Diffusion in condensed matter methods materials models

971 Pages·2005·17.68 MB·english

by  Paul Heitjans

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:[e-mail]
Email:[e-mail]
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