Diffusion in Minerals and Melts PDF
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REVIEWS IN MINERALOGY AND GEOCHEMISTRY Volume 72 2010 Diffusion in Minerals and Melts EDITORS Youxue Zhang University of Michigan Ann Arbor, Michigan, U.S.A. Daniele J. Cherniak Rensselaer Polytechnic Institute Troy, New York, U.S.A. ON THE COVER: Top Left: A BSE image showing zonation of zircon (Zhang 2008, Geochemical Kinetics). Lower Right: Ar diffusivity in air, water, melts and hornblende, and heat diffusivity as a function of temperature (data are from various sources). Series Editor: Jodi J. Rosso MINERALOGICAL SOCIETY OF AMERICA GEOCHEMICAL SOCIETY Reviews in Mineralogy and Geochemistry, Volume 72 Diffusion in Minerals and Melts ISSN 1529-6466 ISBN 978-0-939950-86-7 COPYRIGHT 2010 THE MINERALOGICAL SOCIETY OF AMERICA 3635 CONCORDE PARKWAY, SUITE 500 CHANTILLY, VIRGINIA, 20151-1125, U.S.A. WWW.MINSOCAM.ORG The appearance of the code at the bottom of the first page of each chapter in this volume indicates the copyright owner's consent that copies of the article can be made for personal use or internal use or for the personal use or internal use of specific clients, provided the original publication is cited. The consent is given on the condition, however, that the copier pay the stated per-copy fee through the Copyright Clearance Center, Inc. for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to other types of copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. For permission to reprint entire articles in these cases and the like, consult the Administrator of the Mineralogical Society of America as to the royalty due to the Society. Diffusion in Minerals and Melts 72 Reviews in Mineralogy and Geochemistry 72 FROM THE SERIES EDITOR The chapters in this volume represent an extensive compilation of the material presented by the invited speakers at a short course on Diffusion in Minerals and Melts held prior (December 11-12,2010) to the Annual fall meeting of the American Geophysical Union in San Francisco, California. The short course was held at the Napa Valley Marriott Hotel and Spa in Napa, California and was sponsored by the Mineralogical Society of America and the Geochemical Society. At the MSA website, www.minsocam.org/MSA/RIM, the supplemental material associated with this volume can be found and the reader is encouraged to have a look at it. Any errata will also be posted there. The reader will also be able to find links to the electronic copies of this and other RiMG volumes. Jodi 3*. P-osso. Series Editor West Richland, Washington October 2010 PREFACE Geologists often need to apply diffusion theory and data to understand the degree of mass transfer, infer temperature-time histories, and address a wide range of geological problems. The aim of this volume is to provide practitioners the necessary background and data for such applications. We have made efforts to present a comprehensive overview, with discussion and assessment of diffusion data in a broad range of rock-forming minerals and all geologically rel- evant melts. Extensive data tables are provided as online supplements (as well as at websites maintained by individual authors), both for general usage by readers, and for experimentalists and theoreticians in the field to develop greater understanding of diffusion and plan future research directions. We would like to take this opportunity to thank the authors of individual chapters, and those who reviewed the chapters. The reviewers are: Don Baker, Harald Behrens, Bill Carlson, Michael Carroll, Fidel Costa, John Farver, John Ferry, Jiba Ganguly, Matt Heizler, Jannick Ingrin, Motoo Ito, David Kohlstedt, Ted Labotka, Chip Lesher, Yan Liang, Thomas Mueller, Jim Mungall, Martin Reich, Rick Ryerson, Jim Shelby, Frank Spera, Jim Van Orman, Yong-Fei Zheng, and anonymous reviewers. This volume and the accompanying short course in Napa Valley were made possible by generous support for student participants from the US National Science Foundation. The preparation of this volume and the short course benefited tremendously from the efforts of Jodi Rosso and Alex Speer. Youxue Zhang Daniele Cherniak Ann Arbor, Michigan Troy, New York 1529-6466/10/0072-0000$05.00 DOT: 10.2138/rmg.2010.72.0 TABLE OF CONTENTS 1 Diffusion in Minerals and Melts: Introduction Y. Zhang, D.J. Cherniak INTRODUCTION: RATIONALE FOR THIS VOLUME 1 SCOPE AND CONTENT OF THIS VOLUME 2 REFERENCES 3 Z. Diffusion in Minerals and Melts: Theoretical Background Y. Zhang INTRODUCTION 5 FUNDAMENTALS OF DIFFUSION 6 Basic concepts 6 Microscopic view of diffusion 9 Various kinds of diffusion 10 General mass conservation and various forms of the diffusion equation 14 Diffusion in three dimensions (isotropic media) 17 SOLUTIONS TO BINARY AND ISOTROPIC DIFFUSION PROBLEMS 18 Thin-source diffusion 18 Comments about fitting data 19 Sorption or desorption 20 Diffusion couple or triple 22 Diffusive crystal dissolution 23 Variable diffusivity along a profile 25 Homogenization of a crystal with oscillatory zoning 26 One dimensional diffusional exchange between two phases at constant temperature 27 Spinodal decomposition 28 Diffusive loss of radiogenic nuclides and closure temperature 29 DIFFUSION IN ANISOTROPIC MEDIA 32 MULTICOMPONENT DIFFUSION 35 Effective binary approach, FEBD and SEBD 36 Modified effective binary approach (activity-based effective binary approach) 39 Diffusivity matrix approach 40 Activity-based diffusivity matrix approach 42 Origin of the cross-diffusivity terms 42 DIFFUSION COEFFICIENTS 43 Temperature dependence of diffusivities; Arrhenius relation 43 Pressure dependence of diffusivities 43 Diffusion in crystalline phases and defects 45 Diffusivities and oxygen fugacity 47 Compositional dependence of diffusivities 47 iv Diffusion in Minerals and Melts - Table of Contents Relation between diffusivity, particle size, particle charge, and viscosity 48 Diffusivity and ionic porosity 50 Compensation "law" 50 Interdiffusivity and self diffusivity 50 CONCLUSIONS 53 ACKNOWLEDGMENTS 53 REFERENCES 53 APPENDIX 1. EXPRESSION OF DIFFUSION TENSOR IN CRYSTALS WITH DIFFERENT SYMMETRY 58 3 Non-traditional and Emerging Methods for Characterizing Diffusion in Minerals and Mineral Aggregates E.B. Watson, R. Dohmen INTRODUCTION 61 THE THIN-FILM METHOD AND PULSED LASER DEPOSITION (PLD): PRINCIPLES AND RECENT DEVELOPMENTS 63 Definition of a thin film 63 Why use thin films? 64 Fitting of diffusion profiles from thin-film diffusion couples 65 Analytical solutions - examples 65 Fitting uncertainties 67 Pulsed laser ablation: a versatile method for thin film deposition 68 Application of PLD to diffusion studies - examples 70 Single layer configurations 71 Double layer configurations 74 THE POWDER-SOURCE TECHNIQUE 78 Overview and history 78 Rationale and details 79 Analytical considerations, advantages and drawbacks 80 ION IMPLANTATION AND DIFFUSION EXPERIMENTS 82 Introduction 82 Interactions between energetic ions and solids 83 Ion implantation 84 Mathematical aspects of implantation and diffusion 85 Complications and examples 87 THE DETECTOR-PARTICLE METHOD FOR STUDIES OF GRAIN-BOUNDARY DIFFUSION 90 Context and history 90 The detector-particle approach: general considerations and examples 91 Numerical simulation: constant-surface model 94 A simple analysis of the detector-particle method 99 Concluding remarks on detector particles 100 ACKNOWLEDGMENTS 101 REFERENCES 101 v Diffusion in Minerals and Melts - Table of Contents Analytical Methods in Diffusion Studies D.J. Cherniak, R. Hervig, J. Koepke, Y. Zhang, D. Zhao INTRODUCTION 107 "CLASSICAL" METHODS FOR MEASURING DIFFUSION PROFILES USING RADIOACTIVE TRACERS 109 Serial sectioning 109 Autoradiography 110 ELECTRON MICROPROBE ANALYSIS Ill Principles of EMPA Ill Instrumentation for EMPA 113 Applications and limitations of EMPA 120 Summary 123 SECONDARY ION MASS SPECTROMETRY (SIMS) 123 Basic principles of SIMS 123 Using SIMS to measure diffusion profiles 125 Depth profile analyses 129 Ion implantation and SIMS 134 Summary comments 134 LASER ABLATION ICP-MS (LA ICP-MS) 134 RUTHERFORD BACKSCATTERING SPECTROMETRY (RBS) 137 Basic principles of RBS 137 Depth and mass resolution 140 Example applications of RBS in diffusion studies 141 NUCLEAR REACTION ANALYSIS (NRA) 143 ELASTIC RECOIL DETECTION (ERD) 147 FOURIER TRANSFORM INFRARED SPECTROSCOPY 148 Vibrational modes and infrared absorption 148 Instrumentation for Infrared Spectroscopy 152 Different types of IR spectra 152 Calibration 153 Applications to geology 155 SYNCHROTRON X-RAY FLUORESCENCE MICROANALYSIS (li-SRXRF) 156 Instrumental setup, spectra acquisition and data processing 156 Sample preparation 158 Applications of |i-SRXRF for measuring trace element diffusivities in silicate melts 158 ACKNOWLEDGMENTS 160 REFERENCES 160 D Diffusion of H, C, and O Components in Silicate Melts Y. Zhang, H. Ni INTRODUCTION 171 vi Diffusion in Minerals and Melts - Table of Contents DIFFUSION OF THE H20 COMPONENT 172 H20 speciation: equilibrium and kinetics 172 H20 diffusion literature 178 H20 diffusion, theory and data summary 180 MOLECULAR H2 DIFFUSION 191 DIFFUSION OF THE CO, COMPONENT 197 OXYGEN DIFFUSION 199 Self-diffusion of oxygen in silicate melts under dry conditions 200 Chemical diffusion of oxygen under dry conditions 207 "Self' diffusion of oxygen in the presence of H20 209 "Self' diffusion of oxygen in natural silicate melts in natural environments 211 Contribution of C02 diffusion to 180 transport in C02-bearing melts 213 Oxygen diffusion and viscosity: applicability of the Eyring equation 216 02 DIFFUSION IN PURE SILICA MELT 217 SUMMARY AND CONCLUSIONS 219 ACKNOWLEDGMENTS 219 REFERENCES 219 O Noble Gas Diffusion in Silicate Glasses and Melts H. Behrens INTRODUCTION 227 EXPERIMENTAL AND ANALYTICAL METHODS 228 Studies at atmospheric and sub-atmospheric pressure 228 Studies at high-pressure 230 DIFFUSION SYSTEMATICS 232 Temperature dependence of diffusivity 232 Pressure dependence of diffusivity 233 Comparison of different noble gases in the same matrix glass 236 COMPOSITIONAL EFFECTS ON NOBLE GAS DIFFUSION 238 He diffusion 238 Ne diffusion 240 Ar diffusion 241 Kr, Xe and Rn diffusion 248 COMPARISON OF NOBLE GASES AND MOLECULAR SPECIES 249 H2 diffusion 249 H20 diffusion 250 O, diffusion 250 N2 diffusion 251 CO, diffusion 252 ACKNOWLEDGMENTS 252 RERERENCES 253 APPENDIX 257 vii Diffusion in Minerals and Melts - Table of Contents Observations and Applications to Magmatic Systems C.E. Lesher INTRODUCTION 269 ADDITIONAL TERMINOLOGY 270 THEORETICAL CONSIDERATIONS 271 Self and tracer diffusion 271 Intradiffusion 276 Polyanionic diffusion 280 EXPERIMENTAL METHODS AND DATA 283 Thin source method 283 Diffusion couple method 284 Capillary-reservoir method 284 Gas exchange method 285 DISCUSSION 285 Background 285 Ionic charge and size 286 Temperature 288 Viscosity and the Eyring diffusivity 291 Pressure 296 CONCLUDING REMARKS 303 ACKNOWLEDGMENTS 305 REFERENCES 305 O Diffusion Data in Silicate Melts Y. Zhang, H. Ni, Y. Chen INTRODUCTION 311 Terminology 312 General comments about experimental methods to extract diffusivities 313 Grouping of the elements 315 Data compilation 315 Quantification of D as a function of '/ . H0, P,f and melt composition 317 2 0l DIFFUSION OF INDIVIDUAL ELEMENTS 317 Diffusion of major elements versus minor and trace elements 317 H diffusion 320 The alkalis (Li, Na, K, Rb, Cs, Fr) 320 The alkali earths (Be, Mg, Ca, Sr, Ba, Ra) 330 B, Al, Ga, In, and T1 340 C, Si, Ge, Sn and Pb 345 N, P,As, Sb, Bi 352 O, S, Se, Te, Po 354 F, CI, Br, I, At 356 He, Ne, Ar, Kr, Xe, Rn 360 viii Diffusion in Minerals and Melts - Table of Contents Sc, Y, REE 360 Ti, Zr, Hf 375 V, Nb, Ta 380 Cr, Mo, W 383 Mn, Fe, Co, Ni, Cu, Zn 383 Tc, Ru, Rh, Pd, Ag, Cd 389 Re, Os, Ir, Pt, Au, Hg 389 Ac,Th, Pa, U 391 DISCUSSION 393 The empirical model by Mungall (2002) 393 Effect of ionic size on diffusivities of isovalent ions 395 Dependence of diffusivities on melt composition 397 Diffusivity sequence in various melts 398 CONCLUDING REMARKS 402 ACKNOWLEDGMENTS 404 REFERENCES 404 s Multicomponent Diffusion in Molten Silicates: Theory, Experiments, and Geological Applications Y. Liang INTRODUCTION 409 IRREVERSIBLE THERMODYNAMICS AND MULTICOMPONENT DIFFUSION 411 The rate of entropy production 411 Diffusing species and choice of endmember component 412 GENERAL FEATURES OF MULTICOMPONENT DIFFUSION 414 Solutions to multicomponent diffusion equations 414 Essential features of multicomponent diffusion 415 EXPERIMENTAL STUDIES OF MULTICOMPONENT DIFFUSION 423 Experimental design and strategy 423 Inversion methods 425 Experimental results 428 EMPIRICAL MODELS FOR MULTICOMPONENT DIFFUSION 434 Empirical models 434 Experimental tests of the empirical models 436 GEOLOGICAL APPLICATIONS 437 Modeling isotopic ratios during chemical diffusion in multicomponent melts 437 Convective crystal dissolution in a multicomponent melt 438 Crystal growth and dissolution in a multicomponent melt 441 FUTURE DIRECTIONS 442 ACKNOWLEDGMENTS 443 REFERENCES 443 ix Diffusion in Minerals and Melts - Table of Contents IU Oxygen and Hydrogen Diffusion in Minerals J.R. Farver INTRODUCTION 447 EXPERIMENTAL METHODS 447 Bulk exchange experiments 447 Single crystal experiments 448 ANALYTICAL METHODS 449 Mass Spectrometry 449 Nuclear Reaction Analysis 450 Fourier Transform Infrared Spectroscopy 450 Other methods 450 RESULTS 451 Quartz 451 Feldspars 455 Olivine 461 Pyroxene 465 Amphiboles 470 Sheet silicates 471 Garnet 472 Zircons 474 Titanite 474 Melilite 475 Tourmaline and beryl 476 Oxides 477 Carbonates 480 Phosphates 482 DISCUSSION 483 Effect of temperature 483 Effect of mineral structure 485 Empirical methods 486 Anisotropy 486 Pressure dependence 488 Effect of water 488 Hydrogen chemical diffusion and the role of defects 489 ACKNOWLEGMENTS 490 REFERENCES 490 I I Diffusion of Noble Gases in Minerals E.F. Baxter INTRODUCTION 509 The interpretive challenge of bulk-degassing experiments 510 HELIUM 513 He in apatite 514 x
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