Disordered Alloys: Diffuse Scattering and Monte Carlo Simulations

128 Pages·1998·6.99 MB·English

by  Werner Schweika

Springer Tracts in Modern Physics
Volume 141
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Werner Schweika
Disordered Alloys
Diffuse Scattering
and Monte Carlo Simulations
With 84 Figures
r e g n~ i r p S
Dr. Werner Schweika
Forschungszentrum Jiilich
Institut fiir Festk6rperforschung
D-52425 Jiilich, Germany
Email: w.schweika@fz-j uelich.de
Library of Congress Cataloging-in-Publication Data
Schweika, Werner, 1956-
Disordered alloys: diffuse scattering and Monte Carlo simulations / Werner Schweika.
p. cm. - (Springer tracts in modern physics; .v 141) Includes bibliographical references and index.
ISBN 3-54o-63445-2 (all paper)
.1 Electronic structure-Measurement. .2 Order-disorder in alloys-Measurement. .3 Kirkendall effect.
4. Monte Carlo method. I. Title. II. Series: Springer tracts in modern physics; .141
QC1.$797 vo1.141 QC176.8.E4 539s-dc21 97-39898 CIP
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Preface
Structural correlations and effective interactions in disordered alloys provide
a basis for the understanding of order-disorder phenomena in real alloys.
Updating this classical subject, I hope that this review provides interesting
and stimulating ideas and results for specialists but also for readers with more
general interests. The disorder in the presented alloy systems is studied by
diffuse scattering experiments and related Monte Carlo simulations, which
seems to be a very fruitful combination of methods.
Emphasis is given to neutron scattering methods, though x-rays are of
complementary importance. The use of neutrons offers several advantages,
and the most important ones are the ability to distinguish static and dy-
namic properties - valuable for in-situ studies at high temperatures- and the
sensitivity to scattering from light elements. The alternative description of
the diffuse scattering might give more insights into the origin of local order
of alloys. The experimental method of diffuse scattering provides unique and
precise results on pair correlations, which challenge and hopefully inspire the
theoretical progress in understanding alloy phase stability.
Structural simulations from scattering experiments are of more general
interest; their limitations as well as their success rest on a surprising con-
finement of higher-order correlation functions by the full extent of the pair-
correlation function. Hence, to give an example, the discussion of the reverse
Monte Carlo method also will be of relevance for the determination of the
structure of liquids. The inverse Monte Carlo method is applied to determine
the most realistic effective pair interactions from the experimental data. This
review discusses possible improvements and variations of this method, includ-
ing, for instance, new ideas to reveal the gradient of the interaction potentials
via charge fluctuations leaving their fingerprints on static displacements.
During recent years, with the availability of new experimental tools and
techniques, the region near the surfaces of crystals has gained increasing in-
terest. Near the surfaces of crystals, one may observe a large variety and com-
plexity of ordering phenomena, different from but not independent of the bulk
ordering properties. Near-surface order-disorder phenomena are viewed from
results of very accurate Monte Carlo simulations, which are of importance
for wetting theories, and predict the possibility of new equilibrium states of
order near the surfaces, while the alloy's bulk is still in the disordered phase.
VIII Preface
Admittedly, this review focuses on my own work and, despite some efforts,
the literature review unfortunately remains incomplete. I apologize to those
whose work I have overlooked.
The work presented here has benefited from various collaborations and
I gratefully acknowledge M. Becker, C. Lamers, M. Pionke (Institut ffir
FestkSrperforschung, Forschungszentrum Jfilich), A.E. Caxlsson (Washing-
ton University, St. Louis), A. Hoser (Universit/it Hannover, HMI Berlin), D.P.
Landau (Center of Simulational Physics, The University of Georgia, Athens,
GA) and K. Binder (Johannes-Gutenberg Universit~it Mainz). Thanks to all
colleagues of my institute for discussions, to A. Broich for technical assis-
tance, to M. Beyss for growing single crystals. For valuable comments and
reading of the manuscript it is my pleasure to acknowledge W.A. Oates
(The University of Newcastle) and C. Sparks (Oak Ridge National Labo-
ratory). My special gratitude, however, is dedicated to T. Springer (Institut
ffir FestkSrperforschung, Forschungszentrum Jiilich) for his support and kind
encouragement.
Jiilich, July 1997 Werner Schweika
Co e s
Introduction .............................................. 1
°
2. Diffuse Scattering of Alloys ............................... 5
2.1 Introduction ........................................... 5
2.2 Disordered Solid Alloys ................................. 8
2.3 Short-Range Order ..................................... 11
2.4 Lattice Displacements ................................... 14
2.5 Data Analysis .......................................... 22
2.6 Experimental Considerations ............................. 26
. Monte Carlo Simulations of Alloys ........................ 31
3.1 Ising Models ........................................... 31
3.2 Metropolis Monte Carlo Method ......................... 35
3.3 Reverse Monte Carlo Method ............................ 39
3.4 Inverse Monte Carlo Method ............................ 41
3.5 Comments on the Uniqueness of the Models and Methods ... 43
4. Applications .............................................. 51
4.1 Clustering Alloys ...................................... 51
4.1.1 Solubility of Co in Cu ........................... 54
4.1.2 Decomposition in the Cu-Ni Alloy System .......... 55
4.2 Ordering Alloys ....................................... 58
4.2.1 Chemical Order in Ferromagnetic Fe-A1 Alloys ...... 58
4.2.2 Short-Range Order and Interactions in the Ni-Cr System 64.
4.2.3 The Temperature Dependence of Short-Range Order
in Cu-Zn ........................................ 70
4.3 Interstitial Alloys ....................................... 74
4.3.1 The Defect Structure of Ferrous Oxide Fel_~O ...... 74
4.3.2 Short-Range Order and Interactions in the Metal Hy-
dride VDx ....................................... 83
4.4 Surface-Induced Ordering and Disordering ................. 90
4.4.1 Surface-Induced Disorder .......................... 92
4.4.2 Surface-Induced Order due to Reduced Frustrations .. 96
4.4.3 Surface-Induced Order due to Effective Surface Fields. 98
X Contents
5. Summary and Conclusions ................................ 105
References .................................................... 111
Index ......................................................... 121