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| موضوع: كتاب Diffusion in Condensed Matter - Methods, Materials, Models الأربعاء 07 يوليو 2021, 11:57 am | |
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أخوانى فى الله 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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