Heitjans P., Karger J. (Eds.). Diffusion in Condensed Matter: Methods, Materials, Models
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Diffusion in Condensed Matter
Paul Heitjans · Jörg Kärger
Diffusion in
Condensed Matter
Methods, Materials, Models
With 448 Figures
ABC
Editors
Professor Dr. Paul Heitjans
Universität Hannover
Institut für Physikalische Chemie
und Elektrochemie
Callinstr. 3–3a
D-30167 Hannover, Germany
Email: heitjans@pci.uni-hannover.de
Professor Dr. Jörg Kärger
Universität Leipzig
Institut für Experimentelle Physik I
Linnéstr. 5
D-04103 Leipzig, Germany
Email: kaerger@physik.uni-leipzig.de
Library of Congress Control Number: 2005935206
ISBN -10 3-540-20043-6 Springer Berlin Heidelberg New York
ISBN -13 978-3-540-20043-7 Springer Berlin Heidelberg Ne w York
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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. As this process shows up in all states of matter over very large time and
length scales, the subject is still very general involving a large variety of nat-
ural sciences such as physics, chemistry, biology, geology and their interfacial
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
metallurgist W.C. Roberts-Austen (1896) and the physicist A. Einstein (1905).
Today, exactly 150 and 100 years after the seminal publications by Fick and
Einstein, respectively, the field is flourishing more than ever with about 10.000
scientific papers per year.
From the foregoing it is evident that a single volume book on atomic and
molecular diffusion has to be further restricted in its scope. As the title says,
the book is confined to diffusion in condensed matter systems, so diffusion
in gases is excluded. Furthermore, emphasis is on the fundamental aspects of
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 of the 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. This has been facilitated by the common classification scheme. Further
VIII Preface
help to the reader in this respect is provided by an extended common list of
contents, in addition to the contents overview, as well as an extensive subject
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,
M¨oßbauer 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,
nanocrystalline materials, micro- and mesoporous systems, inorganic glasses,
polymers and colloidal systems, biological membranes, fluids and liquid 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 theoretical descriptions by, e. g., correlation
functions, lattice models treated by (approximate) analytical methods, the
theory of fractals, percolation models, Monte Carlo simulations, molecular dy-
namics simulations, phenomenological approaches like the counterion model,
the dynamic structure model and the concept of mismatch and relaxation.
Despite the large variety of topics and themes the coverage of diffusion in
condensed matter is of course not complete and far from being encyclopedic.
Inevitably, it reflects to a certain extent also the editors’ main fields 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
research without intending to mimic the topicality of proceedings, which nor-
mally have a short expiry date. It is therefore designed as a textbook or refer-
Preface IX
ence work for graduate and 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
K¨arger, for their patience and encouragement.
Hannover, Germany Paul Heitjans
Leipzig, Germany J¨org K¨arger
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 G¨osele ....................................... 165
5DiffusioninOxides
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
9NMRandβ-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 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 ....................... 857