Modelling of Minerals and Silicated Materials PDF
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Modelling ofMinerals and Silicated Materials TOPICSIN MOLECULAR ORGANIZATIONAND ENGINEERING Volume 15 HonoraryChief Editor: W.N.LIPSCOMB(Harvard,U.S.A.) Executive Editor: JeanMARUANI (Paris,France) EditorialBoard: HenriATLAN(Jerusalem,Israel) AlexandreLAFORGUE(Reims,France) SirDerekBARTON(Texas,U.S.A.) J-M.LEHN(Strasbourg,France) ChristianeBONNELLE(Paris,France) P-O.LÖWDIN(Uppsala,Sweden) PaulCAR0(Meudon,France) PatrickMacLEOD(Massy,France) StefanCHRISTOV(Sofia,Bulgaria) H.M.McCONNELL(Stanford,U.S.A.) I.G.CSIZMADIA(Toronto,Canada) C.A.McDOWELL (Vancouver,Canada) P-G.DEGENNES(Paris,France) RoyMcWEENY(Pisa,Italy) J-E.DUBOIS(Paris,France) IlyaPRIGOGINE(Brussels,Belgium) ManfredEIGEN(Göttingen,Germany) PaulRIGNY(Saclay,France) KenishiFUKUI(Kyoto,Japan) R.G.WOOLLEY (Nottingham,U.K.) GerhardHERZBERG(Ottawa,Canada) Modelling of Minerals and Silicated Materials edited by BernardSilvi Laboratoire deChimie Théorique, Université PierreetMarie Curie, Paris,France and PhilippeD'Arco LaboratoiredeGéologie, EcoleNormale Supérieure, Paris,France KLUWER ACADEMICPUBLISHERS NEW YORK /BOSTON / DORDRECHT / LONDON / MOSCOW eBook ISBN: 0-306-46933-2 Print ISBN: 0-792-34333-6 ©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://www.kluweronline.com and Kluwer's eBookstore at: http://www.ebooks.kluweronline.com TABLE OF CONTENTS INTRODUCTION vii / * J. R. CHELIKOWSKY, N. R. KESKAR and N. BINGGELI The StructuralProperties of Silica Using Classical and Quantum Interatomic Forces 1-37 * R. M. WENTZCOVITCH and G. D. PRICE / High Pressure Studies of Mantle Minerals by Ab initioVariable Cell Shape Molecular Dynamics 39-61 / *R. G. GORDON and D. J. LACKS Calculation of Mineral Properties with the Electron Gas Model 63-79 *M.S.T. BUKOWINSKI, A. CHIZMESHYA, G.H. WOLF and H. / ZHANG Advances in Electron-Gas Potential Models : Applications to some Candidate Lower Mantle Minerals 81-112 / *M. CATTI and A. PAVESE Quantum-Mechanical and Classical Simulations of Mg-Ca Carbonates 113-156 / G. V. GIBBS, F. C. HILL and M. B. BOISEN Jr. The SiO Bond and Electron Density Distributions 157-177 / B. SILVI, A. SAVIN and F. R. WAGNER The Nature of Silicon-Oxygen Bonds in Silica Polymorphs 179-199 * S. TSUNEYUKI / Molecular Dynamics Simulation of Silica with a First-Principles Interatomic Potential 201-226 / *A. N. CORMACK and YUAN CAO Molecular Dynamics Simulation of Silicate Glasses 227-271 / M. HENRY Application of the partial chargemodel tothe aqueous chem- istry of silica and silicates 273-334 INDEX 335-341 * Contributions marked with an asterisk also appear in the journal Molecular Engineering, Volume6, 1996. Introduction The modeling of minerals and silicated materials is a.difficult challenge faced by Solid StatePhysics, Quantum Chemistry and Molecular Dynamics communities. The difficulty of such amodeling is due to the wide diversity of elements, including heavy atoms, and types of bonding involved in such systems. Moreover,onehas toconsider infinite systems: either perfect crys- tals or glasses and melts. In the solid state a given chemical composition gives rise to numerous polymorphs, geometrically closely related. These polymorphs have very similar energies and related thermodynamical prop- erties which explain the complexity of their phase diagrams. The modeling of silicates and minerals covers a wide field of applications ranging from basic research totechnology,fromSolid StatePhysics toEarth and Planetary science. The use of modeling techniques yields information of different nature. In the case of chemical studies, we can mention inves- tigations on catalytic processes occurring on surfaces and in zeolite cages. These calculations find possible applications in chemical engineering, in particular in the oil industry. Physical properties, such as elastic constants, are currently investigated in order to get better insights on their relationships to the structure and chemistry. In this respect, the understanding of the phase transition mech- anismsisofprimary importance. Theestimationofthermodynamical prop- erties under extreme conditions of pressure and temperature supplies the difficulty of performing experimental measurements. In Earth and Plane- tary Science, the deep internal pressure and temperature are very high (at Earth core-mantle boundary P~ 300 GPa, T~ 3000 K). Our knowledge of Earth interior is mainly inductive. The principal sources of information are seismic data from which models have been built. The validation of the hypothesis underlying the construction of interior models relies on difficult high pressure and temperature experiments as well as on the results of cal- culations. In this field, the calculations are expected to be as accurate as the experiments which are not always technically feasible. Another important field of application directly related to technology is the design of new materials such as ceramics. The prediction of their physical properties, at least the order of magnitude, allows the selection of those systems for which investments in further investigations arejustified. vii viii The basic tools for the modeling of the solid and liquid states belong to three main categories. Wecan mention first theMolecular Mechanicswhich rely on site-siteor covalent potentialsand which areused tostudy in partic- ular defect formations, to calculate accousticand optical phonon modes by lattice dynamics and toestimate mechanical and thermodynamical proper- ties. Theeasy implementation of the Molecular Mechanics scheme supports its intensive use in the past and its success in commercial softwares. Molecular Dynamics and Monte Carlo simulations also rely on site-site potentials, but the point of view is now that of Statistical Mechanics which allows to explicitly account for temperature and pressure. The price to be paid in order to include the temperature is that the sampling must be statistically significant. This implies that a large number of particles (~ 700) and a much more larger number of configurations (typically > 10000) have to be considered. In Quantum Mechanical calculations, the energy is computed from the exact hamiltonian. It is then possible to build a Born-Oppenheimer energy surface which can be used later toperform lattice dynamics or to study the reaction path of a displacive phase transition. These methods give access to the electron density, the spin density and the density of states which are useful to predict electric and optical properties as well as to analyze the bonding. Recently, methods combining a quantum mechanical calculation of the potential and the Molecular Dynamics scheme have been developed after the seminal work of R. Car and M. Parrinello. The quality of the potential is the key of a reliable simulation. Historically, the first potential were derived from experimental data and with simple assumptions on the bonding. These potentials are basically of the Born- Mayer type and polarization effects can be accounted for by a shell model. Anewtrail to derivepotentials isto fitthe parameters to the ab initio Born- Oppenheimer energy surfaces ofprototype moleculessuch as Si(OH) and 4 (OH) SiOSi(OH) . 3 3 The first principle calculations on minerals have been pioneered by geo- chemists : G. V. Gibbs, J. A. Tossel, M. O’Keefe. They began to perform semi-empirical calculations on prototype molecules derived from mineral fragments in the early seventies. With the advent of efficient user friendly ab initiocodesthey evolved towardsmore accuratecalculationsin theeight- ix ies. The prototype molecule technology provided significant results, but it is very limited because the same prototype molecule represents several polymorphs. Moreover, the periodicity is not taken into account and the dangling bonds are saturated by hydrogens in order to neutralize the sys- tem. These methods are now replaced by periodic schemes working either within the Hartree-Fock theory or within the density functional theory. In both cases core pseudopotentials are very useful to represent heavy atoms. In spite of the increase in the performances of the available computational facilities such periodic calculations remain extremelyintensive both in CPU time and storage requirements. This prevents from the study of compound with large unit cell and low symmetry. An approximate scheme has been derived from the Electron Gas Approximation of Gordon and Kim which allows to consider large cells. Thebondingin silicateshas been first investigated by Pauling. In particular it is difficult to decide the multiplicity of the SiO bond and its mostly ionic or covalent Character through a series of polymorphs. The advent of new tools of analysis which rely on the topology of local functions are shown to be useful to bring a more objective information on a controversial subject. Molecular Dynamics of solids have made considerable progress during the ten past years. It is now possible to reproduce order-disorder phase transi- tions as well as the local structure of glasses. The chapters in this book address the different points briefly sketched above. Our goal is to present the most efficient and reliable modeling approaches and to give the present state of the art. Though the prediction of the structure and properties of any solid mate- rial is still out of reach, it is now possible to make reliable predictions on moderately complex structures. Therefore, the “scandal” revealed by John Maddox in 1988is ending. Bernard SILVI and Philippe D’ARCO THE STRUCTURAL PROPERTIES OFSILICAUSING CLASSICAL AND QUANTUM INTERATOMIC FORCES JAMES R.CHELIKOWSKY,NITIN R.KESKAR Department of Chemical Engineering and Materials Science, Minnesota Super computer Institute, Universityof Minnesota, Minneapolis, MN 55455 USA AND NADIA BINGGELI Institut Romand de Recherche Numérique enPhysique des Matériaux (IRRMA), PHB-Ecublens, 1015 Lausanne, Switzerland 1. Introduction It is well known that SiO exists in amorphous or glassy phases as well 2 as in numerous crystalline polymorphs. What is not well known are the structural details of amorphous silica, or the driving forces which produce numerous polymorphs. The crystalchemistry of silica in some ways is anal- ogous to organic chemistry. Not only do numerous SiO structures occur 2 which differ only slightly in terms of the free energies, but nature of the Si-O bond is such that multiple coordination states can occur. This anal- ogy while useful cannot be taken tooliterally assilica chemistry (geology)is quite different from organic chemistry (biology). Nonetheless, the theoreti- calobstacles which onefacesin modeling silica arealmost as challenging as biologicalsystems. There are a number oftheoretical methods available for the description of condensed matter systems. One would like such meth- ods to be accurate, yet computationally simple, but the complex nature of the chemical bond in silica places stringent conditions on the available methods. Since the Si -O bond cannot be viewed as a purely ionic bond, it is not apparent that complete descriptions of silica can be handled by pairwise interatomic potentials. Amorerigorous approachtomodeling silica centerson quantum descrip- tions of condensed matter systems. Thesemethods can adequately describe 1 B.SilviandP.D'Arco(eds.),Modellingof MineralsandSilicatedMaterials,1-37. ©1997KIuwerAcademicPublishers. Printed intheNetherlands. 2 J. R.CHELIKOWSKY, N. R.KESKAR AND N.BINGGELI structuralenergies, e.g.atypical error in theequilibrium bond length might be lessthan ~1%.Unfortunately, these methods tend to be computation- ally intensive. This problem can be compounded by large number of atoms in the unit cell of silica, e.g., the coesite crystal form of silica contains 48 atoms in the unit cell. If one wishes to examine models for amorphous solids, the number can exceed several hundred atoms in the unit cell. At present, it is decidedly nontrivial to perform quantum calculations on cells which contain more than a few dozen atoms. Perhaps a sensible procedure is to consider an approach which incor- porates both interatomic potentials (classical forces) and fully quantum mechanical methods. One can compute the properties of smaller systems with quantum mechanical approaches and establish the accuracy, or in- accuracy, of interatomic potentials. For example, some elastic anomalies have been reported for α-cristobalite.Theseelastic anomalies indicated the presence of a negative Poisson ratio in this crystalline form of silica. With the use of interatomic potentials, it is a trivial matter to compute these properties. If the anomalies are confirmed via such calculations, it is likely that the experimental measurements are accurate, and more computation- ally intense calculations with quantum forces are merited. Another useful role ofinteratomic potentials istoperformmolecular dynamics simulations, e.g.,toexamine theamorphizationof quartzunder pressure. Onecan easily compute thefree energy of large systems as afunction of both temperature and pressure via interatomic potentials. Such calculations can be useful as guides if interpreted in ajudicious fashion. Given an accuratemethod for determining theenergy (structuralor free energies) of a condensed matter system, a number of important issues can be addressed. If accurate theoretical phase diagrams can be obtained, then hypothetical high pressure forms of silica can be examined. It may be that a low density form of silica,under geologicpressures may be unstable against ahigh pressure form of silica. Direct calculationsof thefree energy of hypo- thetical forms of silica can give guidance to establishing arealistic picture of the interior of the Earth. At a more fundamental level, questions con- cerning the structural nature of silica glass can be addressed. For example, it is possible to create high pressure forms of silica glass by different routes. Consider twocases. In thefirst case,onequenches liquid silica, and subjects the resulting glass to high pressure. In the second case, one subjects quartz to a high pressure to create amorphous silica. Are the resulting forms of silica in these two cases the same, or are they fundamentally different in their structural attributes?
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