Table Of ContentReine und angewandte Metallkunde in Einzeldarstellungen
Herausgegeben von W Köster
Band 24
Order-Disorder
Transformations in Alloys
Proceedings of the International Symposium on
Order-Disorder Transformations in Alloys
held 3-6 September 1973 in Tübingen, Germany
Sponsor
Deutsche Gesellschaft für Metallkunde
Editor
Hans Warlimont
Springer-Verlag Berlin Heidelberg GmbH 1974
Dr. Hans Warlimont
Wissenschaftlicher Mitarbeiter am Max-Planck-Institut
für Metallforschung, 8tuttgart
Professor am Institut für Metallkunde der Universität 8tuttgart
With 304 Figures
ISBN 978-3-642-80842-5 ISBN 978-3-642-80840-1 (eBook)
DOI 10.1007/978-3-642-80840-1
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© by Springer-Verlag Berlin Heidelberg 1974
Softcover reprint of the hardcover 1st edi tion 1974
Originally published by Springer Verlag, Berlin /Heidelberg in 1974
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PREFACE
This book contains 18 invited contributions to the first Inter-
national Symposium on Order-Disorder Transformations in Alloys+. They
cover the major aspects of this group of phase transformations. Although
structural order-disorder transformations have been investigated for
over 50 years the invited papers, the research papers - whose titles
and authors are listed in the appendix - and the discussions at the
Symposium have demonstrated very active continued interest and con-
siderable recent progress in the subject. This is true for theoretical
work as weIl as for experimental studies and for the development of
materials whose properties result from order-disorder transformations.
+
Some major national conferences on ordering were held in the USA and
in the USSR in recent years; the proceedings are available in the
following pUblications:
Local Atomic Arrangements Studied by X-Ray Diffraction, Gordon &
Breach, New York 1966
2 Ordered Alloys, Claitor's Publ. Div., Baton Rouge, La. 1970
3 Summaries of the Proceedings of the 2nd Union Conference on Atomic
Ordering and its Influence on the Properties of Alloys, Naukova
Dumka, Kiev 1966
4 Atomic Ordering and its Influence on the Properties of Alloys,
Naukova Dumka, Kiev 1968
5 Atomic Ordering and its Influence on the Properties of Alloys,
TGU, Tomsk 1973
111
In assembling these papers it vas attempted to compile a systematic
and approximately complete compendium of the sUbject. All authors are
giving a survey of their topic as vell as an account of their ovn
contributions and particular vievs. Thus, the papers are revievs as
vell as reports of recent developments including the arguments on
controversial issues. Seven papers are devoted to the theoretical
aspects of order-disorder transitions, structures, equilibria and
kinetics; six are concerned vith experimental observations of struc-
tures and structural states; the remaining five are treating the
theory, observations and development of mechanical properties due to
ordering and the application of ordered alloys as materials.
The occurrence of superlattice structures and of order-disorder
transitions is tractable on tvo different theoretical bases: either
by considering the electronic structure and size effects of the com-
ponents and deriving the resulting structural states or by assuming
the interatomic forces to be knovn and by computing the atom distri-
bution on the given lattice sites, as a function of temperature and
composition - and, thus, the phase diagrams - thermodynamically. The
first approach is described and applied under different aspects in
the papers by Friedel, Panin and Fadin, ahd Kozlov and covorkers.
The second approach vhose basis is the classical statistical Bragg-
Williams-Gorski theory of order-disorder transitions has been essen-
tially extended through recent vork summarised in the paper by
Heychenko and Smirnov. In the subsequent contribution by Khachaturyan
a nev theoretical treatment of order-disorder transitions based on
static concentration vaves is described. The paper by Kornilov emphasi-
ses the frequent occurrence and appropriate representation of hetero-
geneous equilibria betveen disordered and ordered phases. Yamauchi and
de Fontaine present a unified treatment of the various theories of
order-disorder kinetics.
Since electron microscopy and electron diffraction have recently
become the most videly applied experimental methods for investigating
structural aspects of order-disorder transformations the paper by
Tanner and Leamy vhich is based on these methods is leading the second
section of the book. Most of the common structures of substitutional
binary and ternary superlattice phases have been determined in the past
such that they have become standard content of reference books. The
long-period structures, hovever, vhich are revieved by Ogava are of
particular continued interest because of their implications concerning
the factors affecting the stability of superlattice phases. The survey
by Hirabayashi and covorkers of investigations of interstitial ordering
gives insight into a rapidly groving subject vhich had received less
attention in the past. Short-range order and some of its nev develop-
IV
ments and controversial aspects are reviewed by Iveronova and Katsnelson.
The papers by Das and Thomas and by Mishra and Beck represent two ap-
proaches to the determination of local atomic environment which are par-
ticularly promising for providing experimental data leading beyond the
information yielded by the classical x-ray diffraction methods.
The theoretical and experimental aspects of the mechanieal behaviour
of superlattiee phases are reviewed by Mareinkowski with emphasis on
bee based struetures and by Popov and Koneva with regard to the work
hardening of fee based struetures. Kear reviews the meehanisms of the
most important applieation of a heterogeneous order-disorder transfor-
mation, the high-temperature strengthening of niekel-based superalloys.
Stoloff deseribes new developments of high temperature materials based
on a combination of euteetie eomposite formation and order strengthening.
The eoneluding paper by Westbrook shows that order-disorder transfor-
mations play an important role for the properties of a wide variety of
materials and that there is seope for essential improvements and new
developments by exploiting the partieular structure-property relation-
ships yielded by this group of phase transformations. -
Thanks are due to all authors of this book for their eontributions
and ready cooperation, but in particular to those whose personal parti-
eipation in the eonferenee was impossible and who still agreed to fur-
nish their papers for these proceedings: Dr. E.V. Kozlov and his col-
leagues, Dr. V.V. Heychenko and Prof. A.A. Smirnov, Prof. 1.1. Kornilov
and Dr. J.H. Westbrook. The preparation of the eonferenee program and,
thus, of this volume has been possible only through the intensive co-
operation of Prof. W. Pitseh, Düsseldorf, and the suggestions and
support by Prof. R.W. Cahn, Brighton, Prof. M. Fayard, Paris, Prof.
V.I. Iveronova, Moscow, Dr. B.H. Kear, Middletown, Prof. M.J. Marcinkowski,
College Park, Dr. V. Sehumaeher, Oberursel, and Prof. D. Watanabe, Sendai.
The reviews eontained in this book were reprodueed from manuseripts
as supplied by the authors. Some inadvertent linguistie and graphical
defieienees eould be handled editorially but in the interest of fast
and eeonomie publieation eorreetions were restrieted to instanees where
the contents eould otherwise be misunderstood. It is hoped that the
reader will find this to be an acceptable eompromise.
Finally, I wish to thank Prof. W. Köster for offering this book to
become part of the series "Reine und angewandte Metallkunde in Einzel-
darstellungen", Miss V. Bacher and Miss G. Frommleth for their pains-
taking help in the editorial work and the Springer-Verlag for the fast
pUblication of these proeeedings.
Stuttgart
January 1974 H. Warlimont
V
LIST OF CONTENTS
THEORY
Electron theoretical fundamentals in order disorder
transformations of metallic alloys
J. Friedel
Electronic structure and nature of ordering in alloys
of transition elements
V.E. Panin, V.P. Fadin 28
Symmetry, pair interatomic interaction and electronic
states in ordering alloys
E.V. Kozlov, V.M. Dementryev, V.N. Emelyanov, N.M. Kormin,
A.S. Taylashev, D.M. Stern 58
The theory of order-disorder transformations in alloys
with several phase-transition points
V.V. Heychenko, A.A. Smirnov 80
Static concentration waves in the theory of order-
disorder phenomena in substitutional and interstitial
solid solutions
A.G. Khachaturyan 114
Heterogeneity of the reactions of formation of
compounds with ordered structures from solid
solutions
I.I. Kornilov 132
Kinetics of order-disorder
H. Yamauchi, D. de Fontaine 148
VI
EXPERIMENT
The microstructure of order-disorder transitions
L.E. Tanner, H.J. Leamy 180
On the long-period ordered alloys
S. Ogawa 240
Order-disorder transformations of interstitial
solutes in transition metals of IV and V groups
M. Hirabayashi, S. Yamaguchi, H. Asano, K. Hiraga 266
Supplement: Ordering of oxygen in vanadium
M. Cambini 303
Modern problems of short-range order
V.I. Iveronova, A.A. Katsnelson 306
On structural interpretation of short range order
S.K. Das, G. Thomas 332
Atomic order-disorder information from magnetic
data
S. Mishra, P.A. Beck 344
PROPERTIES AND APPLICATIONS
The effect of atomic order on the mechanical
properties of alloys with emphasis on FeCo
M.J. Marcinkowski 364
Work-hardening of ordered alloys
L.E. Popov, N.A. Koneva 404
The influence of ordering on the engineering
properties of two phase alloys
Part I - Mechanical properties of y' precipitation
hardened nickel-base superalloys
B.H. Kear 440
VII
Part 11 - Ordering effects in directionally
solidified eutectic alloys
N.S. Stoloff
Applications of atomic ordering reactions
J.H. Westbrook
APPENDIX: Titles of research papers presented
at the Symposium
Statistical thermodynamics of ordering 540
Effects of electronic structure in ordering 541
Development of the microstructures of
ordered states
Superlattice structures
Effects of microstructures of ordered states
on magnetic domain structures
Kinetics of ordering 546
Local order
Effects of ordering on mechanical properties
SUBJECT INDEX 550
VIII
ELECTRON THEORETICAL FUNDAMENTALS IN
ORDER DISORDER TRANSFORMATIONS OF
METALLIC ALLOYS
J. Friedel
Physique des Solides Universite Paris Sud Orsay
LA du CNRS
SUMMARY
One discusses briefly why order-disorder transformations are frequent in metal-
lic alloys. Order can be stabilized by electrostatic interactions or by size effects.
A discussion of alloys of 'normal' (sp) met als shows the main factors involved and
their relation to the Fermi structure. Dilute and concentrated alloys of transitional
met als are then discussed.
INTRODUCTION
Why order-disorder transformations are frequent in metallic alloys.
I want to sketch how the knowledge of the electronic structure of alloys might
help to understand the nature of the interatomic forces responsible for their orde-
ring. I will therefore exclude all thermodynamical analysis of the nature of the
order-disorder transformation once these forces are known, a different if active and
fascinating sUbject.
Furthermore, I gather from the program that I MUSt restrict myself to metallic
alloys , and exclude insulators, either rare gases, covalent, ionic or molecular
structures. The metallic alloys provide however already a very large, very interes-
ting and very specific field, for three reasons. These might be worthwile first to
recall.
a. Most elements of the periodic table are metals.
There are indeed three kinds of solid elements /1/
- The rare-gases, insulators with full valence sp shells and Van der Waals inter-
actions of no interest here.
- The elements with partly filled sp valence shells, and especially light ele-
ments or elements with nearly filled sp shells. Because these sand p states have
symmetries of opposite signs but similar orbital radii, they form sp hybrids !i,n>,
each of which points strongly from one site i in only one direction n. The covalent
structures they build are such that each hybrid is used once and only ~ in a linear
combination, to form an interatomic bond (fig.l) :
As a result, it can be
Fig. Covalent bonds built up with sp hybrids
on neighbouring sites i, j
shown /2/ /3/ /4/, /5/ that the sp valence band is split into two equal halves, a bon-
ding or valence band and an antibonding or conduction band (fig.2).
2
