Diffusion in minerals and melts / ed. by Y.Zhang, D.J.Cherniak. - Chantilly: Mineralogical Society of America; Saint Louis: Geochemical Society, 2010. - xviii, 1038 p.: ill. - (Reviews in mineralogy & geochemistry; vol.72). - Incl. bibl. ref. - ISBN 978-0-939950-86-7; ISSN 1529-6466  Место хранения:   09 | Институт геохимии им. А.П.Виноградова СО РАН | Иркутск | Библиотека

Оглавление / Contents

1 Diffusion in Minerals and Melts: Introduction К. Zhang, D.J. Cherniak INTRODUCTION: RATIONALE FOR THIS VOLUME ...................... 1 SCOPE AND CONTENT OF THIS VOLUME ............................. 2 REFERENCES ................................................... 3 2 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 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 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 ...................................... 111 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 (μ-SRXRF) ..... 156 Instrumental setup, spectra acquisition and data processing .............................................. 156 Sample preparation ...................................... 158 Applications of μ-SRXRF for measuring trace element diffusivities in silicate melts ......................... 158 ACKNOWLEDGMENTS ............................................ 160 REFERENCES ................................................. 160 5 Diffusion of H, C, and О Components in Silicate Melts Y. Zhang, H. Ni INTRODUCTION ............................................... 171 DIFFUSION OF THE H2O COMPONENT ............................. 172 H2O speciation: equilibrium and kinetics ................ 172 H2O diffusion literature ................................ 178 H2O diffusion, theory and data summary .................. 180 MOLECULAR H2 DIFFUSION ..................................... 191 DIFFUSION OF THE CO2 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 CO2 diffusion to 18O transport in CO2-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 6 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 H2O diffusion ........................................... 250 O2 diffusion ............................................ 250 N2 diffusion ............................................ 251 CO2 diffusion ........................................... 252 ACKNOWLEDGMENTS ............................................ 252 RERERENCES ................................................. 253 APPENDIX ................................................... 257 7 Self-diffusion in Silicate Melts: Theory, 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 8 Diffusion Data in Silicate Melts К. 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 T, H20, ƒо2- and melt composition ........................................ 317 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 Tl ................................... 340 C, Si, Ge, Sn and Pb .................................... 345 N, P, As, Sb, Bi ........................................ 352 O, S, Se, Те, Ро ........................................ 354 F, Cl, Br, I, At ........................................ 356 He, Ne, Ar, Kr, Xe, Rn .................................. 360 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 9 Multicomponent Diffusion in Molten Silicates: Theory, Experiments, and Geological Applications К. 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 10 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 ACKNOWLEDGMENTS ............................................ 490 REFERENCES ................................................. 490 11 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 He in titanite .......................................... 520 He in zircon and zircon-structure rare earth element orthophosphates ......................................... 520 He in monazite and monazite-structure rare earth element orthophosphates ................................. 523 He diffusion in other minerals .......................... 523 ARGON ...................................................... 527 Ar in micas ............................................. 528 Ar in amphibole ......................................... 529 Ar in feldspar .......................................... 529 Ar diffusion in other minerals .......................... 530 THE OTHER NOBLE GASES: NEON, KRYPTON, XENON, RADON ......... 532 THEMES IN NOBLE GAS DIFFUSION IN MINERALS .................. 534 Effect of radiation damage .............................. 534 Effect of deformation ................................... 535 Multi-domain diffusion .................................. 536 Multi-path diffusion .................................... 537 Synthesis: relative diffusivities of the noble gases in minerals ............................................. 539 CHOOSING THE "RIGHT" DIFFUSION DATA ........................ 542 Role of noble gas diffusion data in Ar/Ar and (U-Th)/He thermochronology .............................. 545 SUGGESTIONS FOR FUTURE STUDY ............................... 548 Diffusion at high pressures and temperatures ............ 548 Diffusion of Ar and He in common mantle minerals ........ 548 In situ depth profile analysis .......................... 551 Quantification of noble gas diffusion within "fast paths" .................................................. 551 Integrated studies with multiple noble gases ............ 551 Quantification of effects of radiation damage, defects, and deformation ................................ 551 ACKNOWLEDGMENTS ............................................ 552 REFERENCES ................................................. 552 12 Cation Diffusion Kinetics in Aluminosilicate Garnets and Geological Applications J. Ganguly INTRODUCTION ............................................... 559 NOMENCLATURE OF DIFFUSION COEFFICIENTS ..................... 560 EXPERIMENTAL DETERMINATION OF DIFFUSION COEFFICIENTS ....... 561 Experimental methods .................................... 561 Modeling of experimental data ........................... 564 EXPERIMENTAL DATA AND DISCUSSION ........................... 566 Self/tracer diffusion coefficients of Mn, Fe2+ and Mg ...................................................... 566 Diffusion properties of Ca .............................. 573 Tracer diffusion coefficients of trivalent rare earth ions .................................................... 575 D-MATRIX, UPHILL DIFFUSION AND CHEMICAL WAVES .............. 578 COMMENTS ON EXTRAPOLATION AND GEOLOGICAL APPLICATION OF EXPERIMENTAL DIFFUSION DATA ................................ 580 Change of diffusion mechanism and extrapolation of diffusion data .......................................... 580 Modeling prograde vs. retrograde profiles ............... 580 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 diffusion formulation .................. 586 Cooling rates of metamorphic rocks: diffusion modeling of garnet vs. geochronological constraints ..... 587 Subduction and exhumation rates ......................... 587 Modeling partially modified growth zoning of garnets in metamorphic rocks .................................... 589 Interpretation of REE patterns of basaltic magma ........ 592 Sm-Nd and Lu-Hf geochronology of garnets in metamorphic rocks ....................................... 594 CONCLUDING REMARKS ......................................... 596 ACKNOWLEDGMENTS ............................................ 598 REFERENCES ................................................. 598 APPENDIX: COMBINED ANALYTICAL AND NUMERICAL METHOD FOR MODELING MULTICOMPONENT DIFFUSION PROFILES ................. 600 13 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 SOLID SOLUTIONS .................................................. 627 SPECTROSCOPIC MEASUREMENTS ................................. 628 COMPUTER CALCULATIONS ...................................... 628 WADSLEYITE AND RINGWOODITE ................................. 629 Diffusion of divalent cations ........................... 630 Diffusion of silicon and oxygen ......................... 631 Diffusion of ions that are incorporated by heterovalent substitutions .............................. 633 A SUMMARY, AND APPLICATIONS OF DIFFUSION DATA IN OLIVINE, WADSLEYITE AND RINGWOODITE ........................ 633 ACKNOWLEDGMENTS ............................................ 635 REFERENCES ................................................. 635 14 Diffusion in Pyroxene, Mica and Amphibole D.J. Cherniak, A. Dimanov INTRODUCTION ............................................... 641 CATION DIFFUSION IN PYROXENES .............................. 641 Pioneering approaches ................................... 643 More recent investigations of major element diffusion ............................................... 644 Diffusion of major element cations in clinopyroxenes .... 645 Diffusion in synthetic versus natural crystals .......... 656 Major element cation diffusion in orthopyroxenes ........ 656 Pyroxene point defect chemistry ......................... 658 Diffusion of minor and trace elements in pyroxene ....... 661 Comparison of diffusion of cations in pyroxene .......... 672 DIFFUSION IN AMPHIBOLES AND MICAS .......................... 676 F-OH interdiffusion in tremolite ........................ 677 Sr diffusion in tremolite and hornblende ................ 678 Sr diffusion in fluorphlogopite ......................... 679 К and Rb diffusion in biotite ........................... 679 ACKNOWLEDGMENTS ............................................ 680 REFERENCES ................................................. 680 APPENDIX ................................................... 685 15 Cation Diffusion in Feldspars D.J. Cherniak INTRODUCTION ............................................... 691 DIFFUSION OF MAJOR CONSTITUENTS ............................ 692 Sodium .................................................. 692 Potassium ............................................... 695 K-Na interdiffusion ..................................... 696 Calcium ................................................. 698 Barium .................................................. 699 CaAl-NaSi interdiffusion ................................ 700 Silicon ................................................. 703 DIFFUSION OF MINOR AND TRACE ELEMENTS ...................... 705 Lithium ................................................. 705 Rubidium ................................................ 705 Magnesium ............................................... 707 Iron .................................................... 708 Strontium ............................................... 708 Lead .................................................... 717 Radium .................................................. 721 Rare Earth Elements ..................................... 721 COMPARISON OF RELATIVE DIFFUSIVITIES OF CATIONS IN VARIOUS FELDSPAR COMPOSITIONS .............................. 723 Albite .................................................. 723 K-feldspar .............................................. 723 Intermediate alkali feldspars ........................... 725 Anorthite ............................................... 725 Labradorite ............................................. 726 Oligoclase .............................................. 728 ACKNOWLEDGMENTS ............................................ 728 REFERENCES ................................................. 728 16 Diffusion in Quartz, Melilite, Silicate Perovskite, and MuUite D.J. Cherniak INTRODUCTION ............................................... 735 DIFFUSION IN QUARTZ ........................................ 735 Silicon ................................................. 736 Aluminum and gallium .................................... 738 Alkali elements - Li, Na, К ............................. 739 Calcium ................................................. 741 Titanium ................................................ 741 Diffusion in quartz - a summary ......................... 742 DIFFUSION IN MELILITE ...................................... 743 Al + Al ↔ Mg + Si interdiffusion ........................ 743 Mg ...................................................... 743 Mn, Fe, Co, and Ni ...................................... 746 Ca, Sr, and Ba .......................................... 748 Potassium ............................................... 749 Diffusion in melilite - a summary ....................... 750 DIFFUSION IN SILICATE PEROVSKITE ........................... 751 Silicon ................................................. 751 Fe-Mg interdiffusion .................................... 753 DIFFUSION IN MULLITE ....................................... 753 ACKNOWLEDGMENTS ............................................ 754 REFERENCES ................................................. 754 17 Diffusion in Oxides J.A. Van Orman, K.L. Crispin INTRODUCTION ............................................... 757 PERICLASE .................................................. 758 General considerations .................................. 758 Oxygen .................................................. 759 Magnesium ............................................... 763 Other group IIA divalent cations ........................ 766 Group IIIA and IIIB trivalent cations ................... 769 Tetravalent cations ..................................... 771 Transition metals ....................................... 771 Hydrogen ................................................ 783 SPINEL ..................................................... 783 Oxygen .................................................. 784 Magnesium ............................................... 785 Fe-Mg interdiffusion .................................... 786 Mg-Al interdiffusion .................................... 787 Cr-Al interdiffusion .................................... 787 Hydrogen ................................................ 788 MAGNETITE .................................................. 788 Oxygen .................................................. 789 Iron .................................................... 791 Other cations ........................................... 794 RUTILE ..................................................... 796 Oxygen .................................................. 797 Tetravalent and pentavalent cations ..................... 799 Divalent and trivalent cations .......................... 801 Monovalent cations ...................................... 803 ACKNOWLEDGMENTS ............................................ 804 REFERENCES ................................................. 804 APPENDIX ................................................... 810 18 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 .................. 838 DIFFUSION IN TITANITE ...................................... 841 Strontium and Lead ...................................... 841 Neodynium ............................................... 843 Zirconium ............................................... 843 Summary of diffusion data for titanite .................. 844 DIFFUSION IN MONAZITE ...................................... 844 Calcium and Lead ........................................ 845 Thorium ................................................. 847 DIFFUSION IN XENOTIME ...................................... 848 DIFFUSION IN APATITE ....................................... 850 Lead and Calcium ........................................ 850 Strontium ............................................... 852 Manganese ............................................... 853 Rare Earth Elements (REE) ............................... 854 Phosphorus .............................................. 858 Uranium and Thorium ..................................... 858 F-OH-Cl ................................................. 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 19 Diffusion in Carbonates, Fluorite, Sulfide Minerals, and Diamond D.J. Cherniak INTRODUCTION ............................................... 871 CARBONATES ................................................. 871 Carbon .................................................. 872 Calcium ................................................. 875 Magnesium ............................................... 876 Strontium 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 .................................................. 886 Pyrrhotite .............................................. 888 Sphalerite .............................................. 889 Chalcopyrite ............................................ 891 Galena .................................................. 892 Summary of diffusion findings for the sulfides .......... 892 ACKNOWLEDGMENTS ............................................ 893 REFERENCES ................................................. 894 20 Diffusion in Minerals: An Overview of Published Experimental Diffusion Data J.B. Brady, D.J. Cherniak INTRODUCTION ............................................... 899 ARRHENIUS RELATIONS ........................................ 900 DIFFUSION COMPENSATION DIAGRAMS ............................ 904 IONIC POROSITY ............................................. 911 DIFFUSION ANISOTROPY ....................................... 913 CONCLUDING REMARKS ......................................... 917 ACKNOWLEDGMENTS ............................................ 917 REFERENCES ................................................. 917 21 Diffusion in Poly crystalline Materials: Grain Boundaries, Mathematical Models, and Experimental Data R. Dohmen, R. Milke INTRODUCTION ............................................... 921 Geological relevance of grain boundary diffusion ........ 921 Physical nature of a grain/interphase boundary .......... 922 Thermodynamic model for interfaces ...................... 925 THE ISOLATED GRAIN BOUNDARY ................................ 927 Basic mathematical description .......................... 927 Kinetic regimes and diffusion penetration distances ..... 928 THE MONOPHASE POLYCRYSTALLINE AGGREGATE .................... 932 Models and kinetic regimes .............................. 932 Bulk diffusion coefficients ............................. 934 A geological example .................................... 936 Profile analysis- the Le Claire approach ................ 937 Complexities of real and polyphase systems .............. 940 Asymmetric grain boundaries/interphase boundaries ....... 941 The migrating isolated grain boundary ................... 942 Presence of dislocations/sub-grain boundaries ........... 944 Element/isotope exchange mediated by grain boundary diffusion ............................................... 946 EXPERIMENTAL METHODS ....................................... 947 Setup with bi-crystals .................................. 948 Setup with a polycrystalline aggregate .................. 949 Source-sink studies ..................................... 950 EXPERIMENTAL DATA .......................................... 950 Parameters affecting grain boundary diffusion coefficients ............................................ 950 Direct measurement of tracer diffusion in polycrystals of geological relevance .................... 955 Concluding remarks ...................................... 964 ACKNOWLEDGMENTS ............................................ 966 REFERENCES ................................................. 966 22 Theoretical Computation of Diffusion in Minerals and Melts N. de Koker, L. Stixrude 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 23 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 .................... 999 Diffusion 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 during garnet growth .......................... 1011 Chemical diffusive fractionation ....................... 1014 Diffusive fractionation in a thermal gradient .......... 1017 THERMOCHRONOLOGY .......................................... 1018 Background ............................................. 1018 Bulk closure ........................................... 1019 Continuous histories ................................... 1021 Dating metamorphic events .............................. 1024 GEOSPEEDOMETRY ............................................ 1025 The concept of geospeedometry .......................... 1025 Deciphering timescales from kinetic modeling ........... 1026 Diffusion in two or three dimentions and the effect of geometry ............................................ 1027 Example: Deciphering short-term metamorphic events and timescales ......................................... 1029 ACKNOWLEDGMENTS ........................................... 1032 REFERENCES ................................................ 1032