCTION 65
2.2 SELF-CORRELATION FUNCTION AND QUASIELASTIC METHODS 66
2.2.1 QUASIELASTIC METHODS: MOFIBAUER SPECTROSCOPY AND
NEUTRON SCATTERING 68
2.2.2 NUCLEAR RESONANT SCATTERING OF SYNCHROTRON RADIATION. . . 73
2.2.3 NEUTRON SPIN-ECHO SPECTROSCOPY 74
2.2.4 NON-RESONANT METHODS 75
2.3 EXPERIMENTAL RESULTS 77
2.3.1 PURE METALS AND DILUTE ALLOYS 77
2.3.2 ORDERED ALLOYS 78
2.4 CONCLUSION 87
REFERENCES 89
3 DIFFUSION STUDIES OF SOLIDS BY QUASIELASTIC NEUTRON
SCATTERING
TASSO SPRINGER, RUEP E. LECHNER 93
3.1 INTRODUCTION 93
3.2 THE DYNAMIC STRUCTURE FACTOR 94
3.3 THE RATE EQUATION AND THE SELF-CORRELATION FUNCTION 102
3.4 HIGH RESOLUTION NEUTRON SPECTROSCOPY 106
3.5 HYDROGEN DIFFUSION IN METALS AND IN METALLIC ALLOYS 115
3.6 DIFFUSION WITH TRAPS 121
3.7 VACANCY INDUCED DIFFUSION 124
3.8 ION DIFFUSION RELATED TO IONIC CONDUCTION 126
3.9 PROTON DIFFUSION IN SOLID-STA^E PROTONIC CONDUCTORS 131
3.10 PROTON CONDUCTION: DIFFUSION MECHANISM BASED ON A CHEMICAL
REACTION EQUILIBRIUM 139
3.11 TWO-DIMENSIONAL DIFFUSION 143
3.12 COHERENT QUASIELASTIC SCATTERING 149
3.13 CONCLUSION 155
REFERENCES 159
CONTENTS - IN DETAIL XVII
4 DIFFUSION IN SEMICONDUCTORS
TEH YU TAN, ULRICH GOSELE 165
4.1 INTRODUCTION 165
4.2 DIFFUSION MECHANISMS AND POINT DEFECTS IN SEMICONDUCTORS 165
4.3 DIFFUSION IN SILICON 166
4.3.1 SILICON SELF-DIFFUSION 166
4.3.2 INTERSTITIAL-SUBSTITUTIONAL DIFFUSION: AU, PT AND ZN IN SI . 168
4.3.3 DOPANT DIFFUSION 172
4.3.4 DIFFUSION OF CARBON AND OTHER GROUP IV ELEMENTS 177
4.3.5 DIFFUSION OF SI SELF-INTERSTITIALS AND VACANCIES 180
4.3.6 OXYGEN AND HYDROGEN DIFFUSION 182
4.4 DIFFUSION IN GERMANIUM 183
4.5 DIFFUSION IN GALLIUM ARSENIDE 184
4.5.1 NATIVE POINT DEFECTS AND GENERAL ASPECTS 185
4.5.2 GALLIUM SELF-DIFFUSION AND SUPERLATTICE DISORDERING 187
4.5.3 ARSENIC SELF-DIFFUSION AND SUPERLATTICE DISORDERING 194
4.5.4 IMPURITY DIFFUSION IN GALLIUM ARSENIDE 196
4.5.5 DIFFUSION IN OTHER III-V COMPOUNDS 203
4.6 CONCLUSION 203
REFERENCES 205
5 DIFFUSION IN OXIDES
MANFRED MARTIN 209
5.1 INTRODUCTION 209
5.2 DEFECT CHEMISTRY OF OXIDES 210
5.2.1 DOMINATING CATION DISORDER 212
5.2.2 DOMINATING OXYGEN DISORDER 215
5.3 SELF- AND IMPURITY DIFFUSION IN OXIDES 216
5.3.1 DIFFUSION IN OXIDES WITH DOMINATING CATION DISORDER .... 216
5.3.2 DIFFUSION IN OXIDES WITH DOMINATING OXYGEN DISORDER . . . 222
5.4 CHEMICAL DIFFUSION 226
5.5 DIFFUSION IN OXIDES EXPOSED TO EXTERNAL FORCES 228
5.5.1 DIFFUSION IN AN OXYGEN POTENTIAL GRADIENT 229
5.5.2 DIFFUSION IN AN ELECTRIC POTENTIAL GRADIENT 236
5.6 CONCLUSION 242
5.7 APPENDIX 243
REFERENCES 245
6 DIFFUSION IN METALLIC GLASSES AND SUPERCOOLED MELTS
FRANZ FAUPEL, KLAUS RA TZKE 249
6.1 INTRODUCTION 249
6.2 CHARACTERISTICS OF DIFFUSION IN CRYSTALS 250
6.3 DIFFUSION IN SIMPLE LIQUIDS 251
6.4 GENERAL ASPECTS OF MASS TRANSPORT AND RELAXATION IN
SUPERCOOLED LIQUIDS AND GLASSES 254
XVIII CONTENTS - IN DETAIL
6.5 DIFFUSION IN METALLIC GLASSES 259
6.5.1 STRUCTURE AND PROPERTIES OF METALLIC GLASSES 259
6.5.2 POSSIBLE DIFFUSION MECHANISMS 262
6.5.3 ISOTOPE EFFECT 265
6.5.4 PRESSURE DEPENDENCE 268
6.5.5 EFFECT OF EXCESS VOLUME ON DIFFUSION 269
6.6 DIFFUSION IN SUPERCOOLED AND EQUILIBRIUM MELTS 270
6.7 CONCLUSION 276
REFERENCES 278
PART II INTERFACES
7 FLUCTUATIONS AND GROWTH PHENOMENA IN SURFACE DIFFUSION
MICHAEL C. TRINGIDES, MYRON HUPALO 285
7.1 INTRODUCTION 285
7.2 SURFACE DIFFUSION BEYOND A RANDOM WALK 286
7.2.1 THE ROLE OF STRUCTURE AND GEOMETRY OF THE SUBSTRATE . . . 286
7.2.2 THE ROLE OF ADSORBATE-ADSORBATE INTERACTIONS 288
7.2.3 DIFFUSION IN EQUILIBRIUM AND NON-EQUILIBRIUM
CONCENTRATION GRADIENTS 290
7.3 EQUILIBRIUM MEASUREMENTS OF SURFACE DIFFUSION 297
7.3.1 EQUILIBRIUM DIFFUSION MEASUREMENTS FROM DIFFRACTION
INTENSITY FLUCTUATIONS 297
7.3.2 STM TUNNELING CURRENT FLUCTUATIONS 306
7.4 NON-EQUILIBRIUM EXPERIMENTS 313
7.4.1 UNIFORM-HEIGHT PB ISLANDS ON SI(LLL) 313
7.4.2 MEASUREMENTS OF INTERLAYER DIFFUSION ON AG/AG(LLL) .... 320
7.5 CONCLUSION 331
REFERENCES 333
8 GRAIN BOUNDARY DIFFUSION IN METALS
CHRISTIAN HERZIG, YURI MISHIN 337
8.1 INTRODUCTION 337
8.2 FUNDAMENTALS OF GRAIN BOUNDARY DIFFUSION 338
8.2.1 BASIC EQUATIONS OF GRAIN BOUNDARY DIFFUSION 338
8.2.2 SURFACE CONDITIONS 339
8.2.3 METHODS OF PROFILE ANALYSIS 340
8.2.4 WHAT DO WE KNOW ABOUT GRAIN BOUNDARY DIFFUSION? ... 343
8.3 CLASSIFICATION OF DIFFUSION KINETICS 347
8.3.1 HARRISON S CLASSIFICATION : 348
8.3.2 OTHER CLASSIFICATIONS . . 351
8.4 GRAIN BOUNDARY DIFFUSION AND SEGREGATION 353
8.4.1 DETERMINATION OF THE SEGREGATION FACTOR FROM GRAIN
BOUNDARY DIFFUSION DATA 353
CONTENTS - IN DETAIL XIX
8.4.2 BEYOND THE LINEAR SEGREGATION 357
8.5 CONCLUSION 359
REFERENCES 364
9 NMR AND /3-NMR STUDIES OF DIFFUSION IN INTERFACE-
DOMINATED AND DISORDERED SOLIDS
PAUL HEITJANS, ANDREAS SCHIRMER, SYLVIO INDRIS 367
9.1 INTRODUCTION 367
9.2 INFLUENCE OF DIFFUSION ON NMR SPIN-LATTICE RELAXATION AND
LINEWIDTH 369
9.3 BASICS OF NMR RELAXATION TECHNIQUES 375
9.4 METHOD OF /3-RADIATION DETECTED NMR RELAXATION 380
9.5 INTERCALATION COMPOUNDS 384
9.5.1 LITHIUM GRAPHITE INTERCALATION COMPOUNDS 384
9.5.2 LITHIUM TITANIUM DISULFIDE - HEXAGONAL VERSUS CUBIC . . . 386
9.6 NANOCRYSTALLINE MATERIALS 390
9.6.1 NANOCRYSTALLINE CALCIUM FLUORIDE 391
9.6.2 NANOCRYSTALLINE, MICROCRYSTALLINE AND AMORPHOUS
LITHIUM NIOBATE 394
9.6.3 NANOCRYSTALLINE LITHIUM TITANIUM DISULFIDE 397
9.6.4 NANOCRYSTALLINE COMPOSITES OF LITHIUM OXIDE AND BORON
OXIDE 399
9.7 GLASSES 402
9.7.1 INHOMOGENEOUS SPIN-LATTICE RELAXATION IN GLASSES WITH
DIFFERENT SHORT-RANGE ORDER 403
9.7.2 GLASSY AND CRYSTALLINE LITHIUM ALUMINOSILICATES 405
9.8 CONCLUSION 408
9.9 APPENDIX 409
REFERENCES 411
10 PFG NMR STUDIES OF ANOMALOUS DIFFUSION
JORG KARGER, FRANK STALLMACH 417
10.1 INTRODUCTION 417
10.2 THE ORIGIN OF ANOMALOUS DIFFUSION 418
10.3 FUNDAMENTALS OF PFG NMR 421
10.3.1 THE MEASURING PRINCIPLE 421
10.3.2 THE MEAN PROPAGATOR 422
10.3.3 PFG NMR AS A GENERALIZED SCATTERING EXPERIMENT 424
10.3.4 EXPERIMENTAL CONDITIONS 425
10.4 PFG NMR DIFFUSION STUDIES IN REGULAR PORE NETWORKS 427
10.4.1 THE DIFFERENT REGIMES OF DIFFUSION MEASUREMENT 428
10.4.2 INTRACRYSTALLINE SELF-DIFFUSION 430
10.4.3 CORRELATED DIFFUSION ANISOTROPY 431
10.4.4 TRANSPORT DIFFUSION VERSUS SELF-DIFFUSION 432
10.4.5 SINGLE-FILE DIFFUSION 434
XX CONTENTS - IN DETAIL
10.4.6 DIFFUSION IN ORDERED MESOPOROUS MATERIALS 437
10.5 ANOMALOUS DIFFUSION BY EXTERNAL CONFINEMENT 439
10.5.1 RESTRICTED DIFFUSION IN POLYSTYRENE MATRICES 440
10.5.2 DIFFUSION IN POROUS POLYPROPYLENE MEMBRANES 441
10.5.3 TRACING SURFACE-TO-VOLUME RATIOS 444
10.6 ANOMALOUS DIFFUSION DUE TO INTERNAL CONFINEMENT 447
10.6.1 ANOMALOUS SEGMENT DIFFUSION IN ENTANGLED POLYMER
MELTS 448
10.6.2 DIFFUSION UNDER THE INFLUENCE OF HYPERSTRUCTURES IN
POLYMER SOLUTIONS 450
10.6.3 DIFFUSION UNDER THE INFLUENCE OF HYPERSTRUCTURES IN
POLYMER MELTS 453
10.7 CONCLUSION 455
REFERENCES 456
11 DIFFUSION MEASUREMENTS BY ULTRASONICS
ROGER BIEL, MARTIN SCHUBERT, KARL ULLRICH WU RZ, WOLFGANG GRILL 461
11.1 INTRODUCTION 461
11.2 DIFFUSION OF HYDROGEN IN SINGLE-CRYSTALLINE TANTALUM 462
11.3 OBSERVATION OF DIFFUSION OF HEAVY WATER IN GELS AND LIVING
CELLS BY SCANNING ACOUSTIC MICROSCOPY WITH PHASE CONTRAST .... 466
11.4 CONCLUSION 468
REFERENCES 469
12 DIFFUSION IN MEMBRANES
ILPO VATTULAINEN, OLE G. MOURITSEN 471
12.1 INTRODUCTION 471
12.2 SHORT OVERVIEW OF BIOLOGICAL MEMBRANES 473
12.3 LATERAL DIFFUSION OF SINGLE MOLECULES 477
12.3.1 LATERAL TRACER DIFFUSION COEFFICIENT 477
12.3.2 METHODS TO EXAMINE LATERAL TRACER DIFFUSION 479
12.3.3 LATERAL DIFFUSION OF LIPIDS AND PROTEINS 482
12.4 ROTATIONAL DIFFUSION OF SINGLE MOLECULES 491
12.5 LATERAL COLLECTIVE DIFFUSION OF MOLECULES IN MEMBRANES 493
12.5.1 FICK S LAWS 493
12.5.2 DECAY OF DENSITY FLUCTUATIONS 494
12.5.3 RELATION BETWEEN TRACER AND COLLECTIVE DIFFUSION 495
12.5.4 METHODS TO EXAMINE LATERAL COLLECTIVE DIFFUSION 497
12.5.5 LATERAL COLLECTIVE DIFFUSION IN MODEL MEMBRANES 498
12.6 DIFFUSIVE TRANSPORT THROUGH MEMBRANES 500
12.7 CONCLUSION . 503
REFERENCES 505
CONTENTS - IN DETAIL XXI
PART III LIQUIDS
13 VISCOELASTICITY AND MICROSCOPIC MOTION IN DENSE POLYMER
SYSTEMS
DIETER RICHTER 513
13.1 INTRODUCTION 513
13.2 THE NEUTRON SCATTERING METHOD 514
13.2.1 THE NEUTRON SPIN-ECHO TECHNIQUE VERSUS CONVENTIONAL
SCATTERING 516
13.2.2 NEUTRON SPIN MANIPULATIONS WITH MAGNETIC FIELDS 516
13.2.3 THE SPIN-ECHO PRINCIPLE 518
13.3 LOCAL CHAIN DYNAMICS AND THE GLASS TRANSITION 519
13.3.1 DYNAMIC STRUCTURE FACTOR 521
13.3.2 SELF-CORRELATION FUNCTION 527
13.4 ENTROPIC FORCES - THE ROUSE MODEL 529
13.4.1 NEUTRON SPIN-ECHO RESULTS IN PDMS MELTS 531
13.4.2 COMPUTER SIMULATIONS 534
13.5 LONG-CHAINS REPTATION 537
13.5.1 THEORETICAL CONCEPTS 537
13.5.2 EXPERIMENTAL OBSERVATIONS OF CHAIN CONFINEMENT 538
13.6 INTERMEDIATE SCALE DYNAMICS 540
13.7 THE CROSSOVER FROM ROUSE TO REPTATION DYNAMICS 543
13.8 CONCLUSION 550
REFERENCES 552
14 THE MOLECULAR DESCRIPTION OF MUTUAL DIFFUSION PROCESSES
IN LIQUID MIXTURES
HERMANN WEINGDRTNER 555
14.1 INTRODUCTION 555
14.2 EXPERIMENTAL BACKGROUND 558
14.3 PHENOMENOLOGICAL DESCRIPTION OF MUTUAL DIFFUSION 559
14.4 THERMODYNAMICS OF MUTUAL DIFFUSION 564
14.5 LINEAR RESPONSE THEORY AND TIME CORRELATION FUNCTIONS 567
14.6 THE TIME CORRELATION FUNCTION FOR MUTUAL DIFFUSION 569
14.7 PROPERTIES OF DISTINCT-DIFFUSION COEFFICIENTS 571
14.8 INFORMATION ON INTERMOLECULAR INTERACTIONS DEDUCED FROM
DIFFUSION DATA 573
14.9 CONCLUSION 576
REFERENCES 577
15 DIFFUSION MEASUREMENTS IN FLUIDS BY DYNAMIC LIGHT
SCATTERING
ALFRED LEIPERTZ, ANDREAS P. FROBA 579
15.1 INTRODUCTION 579
XXII CONTENTS - IN DETAIL
15.2 BASIC PRINCIPLES 580
15.2.1 SPECTRUM OF SCATTERED LIGHT 580
15.2.2 CORRELATION TECHNIQUE 582
15.2.3 HOMODYNE AND HETERODYNE TECHNIQUES 587
15.3 THE DYNAMIC LIGHT SCATTERING EXPERIMENT 589
15.3.1 SETUP 589
15.3.2 SIGNAL STATISTICS AND DATA EVALUATION 594
15.4 THERMOPHYSICAL PROPERTIES OF FLUIDS MEASURED BY DYNAMIC
LIGHT SCATTERING 597
15.4.1 THERMAL DIFFUSIVITY 597
15.4.2 MUTUAL DIFFUSION COEFFICIENT 600
15.4.3 DYNAMIC VISCOSITY 601
15.4.4 SOUND VELOCITY AND SOUND ATTENUATION 604
15.4.5 LANDAU-PLACZEK RATIO 606
15.4.6 SORET COEFFICIENT 606
15.4.7 DERIVABLE PROPERTIES 607
15.5 RELATED TECHNIQUES 608
15.5.1 SURFACE LIGHT SCATTERING 608
15.5.2 FORCED RAYLEIGH SCATTERING 613
15.6 CONCLUSION 615
REFERENCES 617
16 DIFFUSION IN COLLOIDAL AND POLYMERIC SYSTEMS
GERHARD NDGELE, JAN K. G. DHONT, GERHARD MEIER 619
16.1 INTRODUCTION 619
16.2 PRINCIPLES OF QUASIELASTIC LIGHT SCATTERING 620
16.2.1 THE SCATTERED ELECTRIC FIELD STRENGTH 620
16.2.2 DYNAMIC LIGHT SCATTERING 624
16.2.3 DYNAMIC STRUCTURE FACTORS 626
16.3 HEURISTIC CONSIDERATIONS ON DIFFUSION PROCESSES 628
16.3.1 VERY DILUTE COLLOIDAL SYSTEMS 629
16.3.2 DIFFUSION MECHANISMS IN CONCENTRATED COLLOIDAL SYSTEMS. 636
16.4 FLUORESCENCE TECHNIQUES FOR LONG-TIME SELF-DIFFUSION OF
NON-SPHERICAL PARTICLES 660
16.4.1 FLUORESCENCE RECOVERY AFTER PHOTOBLEACHING 661
16.4.2 FLUORESCENCE CORRELATION SPECTROSCOPY 669
16.5 THEORETICAL AND EXPERIMENTAL RESULTS ON DIFFUSION OF COLLOIDAL
SPHERES AND POLYMERS 675
16.5.1 COLLOIDAL SPHERES , 676
16.5.2 POLYMER BLENDS AND RANDOM PHASE APPROXIMATION 697
16.6 CONCLUSION 709
REFERENCES 712
CONTENTS - IN DETAIL XXIII
17 FIELD-ASSISTED DIFFUSION STUDIED BY ELECTROPHORETIC NMR
MANFRED HOLZ 717
17.1 INTRODUCTION 717
17.2 PRINCIPLES OF ELECTROPHORETIC NMR 719
17.2.1 ELECTROPHORESIS 719
17.2.2 PULSED FIELD GRADIENT NMR FOR THE STUDY OF DRIFT
VELOCITIES 720
17.3 NMR IN PRESENCE OF AN ELECTRIC DIRECT CURRENT. TECHNICAL
REQUIREMENTS, PROBLEMS AND SOLUTIONS 725
17.4 ENMR SAMPLE CELLS 727
17.5 ENMR EXPERIMENTS (ID, 2D AND 3D) AND APPLICATION EXAMPLES 728
17.5.1 ID ENMR APPLICATIONS 729
17.5.2 2D AND 3D EXPERIMENTS 734
17.5.3 MOBILITY AND VELOCITY DISTRIBUTIONS. POLYDISPERSITY AND
ELECTRO-OSMOTIC FLOW 737
17.6 CONCLUSION 738
REFERENCES 741
PART IV THEORETICAL CONCEPTS AND MODELS
18 DIFFUSION OF PARTICLES ON LATTICES
KLAUS W. KEHR, KIARESCH MUSSAWISADE, GUNTER M. SCHILTZ, THOMAS
WICHMANN 745
18.1 INTRODUCTION 745
18.2 ONE PARTICLE ON UNIFORM LATTICES 748
18.2.1 THE MASTER EQUATION 748
18.2.2 SOLUTION OF THE MASTER EQUATION 749
18.2.3 DIFFUSION COEFFICIENT 751
18.2.4 EXTENSIONS 752
18.3 ONE PARTICLE ON DISORDERED LATTICES 753
18.3.1 MODELS OF DISORDER 753
18.3.2 EXACT EXPRESSION FOR THE DIFFUSION COEFFICIENT IN D = 1 ... 755
18.3.3 APPLICATIONS OF THE EXACT RESULT 757
18.3.4 FREQUENCY DEPENDENCE IN D = 1: EFFECTIVE-MEDIUM
APPROXIMATION 758
18.3.5 HIGHER-DIMENSIONAL LATTICES: APPROXIMATIONS 762
18.3.6 HIGHER-DIMENSIONAL LATTICES: APPLICATIONS 766
18.3.7 REMARKS ON OTHER MODELS 769
18.4 MANY PARTICLES ON UNIFORM LATTICES 771
18.4.1 LATTICE GAS (SITE EXCLUSION) MODEL 771
18.4.2 COLLECTIVE DIFFUSION 772
18.4.3 TRACER DIFFUSION FOR D 1 773
18.4.4 TAGGED-PARTICLE DIFFUSION ON A LINEAR CHAIN 774
18.5 MANY PARTICLES ON DISORDERED LATTICES 778
XXIV CONTENTS - IN DETAIL
18.5.1 MODELS WITH SYMMETRIC RATES 778
18.5.2 SELECTED RESULTS FOR THE COEFFICIENT OF COLLECTIVE
DIFFUSION IN THE RANDOM SITE-ENERGY MODEL 780
18.6 CONCLUSION 783
18.7 APPENDIX 784
18.7.1 DERIVATION OF THE RESULT FOR THE DIFFUSION COEFFICIENT FOR
ARBITRARILY DISORDERED TRANSITION RATES 784
18.7.2 DERIVATION OF THE SELF-CONSISTENCY CONDITION FOR THE
EFFECTIVE-MEDIUM APPROXIMATION 787
18.7.3 RELATION BETWEEN THE RELATIVE DISPLACEMENT AND THE
DENSITY CHANGE 789
REFERENCES 790
19 DIFFUSION ON FRACTALS
UWE RENNER, GUNTER M. SCHU TZ, GIINTER VOJTA 793
19.1 INTRODUCTION: WHAT A FRACTAL IS 793
19.2 ANOMALOUS DIFFUSION: PHENOMENOLOGY 797
19.3 STOCHASTIC THEORY OF DIFFUSION ON FRACTALS 802
19.4 ANOMALOUS DIFFUSION: DYNAMICAL DIMENSIONS 803
19.5 ANOMALOUS DIFFUSION AND CHEMICAL KINETICS 806
19.6 CONCLUSION 809
REFERENCES 810
20 IONIC TRANSPORT IN DISORDERED MATERIALS
ARMIN BUNDE, WOLFGANG DIETERICH, PHILIPP MAASS, MARTIN MEYER 813
20.1 INTRODUCTION 813
20.2 BASIC QUANTITIES 816
20.2.1 TRACER DIFFUSION 816
20.2.2 DYNAMIC CONDUCTIVITY 817
20.2.3 PROBABILITY DISTRIBUTION AND INCOHERENT NEUTRON
SCATTERING 817
20.2.4 SPIN-LATTICE RELAXATION 818
20.3 ION-CONDUCTING GLASSES: MODELS AND NUMERICAL TECHNIQUE 819
20.4 DISPERSIVE TRANSPORT 822
20.5 NON-ARRHENIUS BEHAVIOR 832
20.6 COUNTERION MODEL AND THE NEARLY CONSTANT DIELECTRIC LOSS
RESPONSE 835
20.7 COMPOSITIONAL ANOMALIES 839
20.8 ION-CONDUCTING POLYMERS 843
20.8.1 LATTICE MODEL OF POLYMER ELECTROLYTES 843
20.8.2 DIFFUSION THROUGH A POLYMER NETWORK: DYNAMIC
PERCOLATION APPROACH 846
20.8.3 DIFFUSION IN STRETCHED POLYMERS 849
20.9 CONCLUSION 850
REFERENCES 852
CONTENTS - IN DETAIL XXV
21 CONCEPT OF MISMATCH AND RELAXATION FOR SELF-DIFFUSION
AND CONDUCTION IN IONIC MATERIALS WITH DISORDERED STRUCTURE
KLAUS FUNKE, CORNELIA CRAMER, DIRK WILMER 857
21.1 INTRODUCTION 857
21.2 CONDUCTIVITY SPECTRA OF ION CONDUCTING MATERIALS 861
21.3 RELEVANT FUNCTIONS AND SOME MODEL CONCEPTS FOR ION TRANSPORT
IN DISORDERED SYSTEMS 864
21.4 CMR EQUATIONS AND MODEL CONDUCTIVITY SPECTRA 867
21.5 SCALING PROPERTIES OF MODEL CONDUCTIVITY SPECTRA 871
21.6 PHYSICAL CONCEPT OF THE CMR 874
21.7 COMPLETE CONDUCTIVITY SPECTRA OF SOLID ION CONDUCTORS 877
21.8 ION DYNAMICS IN A FRAGILE SUPERCOOLED MELT 880
21.9 CONDUCTIVITIES OF GLASSY AND CRYSTALLINE ELECTROLYTES BELOW
10MHZ 883
21.10 LOCALISED MOTION AT LOW TEMPERATURES 887
21.11 CONCLUSION 891
REFERENCES 892
22 DIFFUSION AND CONDUCTION IN PERCOLATION SYSTEMS
ARMIN BUNDE, JAN W. KANTELHARDT 895
22.1 INTRODUCTION 895
22.2 THE (SITE-)PERCOLATION MODEL 895
22.3 THE FRACTAL STRUCTURE OF PERCOLATION CLUSTERS NEAR P
C
897
22.4 FURTHER PERCOLATION SYSTEMS 901
22.5 DIFFUSION ON REGULAR LATTICES 903
22.6 DIFFUSION ON PERCOLATION CLUSTERS 904
22.7 CONDUCTIVITY OF PERCOLATION CLUSTERS 905
22.8 FURTHER ELECTRICAL PROPERTIES 906
22.9 APPLICATION OF THE PERCOLATION CONCEPT: HETEROGENEOUS IONIC
CONDUCTORS 908
22.9.1 INTERFACIAL PERCOLATION AND THE LIANG EFFECT 908
22.9.2 COMPOSITE MICRO- AND NANOCRYSTALLINE CONDUCTORS 910
22.10 CONCLUSION 912
REFERENCES 913
23 STATISTICAL THEORY AND MOLECULAR DYNAMICS OF DIFFUSION
IN ZEOLITES
REINHOLD HABERLANDT 915
23.1 INTRODUCTION 915
23.2 SOME NOTIONS AND RELATIONS OF STATISTICAL PHYSICS 916
23.2.1 STATISTICAL THERMODYNAMICS 916
23.2.2 STATISTICAL THEORY OF IRREVERSIBLE PROCESSES 919
23.3 MOLECULAR DYNAMICS 922
23.3.1 GENERAL REMARKS 922
23.3.2 PROCEDURE OF AN MD SIMULATION 923
XXVI CONTENTS - IN DETAIL
23.3.3 METHODICAL HINTS 925
23.4 SIMULATION OF DIFFUSION IN ZEOLITES 925
23.4.1 INTRODUCTION 925
23.4.2 SIMULATIONS 926
23.4.3 RESULTS 928
23.5 CONCLUSION 942
REFERENCES 944
LIST OF CONTRIBUTORS 949
INDEX 955
|
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| id | DE-604.BV019604364 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:01:08Z |
| institution | BVB |
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| language | English |
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| spelling | Diffusion in condensed matter methods, materials, models Paul Heitjans ... [(ed.)] Berlin [u.a.] Springer 2005 XXVI, 965 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Condensed matter Diffusion Diffusion processes Kondensierte Materie (DE-588)4132810-3 gnd rswk-swf Diffusion (DE-588)4012277-3 gnd rswk-swf Festkörper (DE-588)4016918-2 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content 2\p (DE-588)1071861417 Konferenzschrift 1996 Leipzig gnd-content Festkörper (DE-588)4016918-2 s Diffusion (DE-588)4012277-3 s DE-604 Kondensierte Materie (DE-588)4132810-3 s 3\p DE-604 Heitjans, Paul 1946- Sonstige (DE-588)1200416309 oth DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012934218&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Diffusion in condensed matter methods, materials, models Condensed matter Diffusion Diffusion processes Kondensierte Materie (DE-588)4132810-3 gnd Diffusion (DE-588)4012277-3 gnd Festkörper (DE-588)4016918-2 gnd |
| subject_GND | (DE-588)4132810-3 (DE-588)4012277-3 (DE-588)4016918-2 (DE-588)4143413-4 (DE-588)1071861417 |
| title | Diffusion in condensed matter methods, materials, models |
| title_auth | Diffusion in condensed matter methods, materials, models |
| title_exact_search | Diffusion in condensed matter methods, materials, models |
| title_full | Diffusion in condensed matter methods, materials, models Paul Heitjans ... [(ed.)] |
| title_fullStr | Diffusion in condensed matter methods, materials, models Paul Heitjans ... [(ed.)] |
| title_full_unstemmed | Diffusion in condensed matter methods, materials, models Paul Heitjans ... [(ed.)] |
| title_short | Diffusion in condensed matter |
| title_sort | diffusion in condensed matter methods materials models |
| title_sub | methods, materials, models |
| topic | Condensed matter Diffusion Diffusion processes Kondensierte Materie (DE-588)4132810-3 gnd Diffusion (DE-588)4012277-3 gnd Festkörper (DE-588)4016918-2 gnd |
| topic_facet | Condensed matter Diffusion Diffusion processes Kondensierte Materie Festkörper Aufsatzsammlung Konferenzschrift 1996 Leipzig |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012934218&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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