DiffusioninCondensed Matter · Paul Heitjans Jörg Kärger Diffusion in Condensed Matter Methods, Materials, Models With448 Figures ABC Editors ProfessorDr.PaulHeitjans ProfessorDr.JörgKärger UniversitätHannover UniversitätLeipzig InstitutfürPhysikalischeChemie InstitutfürExperimentellePhysikI undElektrochemie Linnéstr.5 Callinstr.3–3a D-04103Leipzig,Germany D-30167Hannover,Germany Email:[email protected] Email:[email protected] LibraryofCongressControlNumber:2005935206 ISBN-10 3-540-20043-6 SpringerBerlinHeidelbergNewYork ISBN-13 978-3-540-20043-7 SpringerBerlinHeidelbergNewYork Thisworkissubjecttocopyright. Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliableforprosecutionundertheGermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia springeronline.com (cid:1)c Springer-VerlagBerlinHeidelberg2005 PrintedinTheNetherlands Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws andregulationsandthereforefreeforgeneraluse. Typesetting:bytheauthorsandS.IndrisusingaSpringerLATEXmacropackage Coverdesign:Coverdesign:design&productionGmbH,Heidelberg Printedonacid-freepaper SPIN:10816487 56/3141/jl 543210 To Maria and Birge Preface Diffusion as the process of migration and mixing due to irregular movement of particles is one of the basic and ubiquitous phenomena in nature as well as in society. In the latter case the word “particles” may stand for men or ideas, and in the former for atoms or galaxies. In this sense diffusion is a truly universal and transdisciplinary topic. The present book is confined, of course, to diffusion of atoms and mole- cules.Asthisprocessshowsupinallstatesofmatteroververylargetimeand lengthscales,the subjectis stillverygeneralinvolvinga largevarietyofnat- uralsciencessuchasphysics,chemistry,biology,geologyandtheirinterfacial disciplines. Besides its scientific interest, diffusion is of enormous practical relevance for industry and life, ranging from steel making to oxide/carbon dioxide exchange in the human lung. It therefore comes as no surprise that the early history of the subject is marked by scientists from diverse communities, e.g., the botanist R.Brown (1828), the chemist T.Graham (1833), the physiologist A.Fick (1855), the metallurgistW.C.Roberts-Austen(1896)andthephysicistA.Einstein(1905). Today, exactly 150 and 100 years after the seminal publications by Fick and Einstein,respectively,thefieldisflourishingmorethaneverwithabout10.000 scientific papers per year. Fromthe foregoingitis evidentthat a singlevolume book onatomic and moleculardiffusionhas tobe further restrictedinits scope.As the title says, the book is confined to diffusion in condensed matter systems, so diffusion ingasesisexcluded.Furthermore,emphasisisonthe fundamentalaspectsof the experimental observations and theoretical descriptions, whereas practi- cal considerations and technical applications have largely been omitted. The contents are roughly characterized by the headings Solids, Interfaces, Liq- uids, andTheoretical Concepts and Models ofthe four parts under which the chapters have been grouped. The book consists of 23 chapters written by leading researchers in their respective fields. Although each chapter is independent and self-contained (using its own notation, listed at the end of the chapter), the editors have taken the liberty of adding many cross-references to other chapters and sec- tions.Thishasbeenfacilitatedbythecommonclassificationscheme.Further VIII Preface help to the reader in this respect is provided by an extended common list of contents,inadditiontothecontentsoverview,aswellasanextensivesubject index. The book is a greatly enlarged(more than twice) and completely revised edition of a volume first published with Vieweg in 1998. Although the first edition was very well received (and considered as a “must for students and workers in the field”), it was felt that, in addition to the broad coverage of modern methods, materials should also be discussed in greater detail in the new edition. The same applies to theoretical concepts and models. This, in fact, is represented by the new subtitle Methods, Materials, Models of Diffusion in Condensed Matter. The experimental Methods include radiotracer and mass spectrometry, Mo¨ßbauer spectroscopy and nuclear resonant scattering of synchrotron ra- diation, quasielastic neutron scattering and neutron spin-echo spectroscopy, dynamic light scattering and fluorescence techniques, diffraction and scan- ning tunneling microscopy in surface diffusion, spin relaxation spectroscopy by nuclear magnetic resonance (NMR) and beta-radiation detected NMR, NMR in a magnetic field gradient, NMR in the presence of an electric field, impedance spectroscopy and other techniques for measuring frequency de- pendent conductivities. Materials now dealt with are, among others, metals and alloys, metallic glasses, semiconductors, oxides, proton-, lithium- and other ion-conductors, nanocrystallinematerials,micro-andmesoporoussystems,inorganicglasses, polymers andcolloidalsystems,biologicalmembranes,fluids andliquid mix- tures. The span from simple monoatomic crystals, with defects in thermal equilibrium enabling elementary jumps, to highly complex systems, exem- plarily represented by a biomembrane (cf. Fig.12.3), is also indicated on the book cover. Models in the subtitle stands for theoreticaldescriptions by, e.g., correlation functions, lattice models treated by (approximate) analytical methods, the theoryoffractals,percolationmodels,MonteCarlosimulations,moleculardy- namics simulations,phenomenologicalapproacheslike the counterionmodel, the dynamic structure model and the concept of mismatch and relaxation. Despite the largevarietyoftopics andthemes the coverageofdiffusionin condensedmatter is of coursenotcomplete andfar frombeing encyclopedic. Inevitably,it reflects to a certainextentalsothe editors’mainfields of inter- est. Nevertheless the chapters are believed to present a balanced selection. The book tries to bridge the transition from the advanced undergradu- ate to the postgraduate and active research stage. Accordingly, the various chapters are in parts tutorial, but they also lead to the forefront of current researchwithoutintendingtomimicthetopicalityofproceedings,whichnor- mallyhaveashortexpirydate.Itisthereforedesignedasatextbookorrefer- Preface IX ence work for graduateand undergraduate students as well as a source book for active researchers. The invaluable technical help of Dr. Sylvio Indris (University of Han- nover)in the laborious editing of the chapters,which in some cases included extensive revision, is highly acknowledged. We also thank Jacqueline Lenz and Dr. T.Schneider from Springer-Verlag for accompanying this project. As ever, the editors have to thank their wives, Maria Heitjans and Birge Ka¨rger,for their patience and encouragement. Hannover, Germany Paul Heitjans Leipzig, Germany J¨org Ka¨rger August 2005 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 Go¨sele....................................... 165 5 Diffusion in Oxides Manfred Martin................................................. 209 6 Diffusion in Metallic Glasses and Supercooled Melts Franz Faupel, Klaus Ra¨tzke....................................... 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 Interface- Dominated and Disordered Solids Paul Heitjans, Andreas Schirmer, Sylvio Indris ..................... 367 XII Contents– Overview 10 PFG NMR Studies of Anomalous Diffusion J¨org Ka¨rger, Frank Stallmach..................................... 417 11 Diffusion Measurements by Ultrasonics Roger Biel, Martin Schubert, Karl Ullrich Wu¨rz, 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. Schu¨tz, Thomas Wichmann ..................................................... 745 19 Diffusion on Fractals Uwe Renner, Gunter M. Schu¨tz, Gu¨nter 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 ....................... 857 Contents – 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......................................................... 955