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 |  موضوع: كتاب Diffusion in Condensed Matter - Methods, Materials, Models الأربعاء 07 يوليو 2021, 11:57 am | |
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أحضرت لكم كتاب
Diffusion in Condensed Matter - Methods, Materials, Models
With 448 Figures
Paul Heitjans, Jörg Kärger
و المحتوى كما يلي :
Contents – Overview
Part I Solids
1 Diffusion: Introduction and Case Studies in Metals and
Binary Alloys
Helmut Mehrer . 3
2 The Elementary Diffusion Step in Metals Studied by the
Interference of Gamma-Rays, X-Rays and Neutrons
Gero Vogl, Bogdan Sepiol 65
3 Diffusion Studies of Solids by Quasielastic Neutron
Scattering
Tasso Springer, Ruep E. Lechner . 93
4 Diffusion in Semiconductors
Teh Yu Tan, Ulrich G¨ osele . 165
5 Diffusion in Oxides
Manfred Martin . 209
6 Diffusion in Metallic Glasses and Supercooled Melts
Franz Faupel, Klaus R¨ atzke . 249
Part II Interfaces
7 Fluctuations and Growth Phenomena in Surface Diffusion
Michael C. Tringides, Myron Hupalo 285
8 Grain Boundary Diffusion in Metals
Christian Herzig, Yuri Mishin 337
9 NMR and β-NMR Studies of Diffusion in InterfaceDominated and Disordered Solids
Paul Heitjans, Andreas Schirmer, Sylvio Indris . 367XII Contents – Overview
10 PFG NMR Studies of Anomalous Diffusion
J¨org K¨ arger, Frank Stallmach . 417
11 Diffusion Measurements by Ultrasonics
Roger Biel, Martin Schubert, Karl Ullrich W¨ urz, Wolfgang Grill 461
12 Diffusion in Membranes
Ilpo Vattulainen, Ole G. Mouritsen 471
Part III Liquids
13 Viscoelasticity and Microscopic Motion in Dense Polymer
Systems
Dieter Richter 513
14 The Molecular Description of Mutual Diffusion Processes
in Liquid Mixtures
Hermann Weing¨artner . 555
15 Diffusion Measurements in Fluids by Dynamic Light
Scattering
Alfred Leipertz, Andreas P. Fr¨oba . 579
16 Diffusion in Colloidal and Polymeric Systems
Gerhard N¨agele, Jan K. G. Dhont, Gerhard Meier . 619
17 Field-Assisted Diffusion Studied by Electrophoretic NMR
Manfred Holz . 717
Part IV Theoretical Concepts and Models
18 Diffusion of Particles on Lattices
Klaus W. Kehr, Kiaresch Mussawisade, Gunter M. Sch¨ utz, Thomas
Wichmann . 745
19 Diffusion on Fractals
Uwe Renner, Gunter M. Sch¨ utz, G¨ unter Vojta 793
20 Ionic Transport in Disordered Materials
Armin Bunde, Wolfgang Dieterich, Philipp Maass, Martin Meyer . 813
21 Concept of Mismatch and Relaxation for Self-Diffusion
and Conduction in Ionic Materials with Disordered Structure
Klaus Funke, Cornelia Cramer, Dirk Wilmer . 857Contents – Overview XIII
22 Diffusion and Conduction in Percolation Systems
Armin Bunde, Jan W. Kantelhardt 895
23 Statistical Theory and Molecular Dynamics of Diffusion
in Zeolites
Reinhold Haberlandt . 915
List of Contributors 949
Index . 955Contents – 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 fcc 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 42XVI 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 Cu3Au 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: M¨ oßbauer 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-State 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 . 159Contents – In Detail XVII
4 Diffusion in Semiconductors
Teh Yu Tan, Ulrich G¨ osele . 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 R¨ atzke . 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 . 254XVIII 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(111) . 313
7.4.2 Measurements of Interlayer Diffusion on Ag/Ag(111) 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 . 353Contents – In Detail XIX
8.4.2 Beyond the Linear Segregation 357
8.5 Conclusion 359
References . 364
9 NMR and β-NMR Studies of Diffusion in InterfaceDominated 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 β-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
J¨org K¨ arger, 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 . 434XX 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 W¨ urz, 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 . 505Contents – 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 Weing¨artner . 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. Fr¨oba . 579
15.1 Introduction 579XXII 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 N¨agele, 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 . 712Contents – 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 (1D, 2D and 3D) and Application Examples 728
17.5.1 1D 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. Sch¨ utz, 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 . 778XXIV 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. Sch¨ utz, G¨ unter 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 . 852Contents – 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
10 MHz . 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 pc 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 . 923XXVI 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 .
Index
acoustic microscopy 466
activation energy 19, 344, 813
activation enthalpy 18
activation volume 19, 40, 268
adsorbate-adsorbate interactions 288
Ag/Ag(111) 320
0.5Ag2S·0.5GeS2 877
0.3Ag2SO4·0.7AgPO3 884
alloys
binary 49, 53
ordered 78
aluminium 39, 77
amino acid 729
amorphous alloys 259
anomalous diffusion 417–421, 428,
434, 441, 448, 479, 488, 731, 797,
803, 806, 867, 904
anticorrelation in anomalous diffusion
801
antiphase boundaries 77
antistructure defects 71, 72, 78
antistructure-bridge mechanism 46,
81
Arrhenius law 18, 289, 746, 753, 813,
925
association degree 220
asymmetric double well potential
(ADWP) model 836, 866, 888
Auger electron spectroscopy (AES)
14
autocorrelation function 817, 920, see
also correlation function
electric field 625
light intensity 625
orientation 636
average
ensemble 919, 923
time 923
β-NMR
method 380–384
relaxation 370, 383, 384, 403, 407,
409
spectrometer 383
β-radiation asymmetry 383
β-relaxation 520
β-titanium 77
B2 structure 71, 72, 76, 78
backbone of percolation cluster 900
BaF2 394
ballistic diffusion 867
binary intermetallics 42
binary non-electrolyte mixtures 573
blocking factor 104, 150
Bloembergen-Purcell-Pound (BPP)
behaviour 369, 819
body-centered cubic metals 34
Boltzmann-Matano method 49, 294,
498
bond percolation 901
Boson peak 520
Bragg equation 108
Brillouin lines 581, 604
Brownian dynamics simulation method
687
Brownian motion 472, 632, 717, 794
CaF2 391
caloric glass transition temperature
255
capacitance 907
capillary electrophoresis 738
cation sublattice 209
central limit theorem 420, 423, 625,
799
charge diffusion coefficient 126, 127,
148956 Index
charge of transport 222, 238
chemical diffusion 6, 49, 556
chemical diffusion coefficient 231
chemical potential 8, 226, 291, 918,
941
Chudley-Elliott model 69, 71, 102,
130, 149, 150
cobalt oxide 217
CoGa 82
coherent diffuse scattering 153
coherent quasielastic scattering 149
coherent scattering function 102, 150
collective diffusion 495, 641, 648, 747,
772
coefficient of 289, 646, 771, 778
colloidal rods 666
colloidal spheres 676
colloidal systems 619
collective diffusion 641
interdiffusion 651
rotational diffusion 658
self-diffusion 637
component diffusion coefficient 10
compressibility, isentropic 607
computer simulations see simulations
concept of mismatch and relaxation
(CMR) 867, 874
conductivity
electrical 219, 905, 906
frequency dependence 768, 861
thermal 597
conductivity spectroscopy 861
continuity equation 5
continuous time random walk model
824
continuum percolation 902
copper 77
correlated jumps 118, 124, 127, 858
correlation effects 127
correlation factor 19, 222, 773, 816,
848
correlation function 369, 515, 525,
527, 582, 915, 916, 919–921, 923
long-time tail 633
of coverage 291
of current density 864
Van Hove 66, 96, 98, 921, 935, 937
velocity auto- 928, 930
correlation length 897
correlation technique 582–587
correlation time 369, 586, 832
correlator 594
Coulomb interaction 215, 819, 830
Coulomb lattice gas 820, 840
Coulomb trap 835
counterion model 835, 866
coupled diffusion in B2 intermetallics
44
coupling concept 866
coverage 290
critical fluctuation 295
fluctuation 290, 293
step 299
Co-Zr glasses 268
critical concentration 896, 901, 902
critical dimension 808
critical exponent 897, 905
critical percolation path 832
critical slowing down 600, 650, 703
critical-path approach 763
cross coefficients 236
crossover time 905
Cu3Au rule 47
current density autocorrelation function
864
D03 structure 84
Darken equation 51, 296, 433, 557,
562, 573, 941
Darken-Manning relation 52
Darwin width 110
dc conductivity plateau 862
de Broglie wavelength 99, 919
Debye length 720
Debye-H¨ uckel-Onsager-Falkenhagen
effect 859
Debye-Waller factor 67, 70, 74, 99,
113, 119, 138
defect chemistry 210
defect cluster 226
defect structure 210, 215
demixing 234, 236, 240, 703
density distribution 931
detailed balance 71, 767, 786
dichalcogenides 386
dielectric loss 835, 863Index 957
differential effective-medium theory
849
diffusant 6
diffuse scattering 76
diffuser 6
diffusion
ambipolar 227
anomalous 417–421, 428, 434, 441,
448, 479, 488, 731, 797, 803, 867
cation 217, 224
chemical 226
collective 495, 641
continuous jump 371
correlated diffusion anisotropy
431–432
effective diffusivity 428
experimental methods 10
field-assisted 717
in aluminium 39
in amorphous alloys 262
in B2 intermetallics 44, 78
in bcc metals 35
in D03 intermetallics 84
in fcc metals 33
in gallium arsenide 184
in germanium 183
in L12 intermetallics 49
in lead 41
in liquids 251
in membranes 471
in nickel 31
in niobium 28, 29
in polymers 447, 519, 531, 675, 733,
843
in regular pore networks 427
in semiconductors 165
in silicon 166
in silver 38
in zeolites 427, 925
interstitial-substitutional 168
intracrystalline self-diffusion 429,
430, 445
isotope effects 13, 30, 253, 265, 272
lateral 477, 493
long-range 133
low-dimensional 371
molecular mechanism 132
multicomponent 427
mutual 556, 569, 600
normal 417–420, 426, 435, 450, 479,
555, 777, 798, 799
on percolation clusters 904
oxidation-enhanced 174
oxidation-retarded 174
oxygen 222, 223
pressure dependence 18
proton diffusion 131
reactive 54
rotational 477, 491, 635
single-file diffusion 434–437, 775
solute diffusion 35
solvent diffusion 35
surface diffusion 285, 302, 339
through membranes 500
transport diffusion 432–434, 943
diffusion coefficient 904, 921, 929, 931,
941
chemical 6, 8, 151, 227, 244
collective 289, 646, 780
distinct-diffusion 570, 571
foreign atom 8
frequency dependence 762
impurity 8
in grain boundaries 338
interdiffusion 654
self-diffusion 7
Stokes-Einstein 630
thermodynamic 561
tracer 7, 219, 286, 478
transport 941
vacancy 231
diffusion coefficient tensor 4, 439, 676
diffusion entropy 18
diffusion equation 5, 289, 494, 632,
752, 798, 928, see also Fick’s
second law
error function solution 6
source solution 230
thin-film solution 5
diffusion length 5, 479
diffusion mechanisms 23
diffusion-limited reaction 806–808
diffusional line broadening 70, 72, 94
diffusivity 4
effective 41, 170, 348, 420, 429, 453
thermal 597958 Index
diffusivity tensor 4, 439, 676
direct current NMR (DCNMR) 718,
725
disorder models 753, 820
disordered solids
homogeneously 402
inhomogeneously 367, 390
disordered systems 372, 746, 753, 813,
857, 895
dispersive transport 822
dissociative mechanism 26
distribution of site energies 257
divacancy mechanism 25
dopant diffusion 172, 235
Doppler drive 111
double differential scattering crosssection 95
drift flux 230, 232, 236
drift velocity 237, 717–720
dynamic conductivity 817
dynamic light scattering (DLS) 579,
589–597, 624
coherence 593
dynamic percolation 846
dynamic rotational disorder 153
dynamic structure factor 94, 521–526,
531, 538, 545, 568, 626, see also
scattering function
distinct 628
self- 628
dynamic structure model 840
effective activation energy 273
effective charge 236, 239
effective diffusivity 41, 170, 348, 420,
429, 453
effective-medium approximation 746,
758, 762, 912
self-consistency condition 761, 787
Einstein diffusion coefficient 8
Einstein relation 227, 420, 434, 555,
717, 903, 920
Einstein-Debye relation 635
Einstein-Smoluchowski relation 19,
see also Einstein relation
elastic incoherent structure factor
(EISF) 98, 119, 138, 139, 141
electric potential 226, 236
electric potential gradient 228
electro-osmosis 726, 737
electrochemical potential 226
electrokinetic potential 720
electrolyte solution 566, 574
electron hole 211, 212
electron microprobe analysis (EMPA)
14
electrophoresis 718
electrophoretic NMR (ENMR) 717
elementary diffusion step 65, 66, 68
encounter model 124, 128, 370
energy resolution 98
ensemble
canonical 917
microcanonical 917
entanglements 513, 531, 543
enthalpy of migration 22
entropic forces 529
entropy of migration 22
equivalent circuit model 906
error function solution 6
escape rate 121
eucryptite 405
excess charge 210, 228, 231
excess volume 269
exchange mechanism
interstitial-substitutional 26
ring 127
face-centered cubic metals 32
fast solute diffusion 40
FeAl 78
Fe3Al 80
Fermi level effect 172
Fe3Si 84
Fick’s first law 4, 494, 559, 798
non-local 643
Fick’s second law 5, 6, 165, 494, 752
field-assisted diffusion 717
Fisher model 337, 338
five-frequency model 36, 233
fixed-window method 113
fluctuation-dissipation relation 632
fluorescence correlation spectroscopy
(FCS) 669
fluorescence recovery after photobleaching (FRAP) 481, 497,
661
forced Rayleigh scattering 613Index 959
Fourier time window 100, 106
fractal 793
chemical kinetics 806
fractal dimension 446, 793, 897, 898,
904
fractional Brownian motion 794
fragile glass 254
fragile supercooled melt 880
Frank-Turnbull mechanism 26, 168
free induction decay (FID) 376, 400
free-volume model 253, 486
Frenkel
defects 211
equilibrium 210, 212
Γ -space 918
generalized force 919
Gibbs free energy of activation 19
Gibbs free energy of binding 24
Gibbs free energy of migration 22
glass
electrolyte 403
ion-conducting 402, 819
metallic 259
oxide 403, 405, 884
glass transition 255, 272, 519, 638
Gorski effect 16
grain boundary 337
diffusion coefficient 338
in nanocrystalline materials 352,
390, 391
large-angle 345, 346
segregation 339, 353, 357, 361
segregation energy 353
segregation factor 339, 353
small-angle 345, 346
width 338, 343, 911
grain boundary diffusion 337
activation energy 344
anisotropy 345
Arrhenius law 344
atomistic mechanisms 347, 362
comparison with bulk, surface, liquid
344
empirical rules 344
in intermetallic compounds 361
in moving boundaries 362
kinetic regimes 347
orientation dependence 346
Green-Kubo relation 495, 568, 638,
920
Grotthuß mechanism 131
growth constant 54
gyromagnetic ratio see magnetogyric
ratio
Harrison’s classification 348
Hart’s formula 349
Hartley-Crank relation 557
Hausdorff dimension 793
Haven ratio 127, 137, 148, 817, 865
Henry isotherm (of grain boundary
segregation) 358
heterodyne technique 587
homodyne technique 587
hopping rate see jump rate
H/Si(111) 308
Huang scattering 119, 153, 155
hybrid solutes 41
hydrodynamic function 678
hydrodynamic interaction 637, 659
hydrogen bond 131
hydrogen diffusion 29, 115
immobile (trapped) state 121
impedance spectroscopy 861
impurity diffusion
in grain boundaries 339
in metals 35, 77
in oxides 216
in semiconductors 168, 172, 177,
182, 183, 196
impurity diffusion coefficient 8
impurity-vacancy binding 219
impurity-vacancy pair 233, 239
incoherent scattering function 97–99,
102, 133, 141, 154, 818
incoherent structure factor see
incoherent scattering function
infinite percolation cluster 896
intercalation 367
intercalation compounds 384
graphite 384
titanium disulfide 386
interdiffusion 6, 49, 187, 263, 556, 651,
654
interdiffusion coefficient 6, 8, 191, 654
interfacial region 50, 352, 367, 390960 Index
diffusion in 392, 908
intermediate dynamic structure factor
521
intermediate scattering function 73,
95, 100, 523, 818, 828
internal interfaces 360, 367
density of 367
interstitial cation 213, 217
interstitial diffusion 27, 242, 745
interstitial impurities 165
interstitial mechanism 23
interstitial-substitutional exchange
mechanism 26
interstitialcy mechanism 25
intrinsic diffusion coefficient 10
inversion-recovery experiment 378
ion-conducting glasses 402, 819, 861
ion-conducting materials 861
ion-conducting polymers 843
ionic conductivity 126, 224, 817, 861,
908
ionic mobility 717, 729, 737
ionic self-diffusion coefficient 717, 729
irreversible processes 564, 919
isotope effects 13, 30, 253, 265, 272
Jonscher power law 863, see also
universal dielectric response
jump length 7, 20, 105, 866, 903
jump rate 19–23, 65, 70–73, 124, 233,
373, 763, 866
jump relaxation 823, 866
jump vector 20, 65, 67, 68, 102, 140
kick-out mechanism 26, 168
kink atoms 286
Kirkendall effect 10, 51
opposite 263
Kirkwood-Buff theory 575
K2O·2BaO·4SiO2 885
Kohlrausch behavior 255, 521, 866
Kohlrausch-Williams-Watts (KWW)
behavior see Kohlrausch
behavior
Kr¨oger-Vink
diagram 214
notation 210
Kubo formula 817, 941
Lamb-M¨oßbauer factor 67
Landau-Placzek ratio 582, 606
Langevin equation 530, 632
Langmuir-Hinshelwood reaction 808
lanthanum gallate 216, 225, 235
Laplace transformation 644, 760
Larmor condition 421
Larmor precession 74, 516
Larmor precession frequency 369, 814
layer-crystalline materials 367
LiC6, LiC12 384
LiCl·4D2O 403
LiCl·7H2O 881
line broadening in M¨oßbauer spectroscopy 68
line broadening in neutron scattering
68, 94
line narrowing in neutron scattering
104, 151
line narrowing in nuclear magnetic
resonance 374
linear response theory 150, 567, 858,
919
0.3Li2O·0.7B2O3 884
lipid 473
lipid bilayer 475
lithium 370
lithium aluminosilicates 405
lithium intercalation compounds 384
lithium ion conductors 390
lithium niobate 394
lithium oxide 399
lithium titanium disulfide 386
local reptation model 538
localized motion 106, 134, 405, 528,
887
Longini mechanism 26, 193
low energy electron diffraction (LEED)
304
low energy electron microscopy (LEEM)
305
macroscopic diffusion methods 11–15,
65, 368
magnetic field gradient 421, 720
magnetic relaxation methods 16
magnetite 217, 231
magnetogyric ratio 369, 375, 517, 720
majority defect 213Index 961
Mandelbrot dimension 793
Markovian process 70, 749, 802, 804
mass action law 25, 40, 211, 807
master curves of ionic conductivity
863
master equation 102, 748, 772
McLean’s isotherm 358
mean residence time 7, 17, 21, 68,
70–72, 80, 127, 322, 369, 816
mean square displacement 20, 252,
286, 418–449, 478, 516, 531, 555,
629, 751–777, 799, 816, 826, 868,
903, 929
long time tail 761
mean-field theory 808
mechanical relaxation methods 16
mechanical sectioning technique 11
membrane 441, 471, 733
biological 145, 473
lateral diffusion 477
polypropylene 441
transverse diffusion 500
memory effect 117, 127, 632, 643
mesoporous materials 437–439
MCM-41 438
metallic glasses 264
metalorganic chemical vapor deposition
(MOCVD) 187
Meyer-Neldel compensation rule 835
micelles 736
microemulsion 737
microporous materials 427, 925
microscopic diffusion methods 15–17,
65, 368
minority defect 212, 213
mismatch relaxation 866
mixed alkali effect 840
mixed conductor 216
mobility of ions 717, 729, 737
mode coupling theory 256, 275, 691
molecular beam epitaxy (MBE) 187
molecular dynamics simulations 118,
480, 534, 916, 922–925
molecular traffic control 437
molten salt mixtures 566
Monte Carlo simulations 325, 491,
759, 815, 821, 830, 836, 840, 909,
917, 922
M¨oßbauer spectroscopy 65–68
motional narrowing of NMR lines
374, 393, 395
moving grain boundary 362
multifractal 797
multiphase diffusion 53
multiple scattering 115, 135, 528
muon 30
muon spin resonance (µSR) 31
mutual diffusion 556, 569, 600
nanocrystalline BaF2 394
nanocrystalline CaF2 391
nanocrystalline composites 399, 908
nanocrystalline LiNbO3 394
nanocrystalline LiTiS2 397
nanocrystalline materials 352, 367,
390
Na3PO4 154
nearly constant loss (NCL) behaviour
814, 835, 863, 888
Nernst field 227
Nernst-Einstein equation 126, 131,
817, 865, 880, 904
neutron backscattering (BSC)
spectrometer 106, 109, 111
neutron capture 382
neutron scattering 65, 68, 93, 514, 817
neutron spin-echo (NSE) spectrometer
519, 520
neutron spin-echo (NSE) spectroscopy
74, 516, 518
neutron time-of-flight (TOF) spectrometer 106, 114
NiGa 82
Ni3Sb 86
NMR 368, 417, 717
correlation function 369, 818
correlation time 369, 373, 830
flow measurements 720
linewidth 373
PFG diffraction pattern 424–425
PFG effective observation time 426
PFG observation time 418, 421,
426, 427, 449, 455
pulsed field gradient (PFG) technique
417, 421–427
relaxation 369, 426, 814
relaxation techniques 375–380962 Index
spectral density 369, 409, 818
spectrometer 379
spin echo 378, 379, 421, 721
spin-alignment echo technique 390
spin-echo attenuation 422, 424, 426,
440, 452
spin-locking experiment 378
static field gradient (SFG) technique
427
non-Arrhenius behaviour 767, 832
non-stoichiometric oxide 210, 219
normal diffusion 417–420, 426, 435,
450, 479, 555, 777, 798, 799
nuclear
magnetization 375, 421
methods in diffusion 16, 65, 368
polarization 380, 404
reactions for polarized β-emitters
381
spin-lattice relaxation 369
nuclear magnetic relaxation see NMR
relaxation
nuclear magnetic resonance see NMR
nuclear reaction analysis (NRA) 15
nuclear resonance scattering (NRS)
65
Onsager reciprocity relation 566, 919
Onsager regression hypothesis 579
Onsager transport coefficient 226, 566
O/Si(111) 307
O/W(110) 295
oxygen activity 209
oxygen deficit 211
oxygen excess 211
oxygen ion conductor 216
oxygen partial pressure 209
oxygen potential gradient 228
oxygen sublattice 209
paddle-wheel mechanism 153
pair correlation function 251, 575
particle distribution function 917
partition function 915, 919
Pb/Si(111) 313
percolation
bond 901
continuum 902
interface 908
site 895
percolation cluster 897
conductivity of 905
diffusion on 904
percolation model 755, 820, 895
percolation threshold 896
permeation 500
perovskite structure 225
petalite 405
phenomenological coefficient see
Onsager transport coefficient
phonon dispersion 125
phonon spectroscopy 77
photon correlation spectroscopy 579
plasma parameter 822
Poisson process 803
polarized neutron capture 382
polybutadiene 519, 528
polydimethylsiloxane (PDMS) 440,
443, 453, 531
polyethylene oxide (PEO) 451, 843
polyethylethylene (PEE) 453
polyisobutylene 528
polyisoprene 528
polymer
blends 697
diblock copolymer 453
electrolytes 843
reptation 449, 450
triblock copolymer 450, 451
polymeric systems 619
polypropylene membrane 441
polypropylene oxide (PPO) 451
polystyrene (PS) 440
polyvinylether 528
potential 922, 927
chemical 226
electric 226, 236
electrochemical 226
Lennard-Jones 923, 927, 932
square well 922
pre-exponential factor 18
pressure dependence of diffusion 268
principal diffusivities 4
propagator 419, 420, 422, 424, 429,
435, 798, 802, 928
mean 422–424, 935
proton conduction 139Index 963
proton pump 146
proton tunneling 123
protonic conductor 131
pseudo Fermi level 782
pulsed field gradient (PFG) NMR
417, 421–427, 720
quantum diffusion 30
quasi-vacancies 261
quasielastic coherent structure factor
154
quasielastic helium scattering 293
quasielastic incoherent neutron
scattering (QINS) 136
quasielastic incoherent structure factor
141, 154
quasielastic light scattering 620
quasielastic linewidth 103, 105, 124,
151
quasielastic M¨oßbauer spectroscopy
67, 68
quasielastic methods 65, 66, 68, 73
quasielastic neutron scattering (QENS)
67, 68, 93
observation function 100, 105
observation time 100, 105, 133
observation volume 105
resolution function 105
radiotracer sectioning method 217,
340, see also tracer method
random barrier model 753, 867
random phase approximation 699
random trap model 754
random walk 747, 802, 806, 858, 865,
903
randomly blocked sites 755, 765
Rayleigh line 581
RbAg4I5 878, 890
reaction constant 806
reaction rate 120, 143
reactive diffusion 54
reflection high energy electron
diffraction (RHEED) 324
renewal theory 847
reptation
crossover 543
diffusion 537
model 514, 537–540, 543
residence time see mean residence
time
residual activity method 217
rotational diffusion 138, 491, 635, 658
Rouse model 514, 529–536, 844
generalized 538
rubber-like model 538
Rutherford backscattering spectrometry (RBS) 14
scanning tunneling microscopy (STM)
306
scattering amplitude 622
scattering cross section 95
scattering function 94, 149, 523, 921
scattering length 95, 101
scattering strength 621
scattering vector 93
Schottky
defects 211
equilibrium 210, 224
secondary ion mass spectrometry
(SIMS) 13, 222
sedimentation 647
sediments 446–447
segregation 234
self-affine fractal 797
self-correlation function 66–76, 97,
102, 419
self-diffusion 31, 121, 127, 136, 144,
152, 370, 555, 557, 637, 943
self-diffusion coefficient 7, 120, 128,
135, 147, 152, 216, 227, 659
self-interstitial charge state 166
self-similarity 795, 897
short-range order 260
Siegert relation 584, 626
Sierpinski fractal 794
silicon self-diffusion 166
simulations
molecular dynamics (MD) 925, 941
Monte Carlo (MC) 815, 821, 915,
922
Sinai model 746, 769
single-file diffusion 434–437, 775
site energy
disorder 747
exponential distribution 766, 781
site exclusion model 771964 Index
site occupancy 104, 150
site percolation 895
six-jump cycle mechanism 46, 81
Smoluchowski equation 675
Smoluchowski theory 807
Snoek effect 16
soft phonon modes 77, 86
solid rotator phase 156
solid-state protonic conductor 131
solute diffusion 35
solute-vacancy pair 215, 220
solvent diffusion 35
Soret effect 606
sound attenuation 604
sound velocity 461, 604
specific surface area 446
spectral density 921
spin diffusion 382, 400, 403
spin echo
neutron 74, 516
NMR 378, 379, 421, 721
spin incoherent scattering 115
spin-lattice relaxation 369, 818
disorder effects 372
frequency dependence 372, 386,
387, 398, 407
homogeneous 404
inhomogeneous 404
laboratory frame 377, 409
low-dimensionality effects 372
rate 370
rotating frame 379, 409
spin-spin relaxation 378, 409
spinel 217
spodumene 405, 406
sputter sectioning technique 12
SrCl2 128
static field gradient (SFG) NMR 427
static structure factor 95, 150
stochastic process 800
stoichiometric point 212, 216, 228
Stokes-Einstein diffusion coefficient
630
Stokes-Einstein equation 254, 601,
660, 719
Stokesian dynamics simulation method
689
strain field 119, 130, 153
stretched polymers 849
structural relaxation 260
structure factor 153, 298, 919
dynamic 521–526, 921, 937
partial 652
static 918, 921
subdiffusive behaviour 417, 421, 801,
867
substitutional impurities 165
Summerfield scaling 863, 866
superlattice disordering 187
surface diffusion 285, 339
equilibrium measurements 297
non-equilibrium measurements 313
step 302
terrace 302
surface exchange coefficient 222
surface light scattering 608
surface tension 608
surface-to-volume ratio 444–447
synchrotron radiation 65, 73
thermal conductivity 597
thermal diffusivity 597
thermal grating 613
thermodynamic factor 10, 227, 243,
562
time correlation function 567, 920, see
also correlation function
time-dependent correlation factor 867
time-domain interferometry 76
time-temperature superposition
principle 863, 866
titanium 65, 77
titanium disulfide 386
topological distance 900
tortuosity 443, 454, 731
total scattering cross section 102
tracer diffusion 7, 230, 745, 771, 773,
816
tracer diffusion coefficient 7, 286
tracer method 11
tracer self-diffusion coefficient 7
transference number 227, 719, 729
transition rate 746, see also jump rate
transition state theory 943
transport coefficient 919–921, see also
Onsager transport coefficient
transport diffusion 432–434, 556, 943Index 965
traps 121
saturation of 781
trapping rate 123
triple-defect mechanism 46, 81
tunneling of protons 123
two-dimensional diffusion 130, 143,
145, 372, 386, 387
two-state model 121, 122, 752
ultrasonic interferometer 462
ultrasonic wave velocity 462
universal dielectric response 814, 863
universal dynamic response see
universal dielectric response
vacancy
cation 212, 217
charge state 166
oxygen 211
vacancy availability factor 22
vacancy mechanism 23, 65, 124, 169,
232, 347
vacancy-pair mechanism 47
vacancy-wind corrections 52
Van Hove correlation function 66, 96,
98, 419, 689, 921, 935, 937
van Liempt rule 33
vehicle mechanism 132, 148
velocity autocorrelation function 858,
865, 920
velocity cross-correlation coefficients
570
Verlet algorithm 924, 928
vesicles 736
viscoelasticity 513
viscosity 601, 607, 608
Vogel-Fulcher-Tammann (VFT)
equation 255, 520, 845, 882
volume diffusion 339
Wagner formula 227
waiting time distribution 802, 825
walk dimension 801, 804
water in gels 466
water in living cells 466
Wiener process 794, 804
x-ray photon correlation spectroscopy
(XPCS) 76
Zener effect 16
zeolite 426–437, 925, 926
A-type 422, 427, 433
AlPO4-5 436
LTA-type 926
structure 926
X-type 445
ZK4 926
ZSM-5 type 431
zeta potential 720
zirconia 216, 224, 235
List of Contributors
Dipl.-Phys. Roger Biel
CIBA Vision GmbH
Postfach 74
63702 Aschaffenburg
Germany
Prof. Armin Bunde
Justus-Liebig-Universit¨at Gießen
Institut f¨ ur Theoretische Physik III
Heinrich-Buff-Ring 16
35392 Gießen
Germany
bunde@physik.uni-giessen.de
Dr. Cornelia Cramer
Westf¨alische Wilhelms-Universit¨at
M¨ unster
Institut f¨ ur Physikalische Chemie
Corrensstraße 30/36
48149 M¨ unster
Germany
cramerc@uni-muenster.de
Prof. Jan K. G. Dhont
Forschungszentrum J¨ ulich GmbH
Institut f¨ ur Festk¨ orperforschung
52425 J¨ ulich
Germany
J.K.G.Dhont@fz-juelich.de
Prof. Wolfgang Dieterich
Universit¨ at Konstanz
Fachbereich Physik
78457 Konstanz
Germany
wolfgang.dieterich
@uni-konstanz.de
Prof. Franz Faupel
Universit¨ at Kiel
Lehrstuhl f¨ ur Materialverbunde
Kaiserstr. 2
24143 Kiel
Germany
ff@tf.uni-kiel.de
Dr.-Ing. Andreas P. Fr¨ oba
Universit¨ at Erlangen
Lehrstuhl f¨ ur Techn. Thermodynamik
Am Weichselgarten 8
91058 Erlangen
Germany
apf@ltt.uni-erlangen.de
Prof. Klaus Funke
Westf¨alische Wilhelms-Universit¨at
M¨ unster
Institut f¨ ur Physikalische Chemie
Corrensstraße 30/36
48149 M¨ unster
Germany
K.Funke@uni-muenster.de
Prof. Ulrich G¨osele
Max-Planck-Institut f¨ ur Mikrostrukturphysik
Weinberg 2
06120 Halle
Germany
goesele@mpi-halle.de950 List of Contributors
Prof. Wolfgang Grill
Universit¨ at Leipzig
Institut f¨ ur Experimentelle Physik II
Linn´estr. 5
04103 Leipzig
Germany
grill@uni-leipzig.de
Prof. Reinhold Haberlandt
Universit¨ at Leipzig
Institut f¨ ur Theoretische Physik
Augustusplatz 10/11
04109 Leipzig
Germany
Reinhold.Haberlandt
@physik.uni-leipzig.de
Prof. Paul Heitjans
Universit¨ at Hannover
Institut f¨ ur Physikalische Chemie
und Elektrochemie
Callinstr. 3-3a
30167 Hannover
Germany
heitjans@pci.uni-hannover.de
Prof. Christian Herzig
Westf¨alische Wilhelms-Universit¨at
M¨ unster
Institut f¨ ur Materialphysik
Wilhelm-Klemm-Straße 10
48149 M¨ unster
Germany
herzig@uni-muenster.de
Dr. Manfred Holz
Universit¨ at Karlsruhe
Institut f¨ ur Physikalische Chemie
Kaiserstr. 12
76128 Karlsruhe
Germany
Manfred.Holz
@chemie.uni-karlsruhe.de
Dr. Myron Hupalo
Iowa State University
Dept. of Physics and Astronomy
Ames, Iowa 50011
U.S.A.
hupalo@ameslab.gov
Dr. Sylvio Indris
Universit¨ at Hannover
Institut f¨ ur Physikalische Chemie
und Elektrochemie
Callinstr. 3-3a
30167 Hannover
Germany
indris@pci.uni-hannover.de
Prof. Jan W. Kantelhardt
Martin-Luther-Universit¨ at HalleWittenberg
FG Theoretische Physik
von Senckendorff-Platz 1
06099 Halle
Germany
kantelhardt@physik.uni-halle.de
Prof. J¨org K¨arger
Universit¨ at Leipzig
Institut f¨ ur Experimentelle Physik I
Linn´estr. 5
04103 Leipzig
Germany
kaerger@physik.uni-leipzig.de
Dr. Ruep E. Lechner
Hahn-Meitner-Institut
Glienicker Straße 100
14109 Berlin
Germany
lechner@hmi.de
Prof. Alfred Leipertz
Universit¨ at Erlangen
Lehrstuhl f¨ ur Technische Thermodynamik
Am Weichselgarten 8
91058 Erlangen
Germany
sek@ltt.uni-erlangen.deList of Contributors 951
Prof. Philipp Maass
Technische Universit¨ at Ilmenau
Fachgebiet Theoretische Physik II
Weimarer Straße 25
98684 Ilmenau
Germany
philipp.maass@tu-ilmenau.de
Prof. Manfred Martin
RWTH Aachen
Institut f¨ ur Physikalische Chemie I
Landoltweg 2
52074 Aachen
Germany
martin@rwth-aachen.de
Prof. Helmut Mehrer
Westf¨alische Wilhelms-Universit¨at
M¨ unster
Institut f¨ ur Materialphysik
Wilhelm-Klemm-Straße 10
48149 M¨ unster
Germany
mehrer@nwz.uni-muenster.de
Dr. Gerhard Meier
Forschungszentrum J¨ ulich GmbH
Institut f¨ ur Festk¨ orperforschung
52425 J¨ ulich
Germany
G.Meier@fz-juelich.de
Dr. Martin Meyer
Justus-Liebig-Universit¨at Gießen
Institut f¨ ur Theoretische Physik III
Heinrich-Buff-Ring 16
D-35392 Gießen
Germany
Prof. Yuri Mishin
George Mason University
School of Computational Sciences
4400 University Drive, MSN 5C3
Fairfax, VA 22030-4444
U.S.A.
ymishin@gmu.edu
Prof. Ole G. Mouritsen
University of Southern Denmark
Physics Department
Campusvej 55
5230 Odense M
Denmark
ogm@memphys.sdu.dk
Dr. Kiaresch Mussawisade
Forschungszentrum J¨ ulich GmbH
Institut f¨ ur Festk¨ orperforschung
52425 J¨ ulich
Germany
k.mussawisade@fz-juelich.de
Prof. Gerhard N¨agele
Forschungszentrum J¨ ulich GmbH
Institut f¨ ur Festk¨ orperforschung
52425 J¨ ulich
Germany
G.Naegele@fz-juelich.de
Dr. Klaus R¨atzke
Universit¨ at Kiel
Lehrstuhl f¨ ur Materialverbunde
Kaiserstr. 2
24143 Kiel
Germany
kr@tf.uni-kiel.de
Dr. Uwe Renner
Wissenschaftszentrum LeipzigF¨ orderverein
Goldschmidtstr. 26
04103 Leipzig
Germany
Prof. Dieter Richter
Forschungszentrum J¨ ulich GmbH
Institut f¨ ur Festk¨ orperforschung
52425 J¨ ulich
Germany
D.Richter@fz-juelich.de952 List of Contributors
Dr. Andreas Schirmer
Strahlenmessstelle der Bundeswehr
Humboldtstraße
29633 Munster
Germany
Dr. Martin Schubert
Universit¨ at Leipzig
Institut f¨ ur Experimentelle Physik II
Linn´estr. 5
04103 Leipzig
Germany
Prof. Gunter M. Sch¨ utz
Forschungszentrum J¨ ulich GmbH
Institut f¨ ur Festk¨ orperforschung
52425 J¨ ulich
Germany
G.Schuetz@fz-juelich.de
Prof. Bogdan Sepiol
Universit¨ at Wien
Institut f¨ ur Materialphysik
Strudlhofgasse 4
1090 Wien
Austria
bogdan.sepiol@ap.univie.ac.at
Prof. Tasso Springer
Geigerstr. 7
82166 Gr¨ afeling
Germany
Dr. Frank Stallmach
Universit¨ at Leipzig
Institut f¨ ur Experimentelle Physik I
Linn´estr. 5
04103 Leipzig
Germany
stallmac@physik.uni-leipzig.de
Prof. Teh Yu Tan
Duke University
Department of Mechanical Engineering & Materials Science
Box 90300 Hudson Hall
Durham, NC 27708-0300
U.S.A.
ttan@acpub.duke.edu
Prof. Michael C. Tringides
Iowa State University
Dept. of Physics and Astronomy
Ames, Iowa 50011
U.S.A.
tringides@ameslab.gov
Prof. Ilpo Vattulainen
Helsinki University of Technology
Laboratory of Physics
P.O. Box 1100
02015 HUT Helsinki
Finland
ilp@fyslab.hut.fi
Prof. Gero Vogl
Universit¨ at Wien
Institut f¨ ur Materialphysik
Strudlhofgasse 4
1090 Wien
Austria
gero.vogl@ap.univie.ac.at
Prof. G¨ unter Vojta
Donndorfstr. 20
01217 Dresden
Germany
Prof. Hermann Weing¨artner
Ruhr-Universit¨ at Bochum
Lehrstuhl f¨ ur Phys. Chemie II
Universit¨ atsstr. 150
44780 Bochum
Germany
Hermann.Weingaertner
@ruhr-uni-bochum.de
Dr. Thomas Wichmann
Weilerswisterstr. 6
50968 K¨ oln
GermanyList of Contributors 953
Dr. Dirk Wilmer
Westf¨alische Wilhelms-Universit¨at
M¨ unster
Institut f¨ ur Physikalische Chemie
Corrensstraße 30/36
48149 M¨ unster
Germany
wilmer@uni-muenster.de
Dr. Karl Ullrich W¨ urz
PBS Softwareberatung
Schwanheimer Str. 144a
64625 Bensheim
GermanyIndex
acoustic microscopy 466
activation energy 19, 344, 813
activation enthalpy 18
activation volume 19, 40, 268
adsorbate-adsorbate interactions 288
Ag/Ag(111) 320
0.5Ag2S·0.5GeS2 877
0.3Ag2SO4·0.7AgPO3 884
alloys
binary 49, 53
ordered 78
aluminium 39, 77
amino acid 729
amorphous alloys 259
anomalous diffusion 417–421, 428,
434, 441, 448, 479, 488, 731, 797,
803, 806, 867, 904
anticorrelation in anomalous diffusion
801
antiphase boundaries 77
antistructure defects 71, 72, 78
antistructure-bridge mechanism 46,
81
Arrhenius law 18, 289, 746, 753, 813,
925
association degree 220
asymmetric double well potential
(ADWP) model 836, 866, 888
Auger electron spectroscopy (AES)
14
autocorrelation function 817, 920, see
also correlation function
electric field 625
light intensity 625
orientation 636
average
ensemble 919, 923
time 923
β-NMR
method 380–384
relaxation 370, 383, 384, 403, 407,
409
spectrometer 383
β-radiation asymmetry 383
β-relaxation 520
β-titanium 77
B2 structure 71, 72, 76, 78
backbone of percolation cluster 900
BaF2 394
ballistic diffusion 867
binary intermetallics 42
binary non-electrolyte mixtures 573
blocking factor 104, 150
Bloembergen-Purcell-Pound (BPP)
behaviour 369, 819
body-centered cubic metals 34
Boltzmann-Matano method 49, 294,
498
bond percolation 901
Boson peak 520
Bragg equation 108
Brillouin lines 581, 604
Brownian dynamics simulation method
687
Brownian motion 472, 632, 717, 794
CaF2 391
caloric glass transition temperature
255
capacitance 907
capillary electrophoresis 738
cation sublattice 209
central limit theorem 420, 423, 625,
799
charge diffusion coefficient 126, 127,
148956 Index
charge of transport 222, 238
chemical diffusion 6, 49, 556
chemical diffusion coefficient 231
chemical potential 8, 226, 291, 918,
941
Chudley-Elliott model 69, 71, 102,
130, 149, 150
cobalt oxide 217
CoGa 82
coherent diffuse scattering 153
coherent quasielastic scattering 149
coherent scattering function 102, 150
collective diffusion 495, 641, 648, 747,
772
coefficient of 289, 646, 771, 778
colloidal rods 666
colloidal spheres 676
colloidal systems 619
collective diffusion 641
interdiffusion 651
rotational diffusion 658
self-diffusion 637
component diffusion coefficient 10
compressibility, isentropic 607
computer simulations see simulations
concept of mismatch and relaxation
(CMR) 867, 874
conductivity
electrical 219, 905, 906
frequency dependence 768, 861
thermal 597
conductivity spectroscopy 861
continuity equation 5
continuous time random walk model
824
continuum percolation 902
copper 77
correlated jumps 118, 124, 127, 858
correlation effects 127
correlation factor 19, 222, 773, 816,
848
correlation function 369, 515, 525,
527, 582, 915, 916, 919–921, 923
long-time tail 633
of coverage 291
of current density 864
Van Hove 66, 96, 98, 921, 935, 937
velocity auto- 928, 930
correlation length 897
correlation technique 582–587
correlation time 369, 586, 832
correlator 594
Coulomb interaction 215, 819, 830
Coulomb lattice gas 820, 840
Coulomb trap 835
counterion model 835, 866
coupled diffusion in B2 intermetallics
44
coupling concept 866
coverage 290
critical fluctuation 295
fluctuation 290, 293
step 299
Co-Zr glasses 268
critical concentration 896, 901, 902
critical dimension 808
critical exponent 897, 905
critical percolation path 832
critical slowing down 600, 650, 703
critical-path approach 763
cross coefficients 236
crossover time 905
Cu3Au rule 47
current density autocorrelation function
864
D03 structure 84
Darken equation 51, 296, 433, 557,
562, 573, 941
Darken-Manning relation 52
Darwin width 110
dc conductivity plateau 862
de Broglie wavelength 99, 919
Debye length 720
Debye-H¨ uckel-Onsager-Falkenhagen
effect 859
Debye-Waller factor 67, 70, 74, 99,
113, 119, 138
defect chemistry 210
defect cluster 226
defect structure 210, 215
demixing 234, 236, 240, 703
density distribution 931
detailed balance 71, 767, 786
dichalcogenides 386
dielectric loss 835, 863Index 957
differential effective-medium theory
849
diffusant 6
diffuse scattering 76
diffuser 6
diffusion
ambipolar 227
anomalous 417–421, 428, 434, 441,
448, 479, 488, 731, 797, 803, 867
cation 217, 224
chemical 226
collective 495, 641
continuous jump 371
correlated diffusion anisotropy
431–432
effective diffusivity 428
experimental methods 10
field-assisted 717
in aluminium 39
in amorphous alloys 262
in B2 intermetallics 44, 78
in bcc metals 35
in D03 intermetallics 84
in fcc metals 33
in gallium arsenide 184
in germanium 183
in L12 intermetallics 49
in lead 41
in liquids 251
in membranes 471
in nickel 31
in niobium 28, 29
in polymers 447, 519, 531, 675, 733,
843
in regular pore networks 427
in semiconductors 165
in silicon 166
in silver 38
in zeolites 427, 925
interstitial-substitutional 168
intracrystalline self-diffusion 429,
430, 445
isotope effects 13, 30, 253, 265, 272
lateral 477, 493
long-range 133
low-dimensional 371
molecular mechanism 132
multicomponent 427
mutual 556, 569, 600
normal 417–420, 426, 435, 450, 479,
555, 777, 798, 799
on percolation clusters 904
oxidation-enhanced 174
oxidation-retarded 174
oxygen 222, 223
pressure dependence 18
proton diffusion 131
reactive 54
rotational 477, 491, 635
single-file diffusion 434–437, 775
solute diffusion 35
solvent diffusion 35
surface diffusion 285, 302, 339
through membranes 500
transport diffusion 432–434, 943
diffusion coefficient 904, 921, 929, 931,
941
chemical 6, 8, 151, 227, 244
collective 289, 646, 780
distinct-diffusion 570, 571
foreign atom 8
frequency dependence 762
impurity 8
in grain boundaries 338
interdiffusion 654
self-diffusion 7
Stokes-Einstein 630
thermodynamic 561
tracer 7, 219, 286, 478
transport 941
vacancy 231
diffusion coefficient tensor 4, 439, 676
diffusion entropy 18
diffusion equation 5, 289, 494, 632,
752, 798, 928, see also Fick’s
second law
error function solution 6
source solution 230
thin-film solution 5
diffusion length 5, 479
diffusion mechanisms 23
diffusion-limited reaction 806–808
diffusional line broadening 70, 72, 94
diffusivity 4
effective 41, 170, 348, 420, 429, 453
thermal 597958 Index
diffusivity tensor 4, 439, 676
direct current NMR (DCNMR) 718,
725
disorder models 753, 820
disordered solids
homogeneously 402
inhomogeneously 367, 390
disordered systems 372, 746, 753, 813,
857, 895
dispersive transport 822
dissociative mechanism 26
distribution of site energies 257
divacancy mechanism 25
dopant diffusion 172, 235
Doppler drive 111
double differential scattering crosssection 95
drift flux 230, 232, 236
drift velocity 237, 717–720
dynamic conductivity 817
dynamic light scattering (DLS) 579,
589–597, 624
coherence 593
dynamic percolation 846
dynamic rotational disorder 153
dynamic structure factor 94, 521–526,
531, 538, 545, 568, 626, see also
scattering function
distinct 628
self- 628
dynamic structure model 840
effective activation energy 273
effective charge 236, 239
effective diffusivity 41, 170, 348, 420,
429, 453
effective-medium approximation 746,
758, 762, 912
self-consistency condition 761, 787
Einstein diffusion coefficient 8
Einstein relation 227, 420, 434, 555,
717, 903, 920
Einstein-Debye relation 635
Einstein-Smoluchowski relation 19,
see also Einstein relation
elastic incoherent structure factor
(EISF) 98, 119, 138, 139, 141
electric potential 226, 236
electric potential gradient 228
electro-osmosis 726, 737
electrochemical potential 226
electrokinetic potential 720
electrolyte solution 566, 574
electron hole 211, 212
electron microprobe analysis (EMPA)
14
electrophoresis 718
electrophoretic NMR (ENMR) 717
elementary diffusion step 65, 66, 68
encounter model 124, 128, 370
energy resolution 98
ensemble
canonical 917
microcanonical 917
entanglements 513, 531, 543
enthalpy of migration 22
entropic forces 529
entropy of migration 22
equivalent circuit model 906
error function solution 6
escape rate 121
eucryptite 405
excess charge 210, 228, 231
excess volume 269
exchange mechanism
interstitial-substitutional 26
ring 127
face-centered cubic metals 32
fast solute diffusion 40
FeAl 78
Fe3Al 80
Fermi level effect 172
Fe3Si 84
Fick’s first law 4, 494, 559, 798
non-local 643
Fick’s second law 5, 6, 165, 494, 752
field-assisted diffusion 717
Fisher model 337, 338
five-frequency model 36, 233
fixed-window method 113
fluctuation-dissipation relation 632
fluorescence correlation spectroscopy
(FCS) 669
fluorescence recovery after photobleaching (FRAP) 481, 497,
661
forced Rayleigh scattering 613Index 959
Fourier time window 100, 106
fractal 793
chemical kinetics 806
fractal dimension 446, 793, 897, 898,
904
fractional Brownian motion 794
fragile glass 254
fragile supercooled melt 880
Frank-Turnbull mechanism 26, 168
free induction decay (FID) 376, 400
free-volume model 253, 486
Frenkel
defects 211
equilibrium 210, 212
Γ -space 918
generalized force 919
Gibbs free energy of activation 19
Gibbs free energy of binding 24
Gibbs free energy of migration 22
glass
electrolyte 403
ion-conducting 402, 819
metallic 259
oxide 403, 405, 884
glass transition 255, 272, 519, 638
Gorski effect 16
grain boundary 337
diffusion coefficient 338
in nanocrystalline materials 352,
390, 391
large-angle 345, 346
segregation 339, 353, 357, 361
segregation energy 353
segregation factor 339, 353
small-angle 345, 346
width 338, 343, 911
grain boundary diffusion 337
activation energy 344
anisotropy 345
Arrhenius law 344
atomistic mechanisms 347, 362
comparison with bulk, surface, liquid
344
empirical rules 344
in intermetallic compounds 361
in moving boundaries 362
kinetic regimes 347
orientation dependence 346
Green-Kubo relation 495, 568, 638,
920
Grotthuß mechanism 131
growth constant 54
gyromagnetic ratio see magnetogyric
ratio
Harrison’s classification 348
Hart’s formula 349
Hartley-Crank relation 557
Hausdorff dimension 793
Haven ratio 127, 137, 148, 817, 865
Henry isotherm of grain boundary segregation
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