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Physical Properties and Thermodynamic Behaviour of Minerals
NATO ASI Series Advanced Science Institutes Series
A Series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities.
The series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division
A Life Sciences Plenum Publishing Corporation B Physics London and New York
C Mathematical D. Reidel Publishing Company and Physical Sciences Dordrecht, Boston, Lancaster and Tokyo
D Behavioural and Social Sciences Martinus Nijhoff Publishers E Applied Sciences Dordrecht, Boston and Lancaster
F Computer and Systems Sciences Springer -Verlag G Ecological Sciences Berlin, Heidelberg, New York, London, H Cell Biology Paris, and Tokyo
Series C: Mathematical and Physical Sciences Vol. 225
Physical Properties and Thermodynamic Behaviour of Minerals
edited by
Ekhard K. H. Salje Department of Earth Sciences, University of Cambridge, U.K.
D. Reidel Publishing Company
Dordrecht / Boston / Lancaster / Tokyo
Published in cooperation with NATO Scientific Affairs Division
Proceedings of the NATO Advanced Study Institute on Physical Properties and Thermodynamic Behaviour of Minerals Cambridge, U.K. July 27 - August 8, 1987
Library of Congress Cataloging in Publication Data
NATO Advanced Study Institute on Physical Properties and Thermodynamic Behaviour of Minerals (1987: Cambridge, Cambridgeshire)
Physical properties and thermodynamic behaviour of minerals / edited by Ekhard K. H. Salje.
p. cm. - (NATO ASI series. Series C, Mathematical and physical sciences, vol. 225)
"Proceedings of the NATO Advanced Study Institute on Physical Properties and Thermodynamic Behaviour of Minerals, Cambridge, U.K., July 27-August 8, 1987"-T.p. verso.
"Published in cooperation with NATO Scientific Affairs Division." Includes bibliographies and index.
ISBN-13:978-94-010-7802-3 001: 1 0.1 007/978-94-009-2891-6
e-ISBN-13:978-94-009-2891-6
1. Mineralogical chemistry-Congresses. 2. Thermodynamics-Congresses. I. Salje, Ekhard K. H. II. North Atlantic Treaty Organization. Scientific Affairs Division. III. Title. IV. Series: NATO ASI series. Series C, Mathematical and physical sciences; no. 225. QE371.N38 1987 549'.12-c1c 19 87-28892
Published by D. Reidel Publishing Company P.O. Box 17, 3300 AA Dordrecht, Holland
Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A.
In all other countries, sold and distributed by Kluwer Academic Publishers Group, p.o. Box 322, 3300 AH Dordrecht, Holland
CIP
D. Reidel Publishing Company is a member of the Kluwer Academic Publishers Group
All Rights Reserved © 1988 by D. Reidel Publishing Company, Dordrecht, Holland. Softcover reprint of the hardcover 1 st edition 1988
No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any informatior1"Storage and retrieval system, without written permission from the copyright owner.
TABLE OF CONTENTS
Preface xv
List of Participants xvii
1.
2.
THE MICROSCOPIC MECHANISMS OF COMPLEX STRUCTURAL PHASE TRANSITIONS
V. Heine
1. Introductory remarks 2. Microscopic mechanisms 3. Computer modelling 4. The Landau free energy function 5. Critical fluctuations
References
THE THERMODYNAMICS OF SHORT RANGE ORDER
J. D. C. McConnell
1. Introduction 2. Symmetry Principles for interactions in modulated
1
1 2 7 9
11 15
17
18
structures 19 2.1 Symmetry groups and their irreducible
representations 19 2.2 The origin of selection rules for interactions 19 2.3 The nature of irreducible representations of
the space group 21 2.4 Symmetry criteria for the interaction of
modulation components 22 2.5 Summary of the theory of short range interactions
in crystals 23 3. The group theoretical description of short range order
in crystals 25 3.1 Long range order and the importance of the special
point vectors 25 3.2 The general characteristics of short-range order 26 3.3 The development of an energy band theory for short
range order 27
vi
3.
4.
3.4 The nature of interband interactions in order-disorder 27
3.5 Ordering modulations associated with an invariant point 29
3.6 The interaction between ordering and phonon bands 30 3.7 Summary of stable order modulations in crystals 31
4. Short range order interactions in incommensurate structures 32 4.1 Feldspars 32 4.2 The ordering behaviour in mullite 33 4.3 The ordering interactions in yoderite 34
5. Order-phonon modulation structures in minerals 37 5.1 The order-phonon modulated structure of potassium
feldspar 37 5.2 Order-phonon interactions in modulated cordierite 40
6. Thermodynamic aspects of the occurrence of modulated structures 6.1 Thermodynamically stable order-modulated
structures 6.2 Order-modulation in the mechanism of order
disorder transitions 7. References
INCOMMENSURABILITY IN TWO CLASSES OF SOLIDS: MODULATED INSULATORS AND QUASICRYSTALLINE ALLOYS
F. Denoyer
44
44
45 47
49
1. Introduction 49 2. Characterization of incommensurate crystals:
"Standard" behaviour 49 3. Incommensurate phase transition: the "soft-mode"
precursor effect 53 4. Specific dynamic properties of incommensurate phases:
"phasons" 54 5. Present situation concerning the static properties of
incommensurate phases 58 5.1 Some examples of experimental typical phase
diagrams 58 5.2 Other specific properties: global hysteresis,
satellite broadening 62 5.3 Discussion 63
6. Quasicrystals 67 References 72
STRUCTURAL PHASE TRANSITIONS AND SPECIFIC HEAT ANOMALIES
E. Salje
1. Introduction 2. Experimental methods
75
75 77
vii
2.1 Scanning calorimetr~ 77 2.2 AC calorimetry 79 2.3 Adiabatic calorimetry 80
3. Reduction of. background heat capacities 82 4. Application of Landau theory 84 5. Fluctuations of the order parameter and
critical exponents 87 6. The influence of lattice imperfections 91 7. Order parameter coupling and excess specific heats 96 8. Coupled order parameters in feldspar 102
8.1 Na-feldspar 104 8.2 Ca-feldspar 106
9. Selected examples of structural phase trans~t~ons 110 10. Charge carrier induced structural phase transitions 112
References 114
5. WHAT CAN SPIN MODELS TELL US ABOUT THE BEHAVIOUR OF MINERALS?' 119
J. Yeomans
1. Introduction 2. Universality and phase diagrams 3. Modulated structures 4. Surfaces and interfaces
References
6. NEW DEVELOPMENTS IN RAMAN SPECTROSCOPY ON STRUCTURAL PHASE TRANSITIONS
U. Bismayer
119 120 127 136 140
143
1. Introduction 143 2. Theory 144 3. Applications of hard mode Raman spectroscopy 147
3.1 Displacive phase transitions and evidence for Na-K site ordering in alkali feldspar -experimental part 147
3.2 Phase transitions and order parameter treatment in feldspars 148
3.3 Phase transition in ferroelastic AS20S 157 3.4 Raman scattering of hard modes in stepwise
phase transitions in Pb3(Pl-xAsx04)2 161 3.5 Sodium nitrate 172 3.6 Magnesium cordierite 176
4. Conclusions 180 5. References 180
viii
7.
8.
9.
LINEAR AND CIRCULAR BIREFRINGENCE AND CRYSTAL STRUCTURES
A. M. Glazer
1. Introduction 2. Linear birefringence
2.1 Methods of measurement 2.2 Applications to crystals
3. Circular birefringence 3.1 Measurement and observation 3.2 Relationship to crystal structure 3.3 Calculation of optical rotation
4 . S urnrnary 5. References
EXSOLUTION, ORDERING AND STRUCTURAL TRANSFORMATIONS: SYSTEMATICS AND SYNERGISTICS
D. E. Laughlin and W. A. Soffa
185
185 187 187 192 198 198 201 206 211 211
213
1. Introduction 213 2. Isostructural decomposition 215
2.1 Introduction 215 2.2 Nucleation and growth 218 2.3 Spinodal decomposition 219
3. Atomic ordering 224 3.1 Single order parameter 224 3.2 Two order parameters 226
4. Magnetic ordering 245 4.1 Introduction 245 4.2 Miscibility gap in ferromagnetic binary systems 245 4.3 Further examples including magnetic transitions 251
5. Bicritical and tetracritical point 254 5.1 Introduction 254 5.2 Bicritical points 254 5.3 Tetracritical point 257
6. Closure 262 References 263
THERMOCHEMISTRY OF ALUMINIUM/SILICON ORDERING IN FELDSPAR MINERALS
M. A. Carpenter
265
1. Introduction 265 2. Some general features of Al/Si ordering transitions
in minerals 268 3. Macroscopic thermodynamic properties 271
3.1 Landau theory 272 3.2 Enthalpy measurements 274 3.3 Spontaneous strain 277
4. Transformation behaviour in feldspars 4.1 Alkali feldspars 4.2 Plagioclase feldspars 4.3 Incommensurate ordering
5. Kinetics 5.1 Disordering in potassium feldspar 5.2 Ordering in anorthite
6. Conclusions References
10. SOLID STATE NMR SPECTROSCOPY AND PHASE TRANSITIONS MINERALS
l. 2.
3. 4.
A. Putnis
Introduction Background theory and terminology 2.1 Magnetic resonance 2.2 Chemical shift 2.3 NMR of solids 2.4 Nuclear quadrupole resonance 2.5 Relaxation times 2.6 Fourier transform techniques 2.7 High resolution solid state NMR Structural phase transitions Displacive phase transitions
IN
4.1 Displ~ci~e transitions in perovskites, ABX3
5.
6.
7.
8.
4.2 The Pl-Il phase transition in anorthite, CaA12Si20a Orientational order-disorder transitions 5.1 N02 ordering in sodium nitrite, NaN02 Magic-angle spinning NMR 6.1 29Si NMR spectra 6.2 Empirical correlations of 29Si chemical shifts 6.3 29Si site assignments 6.4 Al,Si ordering in Mg-cordierite from 29Si NMR
spectra NMR spectra of quadrupolar nuclei 7.1 27Al MAS NMR spectra Conclusions References
ix
280 280 293 306 309 309 309 312 313
325
325 326 326 326 327 327 328 328 329 330 330 331 333 334 334 335 335 337 339
347 352 352 355 356
11. NONLINEAR DYNAMICS OF LATTICE MODELS FOR ELASTIC MEDIA 359
J. Pouget
1. Introduction 359 2. Part I - lattice model for martensitic transformations 361
2.1 The model 361 2.2 Equations of motion 365 2.3 Continuum model 366 2.4 Linear case 369
x
2.5 Solitary wave solutions 2.6 Conclusion
3. Part II - model for deformable lattices equipped with rotary microstructures 3.1 The model 3.2 Configuration A - equations, of motion 3.3 Influence of an applied field on the motion
a soliton 3.4 Configuration B - equations of motion 3.5 Conclusion References
370 379
380 380 382
of 390 392 396 397
12. EXPERIMENTAL STUDIES OF MINERAL ENERGETICS 403
A. Navrotsky
1. Introduction 403 2. Heat capacities, entropies and lattice vibrations 404
2.1 Basic relations and magnitudes 404 2.2 Experimental techniques 405 2.3 The interpretation of lattice heat capacities 407
3. Free energies of mineral reactions 410 3.1 General principles 410 3.2 Oxidation-reduction equilibria 411 3.3 Vapor pressure measurements 413 3.4 High pressure phase equilibria 413
4. Enthalpies of mineral reactions 416 5. Energetics of high pressure phase transitions, with
emphasis on the magnesium silicates 417 5.1 Relations between olivine, modified spinel and
spinel phases 417 5.2 "Pos t spinel" phases 423 5.3 Lattice vibrational models for post-spinel
phase transitions References
13. HEAT CAPACITY OF SOLIDS
M. J. Tello and A. Lopez-Echarri
1. Introduction 2. Importance of the specific heat measurements 3. Experimental systems
3.1 Adiabatic calorimetry 3.2 AC calorimetry
4. Experimental results 4.1 Solid to solid phase transition within the
Landau framework 4.2 Order-disorder systems References
425 430
433
433 434 438 438 441 448
448 453 456
xi
14. MAGNETIC ORDERING AND THERMODYNAMICS IN SILICATES 459
J. M. D. Coey and S. Ghose
1. Introduction 459 1.1 Background 459 1.2 Properties of noninteracting ions 462 1.3 Magnetic interactions and collective behaviour 467 1.4 Cation disorder 475 1.5 Experimental methods 479
2. Magnetic order in silicates 480 2.1 Group structures lf80 2.2 Chain structures 480 2.3 Sheet structures 486 2.4 Framework structures 488
3. Thermodynamic consequences 494 4. Conclusions 496
References 496
15. MOLECULAR DYNAMICS SIMULATIONS IN THE SOLID STATE SCIENCES 501
M. Dove
1. Computer simulations 501 1.1 Introduction 501 1.2 Simulation models 504 1.3 The molecular dynamics simulation technique 506
2. Techniques 508 2.1 Technical details for molecular dynamics
simulations 508 2.2 Ensembles 519 2.3 Potential models 524 2.4 Analysis of results from a simulation 532 2.5 Computers 550
3. Illustrative examples 552 3.1 Introduction 552 3.2 Orientational1y disordered crystals 552 3.3 Simulations of thiourea 577
4. Conclusions: the outlook for the use of molecular dynamics simulations in minerals physics 583 4.1 General summary 583 4.2 Application in the field of minerals physics:
general outlook 585 References 587
16. THE COMPUTER SIMULATION OF THE LATTICE DYNAMICS OF SILICATES
G. D. Price and S. C. Parker
1. Introduction
591
591
2. Atomistic simulation techniques 594 3. The q=O lattice vibrations of forsterite 595 4. The crystal dynamics of forsterite 598 5. Lattice dynamics and thermodynamic properties 603 6. The thermodynamic properties of forsterite 606 7. The thermodynamic properties of the Mg2SiOq polymorphs 611 8. Conclusion 616
References 617
17. COMPUTER MODELLING OF SILICATES
C. R. A. Catlow
1. Introduction 2. Aims and methodology 3. Interatomic potentials
3.1 Potential models for silicates 4. Applications
4.1 Simulation studies of zeolites 4.2 Defect energies in Mg2SiOq
5. Conclusions References
18. UV TO NIR SPECTRA OF SILICATE MINERALS OBTAINED BY MICROSCOPE SPECTROMETRY AND THEIR USE IN MINERAL THERMODYNAMICS AND KINETICS
K. Langer
619
619 619 622 623 627 627 636 637 638
639
1. Introduction 639 2. Some theoretical aspects 640
2.1 Spectroscopy 640 2.2 How does CFSE3d enter thermodynamic functions? 650
3. Methods of microscope-spectrometry 655 4. Applications 657
4.1 Cr 3+, an ion with nondegenerate ground state, in garnet, clinopyroxene and kyanite 657
4.2 Mn3+, an ion with degenerate ground state, in various silicate structures 663
4.3 Fe 3+-bearing point defects in fayalite, an attempt to solve a kinetic problem 672
5. Conclusions 679 References 682
19. RECENT ADVANCES IN THE MINERALOGICAL APPLICATIONS OF THE 57FE MOSSBAUER EFFECT 687
F. Seifert
1. Introduction 2. Mossbauer parameters
687 688
xiii
2.1 Debye-Waller factor 688 2.2 Line shape 688 2.3 Full width at half maximum intensity (half width) 688 2.4 Isomer shift 689 2.5 Quadrupole splitting 689 2.6 Nuclear Zeeman effect 689
3. Valence 690 4. Electron delocalization and homogeneous electronic
equilibrium 690 5. Site characterization 691
5.1 Ferric ion 691 5.2 Ferrous ion 691 5.3 Next nearest neighbours interaction 691
6. Site occupancy 693 7. Magnetic properties 693 8. Cryptocrystalline and amorphous phases 694
8.1 Poorly crystalline lepidocrocite y-FeOOH 694 8.2 Formation of an amorphous intermediate phase on
dehydroxylation of akageneite B-FeOOH 694 8.3 Silicate glasses 695
9. Diffusion studies 696 9.1 Self diffusion of ferric iron in rutile 696 9.2 Vacancy-related self diffusion in magnetite 696
10. Phase transitions 697 11. Two examples for pitfalls 698
11.1 Extraction of thermodynamic data from Mossbauer-derived site occupancies 698
11.2 Ferric iron in melilite 699 References 700
Subject Index 705
Preface
The role played by earth sciences in the scientific community has changed considerably during this century. Since the revolutionary discoveries of global processes such as plate tectonics, there has been an increasing awareness of just how fundamental many of the mechanisms which dominate in these processes depend on the physical properties of the materials of which the earth is made. One of the prime objectives of mineral sciences is now to understand and predict these properties in a truly quantitative manner. The macroscopic properties which are of most immediate interest in this context fall within the conventional definitions of thermodynamics, magnetism, elasticity, dielectric susceptibilities, conductivity etc. These properties reflect the microscopic contributions, at an atomistic level, of harmonic and anharmonic lattice vibrations, ionic and electronic transport as well as a great variety of ordering and clustering phenomena.
The advances made by solid state physicists and chemists in defining the underlying phenomena lnvolved in the thermal evolution of materials have stimulated major new research initiatives within the Earth Sciences. Earth Scientists have combined to form active groups within the wider community of solid state and materials scientists working towards a better understanding of those physical processes which govern not only the behaviour of simple model compounds but also that of complex materials like minerals. Concomitant with this change in direction has come an increasing awareness of the need to use the typical working tools of other disciplines. The experimental facilities in common use now range from neutron sources, spectroscopy and high resolution TEM to newly developed calorimetry and X-ray scattering techniques. Interdisciplinary research without doubt holds many exciting prospects and the ASI-meeting in Cambridge is a visible expression of the growing together of Earth Sciences with Physics and Chemistry in the fields of thermodynamics, phase transitions, kinetics, simulation-modelling, TEM and spectroscopy, including NMR, Mossbauer technique, EXFS, Raman-, infrared- and optical spectroscopy. This volume is a distillation of the meeting and, we hope, will provide fresh stimulation for scientific interaction in the future.
It is a great pleasure for me to use this opportunity of acknowledging the help given by members of the Departments of Earth Sciences and Physics in Cambridge, in the organisation of the meeting. I wish to thank, in particular, the local organising committee consisting of V. Heine, M.G. Bown, M.A. Carpenter , M.T. Dove, M.I. Johnston, J.D.C. McConnell, A. Putnis.
The meeting was generously funded by NATO and travel grants have been made available by NERC, SERC, NSF and NATO. On behalf of all the participants I thank these institutions for their support.
Cambridge Ekhard Salje
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LIST OF PARTICIPANTS
ABS-WURMBACH I.
ALLAN J.
ALVES A.C.P.
AMTHAUER G.
ANGEL R.
BALLET O.
BARBER D.
BAUM E.
BELLUSO E.
BISMAYER U.
BOBERSKI C.
BOLAND J.
BONELLO B.
BOROWITZ J.L.
BOWN M.
BRAMWELL, S.
Institut fur Mineralogie, Bochum University, Postfach 10 21 48, D-4630 Bochum, F.R. Germany
Department of Pure and Applied Physics, Trinity College, Dublin University, Dublin, Ireland
Departamento de Quimica, Coimbra University, 3039 Coimbra, Portugal
Institut fur Ceowissenschaften, Mineralogie, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria
Geophysical Laboratory, 2801 Upton Street, Washington DC 20008, U.S.A.
DRF/SPL-MDN C.E.N.G., 38041 Grenoble, France
Essex University, Wivenhoe Park, Colchester, Essex, C04 3SQ U.K.
Institut fur Mineralogie, Marburg University, Hans Meerwein Strasse, D-3550 Marburg, FR Germany
Dipartimento di Scienze della Terra, Universita degli Studi di Torino, 10123 Torino, Italy
Institut fur Kristallographie und Petrologie, Hannover University, D-3000 Hannover, FR. Germany
Institut f. Mineralogie, Ruhr-Universitat Bochum, D-4630 Bochum, F.R. Germany
Dept. of Earth & Space Sciences, SUNY at Stony Brook, Stony Brook, NY 11794, U.S.A.
Pierre et Marie Curie University, 4 place Jussieu 75005 Paris, France
SOREQ Nuclear Research Centre, 70600 Yavne, Israel
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ U.K.
Inorganic Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QR U.K.
xw
xviii
BREARLEY, A.
BROWN G.
BROWN N.
BROWN W.
BUCKLEY A.
CAPOBIANCO C.
CARPENTER M.A.
CATLOW C.R.A.
CATTI M.
CHRISTY A.
COEY J.M.D.
COPREAUX J.
CRESSEY G.
DACHS H.
DENOYER F.
DEPMEIER W.
DOMENEGHETTI C
DOVE M.T.
Department of Geology, New Mexico University, Albuquerque, NM 87131, U.S.A.
Department of Geology, Stanford University, Stanford, CA 94305, U.S.A.
Department of Geology, Princeton University, Guyot Hall, Princeton, NY 08544, U.S.A.
CNRS-CRPG, BP 20, 54501 Vandoeuvre, France
Inorganic Chemistry Laboratory, Oxford University South Parks Road, Oxford OX1 3QR, U.K.
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EQ U.K.
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EQ U.K.
Department of Chemistry, Keele University, Keele, ST5 5BG, U.K.
Dipartamento di Chimica Fisica ed Elettrochimica, Milan University, 20133 Milan, Italy
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ U.K.
Department of Pure and Applied Physics, Trinity College, Dublin, Ireland
Laboratoire de Mineralogie & Cristallographie, 4 place Jussieu, 75005 Paris, France
Dept of Mineralogy, British Museum (Natural History), Cromwell Road, London SW7 5BD, U.K.
Hahn-Meitner-Institut, Glienicker Str. 100, D-1000 Berlin, F.R. Germany
Laboratoire de Physique des Solides, Paris Sud University, Bat 510, 91450 Orsay, France
Institut fur Kristallographie, Karlsruhe University, D-7500 Karlsruhe, F.R. Germany
CNR-Centro di Studio Cristallografia Strutturale, Via Bassi n.4, 27100 Pavia, Italy
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ U.K.
DUBESSY J.
ESCOBAR V.
FERNANDEZ-DIAZ L.
FEUER H.
FISCHER M.
FRITZER H.P.
GALLIOS G.
GAVRIELI 1.
GHOSE S.
GIAMPAOLO C.
GILLET P.
GLAZER M.A.
GOULD S.
GREGORKIEWITZ M.
GUTTLER B
HATCH D.M.
HAWTHORNE F.
CREGU, 3 rue du Bois de la Champelle, 54501 Vandoeuvre, France
Department of Mineral Resouces Engineering, Imperial College, London SW7 2AZ, U.K.
Dpto. Cristalografia y Mineralogia, Complutense de Madrid University, 28040 Madrid, Spain
Institut fur Kristallographie, Frankfurt University, D-6000 Frankfurt, F.R. Germany
xix
Pierre et Marie Curie University, 4 place Jussieu 75005 Paris, France
Institut of Physical & Theoretical Chemistry, Graz Univ. of Technology, A-8010 Graz, Austria
Aristotelian Univeristy of Thessaloniki, 54006 Thessaloniki, Greece
Department of Geology, The Hebrew University, Givat Ram, 91904 Jerusalem, Israel
Department of Geological Sciences, Washington University, Seattle, WA 98195, U.S.A.
Dip. Scienze della Terra, Univ. di Roma "La Sapienza", P. Ie Aldo Moro 5, 00100 Rome, Italy
Laboratoire de Mineralogie Physique, CAESS, Rennes University, 35042 Rennes, France
Department of Physics, Oxford University, Oxford OX1 2JD, U.K.
Beevers Miniature Models Unit, Dept. Chemistry, Edinburgh University, Edinburgh EH9 3HS, U.K.
Instituto de Ciencia de Materiales, CSIC, Serrano 115 bis, 28006 Madrid, Spain
Department of Earth Science, University of Cambridge, Downing Street, Cambridge CB2 3EQ U.K.
Department of Physics & Astronomy, Brigham Young University, Provo, Utah 84602, U.S.A.
Geological Sciences, Manitoba University, Winnipeg, R3T 2N2, Canada
xx
HEINE V.
HESS N.
HONIG 1.
HOVIS G.L.
HUCRER M.
JACKSON W.
JONES I.
KARATAS C.
KENNEDY J.
KENNEDY S.W.
KIRKPATRICK J.
KRAUSE C.
KUPPERS H.
LANGER K.
LAUGHLIN D.E.
LE BRETON N.
LE CLEAC'H A.
Department of Physics, Univeristy of Cambridge, Cavendish Laboratory, Cambridge, CB3 OHE, U.K.
Department of Geological Sciences, Washington University, Seattle, WA 98112, U.S.A.
Department of Chemistry, Purdue University, West Lafayette, IL 47907, U.S.A.
Department of Geology, Lafayette College, Easton, PA 18042, U.S.A.
Departement des Sciences de la Terre, Orleans, University, 45067 Orleans, France
Department of Geology, Stanford University, Stanford, CA 94305, U.S.A.
Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 ORE, U.K.
Materials Engineering, Middle East Technical University, 06531 Ankara, Turkey
University of Kent at Canterbury, Canterbury, Kent, U.K.
Adelaide University, Adelaide, Australia
Department of Geology, Illinois University, 1301 W. Green Street, Urbana IL 61801, U.S.A.
Kernforschungszentrum Karlsruhe, Postfach 3640, D-7500 Karlsruhe, F.R. Germany
Mineralogisches Institut, Kiel University, Olshausenstr. 40, D-2300 Kiel, F.R. Germany
Institut fur Mineralogie und Kristallographie, Technische University, D-1000 Berlin, F R Germany
Dept. of Metallurgical Engineering & Materials Science, Carnegie Mellon University, Pittsburgh 15213, U.S.A.
Institut fur Mineralogie, Ruhr University, D-4630 Berlin, F.R. Germany
Lab. de Mineralogie Physique, CAESS, Rennes University, 35042 Rennes, France
LIEBERMANN R.
MADON, M.
MAGALHAES C.
MANGHNANI M.
McCAMMON C.
McCONNELL J.D.C.
McKNIGHT A.S.
MEIKE A.
MOTT N.
MULLER K.A.
MURTY K.S.
NAVROTSKY A.
NORD G.
ONEN A.P.
PALMER D.
PALOSZ B.
PAWLEY A.
Department of Earth & Space Sciences, State Univ of New York, Stony Brook, NY 11794, U.S.A.
Department of Geological Sciences, University College London, London, WC1E 6BT, U.K.
Department of Chemistry, Aveiro University, 3800 Aveiro, Portugal
Department of Geophysics, Hawaii University, 2525 Correa Road, Honolulu, Hawaii 96822 U.S.A.
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Department of Geological Sciences, British Columbia University, Vancouver BC, V6T 2B4 Canada
Department of Earth Sciences, Oxford University, Parks Road, Oxford OXI 3PR, U.K.
Department of Geology, Hull University, Cottingham Road, Hull, HU6 8DF, U.K.
Earth Sciences Division, Lawrence Berkeley Lab., 1 Cyclotron Road, Berkeley, CA 94720, U.S.A.
Department of Physics, University of Cambridge, Cavendish Laboratory, Cambridge CB3 OHE, U.K.
IBM Research Division, Zurich Research Laboratory 8803 Ruschlikon, Switzerland
Department of Geology, The University, Law College Compound, 440 001 Nagpur, India
Department of Geological Sciences, Princeton University, Princeton, NJ 08544, U.S.A.
United States Geological Survey, 959 National Center, Reston, VA 22092, U.S.A.
Geological Engineering Department, Middle East Technical University, 06531 Ankara, Turkey
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ U.K.
Institut fur Kristallographie und Mineralogie, Munchen University, D-8000 Munchen, F.R. Germany
Grant Institute of Geology, Edinburgh University West Mains Road, Edinburgh EH9 3JW, U.K.
xxii
PERCIVAL M.J.L.
PERTLIK F.
PETERSON R.C.
PHILLIPS B.L.
PIEROTH M.
POON, W.C-K.
POUGET J.
PREWITT C.
PRICE G.D.
PUTNIS A.
REDFERN S.A.T.
REEDER R.
REMSBERG A.
ROSS II C.R.
ROSS N.L.
ROUX J.
RUBBO M.
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ U.K.
Institut fur Mineralogie und Kristographie, Wi en University, A-1010 Vienna, Austria
Department of Geological Sciences, Queen's University, Kingston, Ontario K7L 3N6, Canada
Department of Geology, Illinois University, 1301 W. Green Street, Urbana, Illinois 61801, U.S.A.
Fak. f. Physik, Konstanz University, Bucklestr. 13, D-7750 Konstanz, F.R. Germany
Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE, U.K.
Mechanique Theorique, Univ Pierre et Marie Curie, 4 place Jussieu, 75230 Paris, France
Geophysical Laboratory, 2801 Upton Street, N.W., Washington DC, 20008, U.S.A.
Department of Geological Sciences, University College London, London, WC1E 6BT, U.K.
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ U.K.
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ U.K.
State University of New York at Stony Brook, Stony Brook, NY 11794, U.S.A.
Department of Earth & Space Sciences, State Univ of New York, Stony Brook, NY 11794, U.S.A.
Bayerisches Geoinstitut, Bayreuth University, D-8580 Bayreuth, F.R. Germany
Geophysical Laboratory, 2801 Upton Street NW, Washington DC 20008, U.S.A.
CNRS-SCM, IA rue de la Ferollerie, Orleans, France
Dipartimento di Scienze della Terra, Via S. Massimo, 10123 Torino, Italy
SALJE E.
SANTAMARIA C.M.
SANZ LAZARO J.
SCHMAHL W.W.
SCHMIDBAUER E.
SEBALD A.
SEIFERT F.
SHI PING
SOBRADOS I.
SOFFA W.A.
STOBBS W.M.
STUCKENSCHMIDT E.
SYKES-NORD J.
TAZZOLI V.
TELLO M.J.
TRIBAUDINO M.
TURNER P.
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Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ U.K.
Dpto. Fisica, Facultad de Ciencias, Pais Vasco University, 48080 Bilbao, Spain
Instituto de Ciencia de Materials, CSIC, Serrano 115 dpdo., 28006 Madrid, Spain
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ U.K.
Institut fur Geophysik, Munchen University, Theresienstr. 41, D-8000 Munchen, F.R. Germany
Department of Chemistry, Durham University, South Road, Durham, DH1 3LE, U.K.
Bayerisches Geoinstitut, Bayreuth University, D-8580 Bayreuth, F.R. Germany
Grant Institute of Geology, Edinburgh University, West Mains Road, Edinburgh EH9 3JW, U.K.
Instituto di Ciencia de Materiales, CSIC, Serrano 115 bis, 28006 Madrid, Spain
Dept of Metallurgical Engineering & Material Science, Carnegie-Mellon Univ, Pittsburg PA 15213
Dept. of Materials Science & Metallurgy, Cambridge University, Cambridge CB2 3QZ, U.K.
Institut fur Kristallographie und Mineralogie, Frankfurt Univ., D-6000 Frankfurt, F.R. Germany
Department of Earth & Environmental Science, CUNY New York, NY 10036, U.S.A.
Dip. Scienze della Terra, Sez. Mineralogia, Pavia University, Via Bassi n.4, 27100 Pavia, Italy
Departamento de Fisica, Facultad de Ciencias, Pais Vasco University, Bilbao, Spain
Dipartimento di Scienze della Terra, Torino University, 10123 Torino, Italy
Bruker Spectrospin Limited, Unit 3, 209 Torrington Avenue, Coventry, CV4 9HN, U.K.
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WALL A.
WANG A.
WEBER H-P.
WRIGHT K.
WRUCK B.
YEOMANS J.
ZANAZZI P.F.
ZOUBOULIS A.
Department of Geological Sciences, University College London, London, WC1E 6BT, U.K.
Lab. Spectrochimie Infrarouge et Raman, Lille I University, 59655 Lille, France
Institut de Cristallographie, Lausanne University B.S.P., CH-1015 Lausanne-Dorigny, Switzerland
Department of Geological Sciences, University College London, London, WC1E 6BT, U.K.
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ U.K.
Department of Physics, Oxford University, Oxford, OX1 2JD, U.K.
Dipartimento di Scienze della Terra, Pizza University, 06100 Perugia, Italy
Department of Chemistry, Aristotelian University, 54006 Thessaloniki, Greece
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