List of Contributors

Dipl.-Phys. Roger Biel Prof. Franz Faupel CIBA Vision GmbH Universit¨at Postfach 74 Lehrstuhl f¨ur Materialverbunde 63702 Aschaffenburg Kaiserstr. 2 Germany 24143 Kiel Prof. Armin Bunde Germany Justus-Liebig-Universit¨at Gießen [email protected] Institut f¨ur Theoretische Physik III Heinrich-Buff-Ring 16 Dr.-Ing. Andreas P. Fr¨oba 35392 Gießen Universit¨at Erlangen Germany Lehrstuhl f¨ur Techn. Thermody- [email protected] namik Dr. Cornelia Cramer Am Weichselgarten 8 Westf¨alische Wilhelms-Universit¨at 91058 Erlangen M¨unster Germany Institut f¨ur Physikalische Chemie [email protected] Corrensstraße 30/36 48149 M¨unster Prof. Klaus Funke Germany Westf¨alische Wilhelms-Universit¨at [email protected] M¨unster Prof. Jan K. G. Dhont Institut f¨ur Physikalische Chemie Forschungszentrum J¨ulich GmbH Corrensstraße 30/36 Institut f¨ur Festk¨orperforschung 48149 M¨unster 52425 J¨ulich Germany Germany [email protected] [email protected] Prof. Wolfgang Dieterich Prof. Ulrich G¨osele Universit¨at Konstanz Max-Planck-Institut f¨ur Mikrostruk- Fachbereich Physik turphysik 78457 Konstanz Weinberg 2 Germany 06120 wolfgang.dieterich Germany @uni-konstanz.de [email protected] 950 List of Contributors

Prof. Wolfgang Grill Dr. Myron Hupalo Universit¨at Leipzig Iowa State University Institut f¨ur Experimentelle Physik II Dept. of Physics and Astronomy Linn´estr. 5 Ames, Iowa 50011 04103 Leipzig U.S.A. Germany [email protected] [email protected] Dr. Sylvio Indris Universit¨at Hannover Prof. Reinhold Haberlandt Institut f¨ur Physikalische Chemie Universit¨at Leipzig und Elektrochemie Institut f¨ur Theoretische Physik Callinstr. 3-3a Augustusplatz 10/11 30167 Hannover 04109 Leipzig Germany Germany [email protected] Reinhold.Haberlandt Prof. Jan W. Kantelhardt @physik.uni-leipzig.de Martin-Luther-Universit¨at Halle- Wittenberg Prof.PaulHeitjans FG Theoretische Physik Universit¨at Hannover von Senckendorff-Platz 1 Institut f¨ur Physikalische Chemie 06099 Halle und Elektrochemie Germany Callinstr. 3-3a [email protected] 30167 Hannover Prof. J¨org K¨arger Germany Universit¨at Leipzig [email protected] Institut f¨ur Experimentelle Physik I Linn´estr. 5 Prof. Christian Herzig 04103 Leipzig Westf¨alische Wilhelms-Universit¨at Germany M¨unster [email protected] Institut f¨ur Materialphysik Dr. Ruep E. Lechner Wilhelm-Klemm-Straße 10 Hahn-Meitner-Institut 48149 M¨unster Glienicker Straße 100 Germany 14109 Berlin [email protected] Germany [email protected] Dr. Manfred Holz Prof. Alfred Leipertz Universit¨at Karlsruhe Universit¨at Erlangen Institut f¨ur Physikalische Chemie Lehrstuhl f¨ur Technische Thermody- Kaiserstr. 12 namik 76128 Karlsruhe Am Weichselgarten 8 Germany 91058 Erlangen Manfred.Holz Germany @chemie.uni-karlsruhe.de [email protected] List of Contributors 951

Prof. Philipp Maass Prof. Ole G. Mouritsen Technische Universit¨at Ilmenau University of Southern Denmark Fachgebiet Theoretische Physik II Physics Department Weimarer Straße 25 Campusvej 55 98684 Ilmenau 5230 Odense M Germany Denmark [email protected] [email protected]

Prof. Manfred Martin RWTH Aachen Dr. Kiaresch Mussawisade Institut f¨ur Physikalische Chemie I Forschungszentrum J¨ulich GmbH Landoltweg 2 Institut f¨ur Festk¨orperforschung 52074 Aachen 52425 J¨ulich Germany Germany [email protected] [email protected]

Prof. Helmut Mehrer Prof. Gerhard N¨agele Westf¨alische Wilhelms-Universit¨at Forschungszentrum J¨ulich GmbH M¨unster Institut f¨ur Festk¨orperforschung Institut f¨ur Materialphysik 52425 J¨ulich Wilhelm-Klemm-Straße 10 Germany 48149 M¨unster [email protected] Germany [email protected] Dr. Klaus R¨atzke Dr. Gerhard Meier Universit¨at Kiel Forschungszentrum J¨ulich GmbH Lehrstuhl f¨ur Materialverbunde Institut f¨ur Festk¨orperforschung Kaiserstr. 2 52425 J¨ulich 24143 Kiel Germany Germany [email protected] [email protected]

Dr. Martin Meyer Dr. Uwe Renner Justus-Liebig-Universit¨at Gießen Wissenschaftszentrum Leipzig- Institut f¨ur Theoretische Physik III F¨orderverein Heinrich-Buff-Ring 16 Goldschmidtstr. 26 D-35392 Gießen 04103 Leipzig Germany Germany Prof.YuriMishin George Mason University Prof. Dieter Richter School of Computational Sciences Forschungszentrum J¨ulich GmbH 4400 University Drive, MSN 5C3 Institut f¨ur Festk¨orperforschung Fairfax, VA 22030-4444 52425 J¨ulich U.S.A. Germany [email protected] [email protected] 952 List of Contributors

Dr. Andreas Schirmer Box 90300 Hudson Hall Strahlenmessstelle der Bundeswehr Durham, NC 27708-0300 Humboldtstraße U.S.A. 29633 Munster [email protected] Germany Prof. Michael C. Tringides Dr. Martin Schubert Iowa State University Universit¨at Leipzig Dept. of Physics and Astronomy Institut f¨ur Experimentelle Physik II Ames, Iowa 50011 Linn´estr. 5 U.S.A. 04103 Leipzig [email protected] Germany Prof. Ilpo Vattulainen Prof. Gunter M. Sch¨utz Helsinki University of Technology Forschungszentrum J¨ulich GmbH Laboratory of Physics Institut f¨ur Festk¨orperforschung P.O. Box 1100 52425 J¨ulich 02015 HUT Helsinki Germany Finland [email protected] [email protected] Prof. Gero Vogl Prof. Bogdan Sepiol Universit¨at Wien Universit¨at Wien Institut f¨ur Materialphysik Institut f¨ur Materialphysik Strudlhofgasse 4 Strudlhofgasse 4 1090 Wien 1090 Wien Austria Austria [email protected] [email protected] Prof. G¨unter Vojta Prof. Tasso Springer Donndorfstr. 20 Geigerstr. 7 01217 Dresden 82166 Gr¨afeling Germany Germany Prof. Hermann Weing¨artner Dr. Frank Stallmach Ruhr-Universit¨at Bochum Universit¨at Leipzig Lehrstuhl f¨ur Phys. Chemie II Institut f¨ur Experimentelle Physik I Universit¨atsstr. 150 Linn´estr. 5 44780 Bochum 04103 Leipzig Germany Germany Hermann.Weingaertner [email protected] @ruhr-uni-bochum.de

Prof. Teh Yu Tan Dr. Thomas Wichmann Duke University Weilerswisterstr. 6 Department of Mechanical Engineer- 50968 K¨oln ing & Materials Science Germany List of Contributors 953

Dr. Dirk Wilmer Dr. Karl Ullrich W¨urz Westf¨alische Wilhelms-Universit¨at PBS Softwareberatung M¨unster Schwanheimer Str. 144a Institut f¨ur Physikalische Chemie 64625 Bensheim Corrensstraße 30/36 Germany 48149 M¨unster Germany [email protected] Index

acoustic microscopy 466 β-NMR activation energy 19, 344, 813 method 380–384 activation enthalpy 18 relaxation 370, 383, 384, 403, 407, activation volume 19, 40, 268 409 adsorbate-adsorbate interactions 288 spectrometer 383 Ag/Ag(111) 320 β-radiation asymmetry 383 0.5Ag2S·0.5GeS2 877 β-relaxation 520 0.3Ag2SO4·0.7AgPO3 884 β-titanium 77 alloys B2 structure 71, 72, 76, 78 binary 49, 53 backbone of percolation cluster 900 ordered 78 BaF2 394 aluminium 39, 77 ballistic diffusion 867 amino acid 729 binary intermetallics 42 amorphous alloys 259 binary non-electrolyte mixtures 573 anomalous diffusion 417–421, 428, blocking factor 104, 150 434, 441, 448, 479, 488, 731, 797, Bloembergen-Purcell-Pound (BPP) 803, 806, 867, 904 behaviour 369, 819 anticorrelation in anomalous diffusion body-centered cubic metals 34 801 Boltzmann-Matano method 49, 294, antiphase boundaries 77 498 antistructure defects 71, 72, 78 bond percolation 901 antistructure-bridge mechanism 46, Boson peak 520 81 Bragg equation 108 Arrhenius law 18, 289, 746, 753, 813, Brillouin lines 581, 604 925 Brownian dynamics simulation method association degree 220 687 asymmetric double well potential Brownian motion 472, 632, 717, 794 (ADWP) model 836, 866, 888 Auger electron spectroscopy (AES) CaF2 391 14 caloric glass transition temperature autocorrelation function 817, 920, see 255 also correlation function capacitance 907 electric field 625 capillary electrophoresis 738 light intensity 625 cation sublattice 209 orientation 636 central limit theorem 420, 423, 625, average 799 ensemble 919, 923 charge diffusion coefficient 126, 127, time 923 148 956 Index charge of transport 222, 238 correlation length 897 chemical diffusion 6, 49, 556 correlation technique 582–587 chemical diffusion coefficient 231 correlation time 369, 586, 832 chemical potential 8, 226, 291, 918, correlator 594 941 Coulomb interaction 215, 819, 830 Chudley-Elliott model 69, 71, 102, Coulomb lattice gas 820, 840 130, 149, 150 Coulomb trap 835 cobalt oxide 217 counterion model 835, 866 CoGa 82 coupled diffusion in B2 intermetallics coherent diffuse scattering 153 44 coherent quasielastic scattering 149 coupling concept 866 coherent scattering function 102, 150 coverage 290 collective diffusion 495, 641, 648, 747, critical fluctuation 295 772 fluctuation 290, 293 coefficient of 289, 646, 771, 778 step 299 colloidal rods 666 Co-Zr glasses 268 colloidal spheres 676 critical concentration 896, 901, 902 colloidal systems 619 critical dimension 808 collective diffusion 641 critical exponent 897, 905 interdiffusion 651 critical percolation path 832 rotational diffusion 658 critical slowing down 600, 650, 703 self-diffusion 637 critical-path approach 763 component diffusion coefficient 10 cross coefficients 236 compressibility, isentropic 607 crossover time 905 computer simulations see simulations Cu3Au rule 47 concept of mismatch and relaxation current density autocorrelation function (CMR) 867, 874 864 conductivity

electrical 219, 905, 906 D03 structure 84 frequency dependence 768, 861 Darken equation 51, 296, 433, 557, thermal 597 562, 573, 941 conductivity spectroscopy 861 Darken-Manning relation 52 continuity equation 5 Darwin width 110 continuous time random walk model dc conductivity plateau 862 824 de Broglie wavelength 99, 919 continuum percolation 902 Debye length 720 copper 77 Debye-H¨uckel-Onsager-Falkenhagen correlated jumps 118, 124, 127, 858 effect 859 correlation effects 127 Debye-Waller factor 67, 70, 74, 99, correlation factor 19, 222, 773, 816, 113, 119, 138 848 defect chemistry 210 correlation function 369, 515, 525, defect cluster 226 527, 582, 915, 916, 919–921, 923 defect structure 210, 215 long-time tail 633 demixing 234, 236, 240, 703 of coverage 291 density distribution 931 of current density 864 detailed balance 71, 767, 786 Van Hove 66, 96, 98, 921, 935, 937 dichalcogenides 386 velocity auto- 928, 930 dielectric loss 835, 863 Index 957 differential effective-medium theory mutual 556, 569, 600 849 normal 417–420, 426, 435, 450, 479, diffusant 6 555, 777, 798, 799 diffuse scattering 76 on percolation clusters 904 diffuser 6 oxidation-enhanced 174 diffusion oxidation-retarded 174 ambipolar 227 222, 223 anomalous 417–421, 428, 434, 441, pressure dependence 18 448, 479, 488, 731, 797, 803, 867 proton diffusion 131 cation 217, 224 reactive 54 chemical 226 rotational 477, 491, 635 collective 495, 641 single-file diffusion 434–437, 775 continuous jump 371 solute diffusion 35 correlated diffusion anisotropy solvent diffusion 35 431–432 surface diffusion 285, 302, 339 effective diffusivity 428 through membranes 500 experimental methods 10 transport diffusion 432–434, 943 field-assisted 717 diffusion coefficient 904, 921, 929, 931, in aluminium 39 941 in amorphous alloys 262 chemical 6, 8, 151, 227, 244 in B2 intermetallics 44, 78 collective 289, 646, 780 in bcc metals 35 distinct-diffusion 570, 571 in D03 intermetallics 84 foreign atom 8 in fcc metals 33 frequency dependence 762 in arsenide 184 impurity 8 in 183 in grain boundaries 338 in L12 intermetallics 49 interdiffusion 654 in lead 41 self-diffusion 7 in liquids 251 Stokes-Einstein 630 in membranes 471 thermodynamic 561 in nickel 31 tracer 7, 219, 286, 478 in niobium 28, 29 transport 941 in polymers 447, 519, 531, 675, 733, vacancy 231 843 diffusion coefficient tensor 4, 439, 676 in regular pore networks 427 diffusion entropy 18 in semiconductors 165 diffusion equation 5, 289, 494, 632, in silicon 166 752, 798, 928, see also Fick’s in silver 38 second law in zeolites 427, 925 error function solution 6 interstitial-substitutional 168 source solution 230 intracrystalline self-diffusion 429, thin-film solution 5 430, 445 diffusion length 5, 479 isotope effects 13, 30, 253, 265, 272 diffusion mechanisms 23 lateral 477, 493 diffusion-limited reaction 806–808 long-range 133 diffusional line broadening 70, 72, 94 low-dimensional 371 diffusivity 4 molecular mechanism 132 effective 41, 170, 348, 420, 429, 453 multicomponent 427 thermal 597 958 Index diffusivity tensor 4, 439, 676 electro-osmosis 726, 737 direct current NMR (DCNMR) 718, electrochemical potential 226 725 electrokinetic potential 720 disorder models 753, 820 electrolyte solution 566, 574 disordered solids electron hole 211, 212 homogeneously 402 electron microprobe analysis (EMPA) inhomogeneously 367, 390 14 disordered systems 372, 746, 753, 813, electrophoresis 718 857, 895 electrophoretic NMR (ENMR) 717 dispersive transport 822 elementary diffusion step 65, 66, 68 dissociative mechanism 26 encounter model 124, 128, 370 distribution of site energies 257 energy resolution 98 divacancy mechanism 25 ensemble dopant diffusion 172, 235 canonical 917 Doppler drive 111 microcanonical 917 double differential scattering cross- entanglements 513, 531, 543 section 95 enthalpy of migration 22 drift flux 230, 232, 236 entropic forces 529 drift velocity 237, 717–720 entropy of migration 22 dynamic conductivity 817 equivalent circuit model 906 dynamic light scattering (DLS) 579, error function solution 6 589–597, 624 escape rate 121 coherence 593 eucryptite 405 dynamic percolation 846 excess charge 210, 228, 231 dynamic rotational disorder 153 excess volume 269 dynamic structure factor 94, 521–526, exchange mechanism 531, 538, 545, 568, 626, see also interstitial-substitutional 26 scattering function ring 127 distinct 628 self- 628 face-centered cubic metals 32 dynamic structure model 840 fast solute diffusion 40 FeAl 78 effective activation energy 273 Fe3Al 80 effective charge 236, 239 Fermi level effect 172 effective diffusivity 41, 170, 348, 420, Fe3Si 84 429, 453 Fick’s first law 4, 494, 559, 798 effective-medium approximation 746, non-local 643 758, 762, 912 Fick’s second law 5, 6, 165, 494, 752 self-consistency condition 761, 787 field-assisted diffusion 717 Einstein diffusion coefficient 8 Fisher model 337, 338 Einstein relation 227, 420, 434, 555, five-frequency model 36, 233 717, 903, 920 fixed-window method 113 Einstein-Debye relation 635 fluctuation-dissipation relation 632 Einstein-Smoluchowski relation 19, fluorescence correlation spectroscopy see also Einstein relation (FCS) 669 elastic incoherent structure factor fluorescence recovery after photo- (EISF) 98, 119, 138, 139, 141 bleaching (FRAP) 481, 497, electric potential 226, 236 661 electric potential gradient 228 forced Rayleigh scattering 613 Index 959

Fourier time window 100, 106 Green-Kubo relation 495, 568, 638, fractal 793 920 chemical kinetics 806 Grotthuß mechanism 131 fractal dimension 446, 793, 897, 898, growth constant 54 904 gyromagnetic ratio see magnetogyric fractional Brownian motion 794 ratio fragile glass 254 fragile supercooled melt 880 Harrison’s classification 348 Frank-Turnbull mechanism 26, 168 Hart’s formula 349 free induction decay (FID) 376, 400 Hartley-Crank relation 557 free-volume model 253, 486 Hausdorff dimension 793 Frenkel Haven ratio 127, 137, 148, 817, 865 defects 211 Henry isotherm (of grain boundary equilibrium 210, 212 segregation) 358 heterodyne technique 587 Γ -space 918 homodyne technique 587 generalized force 919 hopping rate see jump rate Gibbs free energy of activation 19 H/Si(111) 308 Gibbs free energy of binding 24 Huang scattering 119, 153, 155 Gibbs free energy of migration 22 hybrid solutes 41 glass hydrodynamic function 678 electrolyte 403 hydrodynamic interaction 637, 659 ion-conducting 402, 819 hydrogen bond 131 metallic 259 hydrogen diffusion 29, 115 oxide 403, 405, 884 glass transition 255, 272, 519, 638 immobile (trapped) state 121 Gorski effect 16 impedance spectroscopy 861 grain boundary 337 impurity diffusion diffusion coefficient 338 in grain boundaries 339 in nanocrystalline materials 352, in metals 35, 77 390, 391 in oxides 216 large-angle 345, 346 in semiconductors 168, 172, 177, segregation 339, 353, 357, 361 182, 183, 196 segregation energy 353 impurity diffusion coefficient 8 segregation factor 339, 353 impurity-vacancy binding 219 small-angle 345, 346 impurity-vacancy pair 233, 239 width 338, 343, 911 incoherent scattering function 97–99, grain boundary diffusion 337 102, 133, 141, 154, 818 activation energy 344 incoherent structure factor see anisotropy 345 incoherent scattering function Arrhenius law 344 infinite percolation cluster 896 atomistic mechanisms 347, 362 intercalation 367 comparison with bulk, surface, liquid intercalation compounds 384 344 graphite 384 empirical rules 344 titanium disulfide 386 in intermetallic compounds 361 interdiffusion 6, 49, 187, 263, 556, 651, in moving boundaries 362 654 kinetic regimes 347 interdiffusion coefficient 6, 8, 191, 654 orientation dependence 346 interfacial region 50, 352, 367, 390 960 Index

diffusion in 392, 908 Lamb-M¨oßbauer factor 67 intermediate dynamic structure factor Landau-Placzek ratio 582, 606 521 Langevin equation 530, 632 intermediate scattering function 73, Langmuir-Hinshelwood reaction 808 95, 100, 523, 818, 828 lanthanum gallate 216, 225, 235 internal interfaces 360, 367 Laplace transformation 644, 760 density of 367 Larmor condition 421 interstitial cation 213, 217 Larmor precession 74, 516 interstitial diffusion 27, 242, 745 Larmor precession frequency 369, 814 interstitial impurities 165 layer-crystalline materials 367 interstitial mechanism 23 LiC6,LiC12 384 interstitial-substitutional exchange LiCl·4D2O 403 mechanism 26 LiCl·7H2O 881 interstitialcy mechanism 25 line broadening in M¨oßbauer spec- intrinsic diffusion coefficient 10 troscopy 68 inversion-recovery experiment 378 line broadening in neutron scattering ion-conducting glasses 402, 819, 861 68, 94 ion-conducting materials 861 line narrowing in neutron scattering ion-conducting polymers 843 104, 151 ionic conductivity 126, 224, 817, 861, line narrowing in nuclear magnetic 908 resonance 374 ionic mobility 717, 729, 737 linear response theory 150, 567, 858, ionic self-diffusion coefficient 717, 729 919 · irreversible processes 564, 919 0.3Li2O 0.7B2O3 884 isotope effects 13, 30, 253, 265, 272 lipid 473 lipid bilayer 475 lithium 370 Jonscher power law 863, see also lithium aluminosilicates 405 universal dielectric response lithium intercalation compounds 384 jump length 7, 20, 105, 866, 903 lithium ion conductors 390 jump rate 19–23, 65, 70–73, 124, 233, lithium niobate 394 373, 763, 866 lithium oxide 399 jump relaxation 823, 866 lithium titanium disulfide 386 jump vector 20, 65, 67, 68, 102, 140 local reptation model 538 localized motion 106, 134, 405, 528, kick-out mechanism 26, 168 887 kink atoms 286 Longini mechanism 26, 193 Kirkendall effect 10, 51 low energy electron diffraction (LEED) opposite 263 304 Kirkwood-Buff theory 575 low energy electron microscopy (LEEM) K2O·2BaO·4SiO2 885 305 Kohlrausch behavior 255, 521, 866 Kohlrausch-Williams-Watts (KWW) macroscopic diffusion methods 11–15, behavior see Kohlrausch 65, 368 behavior magnetic field gradient 421, 720 Kr¨oger-Vink magnetic relaxation methods 16 diagram 214 magnetite 217, 231 notation 210 magnetogyric ratio 369, 375, 517, 720 Kubo formula 817, 941 majority defect 213 Index 961

Mandelbrot dimension 793 M¨oßbauer spectroscopy 65–68 Markovian process 70, 749, 802, 804 motional narrowing of NMR lines mass action law 25, 40, 211, 807 374, 393, 395 master curves of ionic conductivity moving grain boundary 362 863 multifractal 797 master equation 102, 748, 772 multiphase diffusion 53 McLean’s isotherm 358 multiple scattering 115, 135, 528 mean residence time 7, 17, 21, 68, muon 30 70–72, 80, 127, 322, 369, 816 muon spin resonance (µSR) 31 mean square displacement 20, 252, mutual diffusion 556, 569, 600 286, 418–449, 478, 516, 531, 555, 629, 751–777, 799, 816, 826, 868, nanocrystalline BaF2 394 903, 929 nanocrystalline CaF2 391 long time tail 761 nanocrystalline composites 399, 908 mean-field theory 808 nanocrystalline LiNbO3 394 mechanical relaxation methods 16 nanocrystalline LiTiS2 397 mechanical sectioning technique 11 nanocrystalline materials 352, 367, membrane 441, 471, 733 390 biological 145, 473 Na3PO4 154 nearly constant loss (NCL) behaviour lateral diffusion 477 814, 835, 863, 888 polypropylene 441 Nernst field 227 transverse diffusion 500 Nernst-Einstein equation 126, 131, memory effect 117, 127, 632, 643 817, 865, 880, 904 mesoporous materials 437–439 neutron backscattering (BSC) MCM-41 438 spectrometer 106, 109, 111 metallic glasses 264 neutron capture 382 metalorganic chemical vapor deposition neutron scattering 65, 68, 93, 514, 817 (MOCVD) 187 neutron spin-echo (NSE) spectrometer Meyer-Neldel compensation rule 835 519, 520 micelles 736 neutron spin-echo (NSE) spectroscopy microemulsion 737 74, 516, 518 microporous materials 427, 925 neutron time-of-flight (TOF) spectrom- microscopic diffusion methods 15–17, eter 106, 114 65, 368 NiGa 82 minority defect 212, 213 Ni3Sb 86 mismatch relaxation 866 NMR 368, 417, 717 mixed alkali effect 840 correlation function 369, 818 mixed conductor 216 correlation time 369, 373, 830 mobility of ions 717, 729, 737 flow measurements 720 mode coupling theory 256, 275, 691 linewidth 373 molecular beam epitaxy (MBE) 187 PFG diffraction pattern 424–425 molecular dynamics simulations 118, PFG effective observation time 426 480, 534, 916, 922–925 PFG observation time 418, 421, molecular traffic control 437 426, 427, 449, 455 molten salt mixtures 566 pulsed field gradient (PFG) technique Monte Carlo simulations 325, 491, 417, 421–427 759, 815, 821, 830, 836, 840, 909, relaxation 369, 426, 814 917, 922 relaxation techniques 375–380 962 Index

spectral density 369, 409, 818 site 895 spectrometer 379 percolation cluster 897 spin echo 378, 379, 421, 721 conductivity of 905 spin-alignment echo technique 390 diffusion on 904 spin-echo attenuation 422, 424, 426, percolation model 755, 820, 895 440, 452 percolation threshold 896 spin-locking experiment 378 permeation 500 static field gradient (SFG) technique perovskite structure 225 427 petalite 405 non-Arrhenius behaviour 767, 832 phenomenological coefficient see non-stoichiometric oxide 210, 219 Onsager transport coefficient normal diffusion 417–420, 426, 435, phonon dispersion 125 450, 479, 555, 777, 798, 799 phonon spectroscopy 77 nuclear photon correlation spectroscopy 579 magnetization 375, 421 plasma parameter 822 methods in diffusion 16, 65, 368 Poisson process 803 polarization 380, 404 polarized neutron capture 382 reactions for polarized β-emitters polybutadiene 519, 528 381 polydimethylsiloxane (PDMS) 440, spin-lattice relaxation 369 443, 453, 531 nuclear magnetic relaxation see NMR polyethylene oxide (PEO) 451, 843 relaxation polyethylethylene (PEE) 453 nuclear magnetic resonance see NMR polyisobutylene 528 nuclear reaction analysis (NRA) 15 polyisoprene 528 nuclear resonance scattering (NRS) polymer 65 blends 697 diblock copolymer 453 Onsager reciprocity relation 566, 919 electrolytes 843 Onsager regression hypothesis 579 reptation 449, 450 Onsager transport coefficient 226, 566 O/Si(111) 307 triblock copolymer 450, 451 O/W(110) 295 polymeric systems 619 oxygen activity 209 polypropylene membrane 441 oxygen deficit 211 polypropylene oxide (PPO) 451 oxygen excess 211 polystyrene (PS) 440 oxygen ion conductor 216 polyvinylether 528 oxygen partial pressure 209 potential 922, 927 oxygen potential gradient 228 chemical 226 oxygen sublattice 209 electric 226, 236 electrochemical 226 paddle-wheel mechanism 153 Lennard-Jones 923, 927, 932 pair correlation function 251, 575 square well 922 particle distribution function 917 pre-exponential factor 18 partition function 915, 919 pressure dependence of diffusion 268 Pb/Si(111) 313 principal diffusivities 4 percolation propagator 419, 420, 422, 424, 429, bond 901 435, 798, 802, 928 continuum 902 mean 422–424, 935 interface 908 proton conduction 139 Index 963 proton pump 146 residence time see mean residence proton tunneling 123 time protonic conductor 131 residual activity method 217 pseudo Fermi level 782 rotational diffusion 138, 491, 635, 658 pulsed field gradient (PFG) NMR Rouse model 514, 529–536, 844 417, 421–427, 720 generalized 538 rubber-like model 538 quantum diffusion 30 Rutherford backscattering spectrome- quasi-vacancies 261 try (RBS) 14 quasielastic coherent structure factor 154 scanning tunneling microscopy (STM) quasielastic helium scattering 293 306 quasielastic incoherent neutron scattering amplitude 622 scattering (QINS) 136 scattering cross section 95 quasielastic incoherent structure factor scattering function 94, 149, 523, 921 141, 154 scattering length 95, 101 quasielastic light scattering 620 scattering strength 621 quasielastic linewidth 103, 105, 124, scattering vector 93 151 Schottky quasielastic M¨oßbauer spectroscopy defects 211 67, 68 equilibrium 210, 224 quasielastic methods 65, 66, 68, 73 secondary ion mass spectrometry quasielastic neutron scattering (QENS) (SIMS) 13, 222 67, 68, 93 sedimentation 647 observation function 100, 105 sediments 446–447 observation time 100, 105, 133 segregation 234 observation volume 105 self-affine fractal 797 resolution function 105 self-correlation function 66–76, 97, 102, 419 radiotracer sectioning method 217, self-diffusion 31, 121, 127, 136, 144, 340, see also tracer method 152, 370, 555, 557, 637, 943 random barrier model 753, 867 self-diffusion coefficient 7, 120, 128, random phase approximation 699 135, 147, 152, 216, 227, 659 random trap model 754 self-interstitial charge state 166 random walk 747, 802, 806, 858, 865, self-similarity 795, 897 903 short-range order 260 randomly blocked sites 755, 765 Siegert relation 584, 626 Rayleigh line 581 Sierpinski fractal 794 RbAg4I5 878, 890 silicon self-diffusion 166 reaction constant 806 simulations reaction rate 120, 143 molecular dynamics (MD) 925, 941 reactive diffusion 54 Monte Carlo (MC) 815, 821, 915, reflection high energy electron 922 diffraction (RHEED) 324 Sinai model 746, 769 renewal theory 847 single-file diffusion 434–437, 775 reptation site energy crossover 543 disorder 747 diffusion 537 exponential distribution 766, 781 model 514, 537–540, 543 site exclusion model 771 964 Index site occupancy 104, 150 stretched polymers 849 site percolation 895 structural relaxation 260 six-jump cycle mechanism 46, 81 structure factor 153, 298, 919 Smoluchowski equation 675 dynamic 521–526, 921, 937 Smoluchowski theory 807 partial 652 Snoek effect 16 static 918, 921 soft phonon modes 77, 86 subdiffusive behaviour 417, 421, 801, solid rotator phase 156 867 solid-state protonic conductor 131 substitutional impurities 165 solute diffusion 35 Summerfield scaling 863, 866 solute-vacancy pair 215, 220 superlattice disordering 187 solvent diffusion 35 surface diffusion 285, 339 Soret effect 606 equilibrium measurements 297 sound attenuation 604 non-equilibrium measurements 313 sound velocity 461, 604 step 302 specific surface area 446 terrace 302 spectral density 921 surface exchange coefficient 222 spin diffusion 382, 400, 403 surface light scattering 608 spin echo surface tension 608 surface-to-volume ratio 444–447 neutron 74, 516 synchrotron radiation 65, 73 NMR 378, 379, 421, 721 spin incoherent scattering 115 thermal conductivity 597 spin-lattice relaxation 369, 818 thermal diffusivity 597 disorder effects 372 thermal grating 613 frequency dependence 372, 386, thermodynamic factor 10, 227, 243, 387, 398, 407 562 homogeneous 404 time correlation function 567, 920, see inhomogeneous 404 also correlation function laboratory frame 377, 409 time-dependent correlation factor 867 low-dimensionality effects 372 time-domain interferometry 76 rate 370 time-temperature superposition rotating frame 379, 409 principle 863, 866 spin-spin relaxation 378, 409 titanium 65, 77 spinel 217 titanium disulfide 386 spodumene 405, 406 topological distance 900 sputter sectioning technique 12 tortuosity 443, 454, 731 SrCl2 128 total scattering cross section 102 static field gradient (SFG) NMR 427 tracer diffusion 7, 230, 745, 771, 773, static structure factor 95, 150 816 stochastic process 800 tracer diffusion coefficient 7, 286 stoichiometric point 212, 216, 228 tracer method 11 Stokes-Einstein diffusion coefficient tracer self-diffusion coefficient 7 630 transference number 227, 719, 729 Stokes-Einstein equation 254, 601, transition rate 746, see also jump rate 660, 719 transition state theory 943 Stokesian dynamics simulation method transport coefficient 919–921, see also 689 Onsager transport coefficient strain field 119, 130, 153 transport diffusion 432–434, 556, 943 Index 965 traps 121 velocity cross-correlation coefficients saturation of 781 570 trapping rate 123 Verlet algorithm 924, 928 triple-defect mechanism 46, 81 vesicles 736 tunneling of protons 123 viscoelasticity 513 two-dimensional diffusion 130, 143, viscosity 601, 607, 608 145, 372, 386, 387 Vogel-Fulcher-Tammann (VFT) two-state model 121, 122, 752 equation 255, 520, 845, 882 volume diffusion 339 ultrasonic interferometer 462 ultrasonic wave velocity 462 Wagner formula 227 waiting time distribution 802, 825 universal dielectric response 814, 863 walk dimension 801, 804 universal dynamic response see water in gels 466 universal dielectric response water in living cells 466 Wiener process 794, 804 vacancy cation 212, 217 x-ray photon correlation spectroscopy charge state 166 (XPCS) 76 oxygen 211 vacancy availability factor 22 Zener effect 16 vacancy mechanism 23, 65, 124, 169, zeolite 426–437, 925, 926 232, 347 A-type 422, 427, 433 vacancy-pair mechanism 47 AlPO4-5 436 vacancy-wind corrections 52 LTA-type 926 Van Hove correlation function 66, 96, structure 926 98, 419, 689, 921, 935, 937 X-type 445 van Liempt rule 33 ZK4 926 vehicle mechanism 132, 148 ZSM-5 type 431 velocity autocorrelation function 858, zeta potential 720 865, 920 zirconia 216, 224, 235