Table Of ContentAtom movements
Diffusion
and mass transport
in solids
Jean PHILIBERT
Professor of Materials Science
Université de Paris-Sud
Panslated from the French by
Steven J. Rothman
Metallurgist, Argonne National Laboratory
PREFACE by
David Lazarus
University of Illinois
le3 éditions
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@ Les Éditions de Physique 1991
“To explain that which is visible but complicated
by that which is invisible but simple ...”
Jean Perrin,
in preface to Les Atomes (1912)
a
b
C
Diffusion of an a.datom on a. (11 0) surface of a fcc crystal by the, exchange
mechanism:
a) Adatom in initial position t = to
+
b) Saddle point position t = 20 6 x s
+
c) Final positmion t = to 10 x 10-l2 s
The figures show an “instantaneous” view of two atomic layers, viewed
along a direction that makes an angle of 20’ with the (110) plane ; each plane
contain six <110> strings of eight atoms.
The atom coordinates were calculated by a molecular dynamics simulation
using a Lennard-Jones potential with parameters corresponding to solid argon
at 0.4 T,. (see G. de Lorenzi el al., reference at end of Ch. VI.)
The author thanks Drs. Madeleine Meyer and Vassili Pontikis for prepar-
ing the figure.
Preface
As I write this preface, in January 1989, it is hard for me to believe that
a full 23 years have passed since the publication of “LA DIFFUSION DANS
LES SOLIDES’’ (Presses Universitaires de France, Paris, 1966). This glorious
two-volume work by Yves Adda and Jean Philibert was, until very recently,
the basic “bible” for all serious scientists working in the field of diffusion in
solids. In 1985 Professor Philibert published a condensed, updated version,
suitable as a textbook for advanced students of materials science or solid-
state physics : “DIFFUSION ET TRANSPORT DE MATIERE DANS LES
SOLIDES’ (Monographies de Physique, les Editions de Physique, Paris, 1985).
Unfortunately, the world includes fewer francophones than persons who
wish to, or should, enter into the serious study of the field of solid-state
diffusion- an area which is absolutely fundamental to understanding a virtual
cornucopia of important phenomena in materials science: nucleation, crystal
growth, sintering, hardening, alloying, phase transformations, oxidation, plas-
tic flow, fracture, photography ...... the list is almost endless. Thus, many not
raised with a sufficient knowledge of French, (including most of my own gradu-
ate students over two decades) have either had to learn enough French to wade
slowly and painfully through the Adda-Philibert “bible,” or, far worse, had no
access at all to this most important reference.
Finally, a miracle has occured : Dr. S. J. Rothman of Argonne National
Laboratory, not only a fluent francophone but also a scientist who himself has
made enormous contributions to the field of solid-state diffusion, has made an
English-language translation of Professor Philibert’s 1985 text, now entitled
“ATOM MOVEMENTS”. Moreover, the new edition has been updated in im-
portant ways and includes an extensive set of extremely practical homework
exercises to help the serious reader master the field in a professional manner.
This, if I may steal a line from Shakespeare, is ...a consummation devoutly to
“
be wished.”
The most wonderful aspects of the original Adda-Philibert “bible” are
faithfully preserved in Professor Philibert’s French-language 1985 book and
again in this English-language edition. This is a work of love by a scientist who
understands the field thoroughly and deeply, from its fundamental atomistic
aspects to the most practical of its “real-world’’ applications. The selection of
topics is superb, and the treatment of each subject is thorough and complete,
appropriate iii level for advanced undergraduate or graduate students, as well
as active research workers, who demand a thorough grounding in this vital
area.
Thus, through the joint efforts of Jean Philibert and Steve Rothman, we
finally have available “ATOM MOVEMENTS”, a superb basic text in English,
VI Atom movements
which should be “required reading” for serious students of diffusion throughout
the world. My one sadness is that it comes too late for my own graduate
students (I have now retired from active research), but then, I can always
console myself with the thought that by forcing them ta learn enough French
to read the “bible,” I also made it possible for them to enjoy much more fruitful
visits to France themselves in their post-student lives!
As a final and personal note, I want to express my own sincere thanks
to my old and dear friends and colleagues, Jean Philibert, who wrote the new
book, and Yves Adda, who joined with Jean in writing the original “bible,”
for all that they have done for the field of solid-state diffusion, in general, and
for me and my own research programs over the past decades. Their books,
as well as their own vital and basic scientific work in this field, will endure
for generations. I am delighted that their work, through this English-language
edition, will now be more widely available.
David Lazarus
Loomis Laboratory of Physics
The University of Illinois
Urbana, Illinois, USA
Fore wo r d
This book was written to remedy a deficiency: at this time, an elementary
text on diffusion in solids does not exist either in French or in English. On the
other hand, literature for specialists at an advanced level is abundant ; during
the last fifteen years, a number of colloquia and workshops have resulted in
publications, many of which resemble review articles. Still, there is no first
book that would prepare a graduate student or beginning researcher to use
these review articles or the original literature fruitfully.
The present book is the result of diverse courses on diffusion. It is intended
to give as complete an overview as possible of diffusion in solid media, while
relating the processes of diffusion to both their physical bases and their appli-
cations. In this spirit, certain fundamental aspects of these processes, such as
the calculation of correlation factors or the theory of the atomic jump, which
require long mathematical derivations, have been considered only on an ele-
mentary level, with the important results given without proof. However, when
a simple approach was possible, the important relations have been derived, but
concentrating more on the physics than on the mathematical formalism.
A series of a real situations is covered in this account, from self-diffusion of
radiotracers to the more complex cases of mass flow under chemical or thermal
gradients or under electric fields, or diffusion in structures of lower dimension-
ality (surfaces and interfaces). In all these analyses, no category of materials
was favored ; metals, ionic crystals, oxides, and semiconductors all had their
turn. Only polymers were not specifically touched. One chapter is specifically
devoted to techniques for studying diffusion, including methods of numerical
simulation, and a last and long chapter gives a number of metallurgical phe-
nomena in which diffusion plays a fundamental role.
In the spirit of the book, neither a review of experimental results nor an
exhaustive bibliography has been given. Only a few typical results, with their
references, are given to illustrate important points. The rest of the bibliography
lists references to books and review articles which allow the reader to penetrate
the subject more deeply before going to the original literature.
This work is addressed first of all to graduate students, but may serve a
larger audience in allowing researchers to refresh their memories on some points
of diffusion. They will grasp that the points of view, the approaches, of this
apparently classical subject have recently experienced a significant evolution,
as shown in the series of colloquia held over the last fifteen years and cited in
VI11 Atom movements
the general bibliography. The background is classical ; the new perspectives
open with new materials.
May this small book inspire the reader to futher research and renewal in
a field in which several laboratories in our country have long been active.
* *
*
The author thanks all those who, by reading a part of the manuscript
and by discussion have helped him to clarify a number of points. His thanks
go equally to the secretaries who had to face a difficult stenographic task,
and especially to Mrs. Marie-Claire Dolou, who took care of a large part of
this reproduction, as well as to the publisher, Editions de Physique, who have
lavished much care on the production of this volume.
J. Philibert
Foreword to the English Edition
The good reception given this work in the scientific community and the
urging of several colleagues have encouraged the author to prepare an English
edition.
The title chosen for this edition, evoking that of the AÇM seminar pub-
lished in 1952, is intended to indicate the aim of this book: to understand the
processes encountered in Materials Science which are governed by the move-
ment of atoms. As for the text itself, it has been revised, expanded, and
corrected, and, last but not least, a set of exercices of various levels of difficulty
has been added.
The author wishes to thank all those who have made suggestions about the
book, and especially the translator ; his many suggestions have considerably
improved the original text, so that it may be of even better service to its
readers.
J. Philibert, October 1988
Translator’s Acknowledgments
Dr. Charles Wiley and Prof. Jean Philibert read the translation manu-
script ; I thank them for their many excellent suggestions, which helped greatly
to improve the clarity of the translation. I especially thank Prof. Philibert for
his constant friendly encouragement. I am grateful to Dr. David Price for read-
ing and correcting the parts on neutron diffraction, and to Drs. Alex McKale
and Nestor Zalucec for assistance with word processing. I thank my wife, Ms.
Barbara Rothman, for her frequent suggestions of the right word or the correct
grammar, and for her patience and support during the course of this work.
S. J. Rothman, October 1988
