Diffusion in minerals and melts : [ Short Course on Diffusion in … · 2012. 9. 3. · OXYGENDIFFUSION Self-diffusion ofoxygenin silicate meltsunderdryconditions Chemicaldiffusion

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

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

iv

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 (

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

';

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


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

ix


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

x


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


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


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


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


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

xvi


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


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

xviii

Documents

Diffusion in minerals and melts : [ Short Course on Diffusion in … · 2012. 9. 3. · OXYGENDIFFUSION Self-diffusion ofoxygenin silicate meltsunderdryconditions Chemicaldiffusion