Diffusion in minerals and melts : [ Short Course on Diffusion in … · 2012. 9. 3. ·...
Transcript of Diffusion in minerals and melts : [ Short Course on Diffusion in … · 2012. 9. 3. ·...
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REVIEWS in MINERALOGY
and GEOCHEMISTRY
Volume 72 2010
Diffusion in
Minerals and Melts
EDITORS
Youxue Zhang
Daniele J. Cherniak
University ofMichiganAnn Arbor, Michigan, U.S.A.
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
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TABLE OF CONTENTS
1 Diffusion in Minerals and Melts: Introduction
Y. Zhang, D.J. Chemiak
INTRODUCTION: RATIONALE FOR THIS VOLUME 1
SCOPE AND CONTENT OF THIS VOLUME 2
REFERENCES 3
JL Diffusion in Minerals and Melts:Theoretical Background
K Zhang
INTRODUCTION 5
FUNDAMENTALS OF DIFFUSION 6
Basic concepts 6
Microscopic view of diffusion 9Various kinds of diffusion 10
General mass conservation and various forms of the diffusion equation 14
Diffusion in three dimensions (isotropic media) 17SOLUTIONS TO BINARY AND ISOTROPIC DIFFUSION PROBLEMS 18
Thin-source diffusion 18
Comments about fitting data 19
Sorption or desorption 20Diffusion couple or iriple 22Diffusive crystal dissolution 23Variable diffusivily along a profile 25
Homogenization of a crystal with oscillatory zoning 26One dimensional diffusional exchange between two phases at
constant temperature 27
Spinodal decomposition 28Diffusive loss of radiogenic nuclides and closure temperature 29
DIFFUSION IN ANISOTROPIC MEDIA 32
MULTICOMPONENT DIFFUSION 35
Effective binary approach, FEBD and SEBD 36Modified 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 42DIFFUSION COEFFICIENTS 43
Temperature dependence of diffusivities; Arrhenius relation 43Pressure dependence ofdiffusivities 43Diffusion in crystalline phases and defects 45Diffusivities and oxygen fugacity 47Compositional dependence of diffusivities 47
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Diffusion in Minerals and Melts - Table ofContents
Relation between diffusivity, particle size, particle charge, and viscosity
Diffusivity and ionic porosityCompensation "law"
Interdiffusivity and self diffusivityCONCLUSIONS
ACKNOWLEDGMENTS
REFERENCES
APPENDIX 1. EXPRESSION OF DIFFUSION TENSOR IN CRYSTALS
WITH DIFFERENT SYMMETRY
Non-traditional and Emerging Methods for CharacterizingDiffusion in Minerals and Mineral Aggregates
E.B. Watson, R. Dolimen
INTRODUCTION f<
Why use thin films? '> '>
Fitting of diffusion profiles from thin-film diffusion couples h>
Analytical solutions - examples
Fitting uncertainties ^"
Pulsed laser ablation: a versatile method for thin film deposition (
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Diffusion in Minerals and Melts - Table of Contents
4 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 111
Principles of EMPA IllInstrumentation 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 129Ion implantation and SIMS 134
Summary comments 134LASER ABLATION 1CP-MS (LA ICP-MS) 134RUTHERFORD BACKSCATTERING SPECTROMETRY (RBS) 137
Basic principles of RBS 137
Depth and muss resolution 140Example 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 148Instrumentation for Infrared Spectroscopy 152Different types of IR spectra 152
Calibration 153
Applications to geology 155SYNCHROTRON X-RAY FLUORESCENCE MICROANALYSIS (u-SRXRF) 156
Instrumental setup, spectra acquisition and data processing 156
Sample preparation 158
Applications of (.t-SRXRF for measuring trace element diffusivitiesin 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 OF THE H20 COMPONENT
H20 speciation: equilibrium and kineticsH,0 diffusion literature
H20 diffusion, theory and data summaryMOLECULAR H2 DIFFUSION
DIFFUSION OF THE CO, COMPONENT
OXYGEN DIFFUSION
Self-diffusion of oxygen in silicate melts under dry conditions
Chemical diffusion of oxygen under dry conditions"Self diffusion of oxygen in the presence of H,0
"Self diffusion of oxygen in natural silicate melts in natural environments
Contribution of CO, diffusion to lfiO transport in C02-bearing melts
Oxygen diffusion and viscosity: applicability of the Eyring equationO, DIFFUSION IN PURE SILICA MELT
SUMMARY AND CONCLUSIONS
ACKNOWLEDGMENTS
REFERENCES
6 Noble Gas Diffusion in Silicate Glasses and MeltsH. lichmn
INTRODUCTION '"'
EXPERIMENTAL AND ANALYTICAL METHODS *
Studies at atmospheric and sub-atmospheric pressureStudies at high-pressure
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DIFFUSION SYSTEMATICS '
Temperature dependence of diffusivity ;'
Pressure dependence of diffusivity -1 •
Comparison of different noble gases in the same matrix glass ;'
COMPOSITIONAL EFFECTS ON NOBLE GAS DIFFUSION
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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 280EXPERIMENTAL METHODS AND DATA 283
Thin source method 283
Diffusion couple method 284
Capillary-reservoir method 284Gas exchange method 285
DISCUSSION 285
Background 285Ionic charge and size 286
Temperature 288
Viscosity and the Eyring diffusivity 291Pressure 296
CONCLUDING REMARKS 303
ACKNOWLEDGMENTS 305
REFERENCES 305
O Diffusion Data in Silicate Melts
Y. Zhang, H. M, Y. Chen
INTRODUCTION 311
Terminology 312General comments about experimental methods to extract diffusivities 313
Grouping of the elements 315Data compilation 315Quantification of D as a function of T, H,0, P,f(), and melt composition 317
DIFFUSION OF INDIVIDUAL ELEMENTS '. 317Diffusion of major elements versus minor and trace elements 317H diffusion 320
The alkalis (Li, Na, K, Rb, Cs, Fr) 320The alkali earths (Be, Mg, Ca, Sr, Ba, Ra) 330
B, A1, Ga, In, and TI 340C, Si, Ge, Snand Pb 345N,P, As, Sb,Bi 352O, S, Se, Te, Po 354
F,Cl,Br, I, At 356
He, Ne.Ar, Kr,Xe, Rn 360
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Sc,Y,REE 3o(i
Ti,Zr,Hf 375
V, Nb.Ta 3W>
Cr, Mo, W 3N3
Mn, Fe, Co, Ni, Cu, Zn 383
Tc, Ru, Rh, Pd,Ag, Cd 3JW
Re, Os, Ir, Pt, Au, Hg 3Kli
Ac,Th,Pa, U 3^)1
DISCUSSION 3M3
The empirical model by Mungall (2002) 33
Effect of ionic size on diffusivities of isovalent ions 3l>5
Dependence of diffusivities on melt composition 3')?
Diffusivity sequence in various melts 3l'.SCONCLUDING REMARKS 402
ACKNOWLEDGMENTS 40-1
REFERENCES 404
7 Multicomponent Diffusion in Molten Silicates:
Theory, Experiments, and Geological Applications
Y. Liang
INTRODUCTION 40"
IRREVERSIBLE THERMODYNAMICS AND MULTICOMPONENT DIFFUSION 41 I
The rate of entropy production 411
Diffusing species and choice of endmember component 412GENERAL FEATURES OF MULTICOMPONENT DIFFUSION 411
Solutions to multicomponent diffusion equations 41 -I
Essential features of multicomponent diffusion 41 5EXPERIMENTAL STUDIES OF MULTICOMPONENT DIFFUSION 423
Experimental design and strategy 42.<
Inversion methods 425
Experimental results 42s
EMPIRICAL MODELS FOR MULTICOMPONENT DIFFUSION 434
Empirical models 43-1
Experimental tests of the empirical models 43d
GEOLOGICAL APPLICATIONS 437
Modeling isotopic ratios during chemical diffusion in multicomponent melts 437Convective crystal dissolution in a multicomponent melt 43S
Crystal growth and dissolution in a multicomponent melt 441
FUTURE DIRECTIONS 442
ACKNOWLEDGMENTS 443
REFERENCES 443
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1 0 Oxygen and Hydrogen Diffusion in MineralsJ.R. Farver
INTRODUCTION 447
EXPERIMENTAL METHODS 447
Bulk exchange experiments 447
Single crystal experiments 448
ANALYTICALMETHODS 449
Mass Spectrometry 449
Nuclear Reaction Analysis 450
Fourier Transform Infrared Spectroscopy 450
Other methods 450
RESULTS 451
Quartz 451
Feldspars 4-55
Olivine 461
Pyroxene 4-65
Amphiboles 470Sheet silicates 471
Garnet 472
Zircons 474
Titanite 474
Meliliie 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 486Pressure dependence 488Effect of water 488
Hydrogen chemical diffusion and the role of defects 489ACKNOWLEGMENTS 490
REFERENCES 490
I I Diffusion of Noble Gases in Minerals
E.F. Baxter
INTRODUCTION 509The interpretive challenge ofbulk-degassing experiments 510
HELIUM 513He in apatite 514
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He in titanite 52o
He in zircon and zircon-structure rare earth element orthophosphates 52uHe in monazite and monazite-structure rare earth element orthophosphates 52He diffusion in other minerals 52 '
ARGON 32"
Ar in micas 52k
Ar in amphiboleAr in feldspar 52l*Ar diffusion in other minerals 5
THE OTHER NOBLE GASES: NEON, KRYPTON, XENON, RADON 5 «;
THEMES IN NOBLE GAS DIFFUSION IN MINERALS 5
Effect of radiation damage 5Effect of deformation 5'*
Multi-domain diffusion 5
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Diffusion in Minerals and Melts - Table of Contents
Treatment of diffusion data 580
A SEMI-EMPIRICAL MODEL OF DIVALENT CATION DIFFUSION 581
Carlson model 581
Discussion 582
GEOLOGICAL APPLICATIONS 585
Modeling multicomponent diffusion profiles using effective binary diffusionformulation 586
Cooling rates of metamorphic rocks: diffusion modeling of garnet vs.
geochronological constraints 587Subduction and exhumation rates 587
Modeling partially modified growth zoning of garnets in metamorphic rocks 589
Interpretation of REE patterns of basaltic magma 592Sm-Nd and Lu-Hf geochronology of garnets in metamorphic rocks 594
CONCLUDING REMARKS 596
ACKNOWLEDGMENTS 598
REFERENCES 598
APPENDIX: COMBINED ANALYTICAL AND NUMERICAL METHOD FORMODELING MULTICOMPONENT DIFFUSION PROFILES 600
I j Diffusion Coefficients in
Olivine, Wadsleyite and Ringwoodite
S. Chakraborty
INTRODUCTION 603
OLIVINE 603
Structure of olivine and types of diffusion coefficients 603
Diffusion mechanisms in olivine 605
Diffusion of divalent cations 608
Diffusion of Si and oxygen 620
Diffusion of ions that enter olivine via heterovalent substitutions 623
INFORMATION FROM OLIVINES OTHER THAN Fe-Mg BINARY SOLIDSOLUTIONS 627
SPECTROSCOPIC MEASUREMENTS 628
COMPUTER CALCULATIONS 628
WADSLEYITE AND RINGWOODITE 629
Diffusion of divalent cations 630Diffusion ofsilicon and oxygen 631
Diffusion of ions that are incorporated by heterovalent substitutions 633A SUMMARY, AND APPLICATIONS OF DIFFUSION DATA IN OLIVINE,
WADSLEYITE AND RINGWOODITE 633
ACKNOWLEDGMENTS 635
REFERENCES 635
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\ t- Diffusion in Pyroxene, Mica and Amphibole
D.J. Cherniak, A. Dimanav
INTRODUCTION MlCATION DIFFUSION IN PYROXENES 6-11
Pioneering approaches 64 <More recent investigations of major element diffusion (S-l-lDiffusion of major element cations in clinopyroxenes 645Diffusion in synthetic versus natural crystals 656Major element cation diffusion in orthopyroxenes 6.56Pyroxene point defect chemistry 658Diffusion of minor and trace elements in pyroxene 661
Comparison of diffusion of cations in pyroxene 672DIFFUSION IN AMPH1BOLES AND MICAS 676
F-OH interdiffusion in tremolite 677
Sr diffusion in tremolite and hornblende 67H
Sr diffusion in fluorphlogopite 67l)K and Rb diffusion in biotite 67')
ACKNOWLEDGMENTS 680REFERENCES 6X0
APPENDIX 6X5
1 D Cation Diffusion in Feldspars
D.J. Cherniak
INTRODUCTION M\
DIFFUSION OF MAJOR CONSTITUENTS 62
Sodium
Potassium (W
K-Na interdiffusion 6l)6Calcium
Barium 69l!
CaAl-NaSi interdiffusion 70(1
Silicon
DIFFUSION OF MINOR AND TRACE ELEMENTS 705
Lithium 705
Rubidium 705
Magnesium 707Iron 70X
Strontium 70X
Lead 717
Radium 721
Rare Earth Elements 721
COMPARISON OF RELATIVE DIFFUSIVITIES OF CATIONS IN VARIOUS
FELDSPAR COMPOSITIONS 72 <
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Albite 723
K-feldspar 723
Intermediate alkali feldspars 725
Anorthite 725
Labradorite 726
Oligoclase 728
ACKNOWLEDGMENTS 728
REFERENCES 728
1 6 Diffusion in Quartz, Melilite,Silicate Perovskite, and Mullite
D.J. Cherniak
INTRODUCTION 735
DIFFUSION IN QUARTZ 735Silicon 736
Aluminum and gallium 738
Alkali elements - Li, Na, K 739
Calcium 741
Titanium 741
Diffusion in quartz - a summary 742
DIFFUSION IN MELILITE 743
Al+Al
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Diffusion in Minerals and Melts - Table of Contents
Other group I1A divalent cations 7Ms
Group IIIA and IIIB trivalent cations 7dMTetravalent cations 7" !
Transition metals 77 i
Hydrogen 7 s »
SPINEL 7k;
Oxygen ""s ">
Magnesium 7KS
Fe-Mg interdiffusion 7Hf-<
Mg-Al interdiffusion 7S""
Cr-Al interdiffusion 7K""
Hydrogen 7Ks
MAGNETITE 7KK
Oxygen 7K«*
Iron 71
Other cations 794
RUTILE 7*,
Oxygen 7M'
Tetravalent and pentavalent cations 7'w
Divalent and trivalent cations HO!
Monovalent cations 8()*
ACKNOWLEDGMENTS «IM
REFERENCES 8(M
APPENDIX 8lo
I O Diffusion in Accessory Minerals:
Zircon, Titanite, Apatite, Monazite and Xenotime
D.J. Cherniak
INTRODUCTION 827
DIFFUSION IN ZIRCON 827
Lead 828
Rare Earth Elements (REE) 832
Tetravalent cations 835
Cation diffusion in zircon - a summary 83.H
DIFFUSION IN TITANITE 8-41
Strontium and Lead 841
Neodynium 84 t
Zirconium 843
Summary of diffusion data for titanite 84-1
DIFFUSION IN MONAZITE 844
Calcium and Lead 845
Thorium 84"?
DIFFUSION IN XENOTIME 84S
DIFFUSION IN APATITE 85t >
Lead and Calcium 85f •
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Strontium 852
Manganese 853
Rare Earth Elements (REE) 854
Phosphorus 858
Uranium and Thorium 858
F-OH-C1 859
Comparison of diffusivities of cations and anions in apatite 860
COMPARISON OF DIFFUSIVITIES AMONG ACCESSORY MINERALS 861
Lead 861
Rare Earth Elements (REE) 862
Thorium and Uranium 863
ACKNOWLEDGMENTS 864
REFERENCES 864
I y Diffusion in Carbonates, Fluorite,Sulfide Minerals, and Diamond
D.J. Cherniak
INTRODUCTION 871
CARBONATES 871
Carbon 872
Calcium 875
Magnesium 876Strontium and Lead 877
Rare Earth Elements 878
Diffusion in calcite - an overview 879
FLUORITE 880
Fluorine 881
Calcium 883
Strontium, Yttrium and Rare Earth Elements 883
DIAMOND 885
SULFIDE MINERALS 885
Pyrite 886Pyrrhotite 888
Sphalerite 889
Chalcopyrite 891Galena 892
Summary of diffusion findings for the sulfides 892ACKNOWLEDGMENTS 893
REFERENCES 894
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Diffusion in Minerals and Melts - Table of Contents
ZU Diffusion in Minerals: An Overview ofPublished Experimental Diffusion Data
J.B. Brady, D.J. CherniaA
INTRODUCTION S«*<
ARRHENIUS RELATIONS **>
DIFFUSION COMPENSATION DIAGRAMS '«>-;
IONIC POROSITY »'l l
DIFFUSIONANISOTROPY "I ;
CONCLUDING REMARKS l>)
ACKNOWLEDGMENTS l'l'
REFERENCES '»!"
Z1 Diffusion in Polyerystalline Materials:Grain Boundaries, Mathematical Models, and Experimental Data
R. Dohmen, R. Milkc
INTRODUCTION l>2)
Geological relevance of grain boundary diffusion 'J-1'
Physical nature of a grain/interphase boundary V22
Thermodynamic model for interfaces l>2*
THE ISOLATED GRAIN BOUNDARY
Basic mathematical description l)2~Kinetic regimes and diffusion penetration distances
THE MONOPHASE POLYCRYSTALLINE AGGREGATE l> V
Models and kinetic regimesBulk diffusion coefficients
A geological example l)
Profile analysts - the Le Claire approach
Complexities of real and polyphase systems ^-K*
Asymmetric grain boundaries/interphase boundaries l)4 IThe migrating isolated grain boundary ^2Presence of dislocations/sub-grain boundaries
Element/isotope exchange mediated by grain boundary diffusion 1>-U>
EXPERIMENTAL METHODS 7
Setup with bi-crystals
Setup with a polyerystalline aggregate W>
Source-sink studies
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Diffusion in Minerals and Melts - Table of Contents
in Minerals and Melts
N. de Koker, L. Stixmde
INTRODUCTION 971
THEORETICAL FOUNDATIONS 972
Thermodynamic description 972
Statistical mechanical description 974
COMPUTATIONAL APPROACHES 976
Characterization of bonding 977
Adding temperature 978
Computation of diffusion 980
SELECTED APPLICATIONS 981
Liquids and melts 981
Solids 988
A VIEW TO THE FUTURE 991
ACKNOWLEDGMENTS 991
REFERENCES 991
JL3 Applications of Diffusion Data to
High-Temperature Earth Systems
T. Mueller, E.B. Watson, T.M. Harrison
INTRODUCTION 997
DECIPHERING KINETICALLY CONTROLLED PROCESSES USING DIFFUSION ...999
Mass transport in geological systems 999Diffusion in minerals 1002
Control of solid-state reaction rates and compositions of reaction
products by diffusion 1005
Metamorphic example of diffusion-limited uptake: REE behavior duringgarnet growth 1011
Chemical diffusive fractionation 1014
Diffusive fractionation in a thermal gradient 1017THERMOCHRONOLOGY 1018
Background 1018Bulk closure 1019
Continuous histories 1021
Dating metamorphic events 1024
GEOSPEEDOMETRY 1025
The concept of geospeedometry 1025
Deciphering timescales from kinetic modeling 1026Diffusion in two or three dimentions and the effect of geometry 1027
Example: Deciphering short-term metamorphic events and timescales 1029ACKNOWLEDGMENTS 1032
REFERENCES 1032
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