Diffusion in Minerals and Melts

1056 Pages·2010·138.24 MB·English

by  Youxue Zhang (editor), Daniele J. Cherniak (editor)

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
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CHANTILLY, VIRGINIA, 20151-1125, U.S.A.
WWW.MINSOCAM.ORG
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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
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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
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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
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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
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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
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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
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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