Atomistic Simulation of Materials: Beyond Pair Potentials

453 Pages·1989·13.487 MB·English

by  O. K. Andersen, M. Methfessel, C. O. Rodriguez (auth.), Vaclav Vitek, David J. Srolovitz (eds.)

Atomistic Simulation
of Materials
Beyond Pair Potentials
Atomistic Simulation
of Materials
Beyond Pair Potentials
Edited by
Vaclav Vitek
University of Pennsylvania
Philadelphia, Pennsylvania
and
David J. Srolovitz
The University of Michigan
Ann Arbor, Michigan
Plenum Press • New York and London
Library of Congress Cataloging in Publication Data
Atomistic simulation of materials: beyond pair potentials / edited by Vaclav Vitek and
David J. Srolovitz.
p. em.
"Proceedings of an international symposium on atomistic simulation of materials:
beyond pair potentials, a satellite conference of the ASM World Materials Congress,
held September 25-30, 1988, in Chicago, Illinois" - T .p. verso.
Includes bibliographical references.
ISBN-l3: 978-1-4684-5705-6 e-ISBN-13: 978-1-4684-5703-2
DOl: 10.1007/ 978-1-4684-5703-2
1. Metallography-Congresses. 2. Electronic structure-Congresses. I. Vitek, V. II.
Srolovitz, David J.
TN689.2.A85 1989 89-16268
669' .95 - dc20 CIP
Proceedings of an international symposium on Atomistic Simulation of Materials:
Beyond Pair Potentials, a satellite conference of the ASM World Materials Congress,
held September 25-30, 1988, in Chicago, Illinois
© 1989 Plenum Press, New York
Softcover reprint of the hardcover 1st edition 1989
A Division of Plenum Publishing Corporation
233 Spring Street, New York, N.Y. 10013
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording, or otherwise, without written permission from the Publisher
PREFACE
This book contains proceedings of an international symposium on Atomistic
Simulation of Materials: Beyond Pair Potentials which was held in Chicago from the 25th
to 30th of September 1988, in conjunction with the ASM World Materials Congress. This
symposium was financially supported by the Energy Conversion and Utilization
Technology Program of the U. S Department of Energy and by the Air Force Office of
Scientific Research. A total of fifty four talks were presented of which twenty one were
invited.
Atomistic simulations are now common in materials research. Such simulations are
currently used to determine the structural and thermodynamic properties of crystalline
solids, glasses and liquids. They are of particular importance in studies of crystal defects,
interfaces and surfaces since their structures and behavior playa dominant role in most
materials properties. The utility of atomistic simulations lies in their ability to provide
information on those length scales where continuum theory breaks down and instead
complex many body problems have to be solved to understand atomic level structures and
processes.
The success atomistic simulations have in mimicking nature is most often limited by
the accuracy of the description of the interaction between atoms. While advances in the
state of electronic structure calculations now make it possible to calculate total energies with
tremendous accuracy, these methods (whether real space cluster methods or reciprocal
space supercell methods) are still largely inapplicable to atomistic simulations needed in
materials science owing to their computer resource imposed limitations on the number of
independent atoms which may be accounted for.
Historically, pair-wise interactions (i.e. pair potentials) were first employed in
atomistic simulations. In most cases, these have been obtained by fitting empirical potential
forms to a variety of experimental data while in some cases such potentials have also been
derived from electronic theory (e.g. from pseudo-potential methods for simple metals). In
situations where the bonding is predominantly covalent, three-body (or bond bending)
potentials have been used. Calculations employing pair potentials have revealed a number
of important structural characteristics many of which now became generally accepted
concepts. However, pair potentials possess severe limitations, the most prominent being
that they are not applicable to the situations where the density of the material differs
v
significantly from that of a chosen reference state. This is, of course, the case for many
crystal defects, interfaces and in particular at surfaces. In the latter case, for example, pair
potentials yield atomic relaxations in complete contradiction to experimental fmdings.
Recently, new descriptions of atomic interactions have come to use the common
denominator of which is that they include the many body nature of bonding in the
condensed matter. On the empirical side the most popular are the Embedded Atom Method
and the Finnis-Sinclair type N-body potentials, two approaches which are closely related.
They are principally applicable to metals but analogous developments are now taking place
for semiconductors and ionic crystals. An approach more directly based on the theoretical
quantum mechanical description of atomic interactions is the tight binding method which is
being applied with increasing regUlarity. There are many different realizations of this
approach and the method itself is under active, widespread investigation. The fully self
consistent total energy calculations are, of course, also utilized with increasing frequency in
atomistic simulations.
The purpose of this symposium was to bring together a wide spectrum of
researchers who share an interest in descriptions of atomic interactions. Participants range
from those involved in highly accurate electronic structure methods to those working on
empirical descriptions of atomic interactions and researchers who carry out atomistic
simulations as part of their research. The materials of interest to the participants included
metals, ceramics, and semiconductors. The symposium thus brought together those whose
research leads to the development of new, more accurate descriptions of atomic interactions
with those who apply these developments in studies of materials properties. This
interaction is most important for further development of this field and we believe these
proceedings will serve the same purpose.
We wish to extend our sincere gratitude to Dr. 1. Eberhart of the US Department of
Energy and Dr. A. Rosenstein of the US Air Force Office of Scientific Research whose
encouragement and help was invaluable for the success of the symposium. We also wish
to thank most sincerely Ms. Denice Gilbert whose typing skill and patience made the
preparation of these proceedings possible.
Vaclav Vitek, Philadelphia
David J. Srolovitz, Ann Arbor
April, 1989
vi
CONTENTS
Total Energy and Force Calculations with the LMTO Method ........ . . . . . . . . . . . 1
O.K. Anderson, M. Methfessel, C. O. Rodriguez, P. Blochl, and H. M. Polatoglou
Concentration Dependent Effective Cluster Interactions in Substitutional Alloys. . . . . .. 15
A. Gonis, P.E.A. Turchi, X.-G. Zhang, G.M. Stocks, D.M. Nicholson, and W. H.
Butler
Simulation of Isovalent Impurities in Magnesium Oxide Using Hartree-Fock Clusters. .. 29
J .. Zuo, R. Pandey, and A.B. Kunz
Defect Abundances and Diffusion Mechanics in Diamond, SiC, Si and Ge. . . . . . . . . .. 33
J. Bernholc, A. Antonelli, C. Wang, R.F. Davis, and S.T. Pantelides
A Computational Metallurgical Approach to the Electronic Properties and Structural
Stability ofIntermetallic Compounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 41
A. J. Freeman, T. Hong, and J.-H. Xu
Theory of Defects in Solids and their Interactions. . . . . . . . . . . . . . . . . . . . . . . . . .. 55
A.B. Kunz
The Atomistic Structure of Silicon Clusters and Crystals: From the Finite to the Infmite . 67
J.R. Chelikowsky
Applications of Simulated Annealing in Electronic Structure Studies of Metallic Clusters. 79
M.R. Pederson, M. J. Mehl, B. M. Klein, and J. G. Harrison
Ab-Initio Molecular Dynamics Simulation of Alkali-Metal Microclusters ............ 87
W. Andreoni, P. Ballone, R. Carr, and M. Parrinello
A Simplified First Principles Tight-binding Method for Molecular Dynamics Simulations
and Other Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 95
O.F. Sankey and D. Niklewski
Angular Forces in Transition Metals and Diamond Structure Semiconductors ......... 103
A.E. Carlsson
Pseudopotential Studies of Structural Properties for Transition Metals. . . . . . . . . . . .. 115
E.J. Mele, M. H. Kang, and I. Morrison
Calculation of Ground- and Excited-State Properties of Solids, Surfaces and Interfaces:
Beyond Density Functional Formalism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
S.G. Louie
vii
Molecular Dynamics Simulation of the Physics of Thin Film Growth on Si: Effects of the
Properties of Interatomic Potential Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
W.L. Morgan
Self-Consistent Cluster-Lattice Simulation of Impurities in Ionic Crystals. . . . . . . . . . . 147
J. Meng and A.B. Kunz
The Effective Medium Approach to the Energetics of Metallic Compounds. . . . . . . . . .. 153
A. Redfield and A. Zangwill
Ab-Initio Study of Amorphous and Liquid Carbon. . . . . . . . . . . . . . . . . . . . . . . . . . 159
G. Galli, R.M. Martin, R. Carr, M. Parrinello
Modelling of Inorganic Crystals and Glasses Using Many-Body Potentials. . . . . . . . . . 167
C.RA. Cadow, R A. Jackson, B. Vessal
Embedded Atom Method: Many-Atom Description of Metallic Cohesion. . . . . . . . . . . . 181
M.S.Daw
Application of Many-Body Potentials Noble Metal Alloys. . . . . . . . . . . . . . . . . . . . .. 193
G.J. Ackland and V. Vitek
Many-Body Potentials for Hexagonal Close-Packed Metals. . . . . . . . . . . . . . . . . . . .. 203
M. Igarashi, M. Khantha, and V. Vitek
Derivation of Embedding Functions to Reproduce Elastic and Vibrational Qualities of
FCC and BCC Metals .......................................... 211
J.M. Eridon
An Embedded Atom Potential for BCC Iron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 219
R.J. Harrison, A.F. Voter, and S.P. Chen
Effects of Boron and Sulfur on Ni3AI Grain Boundaries ....................... 223
A.F. Voter, S.P. Chen, R.C. Albers, A.M. Boring, and P.J. Hay
Embedded Atom Method Model for Close-Packed Metals ...................... 233
DJ. Oh and R.A. Johnson
Boundary Conditions for Quantum Clusters Embedded in Classical Ionic Crystals. . . .. 239
J.M. Vail
Physical Properties of Grain-Boundary Materials: Comparison of EAM and Central-
Force Potentials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .. 245
D. Wolf, J.F. Lutsko, and M. Kluge
Temperature Dependence of Interatomic Forces ............................. 265
A.P. Sutton
New, Simple Approach to Defect Energies in Solids via Equivalent Crystals. . . . . . . .. 279
J.R. Smith, T. M. Perry, and A. BaneIjea
Grain-Boundary and Free-Surface Induced Thermodynamic Melting: A Molecular
Dynamics Study in Silicon. ...................................... 295
S.R Phillpot, J.F. Lutsko, D. Wolf, and S. Yip
Interatomic Potentials and the Bonding Energetics of Poly tetrahedral Packing in
Transition Metals. ............................................ 303
R.B. Phillips and A.E. Carlsson
viii
Transferability of Tight-Binding Matrix Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . 309
D.J. Chadi
The Tight-Binding Bond Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 317
D.G. Pettifor, A. J. Skinner and R. A. Davies
Interatomic Forces and Bond Energies in the Tight-Binding Approximation. . . . . . . . . . 327
A.T. Paxton
A New Interatomic Potential for Non-Metals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
M.Heggie
Transferable Tight-Binding Models Direct from Density Functional Theory. . . . . . . . .. 353
W.M.C. Foulkes
Stability of the (110) Face in Noble Metals Analyzed within a Tight-Binding Scheme. .. 361
B. Legrand and M. Guillope
Application of the Tight-Binding Bond Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 369
M.W. Finnis
Interatomic Forces from the Recursion Method with Gaussian Pseudopotentials. . . . . .. 381
R. Haydock
Application of Tight-Binding Recursion Methods to Lattice Defects in Metals and Alloys. 389
K. Masuda-Jindo, K. Kimura, and S. Takeuchi
Atomic Simulation of Superdislocation Dissociation in Ni3Al. . . . . . . . . . . . . . . . . .. 401
M.H. Yoo, M.S. Daw, and M.LBaskes
A New Method for Coupled Elastic-Atomistic Modelling. . . . . . . . . . . . . . . . . . . . .. 411
S. Kohlhoff and S. Schmauder
Self-Diffusion and Impurity Diffusion of FCC Metals Using the Embedded Atom
Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 419
J.B. Adams, S. M. Foiles, and W.G. Wolfer
Simulations of Atomic and Molecular Processes at Solid Surfaces. . . . . . . . . . . . . . .. 425
M. Menon and R.E. Allen
Molecular Dynamics Simulations of Materials: Beyond Pair Interactions ............ 443
U. Landman and W. D. Luedtke
On some Spectacular Surface Segregation Behaviors in CuNi and PtNi Alloys Analyzed
within the Tight-Binding Model. ................................ " 461
B. Legrand, G. Treglia, and F. Ducastelle
Index ........................................................ 467
ix
TOTALENERGYANDFORCECALCULATIONS~
1HE LMTO METIIOO
O.K. Andersen, M. Methfessel, C.O. Rodriguez,
P. BIOchl, and H.M. Polatoglou
Max-Planck-Institut fiir Festkorperforschung
0-7000 Stuttgart 80
Federal Republic of Germany
IN1ROOUCTION AND OVERVIEW
~uring the past 15 years it has become possible to perform quantum-mechanical
calculations of many properties of simple materials with good accuracy using as input
merely the positions of the atoms and the atomic numbers and masses. In particular, low
temperature structural properties of pure crystals and their surfaces have been obtained with
astonishing accuracy through calculation of the total energy as a function of the atomic
positions. Also, the Fermi surfaces of metals, the magnitude and order of magnetic
moments in transition metals and many of their alloys, as well as important aspects of the
electronic and atomic structures of impurities in metals and semiconductors have been
accurately reproduced.1,2,3
This advance has largely been based on the density1unctional formalism4,5 which
reduces the problem of finding properties of the many-electron ground state to that of
solving SchrOdingers equation for one electron moving in the electrostatic potential from
the nuclei and a potential from the electrons. The latter potential is local, i.e. it is the same
Ve (v) for all electrons, and it must be determined self consistently with the electron
density that it generates through solution of the Schrodinger-equation and subsequent
fllling of the one-electron states according to Fermi-Dirac statistics. The exact form of this
potential is unknown, but the so-called local density approximation (LOA) provides an
educated -and, in particular for structural properties, highly successful -guess for it.
The second prerequisite for this advance has, needless to say, been electronic
computers, and the third has been the development of powerful methods for solving the
self-consistent one-electron problem. Here, essentially two lines of thought have been
followed. In one, originating from Fermi,6 the core-electron degrees of freedom are
neglected in the solid and the potential acting on a valence electron is substituted by a
pseudopotential whose wavefunctions are nodeless inside the atoms. As a result,
wave (LAPW) method,9 which is presumably the most accurate, generally applicable
method presently available.14 It is, however, much more cumbersome to work with
sets have been enormously successful in reproducing and predicting structural properties of
materials with broad sp-like valence bands. 1 The pseudopotential, however, becomes deep
for materials containing less broad bands, such as oxides, halides, transition-metal, rare
earth and actinide compounds; so deep, that the use of unsophisticated basis sets becomes
very costly, and the use of PW's often impossible. A material like Si02, for instance, is
presently at the border-line and requires about 400 PWs per atom'?
The other line of thought, going back to Slater,S came from the desire to be able to
compute the electronic structures also for those materials. Based on the observation that the
potential acting the electrons is nearly spherically symmetric near each atom, the idea was to
approximate this potential by its so-called muffin-tin (MT) average which is spherically
symmetric inside non-overlapping MT-spheres and flat in between. For such a potential
the solutions of Schr6dingers equation for the solid can then be constructed from the
solutions for each MT- sphere of the radial Schr6dinger equations, which are trivial to
integrate numerically. There is no need to eliminate the atomic oscillations of the
wavefunctions through pseudizing the potential, and there is no need to exclude (semi-)
core electrons from the calculation.
In the so-called linear band-structure methods2,9 this MT-potential is used to
construct a relatively small, dedicated basis set which is then used to solve Schr6dingers
equation. The linear muffin-tin-orbital (LMTO) method, together with its descendant the
augmented spherical wave (ASW) method,lO use typically 9 orbitals per MT-well (Le., a
Islpld basis) and they have been very successful in calculations of electronic, cohesive,
and magnetic properties for a large number of S-, p-, d-, or f-band materials.2 The LMTO
method has been used for very large supercells, the largest being a 212 atom model for
amorphous Si,11 as well as for Greens-function calculations for localized and extended
defects. The LMTO set may also be transformed exactly into short ranged, so-called fIrst
principles tight-binding basis,2 and this has been used together with the recursion method
for topologically disordered systems,12 and together with the coherent-potential
approximation (CPA) for substitutionally disordered alloys.13
In all these applications the LMTO method has, however, always been used with
the so-called atomic-spheres approximation (ASA) in which the Coulomb energies are
calculated after the charge density has been spheridized inside "space-filling" -and hence
slightly overlapping -MT -spheres. (In the present paper we defIne the ASA to have the so
called combined correction9 included). For open structures, space-filling with acceptable
overlaps can only be obtained by including spheres also at interstitial sites. It is obvious
that the ASA makes it impossible to calculate structural energy differences associated with
symmetry-lowering displacements of the atoms. Such energies are the center of interest in
the present symposium, and their calculation seems to require treating the full, non
spheridized charge density and potential.
Until now this has only been done successfully with the ltnear augmented-plane-
2