Diffusion Phenomena: Cases and Studies

325 Pages·2001·5.559 MB·English

by  Richard Ghez (auth.)

DIFFUSION
PHENOMENA
Cases and Studies
Reprinted by permission from ChasAddams.
DIFFUSION
PHENOMENA
Cases and Studies
Richard Ghez
Springer Science+Business Media, LLC
LibraryofCongressCaraloging-in-Publication Data
Ghez,Richard.
Diffusionphenomena:casesandstudieslRichard Ghez.-[2nded.].
p. cm.
Rev.ed.of:Aprimerofdiffusionproblems. 1988.
Includesbibliographicalreferencesandindex.
1. Diffusionprocesses-Mathematicalmodels. 2. Differentialequations,Partial. I.
Ghez,Richard.Primerofdiffusionproblems. H. Tide.
QA274.75.G482001
515'.353-dc21
2001016498
ISBN978-1-4419-3355-3 ISBN978-1-4757-3361-7(eBook)
DOI10.1007/978-1-4757-3361-7
©2001SpringerScience+BusinessMediaNew York
OriginallypublishedbyKluwerAcademic/PlenumPublishers,New Yorkin200I.
Softcoverreprintofthehardcover Istedition200I
http://www.wkap.nl/
10987654321
AC.I.P.recordforthisbookisavailablefrom theLibrary ofCongress
Allrightsreserved
Nopartofthisbookmaybereproduced,storedinaretrieval system,ortransmitted inany
formorbyanymeans,electronic,mechanical, photocopying, microfilming, recording,or
otherwise,withoutwrittenpermissionfromthePublisher
A Margalit qui,
tout en ne sachant pas laMathematique,
ne cesse de croquer la Pomme.
Preface
This book is a second edition of the one that was published by John
Wiley & Sons in 1988. It carries a new title because the former one, A
Primer of Diffusion Problems, gave the impression of consisting merely
of a set of problems relating to diffusion. Nonetheless, my intention
was clearly spelled out and it remains the same, namely, to teach basic
aspects and methods of solution for diffusion phenomena through
physical examples. Again, I emphasize that the coverage is not
encyclopedic. There exist already several outstanding works of that
nature, for example, J. Philibert's Atom Movements, Diffusion and Mass
Transport in Solids. My emphasis is on modeling and methodology.
This book should thus constitute a consistent introduction to diffusion
phenomena, whatever their origin or further application.
This edition has been largely revised. It contains a completely new
chapter and three new appendices. I have added several new exercises
stemming from my experience in teaching this material over the last
15 years. I hope that they will be instructive to the reader for they were
not chosen perfunctorily. Although they are the bane of authors and
of readers, I have retained footnotes if they might help the reader's
comprehension. Additional, but nonessential material is collected at
the end of chapters, and is indicated in the text by superscripts.
A few words are in order to explain why I have added a new
chapter, the sixth, on surface rate limitations. By its very nature,
diffusion is multidisciplinary; it is also multidimensional. All real
physical systems have boundaries, and these are always dominant
when the system is "small." I had long felt that an introduction to the
influence of boundaries-beyond abstract mathematical statements
vii
viii Preface
for the resolution of specific problems-was lacking in most texts on
diffusion theory. I can but hope that this additional chapter will help
the reader in this regard.
It was my pleasure to have worked with Evelyn Grossberg, editor
for Kluwer Academic/Plenum Publishers, whose editorial remarks I
gladly accepted.
Jerusalem
April 2001
Preface to the First Edition
Most kinetic processes in ponderable media require the redistribution
of mass, energy, momentum, or charge over macroscopic distances.
This redistribution occurs through a random process called diffusion,
and its macroscopic description rests on a particular differential
equation called the diffusion equation. Because this equation is to
ponderable media what the wave equation is to vacuum, it is no
wonder that its solutions should be relevant to widely different
problems: from the heat treatment of alloys to the motion of pro
teins in growing axon membranes; from the dynamics of galactic
structures to the multitude of device-processing steps. Consequently,
the literature Gn diffusion contains at least four different points of
view: as a mathematical topic in partial differential equations, as a
physicochemical topic in nonequilibrium thermodynamics, as an
engineering topic in materials science, and as a topic in stochastic
processes. It would be presumptuous to claim familiarity with all
these areas and to suggest, here, an equal coverage. And yet, they all
derive from the same basic principle, namely, that something or
other is conserved or can be balanced. Conservation is not so much
an expression of longevity - as in "this person is well preserved"
but rather it expresses our ability to distinguish and to reckon.
Nowhere, to my knowledge, is this point of view better illustrated
than in the frontispiece, and I am deeply indebted to Mr. Chas
Addams for his permission to reproduce an example of his always
penetrating wit.
In spite of this formal unity of diffusion problems, it is my
experience that many scientists and engineers remain baffled by the
ix
x Preface to the First Edition
diffusion equation and by its solution in practical cases. Alternatively,
they are perhaps trapped between purely mathematical texts and
others that deal exclusively with diffusion mechanisms. This book
seeks to bridge the gap between physicochemical statements of certain
kinetic processes and their reduction to diffusion problems. It also
attempts to introduce the reader to the many lines of attack, both
analytic and numerical, on the diffusion equation. I have chosen to
teach through physically significant examples taken mainly from my
experience in the areas of metallurgy and semiconductor technology.
The theory is interwoven, I hope, with sufficient rigor so that the tools
that evolve do not immediately crumble with use. Nevertheless, I have
chosen to write an introductory text, whose only prerequisites are a
serious year of calculus, through ordinary differential equations, one
semester of thermodynamics, and, if the reader be uneasy with alge
braic manipulations, that the fear of calculating be controllable.
As its title implies, this is largely a book about solving the
diffusion equation. I also wanted a short and lively text. Consequently,
unless they provide particular insight, intermediate steps of specific
calculations are often only verbally (though completely) expressed. In
other words, the beginner would be well advised to arm himself with
pad and pencil. Exercises, not so numerous as to paralyze the reader,
are sprinkled throughout the text. They are designed either to empha
size a point that has just been made or to suggest some further
clarification or extension of that point. These exercises are an integral
part of the text, and (a word of encouragement) none is so difficult as
to constitute a doctoral thesis.
The text consists of seven chapters and three appendices. These
appendices contain more advanced material, whose inclusion within
chapters would have detracted from the general flow. References, cited
in the text are listed at the end of each chapter, and, in general,
equations are numbered decimally within each chapter. I have some
times labeled equations with an additional Latin letter when they are
closely related. It can happen, therefore, that "well ordering" is not
everywhere preserved.
I might be faulted on at least one count. My choice of topics is
definitely biased, and each specialist will surely be disappointed to find
that his particular area of expertise was not covered. This is unavoid
able in so short a text, and I will simply observe that presentations of
methodology and techniques are useful even though they fail as
encyclopedias.