Triple Oxygen Isotope Geochemistry 9781501524677, 9781946850065

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REVIEWS in MINERALOGY and GEOCHEMISTRY Volume 86

2021

Triple Oxygen Isotope Geochemistry EDITORS Ilya N. Bindeman

University of Oregon, USA

Andreas Pack

Georg-August-Universität Göttingen, Germany

Series Editor: Ian Swainson MINERALOGICAL SOCIETY of AMERICA GEOCHEMICAL SOCIETY

Reviews in Mineralogy and Geochemistry, Volume 86

Triple Oxygen Isotope Geochemistry

ISSN 1529-6466 (print) ISSN 1943-2666 (online) ISBN 978-1-946850-06-5 Copyright 2021

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.

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PREFACE Since the first volume of the Reviews in Mineralogy was published in 1974, this series (expanded to Reviews in Mineralogy and Geochemistry in 2000) has grown to an invaluable library comprising 86 volumes on various topics related to mineralogy and geochemistry. Often a volume from that series is given by an advisor to a young graduate student or postdoc as a roadmap when they enter a new research field. The review volumes are, however, also a steady resource of information and inspiration for more advanced researchers when they need to get an overview of fields outside their everyday scientific expertise. The field of stable isotope geochemistry, founded by Harold C. Urey, now looks back on seven decades of continuing exciting discoveries and developments. Many of these advancements have already been compiled into five volumes on stable isotope geochemistry in the Reviews in Mineralogy and Geochemistry series. Starting in 1986, Volume 16: Stable Isotopes in High Temperature Geological Processes was the first to review the state of the field and was edited by John W. Valley, Hugh P. Taylor (Jr.), and James R. O'Neil. This volume was updated in 2001 to emphasize the developments in laser fluorination approaches. Printed as Volume 43 and entitled Stable Isotope Geochemistry, it was edited by John W. Valley and David Cole. A rapid accumulation of data and research in on meteorites and planetary crusts was summarized in 2008 with Volume 68 Oxygen in the Solar System, edited by Glenn J. MacPherson, David W. Mittlefehldt, John H. Jones, and Steven B. Simon. Due to new technical developments, most importantly the inductively coupled multicollector mass spectrometry, the field of stable isotope geochemistry has branched out to elements other than the traditional H, C, N, O, and S stable isotopes. This development was summarized in 2004 with Volume 55: Geochemistry of Non-Traditional Stable Isotopes, edited by Clark M. Johnson, Brian L. Beard, and Francis Albarède, and revisited in 2017 with Volume 82, entitled Non-Traditional Stable Isotopes, edited by Fang-Zhen Teng, James Watkins, and Nicolas Dauphas. Why this new volume? During the past two decades, two major and exciting fields have emerged in the science of stable isotope geochemistry, both related to understanding tiny variations (down into the lower ppm range) in the minor isotopologue abundances. The first field is related to the distribution of “clumping” of heavy isotopes in molecules, such as CO2 or CH4; the second field is the use of small variations in all three oxygen isotopes. Both approaches allow researchers to resolve absolute temperatures, previously masked process pathways, and exchange between various reservoirs. In this new volume of Reviews in Mineralogy and Geochemistry we concentrate on understanding the latter—understanding of variations among ratios of all three isotopes of oxygen, with primary emphasis on terrestrial systems. Triple oxygen isotope variations may be related to large, mass-independent fractionation effects such observed in the Earth atmosphere or may be small and related to minute variations due to purely mass-dependent processes. 1529-6466/21/0086-0000$00.00 (print) 1943-2666/21/0086-0000$00.00 (online)

http://dx.doi.org/10.2138/rmg.2021.86.00

Triple Oxygen Isotope Geochemistry ‒ Preface Recent advancements in analytical resolution now allow for the identification of processes and distinct reservoirs that were formerly hidden in the paradigm of a “single terrestrial fractionation line”. New, high-resolution measurements are accompanied by advances in theoretical calculations that dovetail with empirical calibrations and applications throughout this volume. Here, we bring together the leading researchers and asked them to summarize the new discoveries in their field of expertise. The result is a volume with 14 chapters spanning a wide range of subjects: from ab-initio theoretical approaches to observation of triple oxygen isotope variations in the Earth litho-, hydro- and atmosphere. Triple Oxygen Isotope Geochemistry is a young and rapidly evolving field and some of the observations reported in this volume will undoubtedly be modified in the future as new discoveries and improved protocols are developed in the coming years. The triple oxygen isotope concepts presented in this volume, however, will hopefully prove valuable to new entrants in this field and lay a foundation for future growth. As editors, we thank all the authors and reviewers that contributed to this volume. It is their chapters and their reviews that ensured the high quality of this book. The staff support of the Mineralogical Society of America, especially Rachel Russell and Ann Benbow, and that of Ian Swainson, greatly made our editorial work easier and their help is more than appreciated. October 09, 2020 Ilya Bindeman, University of Oregon Andreas Pack, Georg-August-Universität Göttingen

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TABLE OF CONTENTS

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Why Measure 17O? Historical Perspective, Triple-Isotope Systematics |and Selected Applications Martin F. Miller, Andreas Pack

INTRODUCTION.....................................................................................................................1 Non-mass-dependent oxygen triple-isotope distributions..............................................3 Non-mass-dependent oxygen triple-isotope distributions generated by processes not involving photochemical reactions........................................................................5 OXYGEN TRIPLE-ISOTOPE SYSTEMATICS.......................................................................6 Experimental measurements of ln(17/16α) /ln(18/16α) = θ..................................................8 Defining and quantifying deviations from a reference fractionation relationship..........8 REFERENCE MATERIALS AND STANDARDS.................................................................12 16 O, 17O AND 18O ABUNDANCES AND ISOTOPE RATIO RANGES IN NATURALLY OCCURRING TERRESTRIAL MATERIALS...........................................15 Oxygen triple-isotope measurements of atmospheric O2............................................................................. 15 Oxygen triple-isotope measurements of terrestrial silicates.........................................16 Oxygen triple-isotope distributions in meteoric waters, snow and ice cores...............18 STANDARDIZING Δ′17O DATA FROM ROCKS AND MINERALS...................................20 SOME EXAMPLES OF THE APPLICATION OF OXYGEN TRIPLE-ISOTOPE RATIO MEASUREMENTS...............................................21 Corrections to δ13C measurements of CO2...................................................................22 Comparisons of the oxygen triple-isotope compositions of the Earth and Moon........22 Investigating the climate of ‘Snowball Earth’ from hydrothermal rocks.....................24 Insights from Δ′17O measurements on basalts, shales and fluvial sediments...............25 Quantifying gross photosynthetic oxygen production in the oceans............................26 Oxygen triple-isotope ratios in bio-apatite: a proxy for CO2 partial pressure in paleo atmospheres.................................................................................................26 CONCLUSIONS AND OUTLOOK........................................................................................27 ACKNOWLEDGEMENTS.....................................................................................................28 REFERENCES........................................................................................................................28 vi

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Discoveries of Mass Independent Isotope Effects in the Solar System: Past, Present and Future Mark H. Thiemens, Mang Lin

THE BEGINNING OF ISOTOPES.........................................................................................35 Discovery and chemical physics..................................................................................35 The dawn of stable isotope geochemistry....................................................................37 AN OVERVIEW OF STABLE ISOTOPE GEOCHEMISTRY...............................................38 Mass dependent effects and applications.....................................................................38 Mass independent isotope effects and applications......................................................42 FUNDAMENTAL CHEMICAL PHYSICS OF MASS INDEPENDENT ISOTOPE EFFECTS: WHAT IS KNOWN AND WHAT NEEDS TO BE KNOWN..........47 Bond formation processes............................................................................................47 The role of symmetry...................................................................................................47 Bond breaking isotope effects......................................................................................52 Physical chemical details of photodissociation general process..................................55 Specific examples of isotope effects in dissociation: carbon dioxide..........................56 PHOTODISSOCIATION IN THE EARLY SOLAR SYSTEM AND SELF-SHIELDING MODELS.............................................................................................59 Self-shielding models...................................................................................................59 Mass independent isotope effects in CO photodissociation.........................................60 High resolution view of isotopic photodissociation.....................................................64 Self-shielding final test and errors................................................................................68 Nebular fate of water and water ice from photodissociation........................................69 Summary......................................................................................................................75 BOX 1: SELF-SHIELDING PROBLEMS..............................................................................77 SOLID FORMATION IN THE EARLY SOLAR SYSTEM...................................................78 Simultaneous formation of the first solids and their isotopic anomalies......................78 Oxygen isotopic composition of the Solar System......................................................82 A NEW MODEL FOR TRIPLE OXYGEN ISOTOPES, METEORITES, AND THE ORIGIN OF THE SOLAR SYSTEM..........................................................................84 Revisiting triple oxygen isotopes of CAI.....................................................................84 Material balance of bulk meteorites oxygen isotopes..................................................85 BOX 2: SUMMARY OF CHEMICAL MECHANISM MODEL FOR PRODUCTION OF METEORITE OXYGEN ISOTOPIC ANOMALIES..........................88 ACKNOWLEDGEMENTS.....................................................................................................89 REFERENCES........................................................................................................................89

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Climbing to the Top of Mount Fuji: Uniting Theory and Observations of Oxygen Triple Isotope Systematics Laurence Y. Yeung, Justin A. Hayles

INTRODUCTION...................................................................................................................97 BASIC CONCEPTS................................................................................................................99 The equations...............................................................................................................99 Quantifying mass-dependent fractionation................................................................102 Natural variability in the triple-oxygen exponents θ..................................................104 A note about anharmonicity.......................................................................................107 ELECTRONIC STRUCTURE CALCULATIONS...............................................................107 Molecular models.......................................................................................................108 Electronic structure methods: different ways of treating chemical interactions........109 Representing electrons using basis sets......................................................................111 Key takeaways............................................................................................................113 A COMPARISON OF THEORETICAL METHODS...........................................................113 Approach....................................................................................................................113 Results........................................................................................................................114 ANALYTICAL CONSIDERATIONS...................................................................................119 Scale distortion and calibration..................................................................................120 Physical and reservoir effects in the real world..........................................................121 CASE STUDY: KINETIC ISOTOPE FRACTIONATION DURING CARBONATE ACID DIGESTION....................................................................................124 The problems..............................................................................................................124 Evaluation of theory and measurements.....................................................................125 CONCLUDING REMARKS.................................................................................................127 ACKNOWLEDGEMENTS...................................................................................................128 REFERENCES......................................................................................................................128

4 Mass Dependence of Equilibrium Oxygen Isotope Fractionation in

Carbonate, Nitrate, Oxide, Perchlorate, Phosphate, Silicate, and Sulfate Minerals

Edwin A. Schauble, Edward D. Young INTRODUCTION.................................................................................................................137 D17O signatures of equilibrium processes...................................................................137 PREDICTING 17O/16O SIGNATURES..................................................................................140 Estimating mass-dependent fractionations in the harmonic approximation..............140 Effects beyond the harmonic approximation..............................................................146 How important are effects beyond the harmonic approximation?..............................150 ∆′17O signatures of equilibrium..................................................................................152 SUMMARY...........................................................................................................................171 REFERENCES......................................................................................................................172

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Standardization for the Triple Oxygen Isotope System: Waters, Silicates, Carbonates, Air, and Sulfates Zachary D. Sharp, Jordan A.G. Wostbrock

INTRODUCTION.................................................................................................................179 INTERCALIBRATING WATERS, CARBONATES AND SILICATES FOR d18O..............182 Water...........................................................................................................................182 Carbonates..................................................................................................................183 Silicates......................................................................................................................184 Comparison of all data...............................................................................................184 STANDARDIZATION FOR D17O VALUES OF SELECTED REFERENCE MATERIALS..............................................................................................185 Method of measurement.............................................................................................185 Water...........................................................................................................................185 Silicates......................................................................................................................187 Air...............................................................................................................................189 Carbonates..................................................................................................................190 Sulfates.......................................................................................................................191 CONCLUSION......................................................................................................................192 ACKNOWLEDGEMENTS...................................................................................................193 REFERENCES......................................................................................................................193

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Mass-Independent Fractionation of Oxygen Isotopes in the Atmosphere Marah Brinjikji, James R. Lyons

INTRODUCTION.................................................................................................................197 PREVIOUS WORK IN THE LOWER ATMOSPHERE.......................................................197 Early measurements...................................................................................................197 Theory and photochemical modeling of O3 MIF signatures......................................198 Applications of oxygen MIF......................................................................................198 MATERIALS AND METHODS...........................................................................................199 VULCAN photochemical model................................................................................199 RESULTS FOR THE LOWER ATMOSPHERE...................................................................200 RESULTS FOR THE UPPER ATMOSPHERE.....................................................................209 DISCUSSION........................................................................................................................212 CONCLUSIONS....................................................................................................................212 ACKNOWLEDGEMENTS...................................................................................................213 REFERENCES......................................................................................................................213

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Isotopic Traces of Atmospheric O2 in Rocks, Minerals, and Melts Andreas Pack

INTRODUCTION.................................................................................................................217 THE ISOTOPE COMPOSITION OF THE ATMOSPHERE................................................217 Modern air O2.............................................................................................................217 Why is the reconstruction of the Δ′17O of air O2 from rocks interesting?..................220 AIR–ROCK INTERACTION................................................................................................220 Meteorite fusion crust.................................................................................................220 Cosmic spherules........................................................................................................222 From air to sulfates and beyond.................................................................................224 Deep sea manganese nodules.....................................................................................225 Tektites.......................................................................................................................227 Air inclusions in tektite glasses..................................................................................231 Skeletal apatite and eggshell carbonate......................................................................232 High temperature technical products..........................................................................232 Using Δ′17O as a new tool to distinguish synthetic and natural gems........................234 CONCLUSIONS....................................................................................................................236 ACKNOWLEDGEMENTS...................................................................................................236 REFERENCES......................................................................................................................236

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Triple Oxygen Isotopes in Evolving Continental Crust, Granites, and Clastic Sediments Ilya N. Bindeman

INTRODUCTION.................................................................................................................241 Shales, what do they reflect?......................................................................................242 Shales, granites and continental crust growth............................................................246 PART I: TRIPLE OXYGEN ISOTOPES IN WEATHERING PRODUCTS FROM MODERN AND RECENT ENVIRONMENTS.................................................................248 Weathering reactions and stable isotopic parameters.................................................248 Using triple oxygen isotopes in weathering products to estimate T and d′18Ow values..................................................................................................249 Computing the weathering product............................................................................253 Weathering in different climate regions.....................................................................253 Effects of diagenesis on d18O and Δ′17O in shales......................................................255 Effects of metamorphism and anatexis on d18O and Δ′17O.........................................260 PART II: SHALES ACROSS THE GEOLOGIC HISTORY.................................................261 Overview of temporal trend of d18O and ∆′17O and Archean vs. post Archean shales.................................................................................................261 The Phanerozoic shale record.....................................................................................266

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Triple Oxygen Isotopes ‒ Table of Contents PART III: THE TRIPLE OXYGEN ISOTOPE ANALYSIS OF GRANITES IN COMPARISON WITH SHALES RECORD: INSIGHT INTO THE EVOLUTION OF THE CONTINENTAL CRUST AND WEATHERING.............................................268 Comparing coeval record of Archean granites and shales..........................................274 Post-Archean granites and shales...............................................................................277 Alternative testable hypotheses of Archean–Proterozoic ∆′17O transition.................278 PART IV. SEDIMENTARY PROXIES SHOWING TEMPORAL D18O INCREASE..........279 SUMMARY: DEFINING THE D′17O CRUSTAL ARRAY...................................................283 ACKNOWLEDGEMENTS...................................................................................................284 REFERENCES......................................................................................................................284

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Triple Oxygen Isotope Variations in Earth’s Crust Daniel Herwartz

INTRODUCTION.................................................................................................................291 GUIDING PRINCIPALS.......................................................................................................292 Definitions, reference frames and the significance of TFL′s, MWL′s and q..............293 Mass dependent isotope fractionation in triple oxygen isotope space.......................295 Mixing........................................................................................................................298 QUANTIFYING FRACTIONATION FACTORS.................................................................301 The two directional approach.....................................................................................301 The three-isotope method...........................................................................................302 Isotope thermometry and geospeedometry.................................................................303 WATER–ROCK INTERACTION..........................................................................................304 Constraining input variables for the water–rock mass balance equation...................305 Constraining the isotopic composition of pristine (paleo-) fluids..............................307 Resolving the d18O composition of snowball Earth glaciers......................................307 Resolving the d18O composition of ancient seawater.................................................310 RESOLVING INDIVIDUAL PROCESSES..........................................................................311 Boiling and phase separation observed in well fluids................................................311 Assimilation of low d18O rocks..................................................................................311 Isotopic exchange with CO2 and SO2.........................................................................313 Decarbonation............................................................................................................313 Dehydration................................................................................................................313 Alteration....................................................................................................................314 CONCLUSIONS AND OUTLOOK......................................................................................315 ACKNOWLEDGEMENTS...................................................................................................316 REFERENCES......................................................................................................................316

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Triple Oxygen Isotope Trend Recorded by Precambrian Cherts: A Perspective from Combined Bulk and in situ Secondary Ion Probe Measurements D.O. Zakharov, J. Marin-Carbonne, J. Alleon, I.N. Bindeman INTRODUCTION.................................................................................................................323 PART I: PRECAMBRIAN CHERTS AS AN ARCHIVE OF ANCIENT SILICA CYCLE.326 The collection of early Precambrian cherts................................................................328 Silica precipitation and diagenesis, and the effect of oxygen isotopes......................332 Triple oxygen isotopes in silica..................................................................................334 Secondary ion mass spectrometry..............................................................................336 Raman spectroscopy...................................................................................................337 PART II: COMBINED SIMS AND TRIPLE OXYGEN ISOTOPE ANALYSIS OF PRECAMBRIAN CHERTS....................338 Methods......................................................................................................................339 Results........................................................................................................................341 Discussion: various origins of Precambrian cherts and record of seawater...............343 Triple oxygen isotope evolution of seawater..............................................................352 FUTURE DIRECTION AND CONCLUSIONS...................................................................355 ACKNOWLEDGEMENTS...................................................................................................357 REFERENCES......................................................................................................................357

11 Triple Oxygen Isotopes in Silica–Water and Carbonate–Water

Systems

Jordan A.G. Wostbrock, Zachary D. Sharp INTRODUCTION.................................................................................................................367 MINERAL–WATER OXYGEN ISOTOPE THERMOMETERS.........................................368 18 O/16O fractionation...................................................................................................368 Triple oxygen isotope fractionation............................................................................370 Equilibrium triple oxygen isotope fractionation—the Δ′17O–δ′18O plot.....................371 KINETIC EFFECTS RESULTING IN OXYGEN ISOTOPE DISEQUILIBRIUM.............372 Disequilibrium effects with dissolved inorganic carbon............................................373 Application to the triple oxygen isotope system........................................................374 SILICA–WATER FRACTIONATION...................................................................................376 Calibration of the triple oxygen isotope silica–water thermometer...........................376 Silica in the terrestrial environment............................................................................377 CARBONATE–WATER FRACTIONATION........................................................................378 Analytical method......................................................................................................378 Triple oxygen isotope fractionation in the calcite (aragonite)–water system.............379 Applications to natural marine samples.....................................................................381 CONSIDERATIONS NECESSARY TO INTERPRET ANCIENT SEDIMENTS...............382 Modelling changing ocean composition in the past...................................................384 Modelling triple oxygen isotope trends during diagenesis.........................................385 Application to carbonate and silica sediments...........................................................388 xii

Triple Oxygen Isotopes ‒ Table of Contents TRIPLE OXYGEN ISOTOPES OF COEXISTING QUARTZ AND CALCITE..................393 CONCLUSION......................................................................................................................395 ACKNOWLEDGEMENTS...................................................................................................395 REFERENCES......................................................................................................................395

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Triple Oxygen Isotope Systematics in the Hydrologic Cycle Jakub Surma, Sergey Assonov, Michael Staubwasser

INTRODUCTION.................................................................................................................401 Analysis......................................................................................................................402 New data presented in this work................................................................................403 TRIPLE OXYGEN ISOTOPES IN WATER.........................................................................404 Triple oxygen isotope fractionation............................................................................404 17 O-excess during the formation of vapor...................................................................404 NATURAL VARIATIONS OF 17O-EXCESS IN WATER.....................................................405 Meaning and purpose of the Global Meteoric Water Line.........................................405 17 O-EXCESS DISTRIBUTION IN ATMOSPHERIC VAPOR..............................................412 FUTURE WORK AND CONCLUSION...............................................................................420 Future work................................................................................................................420 Conclusion..................................................................................................................422 ACKNOWLEDGEMENTS...................................................................................................423 REFERENCES......................................................................................................................423

13 Triple Oxygen Isotopes in Meteoric Waters, Carbonates, and

Biological Apatites: Implications for Continental Paleoclimate Reconstruction

Benjamin H. Passey and Naomi E. Levin INTRODUCTION.................................................................................................................429 METEORIC WATERS...........................................................................................................430 Evaporation from the oceans......................................................................................430 Rayleigh distillation and the triple oxygen isotope meteoric water line....................432 Evaporation from isolated bodies of water.................................................................434 Closed-basin and throughflow lakes...........................................................................435 Special considerations and case studies.....................................................................438 ANIMAL AND PLANT WATERS........................................................................................441 Prospects for reconstructing ∆′17O of past atmospheric O2........................................446 Plant waters................................................................................................................446 ANALYSIS OF CARBONATES AND BIOAPATITES........................................................449 Conversion methods...................................................................................................449 Exchange methods......................................................................................................451 Other methods............................................................................................................452 xiii

Interlaboratory reproducibility...................................................................................453 Fractionation exponents for carbonate–water equilibrium, and acid digestion..........454 FUTURE DIRECTIONS AND CONCLUDING REMARKS..............................................455 ACKNOWLEDGEMENTS...................................................................................................457 REFERENCES......................................................................................................................457

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Small Triple Oxygen Isotope Variations in Sulfate: Mechanisms and Applications Xiaobin Cao, Huiming Bao

INTRODUCTION.................................................................................................................463 TRIPLE OXYGEN ISOTOPE SYSTEM..............................................................................465 SULFOXYANIONS–WATER OXYGEN ISOTOPE EXCHANGE.....................................466 Sulfate–water system..................................................................................................466 Sulfite–water system ..................................................................................................466 Thiosulfate–water system ..........................................................................................468 MICROBIAL SULFATE REDUCTION (MSR)...................................................................468 SULFIDE OXIDATION MECHANISMS.............................................................................469 Thiosulfate oxidation on pyrite surface......................................................................469 Sulfite oxidation by O2 in solution.............................................................................471 Sulfite oxidation by Fe3 +  in solution..........................................................................472 The role of microbes on oxygen isotope composition of sulfate derived from sulfur oxidation .................................................................................473 Comments on laboratory experiments........................................................................475 Constraining intrinsic equilibrium and kinetic oxygen isotope effects during sulfide oxidation...........................................................................................476 APPLICATIONS....................................................................................................................477 Predicted sulfate δ18O and small Δ′17O.......................................................................477 Lake sulfate ...............................................................................................................479 Riverine sulfate...........................................................................................................480 ANALYTICAL METHODS .................................................................................................481 FUTURE OPPORTUNITIES................................................................................................482 ACKNOWLEDGEMENTS...................................................................................................483 REFERENCES......................................................................................................................484

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Reviews in Mineralogy & Geochemistry Vol. 86 pp. 1–34, 2021 Copyright © Mineralogical Society of America

Why Measure 17O? Historical Perspective, Triple-Isotope Systematics and Selected Applications Martin F. Miller Planetary and Space Sciences, School of Physical Sciences The Open University Walton Hall Milton Keynes MK7 6AA UK [email protected]

Andreas Pack Georg-August-Universität, Geowissenschaftliches Zentrum Abteilung Isotopengeologie Goldschmidtstraße 1 37077 Göttingen Germany [email protected]

INTRODUCTION For many years, it was considered that measurements of the least abundant stable isotope of oxygen, 17O, would not provide any information additional to that obtainable from determinations of the 18O/16O abundance ratio, which, by being a factor of ~5.2 larger than 17O/16O, can be measured more easily. Here, we summarize significant events in the historical development of oxygen stable isotope ratio measurements and their application to Earth and planetary sciences, leading to a consideration of the potential information to be gained from high precision measurements of the ‘third isotope’. This is followed by a short description of triple oxygen isotope systematics, together with notation and definitions. In turn, this leads to a discussion of how improvements in measurement precision, coupled with recent theoretical developments and empirical findings, have enabled small variations in the 17O/16O isotope abundance ratio relative to 18O/16O to provide new insights to a remarkable diversity of applications. The foundations of stable isotope geochemistry can arguably be traced to the year 1947, when a theoretical framework for calculating equilibrium constants and their temperature dependence for isotopic exchange reactions was proposed by Urey (1947) and independently by Bigeleisen and Göppert-Mayer (1947). The partitioning of isotopes at equilibrium results was considered as a quantum mechanical process; reduced partition function ratios, in conjunction with the Teller–Redlich approximation (Redlich 1935) formed the basis of the calculations. The latter approximation allowed the rotational partition function contribution to be eliminated from the calculations and it was also assumed that isotope substitution has no direct effect on electronic energies. Thus, equilibrium fractionation factors could be determined from consideration of the respective molecular vibration frequencies only. From the reported results, Urey (1947) also suggested that, as a temperature increase from 0 °C to 25 °C should change the equilibrium 18O abundance in carbonate by a factor of 1.004 relative to that in coexisting water, accurate determination of the 18O/16O ratio in natural carbonates could be used to determine the 1529-6466/21/0086-0001$05.00 (print) 1943-2666/21/0086-0001$05.00 (online)

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temperature at which they formed. Fortunately, these theoretical advances coincided with of the development by Nier (1947) of a gas source mass spectrometer suitable for routine analyses of isotope ratios of the lighter elements. Modifications of the Nier mass spectrometer to increase the precision in relative abundance measurement by an order of magnitude were subsequently proposed by McKinney et al. (1950). Amongst these, a change-over valve was incorporated, to permit rapid switching between sample and reference gases being admitted to the ion source. Furthermore, the delta notation for reporting stable isotope relative abundances was introduced. Thus, for oxygen: 18

 18 O 

Rsample  18 Rreference 18 Rreference

(1)

where 18Rsample is the 18O/16O abundance ratio in the sample; 18Rreference is the corresponding ratio in a reference material. The δ value, being a ratio of dimensionless quantities, is also dimensionless. Because it is of small magnitude (≪ 1) in natural systems, it is usually reported as parts per thousand (designated ‘per mil’, or ‘‰’). The developments in mass spectrometry instrumentation enabled McCrea (1950), Urey et al. (1951) and Epstein et al. (1951) to investigate the carbonate-water isotopic temperature exchange scale in detail. It was shown that δ18O measurements of marine carbonates could be used to determine the ocean water temperatures to ±1 °C on a geologic timescale. Urey et al. (1951) already noted that the approach requires knowledge of the past seawater composition and that the δ18O of the carbonate did not change with time. These two factors persist to be the most important unknowns in paleo-thermometry. Epstein and Mayeda (1953) extended the measurements to include various natural waters and detail the effects of glaciation. Following a preliminary investigation by Baertschi (1950), Baertschi and Silverman (1951) extracted oxygen from silicate crustal rocks by fluorination (with HF and either ClF3 or F2) and reported a δ18O range of 24‰. They also noted that their measurements (made on O2 as the analyte gas) could be used to determine the temperature of equilibration and mineral closure. Conversion of extracted O2 to CO2, by reaction with a heated graphite rod (Clayton 1955) was generally adopted for δ18O measurements in future studies. This was because CO2 molecular ions occur in a region of the mass spectrum not coinciding with the major background ions from air O2 and N2. Furthermore, CO2 is less corrosive to the mass spectrometer filament than is O2. Later, Clayton and Mayeda (1963) used BrF5 as the fluorination reagent for extracting oxygen from silicate rocks, for improved oxygen yields and reduced systematic errors in the isotope data. Besides equilibrium exchange, variations of light element stable isotope ratios in nature may also result from kinetic effects, with the rates of chemical reactions (or physical processes, such as diffusion) differing for isotopically substituted molecules. Early theoretical considerations for quantifying the effects of isotopic substitution on the rates of chemical reactions were published by Bigeleisen (1952) and by Bigeleisen and Wolfsberg (1957). Despite the existence of the least abundant stable isotope of oxygen, 17O, having been suggested and confirmed as early as 1924 (Blackett 1925), and its presence identified in Earth’s atmosphere (Giauque and Johnston 1929) before the discovery of deuterium by H.  C.  Urey in 1931, no mention of 17O was made in the early calculations of equilibrium constants and their temperature dependence for isotope exchange reactions. This was also true for a review three decades later (Richet et al. 1977). The first application of 17O in the isotope geochemistry literature was the ‘Craig correction’ (Craig 1957) for quantifying the contribution of 12C16O17O+ isotopologues1 to the mass 45 ion beam when deriving δ13C values from measurements on CO2. Based on Craig’s (1957) data on CO2 extracted from Peedee Formation calcite by concentrated H3PO4 at 25.2 °C (McCrea 1950), ~6.3% was attributable to 12C16O17O+. In formulating the Isotopologues (a contraction of isotopic homologues) are molecular entities that differ only in isotopic composition, e.g. H216O, H217O, H218O.

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correction procedure, Craig (1957) postulated that: “For systems in thermodynamic equilibrium, consideration of the vibrational frequency decrease for the addition of one and of two neutrons to a nucleus indicates that the fractionation factor for the distribution of 18O between two compounds should be the square of the fractionation factor for 17O”. The relative abundances of the three oxygen isotopes should therefore follow a simple power law:

Rsample  18 Rsample  =  17 Rreference  18 Rreference  17

0.5

(2)

In delta notation 1   17 O  (1   18 O)0.5

(3)

Using the Maclaurin series expansion ln 1  x  x  12 x 2  13 x 3   x

(4)

and neglecting higher order terms, this relationship between the three isotopes can thus be approximated to:  17 O  0.5 18 O

(5)

Isotope ratio modifications that follow this pattern of proportionality are commonly referred to as ‘mass-dependent’ fractionations. Essentially, they result from the mass difference between 17 O and 16O (1.0042 Da) being approximately half the mass difference between 18O and 16O (2.0042 Da). Clearly, if all processes that modify δ18O values followed this simple law exactly, then indeed nothing would be learned from also measuring δ17O. Fortunately, however, oxygen triple-isotope distributions in natural systems are more variable than is suggested by this simple analysis.

Non-mass-dependent oxygen triple-isotope distributions In a study of refractory calcium-aluminum-rich inclusions, fragments, chondrules and isolated crystals in type-2 and type-3 (C2 and C3) carbonaceous chondritic meteorites, Clayton et al. (1973) made the surprising discovery that the apparent δ13C of the CO2 used as the analyte gas for isotope ratio measurements was negatively correlated with the δ18O value, which varied by nearly 40‰. As the standard (heated graphite rod) method for the conversion of O2 to CO2 had been used, the authors correctly attributed the apparent change in δ13C to a change in δ17O. Assuming that the δ13C value was constant, Clayton et al. (1973) found that the oxygen triple-isotope distributions conformed to δ17O ≈ δ18O, rather than to a mass-dependent trend with δ17O ≈ 0.5 δ18O. Approximately half of the samples were from the Allende meteorite (a type CV3). In addition to the data forming an array of slope one on a δ17O versus δ18O plot, the samples were strongly depleted in both minor isotopes. This led the authors to suggest that the oxygen isotopic compositions probably resulted from the admixture of a component of almost pure 16O, of nucleosynthetic origin. That explanation was abandoned almost three decades later (Clayton 2002), however, in favor of a CO ‘self-shielding’ mechanism. This is now widely accepted and involves optical shielding of ultraviolet radiation by the most abundant isotopologue of carbon monoxide, 12C16O. Such a mechanism had previously been suggested by Thiemens and Heidenreich (1983), although uncertainty about the chemical speciation of oxygen in the presolar nebula prevented those authors from assigning specifically which oxygen-bearing gas-phase molecule was most likely to be implicated. Other mechanisms to explain the δ17O ≈ δ18O relationship observed in many meteoritic components continue to be discussed, however (e.g., Chakraborty et al. 2013; Thiemens and Lin 2021, this volume).

4

Miller & Pack

Following the discovery of the unusual relationship between δ17O and δ18O in the hightemperature phases of Allende and other carbonaceous chondrites, further work (with O2 as the analyte) led to the suggestion by Clayton et al. (1976) and Clayton and Mayeda (1983) that groups of meteorites whose δ18O and δ17O values plot on a distinct mass-dependent fractionation line (displaced from one another) originated on separate planetary bodies. The characterization and classification of meteorites on the basis of oxygen triple-isotope measurements (nowadays at significantly higher levels of precision) continues to be of fundamental importance to meteoritics and studies of the solar system. The next major discovery to stimulate interest in 17O was when Thiemens and Heidenreich (1983) showed that the generation of ozone from molecular oxygen by electrical discharge also produces a slope one array on a δ17O versus δ18O plot. This demonstration that massindependent (also referred to as ‘non-mass-dependent’) isotopic fractionation of oxygen can result from a chemical process was of far-reaching significance. At the time, it was suggested that the effect may result from self-shielding by the major isotopologue, 16O2, although that was subsequently shown to be improbable (Navon and Wasserburg 1985). Heidenreich and Thiemens (1986) then suggested that stabilization of the excited transition state during ozone formation is where the anomalous isotope effect occurs and that symmetry may play a role, as may isotope-specific reaction rates. The empirical findings have been discussed from a theoretical perspective in numerous subsequent publications, but details of the mechanism are still not fully understood. See Thiemens and Lin (2021, this volume) for further information. The laboratory findings were followed by the discovery that stratospheric ozone is also characterized by a mass-independent 17O enrichment (Schueler et al. 1990; Krankowsky et al. 2000; Mauersberger et al. 2001), as are stratospheric CO2 (Thiemens et al. 1991, 1995a,b; Lämmerzahl et al. 2002) and stratospheric nitrous oxide (Cliff et al. 1999). Lämmerzahl et al. (2002) showed a tight coupling of the δ17O and δ18O values of stratospheric CO2, with the ratio being surprisingly high, at 1.70 ± 0.03, for the altitude range sampled (19 to 33 km). As shown in the same paper, ozone at this altitude range was found to exhibit a δ17O versus δ18O slope of 0.62 ± 0.06, which was probably controlled largely by the local temperature (Krankowsky et al. 2000). Tropospheric ozone was also found to be unusually enriched in 17 O (Krankowsky et al. 1995; Johnston and Thiemens 1997), as was tropospheric nitrous oxide (Cliff and Thiemens 1997). Transfer of 17O enrichment, directly or indirectly, from stratospheric ozone into most other oxygen-bearing constituents of the atmosphere has since been documented (and reviewed by Thiemens 2013; Thiemens and Lin 2019). Stratospheric– tropospheric exchange results in tropospheric O2 being depleted in 17O (Luz et al. 1999) relative to the mass-dependent composition of photosynthetic O2. Stratospheric CO2 entering the troposphere (Boering et al. 2004; Thiemens et al. 2014; Liang and Mahata 2015) may experience successive isotopic exchange with water, especially leaf water, where the process is promoted by the presence of carbonic anhydrase. The isotopic exchange reduces—and may eventually eliminate—departure from non-mass-dependent composition. Few other occurrences of the generation (rather than inheritance) of mass-independent oxygen isotopic composition have been documented. The fractionation in atmospheric CO as a result of the CO + ∙OH reaction (Röckmann et al. 1998) is one example. A second is photodissociation of CO2 by of 185 nm wavelength (ultraviolet) radiation, generating CO and O2 which are unusually enriched in 17O (Bhattacharya et al. 2000). Carbon monoxide photodissociation at shorter wavelengths (90–108 nm) in vacuum leads to atomic oxygen formation, which reacts with CO to produce CO2 enriched in 17O (Chakraborty et al. 2012). Of considerable significance in a cosmochemical context is the discovery that silica formed during gas phase oxidation of silicon monoxide by OH is characterized by a slope one array on the δ17O versus δ18O plot (Chakraborty et al. 2013).

Historical Perspective, Triple-Isotope Systematics and Selected Applications

5

The first examples of rocks or minerals on Earth that are characterized by non-massdependent oxygen isotope composition were discovered by Bao et al. (2000a) in massive sulfate deposits (gypcretes from the central Namib Desert and sulfate-bearing Miocene volcanic ash-beds in North America); also in sulfates from Antarctic dry valley soils (Bao et al. 2000b) and in desert varnish sulfates from Death Valley, USA (Bao et al. 2001). Substantial non-mass-dependent oxygen isotope distributions were subsequently found in atmospheric nitrate aerosols, sampled at coastal La Jolla, California (Michalski et al. 2003). Nitrate minerals (and, to a lesser extent, sulfates) of the Atacama Desert, northern Chile, also exhibit substantial enrichments of 17O (Michalski et al. 2004), as do nitrates sampled in the dry valleys of Antarctica (Michalski et al. 2005). Modelling indicated that these unusual isotopic compositions could be traced to photochemical reactions in the troposphere and stratosphere. Sulfate in snow and ice sampled at the South Pole (Savarino et al. 2003) was found to be characterized by strongly non-mass-dependent oxygen isotopic compositions. The authors suggested that SO2 from explosive volcanic eruptions which ejected substantial quantities of material into the stratosphere was probably responsible and that reaction with O(3P) in the stratosphere, rather than with coexisting ∙OH, was the most likely mechanism. Similarly, volcanic sulfate from volcanic supereruption ash deposits sampled from dry lake beds in the Tecopa basin, California, contain strong enrichments in 17O relative to mass-dependent isotopic composition (Martin and Bindeman 2009), indicative of the photolysis and oxidation of volcanic SO2 by 17O-enriched ozone or ∙OH, in the stratosphere. Eruptions which did not eject material higher than the troposphere, however, produced sulfate of, or very close to, mass-dependent oxygen isotopic composition (Martin et al. 2014).

Non-mass-dependent oxygen triple-isotope distributions generated by processes not involving photochemical reactions There are three reported examples of non-mass-dependent fractionation of oxygen isotopes—and not involving photochemistry—having been demonstrated in the laboratory. The first is that of ozone thermal decomposition (Bhattacharya and Thiemens 1988; Wen and Thiemens 1990, 1991). Equal 17O and 18O enrichments were found in the product O2 when the decomposition was performed at 110 °C (Wen and Thiemens 1991). In contrast, photolyic decomposition by visible light gave a δ17O/δ18O slope of ~0.53 at room temperature; this increased to ~0.65 if ultraviolet radiation was used. The second example is that associated with the thermal decomposition of divalent metal carbonate minerals (calcite, magnesite and dolomite were the examples used), under conditions that prevent back-reaction and isotopic exchange between the resulting metal oxide and released CO2 gas. For a collection of carbonates covering a wide range of δ18O values (and including NBS 18 carbonatite and NBS 19 calcite), it was found that the decomposition products fitted parallel mass-dependent fractionation arrays, offset from each other by ~ 0.4‰ (Miller et al. 2002). The metal oxides were anomalously depleted in 17O relative to massdependent composition, whereas the CO2 was enriched by a corresponding amount (half the magnitude of the depletion in the metal oxide). There is still no satisfactory explanation for the empirical findings. It has been suggested (J. R. Hulston, pers. comm.) that Fermi resonance might be an influential factor. However, the theoretical analysis required to investigate that hypothesis has yet to be performed. Fermi resonance occurs when two vibrational energy levels associated with different diatomic or polyatomic vibrations have nearly the same energy, that is, may be ‘accidentally degenerate’. It occurs in CO2, where the υ1 vibration at 1337 cm−1 is close to twice the υ2 vibration at 667 cm−1. A splitting of the 1337 cm−1 line results, as observed in the Raman spectrum. Essentially, Fermi resonance causes shifting of the energies and intensities of absorption bands; this has implications for isotope effects. Fermi resonance might be expected to occur during vibrational excitation of carbonates. In calcite, for example, υ3 occurs at 1432 cm−1, which is very close to twice the υ4 value of 714 cm−1

Miller & Pack

6

(both bands are Raman active). Depending on whether or not there is a linear progression in vibrational energy levels associated with substituting 16O by 17O or 18O in the crystalline carbonate lattice could have significant implications for the isotopic composition of the thermal decomposition products, if the reaction pathway is influenced by Fermi resonance. The third example—which does not involve any chemical reaction—is that the diffusion of molecular O2 gas, at low pressure and in a closed volume, defies mass-dependent isotopic distributions when a thermal gradient is applied (Sun and Bao 2011a). In contrast to the more abundant stable isotopes of oxygen, 17O has a non-zero nuclear spin value (5/2). In a follow-up paper, Sun and Bao (2011b) postulated that a—usually negligible—nuclear spin effect on the gas diffusion coefficient, amplified by the temperature gradient, may be responsible for the empirical observations. Such an effect had been predicted, from theoretical considerations, some 35 years earlier (Zel’dovich and Maksimov 1976).

OXYGEN TRIPLE-ISOTOPE SYSTEMATICS The equilibrium mass-dependent distribution of the three stable isotopes of oxygen resulting from isotopic exchange between two chemical entities A and B may be described in terms of the 17O and 18O abundance ratios relative to 16O as 

RA  18 RA  (6)   17 RB  18 RB  which, by definition, gives the relationship between the respective fractionation factors as 17



18/16 17/16 AB   AB





(7)

and as expressed in delta values: 1   17 O A  1   18 O A    1   17 O B  1   18 O B 



(8)

The exact magnitude of the exponent θ depends on the identity of A and B, since the energy differences between the various isotopically-substituted molecules depends not only on the respective masses of 16O, 17O and 18O, but on the reduced masses in the molecular vibrations. The first investigation of such variations, and their temperature dependence, was by Matsuhisa et al. (1978). Calculations were performed according to the procedure of Urey (1947), i.e. with θ obtained as the ratio of natural logarithms of reduced partition function ratios, and with vibrational frequencies for 17O-containing species calculated from published values for the corresponding 16O- and 18O-bearing entities. The harmonic oscillator approximation for molecular vibrations was assumed throughout. The authors reported that, for gas phase equilibrium exchange between CO2 and water, θ ranges from 0.5233 at 0 °C to 0.5251 at 727 °C. This variation appears small, compared with the corresponding ln(α18/16) varying by a factor of approximately twenty, and illustrates that the magnitude of θ is not particularly sensitive to temperature. For large changes in δ18O, however, small variations in θ become important and the resulting influence on oxygen triple-isotope distributions is usually measurable, at current levels of precision. Matsuhisa et al. (1978) also noted that, at low temperatures, the natural logarithm of the ratio of partition function ratios for CO2 and water approach limiting values given by the respective ratios of the zero-point energy differences between the isotopically substituted molecules. For isotope exchange between water vapor and atomic oxygen, this is 0.53052; the comparable figure for CO2 is 0.52554. At high temperatures, the ratio approaches

Historical Perspective, Triple-Isotope Systematics and Selected Applications

7

a constant value of 0.53053 for all oxygen-bearing molecules, as derived from equation 8 of Urey (1947) and is in accord with the simple expression

 17Q   1 1   16Q    m m 1 1  18Q   m m ln  16 18  16Q   

ln 

16

17

(9)

where m16, m17 and m18 are the atomic masses of 16O, 17O and 18O respectively. Matsuhisa et al. (1978) observed that, for temperatures of interest, ratios of the natural logarithms of partition function ratios for oxygen-bearing molecules vary from about 0.527 to 0.530. In exchange reactions, however, the θ values will be somewhat lower and more variable, depending on the specific reaction considered. The authors reported that a range of 0.520 to 0.528 was obtained from various representative reactions (unspecified) for which calculations were made. This was a highly significant finding, which has since been shown experimentally to be largely true. In the same paper, the authors also reported an experimental determination of 103ln(α17/16) and 103ln(α18/16) for oxygen isotope exchange at equilibrium in the quartz–water system at 250 °C. The respective values of 4.75 and 9.03 gave θ as 0.526. This number has been confirmed by more recent theoretical calculations (Cao and Liu 2011) and empirical data (Sharp et al. 2016). In addition to considering equilibrium processes, Matsuhisa et al. (1978) reported that kinetic processes involving isotope exchange can be examined using a comparable formalism. Their calculations for the example of pinhole (Graham’s law) diffusion, however, seem to have been based on an erroneous algorithm; the reported results are at variance with more recent discussions of the same example (Young et al. 2002; Dauphas and Schauble 2016). The relationship as derived in the later works is:

diffusion 

ln 

M16    M17   M16 

(10)

m16  m17 m16  m18

(11)

ln 

  M18  where Mi refers to the masses of the isotopically substituted molecules. This gives values ranging from 0.516, for the diffusion of atomic oxygen, to 0.501 in the high molecular mass limit. As noted by Dauphas and Schauble (2016), the latter value also corresponds to diffusion 

Clayton and Mayeda (2009) showed experimentally that the lower limit value of θ for a kinetic process was approached during thermal dehydration, in vacuum, of Mg–O–H units in the minerals serpentine and brucite. The oxygen isotopic compositions of crustal silicates on Earth generally results from interactions between solids, melts and aqueous fluids, involving many individual processes and with temperature playing an influential role. Therefore, it is to be expected that, as suggested by Matsuhisa et al. (1978), collections of silicate rocks and minerals will be characterized by oxygen triple-isotope distributions that result from the average of the many individual slopes for specific processes. Measurements on diverse rock and mineral samples reported during the past decade (and discussed below) indicate that, as expected, equilibrium processes dominate the slope value and there seems to be little evidence to suggest that the simple diffusion model is relevant in this context.

Miller & Pack

8

Experimental measurements of ln(17/16α) /ln(18/16α) = θ Few experimental measurements of the equilibrium exponent θ for oxygen triple-isotope exchange have been reported to date. Pack and Herwartz (2014) found that, for SiO2 as chert in equilibration with water at ~50 °C, θ is 0.5235 ± 0.003. At 8 °C, a lower value of 0.5212 ± 0.0008 was determined from opal equilibrated with water. Data from high temperature rock assemblages (granite and San Carlos lherzolite) as reported in the same paper indicated that θ was of the order of 0.528 to 0.529, but the associated error bars were significantly larger because of the very limited δ18O ranges of the samples investigated. Sharp et al. (2016) found that, for the temperature range ~0 to 50 °C, θ in the SiO2−water system is 0.523−0.524 (see also Wostbrock and Sharp 2021, this volume). Taken together, these findings are consistent with the value at 250°C being 0.526, as determined experimentally by Matsuhisa et al. (1978). Oxygen triple-isotope exchange between biogenic apatite and water under equilibrium conditions has also been investigated experimentally (Pack et al. 2013), with θ reported to be 0.523 at 37 °C. Barkan and Luz (2005) measured the fractionation factors 17/16α and 18/16α for water liquid–vapor exchange at equilibrium and found the ln(17/16α) / ln(18/16α) ratio, θ, to be 0.529 ± 0.001 over the temperature range 11.4 to 41.5°C. The same authors subsequently conducted evaporation experiments to investigate the relative diffusivities of water vapor isotopologues in air and derived values for the diffusion fractionation coefficients 17/16αdiffusion and 18/16αdiffusion (Barkan and Luz 2007). The ratio ln(17/16αdiffusion) / ln(18/16αdiffusion) was found to be 0.5185 ± 0.0002, in very good agreement with the theoretical value and significantly smaller than the corresponding ratio reported by the same authors for water liquid–vapor equilibrium. For CO2–H2O equilibrium exchange, θ was determined by Barkan and Luz (2012) as 0.5229 ± 0.0001 at 25 °C, which is in good agreement with the value of 0.522 ± 0.002 for the temperature range 2 to 37 °C as reported by Hofmann et al. (2012). Both values, however, are notably lower than the 0.5246 calculated from theoretical considerations by Cao and Liu (2011)2 and also somewhat less than 0.5235 as calculated by Matsuhisa et al. (1978).

Defining and quantifying deviations from a reference fractionation relationship To quantify departures from a specific fractionation relationship between 17O/16O and O/ O, Clayton and Mayeda (1988) proposed the term Δ17O, which they defined as:

18

16

 17 O   17 O – 0.52 18 O

(12)

This famous equation has since been used routinely in studies of meteorites; also for quantifying terrestrial non-mass-dependent isotope effects. It is based on approximating a power law relationship, as discussed above. Assigning 0.52 as the constant of proportionality was attributed to measurements made more than a decade earlier (Clayton et al. 1976; Matsuhisa et al. 1978) of 35 terrestrial samples—including various rocks and waters—which were found to form an array of slope 0.5164 ± 0.0033 (standard error of the mean, SEM) on a δ17O versus δ18O plot. Unfortunately, no details of the samples, nor the actual isotope data, were reported. Matsuhisa et al. (1978) mentioned that, on the basis of those measurements, a slope of 0.520 was chosen for the quartz–water system as a reasonable compromise between theoretical calculations and empirical observations. This defined a reference (terrestrial) fractionation line; the extent to which meteorite samples deviated from this was quantified by the parameter Δ17O. Definitions of Δ17O using different constants of proportionality have since appeared in the literature, according to the particular application and associated mass fractionation characteristics. For example, Cliff and Thiemens (1997) used 0.515 in defining the Δ17O of atmospheric nitrous oxide; Boering et al. (2004) assigned 0.516 for defining the Δ17O of stratospheric carbon dioxide; Luz et al. (1999) used 0.521 as determined from the fractionation of O2 during respiration. 2

The θCO2–water value at 25 °C was later recalculated as 0.523 (Y. Liu, pers. comm. in Hofmann et al. 2012).

Historical Perspective, Triple-Isotope Systematics and Selected Applications

9

A consequence of the δ17O versus δ18O relationship not being truly linear is that the slope given by a collection of data points on such a plot is dependent on the range of δ values associated with the group of samples and on the isotopic composition of the reference material. An example of this is shown in Figure 1. For consistency of reporting and comparison of data sets, it is therefore advantageous to avoid the approximation. The oxygen triple-isotope distributions in a collection of silicate rock and mineral samples (or waters) of diverse origin will generally conform to the mass-dependent fractionation relationship Rsample  18 Rsample    17 Rreference  18 Rreference  17



(13)

as shown experimentally by Meijer and Li (1998) for natural waters. The exponent term in this case is designated as λ rather than θ, to indicate that the isotope exchange processes are undefined. Thus, λ is a purely empirical parameter, the magnitude of which results from the cumulative effects of (unspecified) fractionations associated with the history of the individual samples. To quantify deviations from a specific mass-dependent fractionation curve, an additional term is needed: 

Rsample    Rreference 

17

Rsample  17 Rreference

18

1  k   18



(14)

With δ values rather than absolute ratios, and with k defined to be Δ17O, then, as suggested by Miller (2002)  17 O 

1   17 O

1   O  18



1

(15)

which is of a similar form to the definition of the δ value. In linear format,







ln(1   17 O)  ln 1   17 O   ln 1   18 O



(16)

It needs to be remembered that the δ17O and δ18O data here are not ‘per mil’ values, as conventionally reported, but the absolute numbers (≪1). Therefore, it is useful to include a multiplier of 103 so that the logarithmic terms involving δ17O and δ18O are then of similar magnitude to the corresponding δ17O and δ18O data reported as ‘per mil’:







103 ln(1   17 O)  103 ln 1   17 O  103 ln 1   18 O



(17)

Following similar terminology introduced by Hulston and Thode (1965) in the context of sulfur multiple isotope ratios, the quantities 103ln(1 + δ17O) and 103ln(1 + δ18O) are sometimes denoted as δ′17O and δ′18O respectively. As reported by Miller (2002), a plot of 103ln(1 + δ17O) versus 103ln(1 + δ18O) data obtained from a collection of silicate rocks and minerals (for example) thus gives a linear array of slope λ, invariant to the range of δ values and to the isotopic composition of the reference, and with the ordinate deviation of an individual sample from the mass-dependent reference fractionation line being quantified by 103 ln(1 + Δ17O). With 103ln(1 + Δ17O) written as Δ′17O, similar to the definitions of δ′17O and δ′18O, we then obtain the simple, non-approximated relationship:  17 O   17 O   18 O

(18)

This definition is used throughout this volume. What is perhaps not immediately intuitive is that, instead of assigning the magnitude of λ from a set of measurements, a value may

Miller & Pack

10

alternatively be assigned arbitrarily. For example, reference lines of slope 0.528 (as used throughout this volume) or 0.5305—and passing through VSMOW—have been defined for the reporting of Δ′17O in various recent studies. Not accounted for in this Δ′17O definition, however, is the magnitude of any offset of a reference line from the zero point of the δ scale. At the time that the definition of Δ′17O was proposed, it was considered that fractionation arrays formed from silicates (or meteoric waters) were not offset from VSMOW. This was subsequently found to be incorrect, although quantifying the small magnitude of the offsets generally requires the highest levels of precision and accuracy. Defining a reference line that is offset from the zero point of the δ scale by a specified amount may also be useful under some circumstances. Therefore, an additional term is required in the definition of Δ′17O; it is usually designated as γ, and with γ′ ≡ 103ln(1 + γ). Thus, we now have: (19)

 17 O   17 O   18 O  

If defined from an empirical data array, the exact magnitude of λ is representative of the particular group; there is not necessarily an implied relationship between the individual samples. Different collections of silicate rock and mineral samples generally give slightly different values of λ (usually between 0.522 and 0.529) and of γ′. Recalibration more accurately to the VSMOW scale, on the basis of Pack et al. (2016) and Miller et al. (2020), of Open University measurements of the two silicates arrays reported by Rumble et al. (2007) results in γ′ values of +8 ± 19 ppm (95% confidence interval) for the hydrothermal quartz and chalk flint array; –38 ± 5 ppm for the eclogite garnets. These values are 12 ppm lower than given by Hallis et al. (2010). Similarly, recalibration by Tanaka and Nakamura (2017) of the γ′ value the same authors reported in 2013, results in a revised γ′ value of –33 ± 5 ppm. This small number of examples is probably not indicative of the γ′ range limits. Despite the variations of λ and γ′, individual arrays have frequently been referred to as a ‘Terrestrial Fractionation Line’ (TFL). 20

δ17O (‰)

15

Data reported relative to the ‘working standard’ O2 : δ17O = (0.5240 ± 0.0010) δ18O + (0.310 ± 0.006) R2 = 0.99996, n = 46

10

Data reported relative to VSMOW: δ17O = (0.5213 ± 0.0009) δ18O + (–0.018 ± 0.012) R2 = 0.99996, n = 46

5

–15

–10

5 –5

10

15

20

δ18O

25

30

35

(‰)

–10

Figure 1. Illustrating that a change of reporting reference for δ17O and δ18O measurements (from the laboratory ‘working standard’ O2 to VSMOW, in this example) may be associated with a changed regression line slope and ordinate offset on a δ17O versus δ18O plot. This is caused by the δ scale being non-linear, leading to non-linearity of δ17O versus δ18O data arrays. The extent of non-linearity increases with distance from the zero point of the scale. For this example, the data are from Miller et al. (1999). The δ18O value of the ‘working standard’ O2 was 10.34‰ relative to VSMOW, with corresponding Δ′17O0.528 = +0.387‰ (as derived from Miller et al. 2015). Converting to the VSMOW scale, from data (shown as open circles) reported relative to the working standard O2, therefore involves substantial positive shifts of the respective δ18O and δ17O values. This results in best linear fit to the converted data (filled circles) requiring a different regression line, as shown. Precision values refer to the 95% confidence interval.

Historical Perspective, Triple-Isotope Systematics and Selected Applications 11 The terminology λRL and γRL has recently been introduced to denote that λRL and γRL are defined quantities (with RL referring to ‘reference line’) and is gaining acceptance. The respective values need to be clearly stated, as there is currently no consensus. This is discussed by Hofmann et al. (2017), who identified six different reference lines used in various studies. An advantage of writing Δ′17O rather than Δ17O is that it provides a clear distinction from the original definition introduced by Clayton and Mayeda (1988). For simplicity, the 103 multiplier term is usually omitted from the definition and γ′RL approximated as γRL, on the basis that | γ | –4 is usually < 10 or is defined to be zero. Thus,









(20)

 17 O ln 1   17 O   RL ln 1   18 O   RL

This definition is becoming generally adopted (e.g., Hofmann et al. 2017) and is advocated for future reporting of Δ′17O data. As a ratio, it may be written (in non-approximated form) as:  17 O 

1   17 O

1   RL  1   18 O 

 RL

1

(21)

103 ln(1 + δ17O)

A graphical representation of the relationship between the various parameters is shown in Figure 2. Because of the small magnitude of Δ′17O in many studies, it is usually reported as parts per million (ppm). In some of the earlier literature, the term ‘per meg’ is used instead of ppm.

Δʹ17O

(Sample C)

Δʹ17O

(Sample B)

C

B Δʹ17O

(Sample A)

Intercept (γʹ) of mass-dependent fractionation line defined by the sample group

A

103 ln(1 + δ18O)

Figure 2. Schematic illustration of the relationship between Δ′17O values for a set of rock, water or gas samples and: (i) the reference mass-dependent fractionation line characterized by assigned slope λRL (0.528, for the VSMOW-SLAP scale) and assigned ordinate axis intercept value γ′RL (zero, in this example) on the 103 ln(1 + δ17O) versus 103 ln(1 + δ18O) plot; (ii) the mass-dependent fractionation line of slope λ and ordinate axis intercept value γ′ formed by the collection of samples. Unlike λ, the value of γ′ will depend on the isotopic composition of the reference material (usually VSMOW) relative to which δ17O and δ18O values are reported; also on the accuracy of the calibration of the ‘working standard’ O2 relative to that reference. If λRL differs significantly from λ, Δ′17O will vary with increasing δ18O as an artefact of the increasing divergence (or convergence) of the two mass-dependent fractionation lines.

For completeness, we note that an earlier definition used by Farquhar et al. (1998) also avoided the approximation of a linear relationship between δ17O and δ18O:

 17 O 1   17 O  (1   18 O)0.52

(22)

Miller & Pack

12

With λRL = 0.52 and γRL = 0, this expression gives very similar results to those obtained from the recommended Δ′17O definition, for a given triple-isotope data set. We also note that (rather confusingly) Angert et al. (2003) defined δ′17O − λ δ′18O as 17Δ. The 17Δ notation has not gained general acceptance, however. In much of the literature reporting oxygen triple-isotope ratio measurements of waters, snow and ice cores, Δ′17O is referred to as ‘17O-excess’, a term introduced by Luz and Barkan (2000) and subsequently defined by the same authors (Barkan Luz 2007) as 17







O-excess  ln 1   17 O  0.528 ln 1   18 O



(23)

This does indicate that 17O-excess is ≥ 0 in all cases, otherwise there is the incongruity of a ‘negative excess’. The definition of 17O-excess is identical to the definition of Δ′17O used throughout this volume. The expression ‘17O anomaly’ is also sometimes adopted (e.g., Thiemens et al. 1995b; Dauphas and Schauble 2016), to describe non-mass-dependent isotope distributions. For simplicity and consistency, we suggest that it is preferable to use the term Δ′17O universally and with the values of λRL and γRL clearly stated. For consistency throughout this volume, the Editors have recommended that Δ′17O be defined using λRL = 0.528 and γRL = 0. It should be noted that Δ′17O does not behave linearly with regard to mixing calculations, unlike Δ17O as defined by Clayton and Mayeda (1988). It is therefore necessary to use the associated δ17O and δ18O data for calculating changes in Δ′17O resulting from the mixing of fluids characterized by different isotopic compositions. Finally, a detailed discussion of the theoretical principles and calculations of mass-dependent fractionation processes in the oxygen triple-isotope system is beyond the scope of this introductory section. For further reading, see Schauble and Young (2021, this volume); Yeung and Hayles (2021, this volume); Brinjikji and Lyons (2021, this volume); Thiemens and Lin (2021, this volume). The review by Dauphas and Schauble (2016) is also recommended. Cao and Liu (2011) and Bao et al. (2016) provide additional insights.

REFERENCE MATERIALS AND STANDARDS Early measurements of oxygen triple-isotope ratios (e.g., Clayton et al. 1973) were reported relative to the Standard Mean Ocean Water (SMOW) standard described by Craig (1961); this practice continued for some considerable time. In 1968, the International Atomic Energy Agency (IAEA) began distributing two new water reference materials, Vienna Standard Mean Ocean Water (V-SMOW) and Standard Light Antarctic Precipitation (SLAP). Both were prepared by H. Craig at the University of California San Diego: V-SMOW by mixing distilled Pacific Ocean water (collected in July 1967) with small amounts of other waters in order to make the isotopic composition as close as possible to that of SMOW. V-SMOW is also referred to as RM 8535 by the US National Institute of Standards and Technology (NIST). SLAP was prepared from a firn sample collected in 1967 at Plateau Station, Antarctica, by E. E. Picciotto of the Université Libre de Bruxelles. On the basis of comparative measurements by 36 different institutions, the δ18O value of SLAP was assigned in 1976 as –55.5‰ exactly, by the IAEA (Gonfiantini 1978), with V-SMOW (subsequently re-designated as VSMOW) defined as the zero point of the scale. SLAP is also referred to as RM 8537 by NIST. For improved consistency of reporting δ18O measurements, it was recommended that data be normalized to the VSMOW-SLAP scale (Gonfiantini 1978). Thus, δ18O data (relative to VSMOW) should be scaled by a factor of (–55.5) / (δ18OSLAP/VSMOW) where δ18OSLAP/VSMOW is the measured value of SLAP relative to VSMOW. It has since been suggested that the assigned δ18O value of SLAP may be significantly in error, however. On the basis of a report by Verkouteren and Klinedinst (2004), Kaiser (2008) noted that the ‘true’ δ18O value

Historical Perspective, Triple-Isotope Systematics and Selected Applications 13 seems to be –56.18 ± 0.01‰, illustrating that the VSMOW-SLAP δ18O scale is associated with significant uncertainties for values far removed from VSMOW. Because measurement artefacts such as cross-contamination generally lead to a compression of the δ scale, the value of –56.18 ± 0.01‰ for SLAP is likely to be more accurate. Nevertheless, the value of –55.5‰ has been retained for calibration to the VSMOW-SLAP scale. With stocks of VSMOW and SLAP becoming low, the IAEA ceased to distribute those reference waters after November 2006. However, successor materials VSMOW2 and SLAP2, prepared to have nominally identical isotopic characteristics to VSMOW and SLAP respectively, were produced at the IAEA Isotope Hydrology Laboratory and made available from 2007 onwards. Details of the respective preparations are given by Harms and Gröning (2017). It is important to recognize that the reporting scale for δ18O (and for δ2H) is still denoted and referred to as the VSMOW–SLAP scale, despite VSMOW and SLAP being no longer available. The non-availability of VSMOW and SLAP doesn’t prevent calibration (or normalizing) measurements to VSMOW and SLAP using VSMOW2 and SLAP2, which provide suitable traceability to VSMOW and SLAP respectively (Dunn et al. 2020). Oxygen triple-isotope ratio measurements (especially at high precision) are generally performed using molecular oxygen as the analyte gas and reported relative to the equivalent ratios in a reference material (usually VSMOW). For investigations involving rocks and minerals, the use of a water reference material causes significant calibration challenges. The accuracy of reported δ17O and δ18O data is critically dependent, however, on the accuracy of calibration (relative to VSMOW) of a laboratory ‘working standard’ O2 against which the isotopic composition of molecular oxygen extracted from silicates (or waters) is compared. The extent of instrumental scale compression should also be established, from measurements of molecular oxygen extracted from SLAP. A few silicates, such as the University of Wisconsin garnet standard UWG-2 (Valley et al. 1995) and San Carlos olivine, are widely used for calibrating the δ18O value of individual laboratory’s ‘working standard’ O2, although there remains a lack of consensus about the exact δ18O values of those silicates relative to VSMOW. Furthermore, there are currently no standards for δ17O and recent attempts to characterize the δ17O values of UWG-2 and San Carlos olivine have not resulted in consensus (Pack et al. 2016; Sharp et al. 2016; Miller et al. 2020; Wostbrock et al. 2020). Table 1 lists those recent results. It should be noted that two distinct variations of San Carlos olivine have been identified (designated as Type I and Type II); these are characterized by different δ18O values. It is probable that other variations also exist. Type I is characterized by δ18O = 4.88‰ (Mattey and Macpherson 1993; Thirlwall et al. 2006). Macpherson et al. (2005) reported a value of 4.84 ± 0.09‰, together with 5.22 ± 0.08‰ for the more commonly-used Type II. In a more recent investigation, Starkey et al. (2016) compared δ18O and also δ17O measurements of Types I and II San Carlos olivine. They noted that, despite the variations in δ18O, the corresponding Δ′17O value seemed to be constant. This latter finding was subsequently confirmed by Miller et al. (2020). For further discussion on standardizing oxygen triple-isotope data, see Sharp and Wostbrock (2021, this volume). Despite atmospheric O2 having a deficit of 17O relative to mass-dependent composition, a number of studies have used it as a standard, notably in investigations of the triple-isotope composition of dissolved O2 for estimating global and oceanic biological productivity (e.g., Luz et al. 1999; Luz and Barkan 2000). Because δ17O and δ18O measurements of air O2 are affected by the presence of argon (which was not removed in those investigations), corrections needed to be applied (Barkan and Luz 2003)3. Converting the resulting isotope data to the VSMOW-SLAP scale, however, is complicated by the δ17O and δ18O values of air O2 relative to the VSMOW reference water not having been universally agreed, as discussed below. 3 In more recent studies involving isotopic measurements of air O2 (Yeung et al. 2012; Young et al. 2014; Pack et al. 2017; Wostbrock et al. 2020), all other atmospheric constituents were removed, including Ar.

Miller & Pack

14

Table 1. Recent high-precision oxygen triple-isotope measurements of widely-used silicate standards San Carlos olivine and UWG-2 garnet. Institution

n

δ18OVSMOW (‰)

Δ′17O0.528 (ppm)

Reference

San Carlos olivine Georg-August-Universität Okayama University

30

5.153 ± 0.161

–36 ± 7

Pack et al. (2016)

5

5.287 ± 0.047

–39 ± 7

Pack et al. (2016)

University of New Mexico

12

5.577 ± 0.095

–54 ± 8

Sharp et al. (2016)

University of New Mexico

18

5.268 ± 0.023

–58 ± 5

Wostbrock et al. (2020)

University of New Mexico

9

5.696 ± 0.115

–71 ± 5

Wostbrock et al. (2020)

UWG-2 garnet

Notes: Measurement precision data are 1σ. All data were calibrated directly to VSMOW and SLAP. With the δ18OVSMOW and Δ′17O0.528 values of UWG-2 garnet assigned as 5.75‰ and –46 ppm respectively, for calibration purposes, Miller et al. (2020) reported that the Δ′17O0.528 value of San Carlos olivine is –38 ± 9 ppm (1σ) as measured at Georg-August-Universität Göttingen, with comparable measurements at The Open University giving –38 ± 8 ppm (i.e., in accord with the inter-laboratory comparison reported by Pack et al. 2016).

For maximum accuracy, linear scaling to VSMOW-SLAP requires that ln(1 + δ18O) values be adjusted, rather than the corresponding δ18O data, because of the non-linearity of the δ scale. The ‘true’ scaling factor is therefore ln(1 − 0.0555) / ln(1 + δ18OSLAP/VSMOW), with δ18OSLAP/VSMOW referring to the measured value of SLAP relative to VSMOW. Fortunately, as noted by Kaiser (2008), the numerical differences between the conventional and logarithmic normalization procedures are generally small. Kusakabe and Matsuhisa (2008) did normalize their ln(1 + δ18O) data to VSMOW-SLAP, with the same scale factor of (–57.10) / (–56.20) being applied to their ln(1 + δ17O) results. The same approach was adopted by Ahn et al. (2012). Kaiser (2008) recommended a similar normalization, but in power law format and with λ assigned to be 0.528, as shown to apply to natural waters (Meijer and Li, 1998): 17  17 Osample VSMOW-SLAP normalized   O VSMOW

(1   18 OSLAP/VSMOW, measured )0.528  1 (1   18 OSLAP/VSMOW, assigned )0.528  1

(24)

These scaling procedures preserve the oxygen triple-isotope ratio relationship of the δ17O and δ18O measurements, whilst ensuring that the measured δ18O values are normalized to the VSMOW-SLAP scale. To improve inter-laboratory consistency of Δ′17O data from measurements of water samples, Schoenemann et al. (2013) proposed that δ17O measurements be normalized to the VSMOW-SLAP scale in the same way as recommended by Gonfiantini (1978) for normalizing δ18O data, with the δ17O value of SLAP defined to give Δ′17O of exactly zero, relative to a reference line of λRL = 0.528 and γRL = 0. Schoenemann et al. (2013) reported that the resulting scale factor for the δ17O measurements is therefore approximately (–29.6986) / δ17OSLAP/VSMOW. This recommendation involves scaling of the empirical δ17O results independently of the corresponding δ18O data. Essentially, the experimental data are adjusted so that the measurements of SLAP fit exactly on a reference line of slope 0.528 and which passes through VSMOW on a ln(1 + δ17O) versus ln(1 + δ18O) plot. The twopoint calibration also addresses other instrument-related effects, as discussed by Yeung et al. (2018) and by Pack (2021, this volume). Recent measurements of SLAP indicate that it is characterized by a Δ′17O value slightly less than zero. Schoenemann et al. (2013) obtained a value of –6 ± 8 ppm (1σ). Wostbrock et al. (2020) reported that averaging their own measurements (–15 ± 5 ppm) with the –9 ± 7 ppm result reported by Sharp et al. (2016) and –8 ± 9 ppm obtained at Okayama University (Pack et al. 2016) gives a value of –11 ± 4 ppm.

Historical Perspective, Triple-Isotope Systematics and Selected Applications 15 16

O, 17O AND 18O ABUNDANCES AND ISOTOPE RATIO RANGES IN NATURALLY OCCURRING TERRESTRIAL MATERIALS

Oxygen is characterized by atomic number 8 and is the third most abundant element in the solar system, after hydrogen and helium. It is the most abundant element on Earth, with silicate and oxide minerals of the crust and mantle comprising by far the largest terrestrial reservoir (~99.5% by mass). Table 2 lists the masses of three stable isotopes of oxygen (Holden et al. 2018), together with their natural abundance ranges (Meija et al. 2016) and abundance ratios in VSMOW (IAEA reference sheet on VSMOW and SLAP 2006). Table 2. Mass, natural abundance range, and abundance ratio in the VSMOW reference material, of the three stable isotopes of oxygen. Isotope

Mass (Da)

Natural abundance range (atom%)

Abundance ratio (ppm) in VSMOW, relative to 16O

16

O

15.994914619

99.738–99.776

106

17

O

16.999131757

0.0367–0.400

379.9 ± 0.8

18

O

17.999159613

0.187–0.222

2005.2 ± 0.45

Although 17O is a factor of ~5.3 less abundant than 18O in seawater, it is nevertheless approximately twice as abundant as deuterium. Reported δ18O values of terrestrial silicate rocks and minerals vary from –27.3‰ (Bindeman et al. 2010, 2014), in the most extreme example of interaction with ‘Snowball Earth’-derived synglacial meteoric waters at depth, to as high as 60.2‰ (and with Δ17O ranging from 14–21‰) in nitrate deposits from the Atacama desert (Michalski et al. 2004). However, the largest known 18O enrichments occur in stratospheric ozone (δ18O up to ~110‰), with only slightly lower values in tropospheric ozone and nitrate aerosols. Isotopic data for these three species scatter about a slope one line on a δ17O versus δ18O array (Thiemens 2013). At the other end of the scale, a δ18O value as low as –81.9‰ has been measured in precipitation collected at Dome Fuji, East Antarctica (Fujita and Abe 2006).

Oxygen triple-isotope measurements of atmospheric O2 M. H. Thiemens (comment reported in Bender et al. 1994) first suggested that there should be a deficiency of 17O in atmospheric O2, relative to mass-dependent composition. This was based on a consideration of stratospheric photochemical reactions and mass exchange between the stratosphere and troposphere (Thiemens et al. 1991). The magnitude of the deviation from mass dependent composition was subsequently documented from experiments by Luz et al. (1999). The first high precision δ18O and δ17O measurements of atmospheric O2 relative to VSMOW directly, however, were by Barkan and Luz (2005), who obtained δ18O = 23.88 ± 0.02‰, δ17O = 12.08 ± 0.01‰. Measurements on SLAP were reported in the same paper as –55.11 ± 0.01‰ and –29.48 ± 0.03‰, respectively, giving a Δ′17O value (relative to λRL = 0.528) of 0.007‰. The air O2 δ18O value was in agreement with 23.79 ± 0.06‰ as obtained by Horibe et al. (1973) and also with the 23.8 ± 0.14‰ value (Coplen et al. 2002) obtained by recalibrating the measurements of Kroopnick and Craig (1972). The measurements by Horibe et al. (1973) and Kroopnick and Craig (1972) were made on CO2 equilibrated with water of air O2 isotopic composition. In none of those three studies was instrument-related contraction of the δ scale corrected for, however, which would increase the respective magnitudes of the δ17O and δ18O data. Relative to a reference line of λRL = 0.528 and passing through VSMOW, Δ′17O for air O2 as obtained from the Barkan and Luz (2005) data is –0.453‰. Normalizing their data to the VSMOW-SLAP scale as recommended by Schoenemann et al. (2013) shifts the Δ′17O value by only 2 ppm, to –0.451‰, despite the corresponding δ18O and δ17O values being increased to 24.05‰ and 12.17‰ respectively. This illustrates the comparative robustness of Δ′17O (resulting from the correlation of δ17O and δ18O measurement errors) relative to the δ17O and δ18O data.

16

Miller & Pack

Kaiser (2008) considered how ‘true’ linear scaling (i.e., of δ′17O and δ′18O values rather than δ17O and δ18O) affects the isotope data from Barkan and Luz (2005). If a scaling factor of ln(1 – 0.0555)) / ln(1 – 0.05511) = 1.00728 is applied to the δ′17O and δ′18O values, then Δ′17O becomes –0.456‰. Again, the resulting change is very small. Performing the same scaling but with δ18OSLAP/VSMOW = –56.18‰ as recommended by Kaiser (2008) gives Δ′17O = –0.462‰. This latter value is in close agreement with subsequent measurements by Kaiser and Abe (2012), which gave Δ′17O = –0.460‰. The corresponding δ17O and δ18O data were 12.25 ± 0.03‰ and 24.22 ± 0.04‰, corrected for a 0.8% scale contraction (which the authors noted may be typical for the type of instrument used). Assigning the Δ′17O value of San Carlos olivine on the VSMOW-SLAP scale as –0.051‰ (based on averaging the data from Pack et al. 2016; Sharp et al. 2016; and Wostbrock et al. 2020), the Δ′17O value of air O2 relative to VSMOW as reported by Pack et al. (2017) becomes –0.422‰ (it is –0.409‰ if based on Pack 2016, alone). Applying the same San Carlos calibration to measurements reported by Young et al. (2014) gives the Δ′17O value of air O2 as –0.425‰. If the Yeung et al. (2018) Δ′17O value of UWG-2 garnet relative to air O2 is revised to –0.061‰ (i.e., 10 ppm lower than that of San Carlos olivine), the derived Δ′17O of air O2 is –0.435‰. Anchoring recent data by Wostbrock et al. (2020) to both San Carlos olivine at Δ′17O = –0.051‰ and UWG-2 garnet at –0.061‰ results in the Δ′17O value of air O2 as –0.433‰. Data from different laboratories are thus converging, but more measurements of air O2, silicates and waters (using similar extraction protocols and the same mass spectrometers) are needed for consensus values to emerge. At present, is evident that anchoring the Δ′17O value of air O2 to measurements of silicates results in more positive values than as obtained by direct measurements of VSMOW relative to air O2. The reason for this is currently unknown.

Oxygen triple-isotope measurements of terrestrial silicates The first investigation of oxygen triple-isotope mass fractionation relationships in terrestrial rocks since that reported by Matsuhisa et al. (1978) was by Robert et al. (1992). Modern cherts were compared with well-preserved examples of age up to 3.5 Ga (Precambrian), together with mantle-derived rocks (mid-ocean ridge basalts, ocean island basalts and continental flood basalts). No statistically meaningful distinction was apparent, on a δ17O versus δ18O plot, between the fractionation line derived from the modern cherts and that derived from the Precambrian samples. The authors interpreted this as showing that oxygen isotopic homogeneity between the Precambrian ocean and the Earth’s mantle (through which the modern ocean has been extensively recycled) was already attained by 3.7 ± 0.1 Ga ago. A corollary was that the Precambrian sedimentary rocks presented no evidence for the delivery of extraterrestrial (cometary) water.4 Within measurement error, the mantle-derived rocks all fitted on the mass-dependent fractionation line defined by the cherts. Meijer and Li (1998) noted that if the chert data reported by Robert et al. (1992) are re-formulated to obtain the corresponding λ values, the result is the same (although at significantly lower precision) as that determined by Meijer and Li (1998) for meteoric waters. A significant technical advance in oxygen triple-isotope measurements of rocks and minerals was the demonstration by Sharp (1990) that fluorination of silicates and oxides by BrF5 vapor could be achieved rapidly and quantitatively using a CO2 laser beam (10.6 μm wavelength) as the heat source, directed onto the sample through a BaF2 window in a purpose-designed fluorination cell. Far smaller quantities of material were needed than for the conventional (Clayton and Mayeda 1963) procedure and the attendant blanks were very much reduced. Furthermore, even the most refractory minerals could be fluorinated, by heating to incandescence and without heating the surrounding chamber. In that initial report, the resulting oxygen gas was converted into CO2 by reaction with a hot graphite rod (catalyzed by Pt wire), 4

Rumble (2018) reported that the isotopic homogeneity has since been extended back to 4.3 Ga before present, i.e. earlier than the beginning of the Archean Eon.

Historical Perspective, Triple-Isotope Systematics and Selected Applications 17 for δ18O analysis only. Rumble and Hoering (1994) showed that a similar procedure but using F2 as the fluorinating agent (derived from heating Asprey’s salt, K2NiF6 ∙KF) was also possible and with the extracted O2 used as the analyte gas for mass spectrometric measurements. Oxygen triple-isotope data from quartz and spinel samples were reported by those authors. Laser-assisted fluorination of silicates using focused spot heating by an excimer laser (pulsed, ultraviolet radiation) was also developed during the 1990s (Wiechert and Hoefs 1995; Rumble et al. 1997; Young et al. 1998). This technique, however, was limited to spot sizes in the range ~80–300 µm, was very sensitive with respect to reactive materials in the samples (e.g., carbonates, resin, clay minerals), and has thus been largely discontinued. The development of laser-based silicate fluorination procedures, together with use of O2 as the analyte for oxygen triple-isotope measurements, coincided with new designs of gas source mass spectrometers which were better able to resolve the 17O16O ion beam from that of the major isotopologue, 16O16O, thus facilitating 17O relative abundance measurements at higher precision. At several laboratories where a laser-based silicate fluorination facility was installed, an investigation was made of the mass-dependent fractionation characteristics of a collection of terrestrial rocks and minerals spanning a wide range of δ18O values (Miller et al. 19995; Miller 2002; Rumble et al. 2007; Pack et al. 2007, 2013; Spicuzza et al. 2007; Kusakabe and Matsuhisa 2008; Ahn et al. 2012; Hofmann et al. 2012; Tanaka and Nakamura 2013; Levin et al. 2014; Kim et al. 2019). In many of these studies, an objective was to define a ‘Terrestrial Fractionation Line’ for use as a Δ′17O reference. Despite the diversity of rock and mineral types in most cases, the slope (λ) obtained from 103ln(1 + δ17O) versus 103ln(1 + δ18O) data regression in all of the abovementioned examples were within the range of 0.5240‒0.5270. Furthermore, in several reports the associated 95% confidence interval was better than 0.001. Such λ variations are within the range of theoretical θ values calculated by Matsuhisa et al. (1978) for various oxygen isotope exchange reactions under equilibrium conditions, thus indicating that kinetic fractionation does not play a significant role in rock-forming processes. Rumble et al. (2007), in an inter-laboratory comparison, showed that a mass fractionation line formed from eclogite facies garnets (high-pressure, medium- to high-temperature metamorphism) was statistically distinguishable from a comparable array formed from hydrothermal quartz samples. The respective (best precision) slope values were 0.5262 ± 0.0008 for the garnets and 0.5240 ± 0.0008 (95% confidence interval) for the quartz. This was the first empirical demonstration that the concept of a single ‘Terrestrial Fractionation Line’ for rocks and minerals is inaccurate, and that distinct mass fractionation arrays exist. It was later noted (Hallis et al. 2010) that the two fractionation arrays discussed by Rumble et al. (2007) were offset from one another. At VSMOW, the origin of the δ scale, the 103ln(1 + δ17O) difference was 0.046‰. The precision (95% confidence interval) of the intercept value of the eclogite garnets line was 0.005; that of the hydrothermal quartz line was 0.019. This demonstrated that mass fractionation arrays from silicate rocks and minerals are offset from VSMOW, by an amount dependent on the specific fractionation array. This finding, though important, was overlooked until Tanaka and Nakamura (2013) similarly identified an offset between VSMOW and a fractionation array formed from a collection of silicate and oxide mineral samples. Measurements of VSMOW, SLAP and GISP (Greenland Ice Sheet Precipitation) were made, using the same oxygen purification system and mass spectrometer for the reference waters as for the mineral and oxide samples. The laboratory ‘working standard’ O2 was calibrated against O2 obtained from the fluorination of VSMOW and the magnitude of the ordinate offset (γ′) of Miller et al. (1999) reported the slope in δ17O versus δ18O format. Taking the mean of duplicate measurements (46 samples), the equivalent λ value is 0.5247 ± 0.0010 (95% confidence interval). The same data set was subsequently extended and discussed by Miller (2002), with all raw data being published in Miller et al. (2015). A statistically identical slope value of 0.5251 ± 0.0014 (SEM multiplied by Student’s t factor for a 95% confidence limit) was reported by Hofmann et al. (2012) from >700 measurements. This was unchanged (0.5251 ± 0.0014, 2σ) by increasing the number of samples to 1071 (Pack et al. 2013).

5

18

Miller & Pack

the silicate array from VSMOW was reported to be –0.070 ± 0.005‰ at the 95% confidence interval, for the specific collection of samples selected (λ value of 0.5270 ± 0.0005). The reported γ′ value was later found to be significantly in error (Pack et al. 2016). Tanaka and Nakamura (2017) subsequently gave a revised figure of –33 ppm. Further confirmation that distinct mass fractionation lines are associated with specific rockand mineral-forming processes was provided by Pack and Herwartz (2014) and, independently, by Levin et al. (2014). Pack and Herwartz (2014) demonstrated that variations in Δ′17O relate to the temperature dependence of α and θ for specific fractionations and/or mixing between reservoirs with different isotopic compositions. They suggested that even a fractionation line defined by data points from coexisting and well-equilibrated minerals in a rock is conceptually incorrect, as θ values (by analogy to α values) are specific to two phases that are in equilibrium. Furthermore, low-temperature (4–50 °C) equilibration between silica and water was shown to be associated with low (and temperature-dependent) values of θ (0.5211 at ~8 °C), whereas high-temperature mineral–mineral equilibria in metamorphic and igneous felsic and mafic rocks are characterized by θ values of the order of 0.528–0.529. In their investigation of oxygen triple-isotope variations in sedimentary rocks, including Archean and Phanerozoic cherts, Levin et al. (2014) noted that, although their complete data set produced a fractionation array of λ value 0.523 ± 0.001, different groups gave distinctive slopes (non-overlapping at the 95% confidence level). In accord with Pack and Herwartz (2014), Levin et al. (2014) noted that the slope variations were the result of processes including mass fractionation associated with lowtemperature precipitation during the growth of authigenic minerals; variation in the triple-isotope composition of the waters from which the sedimentary minerals precipitated; and equilibrium exchange after initial authigenic formation. The observations collectively provided further confirmation that no single fractionation line exists for terrestrial materials. Pack and Herwartz (2014) and Levin et al. (2014) also noted that oxygen triple-isotope studies are particularly appropriate for investigating (mass-dependent) low-temperature processes. This is because small variations in θ cause large variations in Δ′17O when the isotope fractionation factors (18/16α and 17/16α) between water and the mineral of interest are large, as at low temperature. Comparisons of empirical and predicted triple-isotope arrays can therefore, in principle, be used to test hypotheses of chert formation and thus inform long-standing debates on the trends in chert δ18O values, from the Archean through the Phanerozoic.

Oxygen triple-isotope distributions in meteoric waters, snow and ice cores In much of the literature, the relative abundance of the isotopologues H216O, H217O and H218O in meteoric precipitation and in the cryosphere has been quantified using the dimensionless parameter 17O-excess (Angert et al. 2004), which was later defined as ln(1 + δ17O) − 0.528 ln(1 + δ18O) by Barkan and Luz (2007). The 17O-excess parameter is therefore identical to the definition of Δ′17O used throughout this volume. The rationale for the approach introduced by Barkan and Luz (2007) is that, as first shown by Meijer and Li (1998) and subsequently confirmed by higher precision measurements (Barkan and Luz 2007; Landais et al. 2008; Luz and Barkan 2010), oxygen triple-isotope distributions in precipitation seemed to conform closely, on a global scale, to the relationship ln(1 + δ17O) = 0.528 ln(1 + δ18O), with only small deviations from this trend. Angert et al. (2004) predicted ppm-scale positive deviations from the array, resulting from kinetic fractionation during the diffusive transport of water vapor from the (marine) source region into undersaturated air. This causes the ln(1 + δ17O) versus ln(1 + δ18O) array for natural waters to be slightly offset from VSMOW. In the same paper it was also suggested that normalized relative humidity at the vapor source largely controls—and inversely correlates with—the magnitude of 17O-excess, if turbulence in the marine boundary layer is taken into consideration. These theoretical predictions could not be tested, however, until a procedure for making oxygen triple-isotope measurements of waters at the required precision (5 ppm) had been devised.

Historical Perspective, Triple-Isotope Systematics and Selected Applications 19 That was achieved by Barkan and Luz (2005), who developed further a fluorination technique described by Baker et al. (2002). Small (~2 μL) samples of water samples were injected into a helium carrier stream which passed through a heated nickel tube containing CoF3 at 370 °C. The resulting O2 was isolated from the HF also formed, prior to δ17O and δ18O measurements. The same fluorination method was subsequently established at a small number of other laboratories. Barkan and Luz (2007) suggested that the difference between the ln(17/16α) / ln(18/16α) value for water vapor diffusion in air (0.5185 ± 0.0002) and the corresponding ratio (0.529) for vapor–liquid equilibrium is responsible for the presence of 17O-excess in meteoric waters. This explanation is in accord with that originally proposed by Angert et al. (2004), although the relevant fractionation factors were not known accurately in 2004. Many studies, as reported elsewhere in this volume, have since used 17O-excess measurements of precipitation as a temperature-insensitive proxy for the humidity at the vapor source region, above the ocean. Experimental evidence for a non-zero value of 17O-excess in water vapor of marine air, and a negative correlation between 17O-excess and relative humidity, was first presented by Uemura et al. (2010). Uechi and Uemura (2019) demonstrated a similar finding, from a two-year record of 17O-excess in precipitation at the sub-tropical maritime island of Okinawa, Japan (in the East Asian monsoon region), in conjunction with the corresponding normalized relative humidity back-calculated from a simple model of evaporation. Their results were in accord with 17O-excess in the precipitation being determined largely by diffusional fractionation during evaporation from the surrounding ocean. From recently published data sets (Li et al. 2015; Tian et al. 2018, 2019), it is evident that precipitation in the temperate and tropical regions actually conforms to a slightly lower and more variable proportionality constant than the 0.528 value used in the 17O-excess definition. Furthermore, it is the inclusion of samples from the polar regions in the earlier data sets of oxygen triple-isotope ratios in meteoric precipitation that essentially constrained the slope to be 0.528. Removal of polar data from the sample collection used by Meijer and Li (1998), and that reported by Luz and Barkan (2010), lowers the slope value significantly (Miller 2018). Nevertheless, a definition based on a λ value of exactly 0.528 and with the corresponding Δ′17O of the VSMOW and SLAP reference waters defined to be zero (Schoenemann et al. 2013) provides the basis of a VSMOW-SLAP scale for reporting Δ′17O values to, as well as the corresponding δ18O data. This is now widely accepted practice for standardizing the reporting of oxygen triple-isotope data from waters. Uechi and Uemura (2019) showed that lowering the proportionality constant slightly from 0.528 in the 17O-excess definition does not generally affect the robustness of using 17O-excess data for normalized relative humidity reconstruction for tropical and subtropical regions (i.e., between 35°S and 35°N), where precipitation δ18O values are generally >–10‰. This is because the resulting change in 17O-excess is generally 500 species and >7600 reactions) to consider these reactions and showed that these side-reactions would not influence the isotopic composition of the large water reservoir. A limitation is that all reactions are presumed to be mass-dependent by estimating reaction rates of isotopologues using reduced masses for collisions between reactants. As shown in Figure 25, there are several mass independent reactions even in a relatively small reaction network. It is clear that the role of these well-known and other unidentified reactions that may lead to significant mass independent isotope effects in a much more complex reaction network should be carefully evaluated.

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Figure 26. (a) Schematic diagram of the CO ice photodesorption experiment (Bertin et al. 2012): By labeling the top layer with 13CO (with varying thickness), the authors found that the desorbed gaseous CO is always from the surface layer of CO ice (< 2 monolayer equivalents for CO, MLeq). A synchrotron monochromatic beam was used in the experiment. (b) Proposed scheme of the photodesorption mechanism: CO molecules in the subsurface of CO ice were excited to its A1Π state by UV photons, and the energy is subsequently transfer to the neighboring CO molecules. The CO molecule in CO ice surface is ejected after receiving enough energy. Modified from Bertin et al. (2012).

The fate of water ice in different astronomical environments is highly complex and there is a rich literature on observations in molecular clouds, proto stellar environments, cold and warm. There are relevant laboratory experiments that help define the role of all contributing processes. This includes the chemistry rates for the reactions shown in Figure 25 as well as photo and thermal desorption, ice properties of crystalline and amorphous ice, photo destruction and chemical reactions within the ice (van Dishoeck et al. 2013), especially the interaction between H2O and CO to form CH3OH as outlined earlier. Many of these processes have been defined by laboratory measurements and models of satellite interferometric observations of D2O/HDO in ice in protosolar cores (Furuya et al. 2016). The measurements show that the D2O/HDO ratios are not that expected by simple ice formation and require secondary chemical evolution to account for the observations. The processing is schematically shown in Figure 27. The models and application of the isotopic fractionation process show the formation of a water ice layer from stage 1 and the layer of pure water ice with a lower D2O ratio than HDO, to the second stage with a chemical evolution and associated fractionation associated with all of the processes mentioned above and re-partitioning of the deuterium (Furuya et al. 2016). This is further evidence that storage in ice is not stable and the processes of formation/sublimation and chemistry within the ice is substantial and interactive with the surrounding gas during transport. The hydrogen isotope effect also provides observational constraints for testing the validity of current models that have already considered isotope effects. Most of the individual contributing factors have been described in the literature (Johnson and Quickenden 1997; Watanabe et al. 2000; Fraser et al. 2001; Andersson et al. 2006; Al-Halabi and Van Dishoeck 2007; Yabushita et al. 2008; Bertin et al. 2012; Noble et al. 2012; van Dishoeck et al. 2013).

Figure 27. Schematic diagram showing the formation of H2O-dominated and CO and CH3OH-rich layers on grains that significantly influence the partitioning of deuterium. Modified from Furuya et al. (2016).

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With the ability to use satellite data, our understanding of these processes has advanced greatly. Using the far infrared spectrometer on the Herschel Space Observatory it was possible to use the emission lines from the cold water vapor around the young star TW Hydrae to map out the distribution of ice (Hogerheijde et al. 2011). The authors being mapped the water/ice lines and the observations amplify understanding of the processes associated with ice formation. The emission lines are measured and derived from the cold water vapor associated with the ice coated dust grains at the edge of the disk. In Figure 28a the number density of H2 is shown in a cut through the protoplanetary disk, and Figure 28b is the associated thermal structure. Note that the blue contours in Figure 28b is the layer of maximum water vapor concentration. Figure 28c is most important as it shows logarithmic variation of the water molecules/water ice. The equilibrium between the photodissociation of water to the photo desorption of water providing an equilibrium water column (Woitke et al. 2009; Hogerheijde et al. 2011) even though it is well below the freezing point of water. It is not until deeper into the disk that the temperature is lower and the amount of photons become too low for photo desorption to occur. Figure 29 shows the effect of photons on water/ice number density distribution in a cut of a solar nebula and a component of the equilibrium (Bethell and Bergin 2009). The self-shielding in this case is not for CO or isotopes but rather the effect of water opacity on its own gas/solid phase processes. The left panel is the complete consideration which includes its self-shielding of photons.

Figure 28. Distribution of (a) H2, (b) dust temperature, and (c) water vapor and ice in the TW Hydrae protoplanetary disk. Modified from Hogerheijde et al. (2011). It is to be noted that there is a significant amount of water vapor into the nebula before it is effectively made into ice.

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Figure 29. Schematic diagram showing the effect of H2O self-shielding on distribution of H2O in solar nebular. Modified from Bethell and Bergin (2009).

In the upper layer there are sufficient photons to photodissociate water and deeper in there remains water but less dissociation due to the decrease of photons. These observations somehow support the theoretical prediction (e.g., Young 2007; Du and Bergin 2014) that water may be “stable” in some region of the protoplanetary disk. However, it does show although the isotopic composition of the ice reflects the CO dissociation process in any way and that requires most importantly, experimental data of ice photochemical processes for all oxygen isotopes and, across all relevant wavelengths. There are aspects of the grand titration associated with the transport of the δ17O = δ18O ice and reacted with nebular CO to form secondary products to consider. This includes, but not limited to (1) the solar nebula is turbulent; and (2) the ice preserved must be formed and transported intact. Ciesla (2014) has provided an analysis of the fate during formation of ice and its cycling in the environment and subsequent transport. The work shows the difficulty from effects of nebular diffusivity, different temperature regimes, gas densities, chemical compositions and photons. Ciesla (2010) discuss the turbulence of the nebula as a significant driving force in condensation. The requirement is that the ice particles before doing the titration to form the many meteorite classes with the preserved is that ice oxygen isotopic composition must survive intact for 105–106 years and transported through the different regimes totally intact. Indeed, Young (2007) considered both chemistry and vertical/radial mixing and showed that the transport of the δ17O = δ18O water ice produced by CO photodissociation and self-shielding from the disk surface to midplane is on a time scale of 105 years. Furuya et al. (2016) however showed that the chemical evolution of water on grains that may lead to additional isotope effects could be less than 105 years (Fig. 27). These reactions have been considered by Young (2007) as mass dependent reactions. Nevertheless, potential mass independent reactions shown in Figure 25 remains not well considered. Whether such reactions significantly alter water triple oxygen isotopic composition is an open question and needy of relevant experimental work to progress. Dominguez (2010) has suggested that δ17O = δ18O water could have been produced without any CO self-shielding effect if some of these mass independent reactions are considered. The sum of the foregoing discussion is that the fate of water formed from self-shielding might not be an isotopically stable reservoir due mostly to ice photolysis and subsequent complicated chemical reactions accompanied with isotopic partitioning. A much more comprehensive

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reaction network that consider all possible mass independent isotope effects is needed. As will be discussed, the oxygen isotopic composition of the meteoritic oxygen isotopes places stringent limits on the source of oxygen and how much it may vary from secondary alteration.

Summary In the foregoing sections the development of the theory and understanding of the triple oxygen isotope chemistry in chemical recombination reactions and photo dissociation have been discussed. Much of the discussion has centered on the oxygen isotopic record stored in the meteorite record and consequences for understanding the earliest formation processes in the solar system. The basic physical chemical principles apply to all processes on earth as well and molecules that have isotopic compositions thought to derive from photochemical shielding. The experimental and theoretical chemical, photo and quantum mechanical basis since the discovery of the mass independent isotope effect (Thiemens and Heidenreich 1983) have advanced considerably and have aided in providing a mechanistically better understanding of these processes in nature. Though not relevant to this special issue, the understanding of the Archean processes using sulfur isotopes have been included in this developmental process. For meteoritic oxygen isotopes the discussion has led to basically two fundamental physical chemical processes: dissociation and bond formation. The intrinsic effects associated with CO self-shielding and the total steps render it unlikely. First, the isotope effects associated with the bond breakage process do not coincide with observed experiments. Secondly, following photolysis, a dissociation effect is immaterial as the reaction that leads to the formation of the solids containing oxygen will eliminate the isotopic record of the shielding in the short-lived transition state of the combination reaction. The consequence is that the most important step in the formation of the solar system, the gas to particle conversion process creates a new isotopic signature that is based upon this step exclusively. The fractionation produces a δ17O = δ18O composition in the condensates (Fig. 5). This is consistent with both contemporary experimental and physical chemical theory. Another uncertainty arises from the inability to store the isotopic anomaly in a species that is stable such as water ice. The assumption is that this ice species will retain the signal of self-shielding, at thousands of ‰ enrichment with near perfect equal 17O,18O enrichment requires transport from the outer edge of the nebulae to the region where it will melt, evaporate and transfer to the local reservoir where it first produces a CAI condensate. Relevant chemical mechanisms are proposed and incorporated in the models for this process, but are significantly incomplete, especially for a thorough consideration of the associated isotope effects across wavelengths. Experiments are required to support the envisioned scenarios. Large oxygen isotopic anomalies of Fe3O4 in new-PCP from one meteorite may originate from other sources and may not be a sufficient evidence to reconstruct the isotopic composition of water in the protoplanetary disk. This issue will be further discussed in the next section. Most importantly, non-CAI components comprise >99 % of solar system materials: the bulk meteorite compositions (Fig. 30). The basic premise is that there are varying mixes between a presumably single valued ice and an inner nebular component. The isotopic difference of two reservoirs are hundreds of per mil. This model for example requires that one mix a component of heavy isotope water ice that survives the transport and mixes it with a titration precision so tight that one can differentiate between eurcrites and diogenites at −0.24‰ and Angrites at −0.04‰! The same is true for all of the features shown in Figure 30. The titration must capture the difference of a 1 to 2‰ between difference between the ordinary chondrites (H, L, LL) and also the original δ17O = δ18O CAI line, all in a turbulent environment and on a short time scale. Alternatively, if the small difference among these materials is interpreted as a “noise” during mixing, the overall small variability of oxygen isotopic composition in all planetary materials that formed over a large distance in the disk implies an extremely thorough mixing on a large spatial scale. Large temporal and spatial variabilities of water isotopic compositions (hundreds of per mil) were however shown in models that carefully considered vertical and radial mixing.

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Figure 30. Triple oxygen isotopic composition of the solar system. Left panel: The close up of major meteorites in the solar system. Adapted and modified from Northern Arizona Meteorite Laboratory. Right Panel: A scaled-down version of Figure 16. Note that with Bulk earth as a starting composition, the formation from the SiO + OH reaction includes nearly all meteorite types and requires no mixing except for the back mixing of CAI which are 1000 oC) flow system with precursor iron (from Fe(CO)5) and Silane (SiH4) in the presence of a third body such as He and with different oxidants, including O2, H2O and N2O in the presence of an electrical discharge to produce reactive oxygen species, a mass independent isotopic composition was observed in the solids produced, with Δ17O extending to greater than 4‰. This is consistent with prediction of a symmetry-based production mechanism for both Fe and Si. The products collected in this system have unreacted Fe and Si present which makes it impossible to state the magnitude of the effect and theory. Even for the well-studied ozone case state of the art quantum mechanically based models do not allow for determination of a single stage fractionation factor. The Δ17O value of 4‰ is a lower limit. In a more recent work, Chakraborty et al. (2013) used a laser-based ablation system to create controlled amounts of gas phase SiO and determine its isotopic fractionation to SiO2 via O (O2) and OH. SiO is the dominant nebular gas leading to the formation of the first condensates and subsequent ones leading to silicates. It is a key step in the very first formational processes in the solar system. In the experiments, pure SiO was laser ablated at 248 nm providing a reproducible number density of gas phase SiO molecules. Oxidants were provided as OH as this is a likely oxidant is the solar nebula. The results are shown in Figure 5c. In these experiments a mass independent fractionation is observed. As in previous experiments there are contributions from more than one reaction, however in this case all of the rate constants for relevant reactions are known and the isotopic contribution for a given reaction may be determined. Consequently, the mass independent component in the reaction network can be unambiguously extracted. The Figure 5c shows the contribution for the SiO + OH reaction, arguably one of the most likely early reactions in the solar system. It is seen in the figure that the slope one required for the meteorites is observed. All variables are known and clearly defined and thus the assumption for this as a mechanism for production of the meteoritic anomalies is consistent with the most recent physical chemical models for production of the anomaly and experiments. In the experiment, the H2/O2 ratio is significant to acquiring a unity slope as that ratio determines the production of OH radical in the laser system. In the solar nebular, if the SiO + OH reaction dominates the production of SiO2 solid, a pure unity slope can be directly observed. A detailed chemical model quantitatively accounting for various SiO2 production pathways is needed in the future. The take-away point is that the assumption that a reaction of mass dependent nebular species may produce a δ17O = δ18O composition in a solid and is likely a meteoritic mineral precursor has been experimentally observed. It has been known since the classic paper of Grossman (1972) that a first condensate should be corundum at around 1758 degrees, followed by perovskite (CaTiO3) and melilite. In each case the oxygen is in a position where a symmetry factor is relevant. The experiments of Chakraborty et al. (2013) show that the slope 1 effect is a feature associated with gas to particle conversion. It also shows that the effect arises and the original oxygen species in ice covered grains of shielding is lost. In the solar nebula this would suggest that the origin is near the bulk earth and Mars. In Figure 16, triple oxygen isotope composition of the putative selfshielding precursor water from self-shielding (Fe3O4 in new-PCP) is shown as well as different terrestrial species. In the model, water is brought to the inner solar system and reacts with troilite either in the pre-condensation of on a planetary surface. The probability of the water possessing the anomaly has been discussed in the previous section. It is stated that these are the heaviest isotopic enrichments in the solar system though stratospheric ozone extends to the same enrichment factors is not discussed. Sakamoto et al. (2007) suggested that the anomalous feature arises from the net stoichiometric reactions with either troilite or native nickel:

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(R12)

3Fe + 4H2O ↔ Fe3O4 + 4H2

(R13)

In this reaction the water is presumed to lie along an extension to the end member somewhere in the outer solar nebula (as high as 1000‰ in δ18O) (Lee et al. 2008; Lyons et al. 2009) and reacts passing along the anomaly to the Fe3O4, which under the ambient conditions is the thermodynamically stable phase. The water δ18O is presumably between 150‰ and 200‰. In the model of Lyons et al. (2009), the δ18O value of water produced by self-shielding that is responsible for creation of the Fe3O4 is at approximately 200‰ (Fig. 31a). A difficulty is that the required isotopic composition (δ17O = δ18O) in water is not widely observed and the two lines (1: CO photodissociation line segments in which δ17O/δ18O slope may not be one based on experimental results; 2: the δ17O = δ18O line of O3 formation that likely involved in the processes) converge for only a limited time. Even in a self-shielding model, for much of the time the δ17O/δ18O ratio in product water is not exactly 1 (Fig. 31a). Furthermore, the ca. 200‰ for δ18O of Fe3O4 in new-PCP (Acfer 094) is required to produce for a minute period of time in this model. Figure 31b further shows that the variation of ice along a hypothesized slope 1 line varies considerably. The δ17O and δ18O values depending on UV light intensity, radial distance and time varies from 0‰ to ca. 1000‰. To achieve the proper value for new-PCP of Acfer 094 at 200‰ it has been suggested there may be mixing of ice at different values must occur. At present measurements are too scarce to evaluate the variability induced by the mixing effect. Photodesorption is included as a factor but it is not stated how. The isotope effect and its wavelength dependence has not been measured for oxygen. Water photolysis is included but only as a rate of oxygen atom formation not isotopes. For the model to explain the Acfer 094 new-PCP measurements there are restrictions in mixing, radial distance, light intensity, time, isotope effects in water dissociation and mixing of ice proportions that may differ by hundreds to thousands of per mil to acquire the right isotopic composition of ice. Also not included directly in the models are the chemical reactions that actually produce the anomalous ice along with their isotopic fractionations or as discussed side reactions with e.g., CO. A significant point is that the chemical production of water is thought to occur on grain surfaces and proceeds by many reactions:

Figure 31. (a) Model results of time-dependent triple oxygen isotopic compositions of H2O at 30 AU from the protosun at the disk midplane (Lyons et al. 2009). (b) Three isotope plot of H2O ice at 125 AU from the protosun at the disk midplane simulated by Lee et al. (2008) with different G0 value, a parameter scaling the strength of the local FUV radiation field relative to the standard interstellar radiation field. Modified from Lyons et al. (2009) and Lee et al. (2008).

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These reactions have been suggested by Tielens and Hagen (1982), Hasegawa et al. (1992), Cuppen and Herbst (2007), Nunn (2015). This reaction network to actually form ice will not necessarily store the shielding record in ice. Young (2007) did consider mass dependent fractionation processes in a relatively large reaction network in the self-shielding model, but the isotope effect was not treated in an isotopically relevant selective chemical reaction mechanism. For the new-PCP results of Sakamoto et al. (2007) shown in Figure 16, the matrix of the material is shown near the origin in the triple oxygen isotope plot at the terrestrial fractionation line of the host meteorite Acfer 094, an ungrouped primitive carbonaceous chondrite (Fig. 30). To account for the data measured in the Fe3O4, the ice composition has numerous restrictions. Apart from the ice compositions, the aqueous alteration reaction is not well known. An analogy is serpentinization in which water reacts with iron-bearing rocks to form oxide, a mass dependent process. In this case, the oxygen isotopic composition of iron oxides is determined by oxygen in the large water reservoir. However, it is noted that the new-PCP are tiny grains. Elemental mapping suggests that most new-PCP grains are less than 7 μm2, with the largest 160 μm2 (Sakamoto et al. 2007). This is very similar to the observation of iron sulfate on terrestrial aerosols measured by NanoSIMS (Li et al. 2017), a reaction product of SO2 and iron oxides formed in the aqueous aerosol surface of some 10s of nanometers. Therefore, water that directly reacted with carbonaceous chondrite to form new-PCP may not be a large reservoir, but potentially a thin surface layer. Therefore, an alternate chemically plausible to interpret the anomalous oxygen in the new PCP comes from heterogeneous reactions on liquid layers of terrestrial aerosols, as thoroughly discussed by Thiemens (2018). It is known that in such reactions, the isotopic anomaly from gaseous ozone is passed along from the 10 nm liquid water layer to the mineral surface. Most carbonate minerals on the Earth are isotopically normal due to their interaction with the large isotopically normal water reservoir. Shaheen et al. (2010) have observed that atmospheric crustal-derived CaCO3 possess a significant mass independent oxygen isotopic composition ranging from 0 to more than 3‰ in Δ17O (Fig. 7). The aerosols were collected as a function of particle size and observed that the sub-micron particles have the smallest value and the micron sized particle the largest. Laboratory experiments defined that the odd oxygen with isotopic anomaly from ozone or OH is transferred to the surface carbonate in the water-solid thin layer. The same scenario would occur on the troilite surface in the presence of the oxidizing water of isotopic composition of new-PCP in Acfer 094. It is well known that water on a surface such as FeS or FeS2 undergoes dissociation via electron transfer reaction producing OH. This is the actual radical that oxidizes the reduced species and not direct reaction with water. A recent paper has performed a density functional theory/plane wave calculation for pyrite. The initial step of the surface, which will be the case for troilite is that the two Fe(II) sites on the surface react with water and produce Fe(III)–OH− (Dos Santos et al. 2016). This species then in reducing environments will successively produce Fe3O4, and these reactions are all subject to symmetry isotopic fractionation effects. In this case, the anomalous oxygen did not originate from water per se but reactive oxidizing species with mass independent isotopic signatures. Indeed, the reaction sequence referenced above by Sakamoto et al. (2007) is not a mechanistic reaction but rather the net stoichiometric reaction of several steps. For the two Reactions (R12) and (R13), it is important to note that water does not react with FeS directly and the initiating step is from an OH reaction, followed by a series of oxidation steps that ultimately produce Fe3O4 (Dos Santos et al. 2016). If the water in the troilite had a composition similar to the host meteorite the anomaly in Fe3O4 would be produced from the reverse of that from self-shielding produced exotic water. The simplest explanation is that the troilite begins with oxidation from OH derived from the host meteorite near the terrestrial fractionation line. OH is produced on surfaces by water dissociation (Dzade et al. 2016). For the beginning of the oxidation processes leading to the thermodynamically stable Fe3O4, the reaction is very much analogous to the SiO + OH reaction and proceeding by successive oxidations such as the intermediate:

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Thiemens & Lin Fe + OH ↔ FeOH ↔ FeO + 1/2 H2

(R14)

FeO + OH ↔ OFeO + H

(R15)

The Reaction (R14) would produce a mass independent fractionation as observed in the experiment of Chakraborty et al. (2013). As seen in Figure 16, the magnitude of the Fe3O4 fractionation is close to that observed in the stratosphere and troposphere in ozone, which derives from O + O2 with an extent as high as 150‰ for δ18O and >26‰ for Δ17O. It should be noted that for the mass independent fractionation process, there is an inverse temperature effect where a higher temperature enhance the isotope effect (Morton et al. 1990). In that case, for the oxidation of troilite oxidation, if the process were at e.g., 200–400 degrees the magnitude of the effect in oxygen would be more than sufficient to produce a fractionation from above mentioned reactions and seen in Figures 5 and 16. The high temperature effect is also observed in the most recent titanium experiment that was carried out at ~1000K and the mass independent isotopic effect mimics the observation from meteorites (Fig. 10) (Robert et al. 2020). Atmospheric ozone (produced from symmetry-dependent reactions) and nitrate (inheriting the isotopic signature from ozone) are also nearly overlapping with the meteoritic Fe3O4 as seen in the figure. Consequently, this process does not require a photochemical process, preservation of an isotopically labeled ice, and transport trans nebula and quantitative reaction without fractionation. The process is a single step starting with water at the mass fractionation line where the bulk meteorite lies. It had been suggested that the ice to solid occurs at high temperature and no isotope effect occurs. The symmetry reactions have a negative temperature effect, and the isotope effect in forming the solids at high temperatures produce a larger effect rather than no effect. In this case it is simply the oxidation process, as in experiments and the atmosphere and no reservoir mixing is required. The reactions are known and the basic physical chemical symmetry relations known at a level to model, and requires no major assumptions. Therefore the bottom line for the presence of heavy water is that it is not required and the indirect evidence in magnetite is not an anomaly from water. Based upon experiments, atmospheric species isotopic composition and chemical reaction theory is most plausible that this is locally produced and hence not subject to secondary processes. The reaction leading to the stable products would be the relevant host phase.

Oxygen isotopic composition of the Solar System Ultimately the main objective is that a model for well-known oxygen isotopic composition of meteorites shown in Figure 16. A prediction of mixing models, inculding self sheilding is that a reservoir of oxygen exisits at a δ17O = δ18O value of approximately −40‰ or lighter (−50‰ is more likely) (Krot et al. 2019). This CAI reservoir was predicted to be the sun. The Genesis spacecraft mission collected solar wind for two years and returned samples for a high precion measurement of the elemental and isotopic composition of the solar wind for a large portion of solar wind elements. In the return samples, the first after Apollo, the oxygen isotopes of the solar wind were measured by MegaSIMS, an instrument that combines the advantages of secondary ion microscopy with accelerator mass spectrometry (McKeegan et al. 2011). At the low concentrations of the solar wind an electrostatic concentrator was used to concentrate the solar wind for a greater quantity of solar wind material. A series of correction factors for instrumental and Genesis concentrator electrostratic fractionations is applied and the data obtained for the measurements after correction is shown in Figure 16. It may be seen that the actual solar wind does not lie at the point predicted by self shielding models at δ17O = δ18O = −50‰ and is at δ18O = −102‰ and δ17O = −80‰. In McKeegan et al. (2011), it was speculated that there is a fractionation in the formation of the solar wind from the solar

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photosphere and the sun lies along a slope one line, with the 40‰ fractionation factor difference in δ18O attributed to solar wind formation. Heber et al. (2012) modeled and deterimened the solar wind isotopic fractionation factor for helium (63‰/amu), neon (4.2‰/amu) and argon (2.6‰/amu). For a charge state of + 6 for oxygen (which may also possesses a component of + 7), a fractionation between sun and solar wind must be known and compared to what is expected to test if the inferred value for the sun is correct (Fig. 16). In a more recent study (Laming et al. 2017), oxygen isotopes were modeled using a electromagneic model and applying a pondermotive inetractive force in the solar chromosphere, with maintainence of the first adiabtic invariant in the lower corona. Laming et al. (2017) developed a solar wind formation mechanism specifically to understand oxygen concentrations and isotopes. In their calculations they have determined the isotopic fractionation factor between the bulk solar wind and the photosphere for low mass dependent fractionation and high mass depeendent fractionation prcesses that typify solar wind energy regimes. It is found for the low mass regime the 16O/18O value ranges between 0.8–0.9 %/amu and for high MDF, 1.57–1.62 %/amu compared to the measured Genesis value at 2.2 %/amu. In their models, the calculated range of 25Mg/26Mg and 15N/14N values agree with the Genesis measurements. The oxygen isotopes do not however, thus there is some component missing in the model or different values for input parameters are needed. In Laming et al. (2017), the elemental abundances have also been calculated by the ponderomotive model and compared to Genesis measurements (Fig. 32). It is observed that the model results for the element concentrations with respect to solar are close and do the best at low values of the First Ionization Potential, or FIP. A most important point is that the modeled elemental abundance of oxygen does not agree with the model by a significant factor, as highlighted in Figure 32. It is suggested that the photospheric values assumed are too small, and the assumed values do not agree with those of von Steiger and Zurbuchen (2016). Part of the issue is concerned with fractionation factors in slow and fast wind regimes and their relation to the first ionization potential. The polar coronal holes are of particular importance. The bulk oxygen isotopic composition of the sun and solar system remains unknown. Laming et al. (2017) conclude that more data and analysis is needed to solve the existing inability to model both the oxygen isotopic and elemental compositions of Genesis. “Once this has been achieved then a full assessment of whether the solar photospheric values may be used as a proxy for the pre-solar nebula.”

Figure 32. Left panel: The close up of triple oxygen isotopic composition of selected CAIs. The fractionation processes of CAI after formation are schematically shown by green dotted line. FUN CAIs distribute in the region with green dotted lines. CCAM and PCM stands for “carbonaceous chondrite anhydrous mineral line” and “primitive chondrule mineral line”, respectively. Modified from Krot et al. (2019). HAL data from Lee et al. (1980). Right Panel: A scaled-down version of Figure 16.

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Thiemens & Lin A NEW MODEL FOR TRIPLE OXYGEN ISOTOPES, METEORITES, AND THE ORIGIN OF THE SOLAR SYSTEM

As reviewed, the history of models on the origin of the meteoritic isotopic anomalies has several categories, ranging from the original nucleosynthetic, to self-shielding, to the origin arising during the bond formation that occurs during the actual formation of the first solids in the proto solar environment due to experimentally and theoretically determined symmetry dependent reactions. A nucleosynthetic case for the anomalies has been ruled out. Self-shielding, while still utilized has been discussed in great detail in the forgoing section is unlikely. This then leaves a mass dependent isotopic fractionation process associated with formation of solids as a source of the meteoritic oxygen isotopic class differences. Here we analyze existing measurements and propose a new Chemical Mechanism Model for production of meteorite oxygen isotopic anomalies and the origin of the solar system.

Revisiting triple oxygen isotopes of CAI Many of the models for solar system formation revolve around CAI and their formation. These objects as well as chondrules are among the most primitive and oldest objects in the solar system and the interest is warranted. This leads to the outstanding issues with the source of meteoritic oxygen isotopic compositions arising from self-shielding/ice transport and addition to an inferred solar system oxygen at δ17O = δ18O = −60‰. The short comings suggest that an alternative route to synthesis of the observations shown in Figure 16 is warranted. It is suggested that the early nebula was at the point in three isotope space resembling the Calcium Aluminum Inclusions (CAI) that is subsequently titrated with ice created in the nebular fringes. As discussed by Laming et al. (2017), the inability to model the oxygen elemental and isotopic data of Genesis solar wind sufficiently well to conclude with certainty that the solar wind is fractionated and to an exact extent that it intersects with the CAI line. The consequence is that the link between solar nebular processes and the sun is not solidly established. Though CAI studies have been a Rosetta stone for development of nebular formation, chemistry, and alteration understanding, they are 15% of a rare meteorite class (CV) that constitute about 0.84% of meteorite falls (Sears 1998) and in the interest of material balance for nebular oxygen, the other classes of meteorites need to be included and how many reservoirs and processes are needed. If one assumes the 18O/17O ratio of the solar system was on the CAI line, it is estimated to be 5.2 ± 0.2, which is quite different from the galactic value of 4.1 (Young et al. 2011). A better evaluation of the triple oxygen isotope composition of our solar system for a deepening understanding of their origins is needed. In the case of oxygen, it is reasonably well established that based on the original paper by Lee et al. (1980) there is a select group of FUN (Fractionated Unknown Nuclear) CAI that possesses isotopic anomalies in oxygen that differ from other CAI and requires a very different interpretation. The range of FUN triple oxygen isotope composition is schematically shown in Figures 16 and 33. Lee et al. (1980) interpret the data as starting with the original CAI at δ17O = δ18O = −40‰ and resembling most CAI. The CAI then undergo an extensive heating that results in evaporative material loss and a 25‰ amu−1 mass-dependent fractionation. A variable amount of this fractionation moves the individual core along a mass fractionation line, with Allende inclusion HAL undergoing a greater fractionation (red stars in Fig. 33). Subsequent to that heating event the CAI core undergoes an exchange with a gas reservoir that converge upon a reservoir that also intersects with the normal CAI line at a point that is very near δ17O = δ18O = 0‰ suggesting that this is a major nebular gas phase reservoir. This finding is later supported by further triple oxygen isotope and detailed mineralogy and petrology studies on FUN CAI (Krot et al. 2010, 2014). These processes are schematically shown in Figure 33. Krot et al. (2019) in a recent review have studied other inclusions (“normal CAI”) and carefully documented the complex mineralogy to define the different processes associated with

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its formation some 3–5 × 106 years before the complete melting of some CAI and meteorite formation. Grossite (CaAl4O7) bearing CAI with the canonical initial 26Al/27Al ratio (5 × 10−5) is a record of the antiquity of these CAI. The Δ17O composition of these CAI is −24 ± 2‰ (Krot et al. 2019). In the ensuing 3–5 million years the CAI will exchange and the most labile oxygen species will exchange the most. Δ17O values of many CAI with Wark–Lovering rims vary between −40 and −5‰ (Krot et al. 2019). As exchange proceeds and planetary body become molten and have incomplete aqueous exchange, their Δ17O values range between 0 and −2‰ as observed in CO and CV meteorites (Krot et al. 2019). The time scale is a few million years post CAI formation. These values (Fig. 33) cover the full range of CAI isotopic composition shown in Figure 16. Figure 33 clearly illustrates the end member, the minerals of exchange, and the final product of exchange being the aqueous exchange near δ17O = δ18O = 0‰. The data are also clear that there is a reservoir at δ17O = δ18O = ca. −50‰ and it is well produced but only resides in a very minor phase with respect to the volume of the other meteorites.

Figure 33. Left panel: The close up of triple oxygen isotopic composition of selected CAIs. The fractionation processes of CAI after formation are schematically shown by green dotted line. FUN CAIs distribute in the region with green dotted lines. CCAM and PCM stands for “carbonaceous chondrite anhydrous mineral line” and “primitive chondrule mineral line”, respectively. Modified from Krot et al. (2019). HAL data from Lee et al. (1980). Right Panel: A scaled-down version of Figure 16.

Material balance of bulk meteorites oxygen isotopes It has been suggested in the self-shielding model that the ice produced from CO photolysis may vary depending on time, UV field and vary from 1000‰ downward (Lee et al. 2008) (Fig. 31). The many problems associated with this have been discussed. The heavy isotope effect observed by Sakamoto et al. (2007) does not require a heavy ice production and may be a consequence of the oxidation process itself with the starting species at Δ17O = 0‰. As discussed, it is well known that the Δ17O in atmospheric nitrate and ozone is near that of the “heavy water” point (new-PCP) and would overlap at slightly higher temperatures. Ozima et al. (2007) noticed that CAI (and some other meteorites with large non-zero Δ17O values) is a minor component and the mean oxygen isotope composition of the solar system should be characterized by Δ17O = 0‰. As shown in Figure 30, the δ18O composition of

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99% of meteorites lie near the point δ18O = 5‰ and δ17O = 2.5‰. This is not considering the CAI. The entire range of bulk meteorites is only ca. 4‰ near terrestrial fractionation line (Δ17O = 0‰). If one uses NASAs meteorite collection (>20,000 Falls) as a very rough guide as to the amount of material, approximately 92% are H, L, LL and carbonaceous 4%. Most carbonaceous chondrites (expect for CI) possess negative Δ17O values and the lowest was found in CV (ca. −6‰). Besides carbonaceous chondrites the other meteorites: ureilites, acapulcoites, lodranites, angrites, aubrites, pallasites, howardites, eucrites and diogenites all have slightly negative Δ17O values and altogether are only 2–3% of falls. Aubrites and eucrites have terrestrial values (Δ17O = 0‰). In addition, Comet 81/P Wild 2 bulk composition (McKeegan et al. 2006) is located near δ18O = 5‰ and δ17O = 2.5‰ and only a small fractionation (polymineralic refractory grain) in the Stardust mission returned sample possess isotopic signature similar to CAI (δ17O = δ18O = −40‰) (Fig. 16). δ18O values of 67P/Churyumov-Gerasimenko dust and CO2 measured by the Rosetta Mission are also near δ18O = 5‰ (3 ± 50‰ and 10 ± 15‰, respectively) (Hassig et al. 2017; Paquette et al. 2018), although there are large uncertainties and δ17O values are unable to measure. We acknowledge that an isotopic balance cannot be quantitatively done since 1) these numbers reflect the survivability of falls and the most fragile ones are least abundant 2) this is a number of falls but one cannot say that this is equivalent to a mass balance 3) in a true mass balance Earth, Mars, Venus (and Vesta) should be included with earth at Δ17O = 0‰, Mars Δ17O = 0.3‰, Vesta Δ17O = −0.2‰ and Venus unknown. The current safest statement with respect to the bulk meteorite, comet and planet compositions is that there are both positive and negative values and the observed range is modest. The basic considerations for a chemical local production of the meteorite oxygen isotopes we note the following: 1. The presence of what has been observed is considered evidence of a heavy water may be produced locally and isotopically similar to components in the terrestrial atmosphere where the reactions are all known and isotopically characterized. The observed meteoritic composition may be explained by chemical reactions of isotopic compositions of water that is the same as the bulk meteorite, which is near terrestrial. 2. Based upon CAI and anomalous FUN (e.g., HAL) CAI oxygen isotopic measurements and the back exchange captured in minerals of CAI converge on the major solar system reservoir at a value near Δ17O = 0‰, this point is the most likely isotopic value to consider as a starting value to explain bulk isotopic values. Given that bulk Earth, moon, Mars and HED meteorites, comets, CAI and “heavy water” lines lie near 5‰, this is reasonable value to assume as a nebular reservoir. Given the data spread in several of the datum, this might vary by 1–2‰. 3. The solar component at δ17O = δ18O = −50‰ has yet to have a model that is capable of quantitatively justifying the large correction applied to Genesis measurement and Genesis inferred. Present models may not account for either elemental or isotopic abundances (Laming et al. 2017). The link between solar nebular processes including CAI may not be directly coupled. If the bulk isotopic values observed in meteorites can be explained by a chemical model, the requirement for multiple isotopic reservoirs that mix vanishes. It is well known from several independent observations that in the symmetry driven reactions, it has been known since the very first experiments that in the reaction both positive and negative reservoirs are created with complete mass balance observed. The positive ozone reservoir is exactly matched by the negative O2 reservoir (Fig. 5). There is no mixing required as it is simply one chemical reaction with extensive theoretical and experimental measurements by numerous laboratories. Indeed, the mass independent effect can be positive or negative according to the type of chemical reaction

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sampling the intermedia complex (Robert et al. 2020). This has been observed for titanium but not for oxygen yet. In a boarder view, a complete mass balance is not a necessary requirement. The positive and negative Δ17O reservoir observed in the solar system could have been due to different chemical reactions, which are required future identification though. If the solar nebula is defined as at a value of Δ17O = 0‰ and approximately somewhere with δ O between 3‰ and 6‰ and we consider a symmetry dependent reaction that produces positive and negative reservoirs, the possible consequences may be see in Figures 5 and 30. The results show that if we use the measured experiments of Chakraborty et al. (2013) for the reaction SiO + OH, one of the first reactions in gas to particle conversion process, for an equal partitioning between a nebular value centered around δ18O = 5 and δ17O = 2.5‰ (presumed starting nebula), all meteorite classes, Earth, Mars, Vesta, comets, CAI positive terminus, “water ice”, chondrules fall within this range. The consequence is that there is a requirement of only one reservoir. The entire solid bodies of the inner solar system are created by one process. Transport, storage and mixing are not required. The chemical reaction is required as SiO does not react with CO or H2O but rather OH is considered the dominant reaction. The fractionation factor has been experimentally measured and the results are interpretable in terms of known theory and a wide range of experimental tests by multiple groups of the symmetry dependent reaction. The use of equal partitioning may be varied and still incorporate all members. In the schematic arrow shown in Figure 30, we have employed a 10‰ fractionation factor, a lower limit. The value may be higher. 18

Another important point to be made is the Earth’s atmosphere. As shown in the Figure 7 there is a δ17O = δ18O fractionation factor observed in the Earth’s atmosphere as those in the solar system (Fig. 16). It should be noted that atmospheric ozone isotope effect is double the magnitude of CAI (Fig. 16). It has more variation from the pure effect because of its exchange reactions in oxidations and secondary photolysis in the stratosphere. Its origin is molecular oxygen, not bulk earth. With the exception of CAI, most meteorites are not plotted in Figure 16 but in an enlarged version in Figure 30 as their range is too small to be seen on Figure 16. An important point to be made with respect to Figures 16 and 30 is the mass balance. In Figure 16, there is a >100‰ enrichment factor in ozone (up to 150‰). As shown in Figure 7 this very large positive effect has a slightly negative counterpart in a large reservoir (O2). The >100‰ enrichment effect arises in the stratosphere in ozone formation, which has a concentration of on average about 3 ppm. Tropospheric ozone has the same large enrichment, and a concentration on average of 40 ppb. The troposphere is ca. 80% and stratosphere ca. 10% of the Earth’s atmosphere by mass. The balance is between the ozone and in part, molecular oxygen. As discussed by Miller and Pack (2021, this volume), there is a mass independent Δ17O of −0.467‰ in O2 that is the counter balance. It is not exact because the ozone enrichment is passed to CO2 in the stratosphere as need first in return balloon and rocket samples by the Thiemens group (Thiemens et al. 1991, 1995) and is maintained in the troposphere (Thiemens et al. 2014) (Fig. 7). This has been modeled by Hoag et al. (2005) and is used to determine global primary productivity. The CO2 loses its signal in steady state by exchange with water in the stomata of green plants as first detected by Luz et al (1999). In a recent model, Young et al (2014) quantified the mass independent component of the negative Δ17O value to be ca. 1/3 while the remaining signature is a result of mass-dependent fractionation due to respiration. Mass-dependent fractionation processes can lead to small Δ17O values but cannot account for all non-zero Δ17O components. Overall, the Earth’s atmosphere is in a steady state with simultaneous positive and negative Δ17O reservoirs. This is a natural proof that in a single interactive environment positive and negative Δ17O reservoirs may be produced and does not require mixing of preserved reservoirs from different places and production times. In Box 2, we summary several critical points of our Chemical Mechanism Model for production of meteorite oxygen isotopic anomalies.

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Thiemens & Lin BOX 2 SUMMARY OF CHEMICAL MECHANISM MODEL FOR PRODUCTION OF METEORITE OXYGEN ISOTOPIC ANOMALIES

1. There is only one reservoir required and no mixing. The basis for the production is the slope one effect discovered for ozone and experimentally observed in SiO + OH reaction, a likely first gas-to-solid formation reaction in the nebula. The process requires no photons. The reaction is the step that determines isotopic composition of the solids independent of the source of the oxygen, consistent with gas phase isotopic models and experiments 2. The fractionation factor associated with the fractionation factor assumes the nebula has isotopic composition on the earths bulk solid fractionation line at about δ18O = 5‰ and δ17O = 2.5‰. The value is at the Nexus of bulk earth, enstatite chondrites, aubrites, CAI and FUN CAI back reaction intersections 3. If the nebula starts a value at δ18O = 5‰ and δ17O = 2.5‰ and assumes the fractionation factor measured for the SiO + OH of 10‰ (ΔΔ17O, θ = ln α17/ln α18 = 1) from that point, one produces two reservoirs with the values dependent upon reservoir sizes. If both are e.g., equal in equal amounts all reservoirs are overlapped: Earth, Mars, Vesta, all meteorite classes, comets, CAI, chondrules. Other proportions will do the same. 4. At higher temperature, the isotope effect increases as it is known to be an inverse isotope effect. The effect is still δ18O = δ17O. The high temperature condition is relevant to the environment where the first solids were formed in the solar system. 5. The earth’s atmosphere shows the same simultaneous partitioning into positive and negative Δ17O reservoirs without mixing and δ18O extends past 100‰; twice that of CAI 6. The nebular reservoir is at a point in part set by the oxygen isotopes in individual minerals in CAI and FUN inclusions. The starting composition of the CAI has no influence on the bulk nebula and the isotope composition. At high temperatures however, the first condensates to form CAI lie along the slope one line and might be a minor but interesting process that chemically produces CAI as proposed by Nobel Laureate Marcus (2004). In this model CAI are produced from the nebula as proposed and not by the sun’s inferred composition. 7. The solar wind measured value at δ18O = −102.3‰ and δ17O = −80.5‰ or the inferred value at δ18O = δ17O = −60‰ does not play a role. As concluded by Laming et al. (2017) the link between the solar wind and solar value and the protosolar nebula has not been proven. The present model depends on the value of the nebula at the time of back reaction of CAI at δ18O = 5‰, δ17O = 2.5‰. Overall, the present model has avoided the need to create reservoirs and transport ice on grains and mix at ultra-high δ18O precision by undefined processes. The major components of the model have been experimentally measured and are consistent with the underlying quantum chemical models by different groups. The measurements and models of the present and past atmosphere on Earth and Mars is a testing ground for how reactions in nature occur, transfer chemically and are preserved. The mass independent isotopic anomaly of water in sulfate on Mars has been preserved for billions of years’ time scale for example (Thiemens 2006). For the future, experiments that lead to a deeper understanding of the gas-to-particle conversion process would be of high value. Isotopic measurements of the oxidation process for different elements and oxidants will be of importance, especially for the magnitude of effects as observed in present-day’s terrestrial atmosphere. Theory cannot predict the models

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due to lack of precise details of the relevant potential energy surfaces. This will lead to better understanding of the first condensates and CAI. The catalytic oxidation on surfaces is fundamental to grain and larger and is not understood at the quantum level. There is a need for studies of the temperature effect of the mass independent fractionation processes at high temperature, especially near condensation temperatures. It is expected to be larger and the reverse of classical mass dependent isotope effects. The CAI do not play a role in influencing the isotopic composition of the meteorites, but they play a highly valuable role in defining the nebular composition and the timing of the major events. Future studies that examine the role of chemical processes in this process might be illuminative. The new model simplifies the larger details in the meteoritic oxygen isotopic formational process. The case for photochemical shielding has been discussed and the details of the obstacles for the models listed, but not all included. The present model based on experiments, theory and atmospheric and meteoritic observations reduces many long-standing barriers and at the same time presents a range of new experiments that would deepen understanding and are needed in the future.

ACKNOWLEDGEMENTS We thank François Robert and Edward Young for their critical reviews and Andreas Pack and Ilya Bindeman for their editorial handling and suggestions. All greatly improved this paper. M.H.T. is supported by the Chancellors Associates fund. M.L. is supported by Key Research Program of Frontier Sciences from Chinese Academy of Sciences (ZDBS-LY-DQC035).

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Reviews in Mineralogy & Geochemistry Vol. 86 pp. 97–137, 2021 Copyright © Mineralogical Society of America

Climbing to the Top of Mount Fuji: Uniting Theory and Observations of Oxygen Triple Isotope Systematics Laurence Y. Yeung Department of Earth, Environmental and Planetary Sciences Rice University Houston, TX 77005, U.S.A. [email protected]

Justin A. Hayles Jacobs, Astromaterials Research and Exploration Science, Johnson Space Center National Aeronautics and Space Administration Houston, TX 77058, U.S.A. [email protected]

INTRODUCTION The near-simultaneous discovery of both minor isotopes of oxygen in 1929 was a watershed moment for modern science, to say nothing of its impacts on isotope geochemistry. At the time, oxygen was the international standard for atomic weight, as it had been for over twenty-five years. However, chemists and physicists had grown fond of different definitions: physicists used the weight of the 16O atom, while chemists used half the weight of atmospheric oxygen (O2) to define the precise weight of 16 atomic mass units. While they usually avoided direct conflicts, these contrasting definitions found an unexpected impasse in the near-infrared absorption spectrum of atmospheric oxygen: it contained a series of faint lines that could not be explained by any known atmospheric constituents (Dieke and Babcock 1927; Mulliken 1928). The key breakthrough came when Herrick Johnston and William Giauque, who were separately studying the thermodynamics of oxygen, realized that small amounts of heavier oxygen isotopes in O2, 17O and 18O, could generate those weak absorptions. With no prior precedent for these isotopes aside from Ernest Rutherford’s α-particle-driven transmutation of 14 N into 17O (Rutherford 1919), Johnston and Giauque relied on the theoretical mass dependence of vibrational frequencies and spectroscopic selection rules from quantum mechanics—then still a young theory—to predict where in the infrared 16O18O and 16O17O would absorb. Their predictions were quantitative and definitive (Giauque and Johnston 1929a,b). Together with subsequent observations by Malcolm Dole, George Lane and others (Dole 1935; Dole and Jenks 1944; Dole et al. 1947; Epstein and Mayeda 1953; Lane and Dole 1956)—the discovery of 17O and 18O led the International Union of Pure and Applied Chemistry to redefine atomic weight relative to carbon-12 in 1962, which is still valid today. Oxygen triple-isotope geochemistry owes its existence to this discovery, which emerged from a clever application of theory to a puzzling observation. Isotope geochemists today still rely on theory to fill this same role: to predict and explain observations of nature, using that nexus to make fundamental advances of broader scientific relevance. However, the targets have evolved; our ability to measure variations in oxygen-isotope abundances in natural materials has been transformed by high-precision isotope ratio mass spectrometry and innovative analytical techniques (Nier 1947; McCrea 1950; Sharp 1990; Baker et al. 2002). These methods have improved in the past few decades to yield parts-per-million (ppm) levels of precision in oxygen-isotope ratios for a wide 1529-6466/21/0086-0003$05.00 (print) 1943-2666/21/0086-0003$05.00 (online)

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variety of natural materials (Luz et al. 1999; Luz and Barkan 2000; Barkan and Luz 2005; Pack et al. 2013; Pack and Herwartz 2014). Concurrently, the explosive growth of computing power, particularly the recent advances in parallel computing, have made first-principles electronic structure calculations more accessible than ever to the geochemist: large chemical systems once considered intractable are being studied routinely in silico. How well can theory and observations work together toward new insights in these much more exacting times? Oxygen triple-isotope geochemistry focuses in two general areas, both of which have been informed and advanced by theory. The mass-independent isotopic fractionation of oxygen preserved in early solar-system condensates (Clayton et al. 1973) and atmospheric ozone (Mauersberger 1981; Thiemens and Heidenreich 1983) stimulated a new wave of theoretical work in the 1990s and 2000s to understand the physical-chemical origins of those anomalies, leading to the discovery of other mass-independent isotope fractionation mechanisms for oxygen and other elements (Röckmann et al. 1998; Hathorn and Marcus 1999; 2000; Farquhar et al. 2001; Gao and Marcus 2001; Clayton 2002; Babikov et al. 2003; Marcus 2004; Schinke et al. 2006; Bergquist and Blum 2007; Sun and Bao 2011). These signals have led to fundamental discoveries about the formation and evolution of the solar system, Earth history, and biogeochemical cycling (Thiemens 2006). Other chapters in this volume will cover those developments, so we will focus here on the second major area of oxygen triple-isotope geochemistry, that of natural variations in mass-dependent fractionation. The role of theory in this area is clear: it provides independent, physics-based reference points for oxygen triple-isotope partitioning. Such reference points are invaluable because of the myriad ways in which oxygen isotopes can be fractionated, transported, and mixed to yield the parts-per-million (ppm) level variability that is routinely observed and interpreted (Juranek and Quay 2013; Herwartz et al. 2014; Luz et al. 2014; Young et al. 2016; Bindeman et al. 2018; Sharp et al. 2018); theory can help distinguish the signal from the noise. Theoretical reference points can also lead to analytical innovations and the characterization of unusual processes (Richet et al. 1977; Thiemens 2006; Eiler 2007; Bao et al. 2015; Hayles et al. 2017).Even when imperfect, a theoretical prediction constitutes a vital third approach to high-precision isotope geochemistry that has a different set of biases from experiments and observations. Are current theoretical methods sufficiently accurate to benchmark oxygen triple-isotope geochemistry? Analogous investigations in the clumped-isotope community (Wang et al. 2004; Schauble et al. 2006; Guo et al. 2009; Piasecki et al. 2016, 2018) suggest that they are not far off: robust features of isotope partitioning have been observed across theory, experiment, and observations to within several tens of ppm. Some disagreements in isotopic fractionation factors have persisted, however (e.g., for acid digestion fractionation: Guo et al. 2009; Murray et al. 2016; Müller et al. 2017; Petersen et al. 2019; Swart et al. 2019; Zhang et al. 2020), resulting in barriers to reproducibility and (in our view) limits the certainty with which isotopic records can be interpreted. Breaking through these barriers to find agreement at the single-digit ppm level would be both a triumph for theoretical approaches and transformative for oxygen triple-isotope geochemistry. This article aims to evaluate how close the state of the art is to this target, and hopefully to guide the way forward. In this article, we will first cover basic concepts and notation relevant to oxygen tripleisotope geochemistry. Second, we will examine what theory predicts for oxygen triple-isotope variability in chemical processes. Third, we will examine the systematic biases that may be present in theoretical approaches, with special attention paid to first-principles electronic structure calculations. Fourth, we will consider the current limits of analytical accuracy and the complications introduced by physical effects in real systems. Finally, we will revisit the triple-isotope mass dependence of carbonate acid digestion as a case study of how theory and experiment can work together to improve both each other and ultimately also our understanding of a process that is vital for the emerging area of carbonate-based paleohydrology.

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BASIC CONCEPTS The equations Molecules as physical entities can be viewed as collections of balls and springs, with the balls being nuclei of atoms and the springs being the bonds that tie them together. The strength of chemical bonds is tied primarily to electrons, which are each about 1/30,000th the mass of an oxygen atom. Consequently, changing the mass of an oxygen atom has little effect on basic molecular structure or chemistry in most cases. This simplification is known as the BornOppenheimer approximation (Born and Oppenheimer 1927). Exchanging an oxygen atom for a heavier isotope, however, will change the frequencies at which a molecule naturally vibrates: heavier masses connected to the same springs will yield lower frequencies of vibration. It is these subtle variations in vibrational frequencies in isotopically substituted molecules, which have subtle effects on molecular enthalpy and entropy, that drive a majority of chemical isotope effects. Bigeleisen, Goeppert-Mayer, and Urey are credited with deriving expressions describing the thermodynamics of isotopically substituted gas-phase molecules (Bigeleisen and GoeppertMayer 1947; Urey 1947). They used the reduced partition function ratio (RPFR) between two isotopic variants of molecules as a building block to describe isotope-exchange reactions. For the exchange of a single isotope, RPFR 

3 N 6

 *i   e Ui / 2   1  e Ui  s  *K   Ui / 2   Ui*   i  MMI  e  ZPE  1  e  EXC s *

 i 1

(1)

Here, νi is the ith harmonic vibrational frequency of the molecule (of 3N – 6 total for nonlinear molecules, 3N − 5 for linear molecules), Ui = hνi / kBT (or hcνi / kBT if νi is expressed in wavenumbers, where c is the speed of light), N is the number of atoms in the molecule, h is Planck’s constant, kB is Boltzmann’s constant, and T is the temperature in Kelvin. This equation represents the thermodynamic preference to form an isotopically substituted molecule (denoted above by an asterisk) compared to the isotopically “normal” molecule in an idealized equilibrium between the species and free atoms (e.g., 16O16O + 18O ⇌ 16O18O + 16O). The RPFR can thus be thought of as the equilibrium constant K for the reaction scaled by the ratio of isotopologue symmetry numbers s/s*, e.g., s = 1 for 16O16O and s* = 2 for 16O18O. The equilibrium 18O/16O isotopic fractionation between species A and species B in the reaction A + B* ⇌ A* + B, in which a single isotope is exchanged, is written as

   

   

18   O / 16 O A   18 O / 16 O  18 RPFR  18 atomic   A (2)   AB  18  18 RPFR B  O / 16 O B   18 O / 16 O   atomic   For exchange of n isotopes of the same atom in a molecule, the reduced partition function ratio in Equation (1) is raised to the 1/n power, i.e., (RPFR)1/n.

Many excellent discussions of Equation (1) exist (Schauble 2004; Liu et al. 2010), so we will highlight only a few elements most germane to this discussion. First, the expression has inherent assumptions: it is derived assuming that bonds are perfect springs holding atoms together (the so-called harmonic oscillator approximation) and that bond lengths are constant (the so-called rigid-rotor approximation). Clearly, these two approximations cannot simultaneously be true, but they simplify the math considerably, and are good approximations of many real systems at Earth-surface temperatures. Moreover, the approximations allow one to separate the energies

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associated with molecular vibrations (ZPE and EXC subscripts) from those involving translations and rotations (MMI subscript). The ZPE (zero-point energy) term corresponds to the ratio of “occupancies” of the lowest-energy vibrational states ν0 and ν0*, i.e., how often an isotopically substituted molecule would be in that state compared to its unsubstituted counterpart at a given temperature. The EXC term corresponds to the occupancies of the higher vibrational states. The MMI term is deceptively simple because it relates the ratio of masses and moments of inertia of the molecule (from classical mechanics) to a ratio of vibrational frequencies (from quantum mechanics) through the Teller–Redlich isotopic product rule (Redlich 1935). Indeed, without the harmonic-oscillator and rigid-rotor approximations, Equation (1) would be much more complicated. There are many notable instances in which these approximations are insufficient for describing isotope fractionation; we will return to these later. In liquids, solutions, and solids—which are in many cases the phases most relevant to oxygen triple isotopes—the potential range of atom–atom interactions broadens considerably compared to an isolated gas-phase molecule. Oxygen atoms in aqueous oxides (e.g., HCO3, SO42−, and H4SiO4) interact meaningfully with the solvent, so one expects aqueous isotopic fractionation of oxygen to depend on the strength and number of these interactions; in addition to influences on vibrations of the solute, there are simply more relevant vibrational modes i to consider in Equation (1), and the “sphere of influence” of an isotopic substitution is larger. These interactions cause narrow, gas-phase vibrational absorption lines to shift and broaden (Fig. 1). Weak long-range interactions, including those arising from long-range order in solids, can comprise an important component of the RPFRs in condensed-phase systems. Schauble (2004) introduced the following equation, based on the work of Kieffer (1982), to represent the reduced partition function ratio in terms of a continuum of vibrations in solids:   max  e U * / 2  * *   0 ln   g  d  3/ 2 U *   1  m 1 e  RPFR   *  exp   U / 2  max n   e m   ln  g    d    U  0    1 e   

 

(3)

Here, m and m* are the masses of the normal and rare (commonly heavy) isotope being exchanged, respectively, n is the number of atoms exchanged in a unit cell, and g is the vibrational density of states, which is proportional to the number of vibrational modes in the frequency window between ν and ν + dν. The upper frequency limit of the integrals is the highest vibrational frequency νmax in the crystal. Note that crystals have exceedingly large molecular weights, rendering insignificant the effect of occasional isotopic substitutions on translations and rotations. The related terms in the Teller–Redlich isotopic product rule thus cancel, leaving only the leading (m/m*)3/2 term. Because many of the terms in Equation (3) are either uncertain or poorly constrained, one often must approximate it. Elcombe and Pryor (1970) showed that the continuous crystal spectrum of the ionic solid CaF2 can be well-approximated by using a set of discrete frequencies as constraints on lattice vibrations simulated to satisfy known physical properties (e.g., the dielectric and elastic constants). This approach has not yet been utilized for predictions of triple oxygen-isotope fractionation, although it has been used to examine bulk 18O/16O fractionation factors in minerals (Bottinga 1968; Kieffer 1982; Chacko et al. 1991; Schauble et al. 2006). Kinetic isotope effects are typically approached through the lens of adiabatic transitionstate theory (Evans and Polanyi 1935; Eyring 1935) using the schematic depicted in Figure 2. Transition-state theory presumes that reactions proceed first through a pre-equilibrium between the reactants and an activated complex (i.e., a transition state, denoted by a “‡” superscript) followed by a unidirectional transformation of that complex into the products. The transformation of reactant A to product B through a transition state TS would thus be written:

Uniting Theory and Observations of Oxygen Triple Isotope Systematics 101

Figure 1. Broadening of vibrational transitions in condensed phases. Data from NIST Mass Spectrometry Data Center (2020).



Figure 2. Schematic of reaction pathway for a generic O-atom exchange reaction.

A ⇌ [TS]‡ → B

The transition state is a saddle point on the potential energy surface, meaning that all nuclear vibrations are bound except that which defines the bond being made or broken. The axis that describes the path of that bond is known as the reaction coordinate (see Fig. 2). The rate of a reaction can be written in terms of the partition functions Q of the reactants (i.e., the product of the partition functions for each reactant) and the transition state: k  tun

E k BT Q ‡ e h Qreactants

‡

k BT

(4)

Here, ηtun is a correction for nuclear tunneling (a uniquely quantum-mechanical effect discussed below) and Q refers to the nuclear partition functions only. The exponential term represents the effects of the electronic activation barrier, ΔE‡. Assuming a full separation of nuclear and electronic motions (i.e., the Born–Oppenheimer approximation; see above), ΔE‡ is the same for all isotopologues because they all lie on the same electronic potential energy surface. The kinetic 18O/16O fractionation factor is thus (Bigeleisen 1949; Bigeleisen and Wolfsberg 1958):

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18

 kin

18

18

16

16

k  k

tun tun

RPFR ‡ RPFR reactants 18

18

(5)

where k is the reaction-rate coefficient and  e U i / 2   ‡*j 3 N 7   ‡* i    ‡     ‡j i  j   ‡i  MMI  e Ui / 2  ‡*

RPFR ‡* 

 1  e U i   1  e Ui‡* ZPE  ‡

    EXC

(6)

The reduced partition function ratio for the transition state, RPFR‡, is nearly identical to that in Equation (1) except that the vibrational mode j that corresponds to the transforming bond is removed from the ZPE and EXC terms. That mode is unbound because it defines the reaction coordinate (Fig. 2); thus it is not free to vibrate in the transition state; consequently, it has an imaginary frequency, νj‡. The MMI term, however, expressed using the Teller–Redlich product rule, includes this imaginary frequency, so the ratio νj‡*/νj‡ remains outside the product. In addition, the ηtun terms in Equation (5) also depend on νj‡; they are approximately equal to 1 + Uj‡2/24 (Wigner 1932; Bigeleisen and Wolfsberg 1958). Note that these expressions also employ the harmonic-oscillator and rigid-rotor approximations.

Quantifying mass-dependent fractionation Triple-isotope variations can be quantified in many ways, but we will restrict the present discussion to several recurring terms used in the mass-dependent fractionation literature: κ, θ, and λ (Bao et al. 2016; Dauphas and Schauble 2016). The three terms cover the spectrum of theoretical to empirical quantities, with κ being theoretically straightforward but difficult to verify by experiment, and λ being observationally straightforward but the least directly related to theory. Each has its utility for different objectives in oxygen triple-isotope geochemistry. The triple-isotope κ value is characteristic of isotope-exchange equilibrium between an isotopically substituted species and a free atom. It is defined as the ratio of the natural logarithms of the RPFRs (Cao and Liu 2011): 

ln 17 RPFR A ln 18 RPFR A

(7)

This term, while abstract, has the benefit of putting all oxygen triple-isotope variations against a common reference state (atomic oxygen, which has no chemical isotopic preferences). Under the approximations used in Equation (1), it is bounded in the tripleoxygen system, in the high-temperature limit, to a maximum value of 0.5305 because κ(T→∞) = (1/m16–1/m17)/(1/m16–1/m18), in which the subscripts denote the isotope masses. Most oxygen-containing species thus far studied have temperature-dependent κ values lying between 0.527 and 0.530 (Young et al. 2002; Cao and Liu 2011; Hayles et al. 2017, 2018). Individual contributions to κ from can be separated by the relation (Hayles et al. 2017):

  ln   ln  18

complete 

i i

18

i

i

(8)

i

in which Πβi = RPFR, and βi refers to the contributions from individual vibrational modes or multiplicative corrections to the RPFR (e.g. anharmonic corrections). Each pair of 17βi and 18βi values thus yields a κi value for that mode. The contribution from the imaginary frequency of a transition state in Equation (6) in this framework is defined as βIF‡ = νj‡*/νj‡. Corrections for deviations from the harmonic-oscillator and rigid-rotor assumptions can also be incorporated this way, allowing one to understand their influence on κcomplete (see below).

Uniting Theory and Observations of Oxygen Triple Isotope Systematics 103 A more empirically tractable quantity is the triple-isotope exponent θ, which describes the triple-isotope fractionation between two species or phases, rather than a single species or phase relative to an atom. The quantity θ is derived from the relation 17αA–B = (18αA–B)θ for fractionation factors and is conventionally defined in logarithmic form, i.e., A  B 

ln 17  A  B ln 18  A  B

(9)

Because uncertainties in 17αA–B and 18αA–B values covary in laboratory measurements, θA–B values for many processes can be derived from laboratory measurements to high precision (Angert et al. 2003, 2004; Helman et al. 2005; Luz and Barkan 2005; Barkan and Luz 2007; Pack and Herwartz 2014; Sharp et al. 2016; Sengupta and Pack 2018; Stolper et al. 2018; Wostbrock et al. 2018, 2020; Ash et al. 2020); thus, θA–B values have been indispensable as a mediator between experiment and theory. To first order, θA–B values are insensitive of temperature (Young et al. 2002), but experimental and theoretical work has shown that a subtle temperature dependence can be observed in many cases (Cao and Liu 2011; Pack and Herwartz 2014; Casado et al. 2016; Sharp et al. 2016; Hayles et al. 2018; Stolper et al. 2018; Wostbrock et al. 2018). The triple-isotope coefficient λ has multiple meanings in the literature. We will simplify them here as λ and λRL. The former is descriptive and used to characterize experimentally observed relationships between isotope ratios (e.g., the meteoric water line has λ = 0.528). In the simplest case, λ describes the differences in δ′ values between two species, but more often it describes a best-fit slope for set of measured data, i.e.,



 17 O  18 O

(10)

The latter quantity λRL, however, is the reference slope against which Δ′17O values are reported:  17 O  17 O   RL   18 O

(11)

Both of these uses serve empirical ends, and do not necessarily represent discrete processes. However, λRL is sometimes tied to λ, θ, or κ values for convenience. One prominent example is the high-temperature limit of κ (i.e., 0.5305; Pack et al. 2013; Pack and Herwartz 2014). We will use λRL = 0.528 to report data. The relationship between observed λ values and the more fundamental θ values relies on an assumed physical model of the system, and thus can vary. For example, for a well-mixed system described by Rayleigh fractionation, one can define λRayleigh (γ in Angert et al. 2003) as  Rayleigh 

1  18   1  18 

(12)

whereas for a diffusion-limited Rayleigh system (He and Bao 2019; Li et al. 2019)  diff  rxn

   1   1

18

18

/2 1/ 2

(13)

Using triple-isotope observations to constrain chemical or thermodynamic quantities (e.g., formation temperature) thus requires that one evaluate and understand the physical constraints on a given problem, often through its extended geochemical context.

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Note that theory meets the “real world” in these three quantities. The experimentalist will almost always measure α and λ values, which, through a suitable model of the system under study, may allow them to infer θA–B values. The theorist will always calculate a set of RPFRs first before obtaining α, κ, and θA–B values for fundamental processes. Interpreting subtle variations in triple-oxygen compositions in natural systems thus requires an understanding of how accurate each of these approaches is, or at least how well they are able to reproduce each other.

Natural variability in the triple-oxygen exponents θ In pursuit of an intuition about triple-oxygen isotope systematics, one may wish to interrogate the bounds of θ values allowed by theory: what are typical ranges for equilibrium and kinetic processes, and when can θ values deviate from these ranges? For equilibrium 18 α, and 18RPFR values (Cao and Liu 2011): processes, eq A  B can be expressed in terms of κ, eq A  B  A    A   B 

ln 18 RPFR B ln 18  A  B

(14)

This expression highlights the larger physically allowable range in eq A  B values compared to κ values, which have a maximum value of 0.5305 at high temperatures (see above). When κA ≠ κB, 18 16 O/ O fractionations, i.e., when ln(18αA–B) = ln 18RPFRA–ln eq A  B values diverge for small 18 RPFRB is near zero. This divergence allows eq A  B to take any value in an isotope-exchange equilibrium in principle; fractionation “crossovers,” where ln(αA–B) changes sign as a function of temperature (e.g., hematite–water equilibrium near 60 °C), have been highlighted before as regions where eq A  B values can deviate strongly from the limits of κ and yield seemingly anomalous isotope effects (Skaron and Wolfsberg 1980; Kotaka et al. 1992; Hayles et al. 2017). Nevertheless, the typically expected range in eq A  B values is between 0.525 and 0.530 at Earthsurface temperatures and above, slightly larger than the range for κ values (Bao et al. 2016). The kinetic triple-isotope exponent Akin B has a typical range that is even larger. Young et al. (2002) first showed, using both transition-state theory and Rice–Ramsperger–Kassel–Marcus theory for unimolecular decomposition (Marcus 1952), that kinetic triple-oxygen isotope effects depend on whether the isotopic substitution is part of the bond being altered. If oxygenatom motions are only relevant along the reaction coordinate (cf. Fig. 2), then the Akin B value approaches the mass dependence of classical particles in motion, i.e., the relative velocities of 16O, 17O, and 18O, approaching Akin B = 0.516 as the masses of the participant fragments increases or the temperature increases. Within the framework of κ values, Equation (6) implies that κcomplete approaches κIF (the imaginary-frequency contribution to κcomplete) when an isotopic substitution only affects motion along the reaction coordinate (Hayles et al. 2017):

 17  ‡   17 ‡  ln  16 ‡j  ln  16 ‡  j   IF   18 ‡    18 ‡      j  ln  16 ‡  ln  16 ‡      j 

(15)

Here, the reduced mass μ, i.e., derived from 1/μ = Σ (1/m), corresponds to that of the two fragments participating in the vibration that becomes the reaction coordinate. In contrast, if the oxygen-atom vibrations are all orthogonal to the reaction coordinate, then Akin B approaches eq A  B. One might then surmise that if oxygen atoms participate in some vibrational modes of both the reactants and transition state, then Akin B lies somewhere in between the classical limit and eq A  B (Dauphas and Schauble 2016). We note that Bao et al. (2015) showed that because is not bounded—e.g., it adopts unusual values near isotopic crossovers—Akin B can also eq AB adopt any value. Nevertheless, this simplified view obscures an important and non-intuitive feature of kinetic fractionation for oxygen triple isotopes: Akin B is not bounded, even for wellbehaved reactions far from where the kinetic isotope fractionation changes sign.

Uniting Theory and Observations of Oxygen Triple Isotope Systematics 105 The loss of one vibrational degree of freedom in Equation (6) relative to Equation (1) is the ultimate origin for the larger potential variability of Akin B relative to its equilibrium counterpart. Importantly, the ratio of imaginary frequencies, βIF‡, is always less than one (Bigeleisen and Wolfsberg 1958). If the substituted oxygen atom participates in some vibrational modes of both the reactants and products, then the remaining, real portion of RPFR‡ in Equation (6) is greater than one (i.e., βreal‡ > 1). This disparity in βi values on either side of unity creates an “internal crossover” for κ‡: the denominator of Equation (8) for the transition state, ln18βIF‡ + ln18βreal‡, is predisposed to be close to zero. κ‡ itself is not bounded, and instead is predisposed to appear anomalous. Higher values of 18βreal‡, arising from lower reaction temperatures and/or substitutions that shift high-frequency vibrations, tend to drive κ‡ toward a canonically more “normal” range. To illustrate this concept, we plot predicted values of κ‡ for a variety of model transition states as a function of 18RPFR‡ = 18βIF‡ × 18βreal‡ in Figure 3. A κ‡ crossover can be seen at 18RPFR‡ = 1 (i.e., ln18βIF‡ + ln18βreal‡ ~ 0), with anomalous nearby κ‡ values. Given this predisposition for high variability in κ‡, then, the values of Akin B typically measured and calculated, between 0.516–0.53 (Bao et al. 2016), are surprising. The absence of anomalous Akin B values in the literature imply that bounds on its value are imposed by chemical and not mathematical limits. For example, the lower zero-point energy of isotopically substituted reactants may mitigate the expression of anomalous 18RPFR‡ values as anomalous kinetic isotope effects.

Figure 3. Monte-Carlo sampling of 18RPFR‡ = 18βIF‡ × 18βreal‡ and κ‡ values for a model transition state. In this model, the harmonic vibration of a diatomic molecule M1‑O is used to obtain 18βreal‡, which characterizes the real vibrations inEquation (6). The force constant for that bond is varied from that of CO to 1/8th that of CO. The imaginary frequency contribution to Equation (6),18βIF‡, is here equal to (μM1 – O + M2/μM1 – O* + M2)1/2, i.e., a function of the reduced mass along the decomposition mode only. Both M1 and M2 are varied from 1–300 amu for Monte Carlo sampling. For comparison, the harmonic vibration of O2 (ν = 1580 cm−1) 18βreal‡ = 1.17 at 25 °C.

Nuclear tunneling is thought to be negligible for oxygen isotopes, leading to the generalizations above (cf. Eqns. 4, 5). However, electron–nuclear tunneling may be relevant in electron-transfer (ET) reactions, which are ubiquitous in biology (Bertini et al. 1994). In this mechanism, electron tunneling through the reaction barrier results in nuclear reorganization, especially at low temperatures (De Vault and Chance 1966; Hopfield 1974); the nuclear motions in this case are a response to the reaction, not the cause of it (sensu stricto). Its mass dependence is not obvious at first glance. Two mechanisms of ET reaction are relevant: inner-sphere and outer-sphere. Innersphere electron transfer involves bond-making and/or breaking, whereas outer-sphere electron transfer does not. The former mechanism is characteristic of enzyme catalysis and has oxygenisotope effects arising from both transition-state properties and tunneling (Roth et al. 2004; Mukherjee et al. 2008). The latter type describes all long-range electron transfers in biological systems (Bertini et al. 1994) and has isotope effects arising primarily from electron–nuclear tunneling. We explore the mass dependence of the latter mechanism below.

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Buhks, Jortner, and coworkers (Buhks et al. 1981a,b) described outer-sphere electron transfer in terms of an electronic coupling term (i.e., the probability of an ET event) and a Franck–Condon overlap factor (i.e., for a given geometry in a given system). The latter term encompasses the Franck–Condon principle, which states that an electronic transition is most likely to occur between states that resemble each other on the potential energy surface. For example, the half-reaction O2 + e− → O2− is most likely to occur when the O–O bond length in O2 (1.21Å on average) is equal to the equilibrium bond length of O2− (1.28Å). Note that changes in the O–O bond length occur naturally as the O2 molecule vibrates, modulating this overlap (Fig. 4, left). The equations describing the tunneling effects on the reaction O2* + O2− → O2−* + O2 are:

4   d   r  p  Up  U  r coth     p coth r 4 4   2

Y

 

 d 

2



2  r  h

(16)

2

(17) (18)

ln  Y  Y *

Here, (Δr)2 is the squared change in equilibrium bond length between reactant (subscript r) and product (subscript p). For harmonic oscillators, the (Δr)2 term and the constants cancel when θ values are computed, rendering the difference between νr and νp (i.e., the change in bond strength upon reaction) the most important factor that determines θET for the ET component of these reactions. We compared the ET and equilibrium θ values for the reaction O2* + O2− → O2−* + O2 using known harmonic vibrational frequencies of 1580 cm−1 and 1090 cm−1 for the neutral and anionic 16O16O species, respectively (Celotta et al. 1972; Huber and Herzberg 1979). The results between 0 °C and 400 °C are shown in Figure 4. Interestingly, the outer-sphere electron transfer mechanism is not mass-anomalous, as one might have guessed for an electron tunneling-driven reaction, or from the dependence of α on (Δr)2. Instead, θET is well behaved and less than θeq over the entire temperature range. Therefore, a kinetically limiting outersphere ET pathway has a mass dependence in the range of more typical kinetic isotope effects: the range in θET values is still between 0.52 and 0.53 in this temperature range.



Figure 4. Effects of outer-sphere electron transfer in the reaction O2 + O2 → + O2. (Left) Schematic depicting outer-sphere ET through electron–nuclear tunneling. (Right) Comparison of θ values between 0 °C and 400 °C predicted for outer-sphere ET and isotopic equilibrium. *

−

O2−*

Uniting Theory and Observations of Oxygen Triple Isotope Systematics 107 The preceding discussion emphasizes the relatively small range of triple-isotope fractionation exponents observed, and the broader range allowed by theory in geochemical systems. These ranges set a target on how accurate theoretical predictions and measurements need to be in order to interpret isotopic trends unequivocally. Systems showing higher variability in θ values such as those influenced by isotopic crossovers, photochemistry, surfaces, and/or low temperatures (Skaron and Wolfsberg 1980; Horita and Wesolowski 1994; Abe 2008; Balan et al. 2009; Sun and Bao 2011; Eiler et al. 2013; Hayles et al. 2017) may have slightly lower accuracy requirements, but their influence in nature is no less important to understand.

A note about anharmonicity The assumptions present in Equations (1, 3, 6, 15) are nontrivial, so an exploration of their effects on calculated triple-isotope fractionation is warranted. The harmonic-oscillator and rigidrotor approximations, in particular, represent idealized behaviors of atoms and bonds, and are generally justified if molecules primarily occupy the lowest vibrational state (e.g., under mild conditions). Relaxing the harmonic-oscillator and rigid-rotor assumptions allows vibrational and rotational modes to influence each other and centrifugal forces to affect bond lengths. More subtle molecular motions, such as hindered internal rotations, may also be relevant (Ellingson et al. 2006). Collectively, these are known as anharmonic effects. While accounting for these effects adds considerable complexity to calculations, it also yields a more accurate description of the physical system and more accurate isotopic fractionations in principle. Richet et al. (1977) and Liu et al. (2010) found that the most significant anharmonic effect for isotopic fractionation is that associated with the lowest vibrational state. While this anharmonic correction can be calculated from spectroscopic constants for some simple molecules, a more typical treatment is to replace the ZPE term in in Equation (1) with an anharmonic zero-point energy obtained directly from electronic structure programs. The resulting expression for RPFR, incorporating this first-order correction, is thus:  e  ZPEanh / kT   *   1  e Ui  (19) RPFR anharm    ZPEanh / kT    i   e  i   i   1  e Ui*  MMI EXC   where ZPEanh is the total anharmonic vibrational zero-point energy of the molecule. These effects are most pronounced for molecules bearing light elements such as hydrogen. *

While the accuracy benefits of anharmonic corrections are apparent for individual RPFRs and α values, there is a certain degree of error cancellation for mass-dependent processes. The accuracy improvements for the quantities κ and θ in the oxygen triple-isotope system therefore are not as obvious. Calculating anharmonic effects is expensive, and may be of limited use if the end result is nearly unchanged from the harmonic result. Cao and Liu (2011) found that The anharmonic correction typically accounts for single-digit percentages of ln(18RPFR) for hydrogen-bearing molecules and even less for non-hydrogen bearing species. For small molecules (i.e., CO2 and N2O), changes to κ values arising from anharmonic effects were therefore found to be 1200 K), and second, the calculated effects have the opposite sign to observed signatures (> 0 for the model potential, vs. < 0 in measured granite and feldspars). Anharmonic effects on the mass fractionation exponent will be ignored in the discussion that follows, excepting the anharmonic zero-point energy correction previously described for H2O(v), CO2, and CO.

∆′17O signatures of equilibrium Based on the discussion and findings above, it appears likely that mass-dependent effects within the Born–Oppenheimer approximation are usually the predominant driver of ∆′17O at equilibrium, including at high (metamorphic and igneous) temperatures, and that even simplified calculations based on these assumptions can generate reasonable estimates of signatures found in natural systems. Newly calculated mass dependent 103 ln18/16β and qa–atoms results from the present work are reported in Table 4. Polynomials in 1/T have been fit to each, in order to facilitate interpolation (Tables 5 and 6) for temperatures above 243.15 K. Fits for 103 ln18/16β are accurate to within 0.03‰, and fits for qa–atoms are accurate within 1 × 10–4 over this temperature range. Model properties for liquid and supercritical water are also tabulated (273.15–647 K for liquid water and 647+ K for supercritical water), by adding 103  ln18/16α for liquid–vapor or supercritical fluid–vapor (Horita and Wesolowski 1994; Rosenbaum 1997) to the present H2O vapor results. qliquid water–atoms is estimated as described above. Uncertainties in estimated mass-dependent fractionations. Leaving aside anharmonicity, which has been addressed in a special case above, more generally by Richet et al. (1977), Schauble et al. (2006) Méheut et al. (2007), and others for the calculation of stable isotope fractionation factors, and in greater detail by Cao and Liu (2011) for estimating qa–b exponents, the main contributors to uncertainty in estimated 18O/16O and qa–b are likely to be errors in calculated

Mass Dependence of Equilibrium Oxygen Isotope Fractionation

153

Figure 4. Contour plots showing variation in the calculated ∆′17O (in per meg), relative to a θ=0.528 reference exponent, for an anharmonic oscillator in a double-well potential, versus the height (B) and sharpness (γ) of the central Gaussian. Temperatures are given for each panel, based on the assumption that the harmonic component of the potential has a characteristic frequency of 200 cm–1. The corresponding ∆′17O for the unperturbed harmonic potential is shown with a white line labelled “B = 0” in each color scalebar. The dashed black line indicates Bγ = 2; it is likely that silicates and other molecules with double-well potentials are best fit by values of B and γ that fall below this line.

vibrational frequencies, errors in the frequency shifts upon isotope substitution, errors from incomplete sampling of the phonon density of states, and errors stemming from the interaction of 18 O or 17O substitutions in adjacent unit cells. We will attempt to address each of these sources of error in turn, though it is still not possible to provide a rigorous quantitative analysis. Scale factor effects. Application of a frequency scale factor is intended to correct for the typical systematic error in the PBE gradient-corrected approximation of the density functional. This work and many previous studies have found consistent underestimation of both measured and harmonic frequencies, by ~3–6% in materials most closely resembling the crystals studied here. However, there are still potentially significant mismatches between measured and calculated frequencies even when the scale factor is applied. One approach to estimating this source of uncertainty is to compare our results with a general fitted PBE scale factor

103.73 107.42 111.51

Phlogopite

Tremolite

Glaucophane 105.10 108.35 110.20 103.09

Diaspore

Xenotime YPO4

Xenotime LuPO4

Monazite LaPO4

96.70

111.96

Kaolinite

Spinel (normal)

99.51

Lizardite

Jadeite

100.67

112.83

Diopside

103.09

104.55

Anorthite (ordered)

Grossular

109.91

Microcline (low)

Zircon

116.71

Albite (low)

99.47

117.11

a-quartz

Forsterite

0 ºC 124.83

Substance

89.19

95.35

93.74

90.65

82.79

96.57

92.96

89.72

97.25

86.28

86.55

88.98

85.60

97.57

90.30

95.18

101.36

101.69

108.70

25 ºC

1000 ln18/16b

60.75

64.97

63.85

61.53

55.02

65.98

63.41

61.19

67.12

59.37

58.10

60.26

57.59

66.37

61.26

64.97

69.67

69.85

75.20

100 ºC

0 ºC

0.528464

0.528401

0.528427

0.529025

0.529026

0.528261

0.528349

0.528512

0.528556

0.528679

0.528798

0.528501

0.528764

0.528331

0.528508

0.528301

0.528091

0.528103

0.527906

0.528660

0.528603

0.528627

0.529193

0.529214

0.528476

0.528561

0.528718

0.528750

0.528875

0.528991

0.528705

0.528955

0.528540

0.528708

0.528509

0.528304

0.528315

0.528118

25 ºC

qa–atoms 100 ºC

0.529127

0.529083

0.529103

0.529552

0.529615

0.528989

0.529062

0.529194

0.529201

0.529320

0.529421

0.529180

0.529387

0.529037

0.529177

0.529005

0.528827

0.528835

0.528653

−90.0

−93.7

−91.6

−30.1

−38.6

−108.8

−100.4

−84.8

−75.7

−70.3

−57.5

−86.3

−61.9

−100.6

−84.8

−104.8

−127.2

−125.9

−149.6

0 ºC

−66.4

−67.8

−66.4

−17.1

−24.7

−79.3

−73.1

−60.9

−52.3

−49.8

−39.5

−62.5

−43.5

−72.5

−61.3

−76.8

−94.4

−93.2

−112.4

25 ºC

−29.0

−27.1

−27.1

−2.0

−8.6

−32.2

−30.1

−24.4

−16.9

−19.1

−14.9

−26.4

−17.6

−28.6

−25.4

−32.2

−39.9

−39.2

−48.4

100 ºC

D′17O vs. H2O vapor (per meg)

Table 4. Calculated 1000 ln18/16b, qa–atoms, and D′17O (vs. H2O vapor) for crystals and molecules at 0 ºC (273.15 K), 25ºC (298.15 K), and 100 ºC (373.15 K). Anharmonic zero-point energy corrections are included in estimated ln18/16b for H2O vapor (anharm.), CO, and CO2. qa–atoms is based on harmonic oscillator models for all species. Liquid water results are based on both anharmonic and harmonic H2O vapor models, and assume the liquid–vapor fractionation of Rosenbaum (1997; R-model) and Horita and Wesolowski (1994; HW-model). qa–atoms for the liquid water results shown here are calculated as the average of H2O vapor and ice-Ih.

154 Schauble & Young

0 ºC 104.31 111.93 107.41 102.18 109.41 87.58 106.54 114.44 113.69 119.53 124.82 121.52 111.71 68.29 71.68 79.81 83.20 80.04 83.43 91.31 91.39 123.57 112.84 100.53

Substance

Fluorapatite

Anhydrite

Barite

Gypsum (all O)

Gypsum (sulfate O)

Gypsum (H2O)

NaClO4

Calcite

Aragonite

Dolomite

Magnesite

Nahcolite

Nitratine

H2O vapor (anharm.)

H2O vapor (harm.)

Liquid water (R-model, anharm.)

Liquid water (R-model, harm.)

Liquid water (HW-model, anharm.)

Liquid water HW-model, harm.)

Water Ice Ih (harm.)

Water Ice XI (harm.)

CO2 vapor (anharm.)

CO vapor (anharm.)

H4SiO4 vapor

88.19

101.33

109.54

81.11

81.04

74.11

71.01

73.75

70.65

64.81

61.70

97.52

106.37

108.68

104.15

99.16

99.75

92.47

78.04

94.94

89.34

93.19

97.16

90.29

25 ºC

1000 ln18/16b

62.54

76.10

79.39

59.48

59.42

54.82

52.34

54.59

52.11

49.74

47.26

67.85

74.67

75.26

72.22

68.91

69.22

63.43

57.88

65.12

62.71

63.89

66.71

61.57

100 ºC

0.529053

0.528128

0.527852

0.529760

0.529760

0.529889

0.529889

0.529889

0.529889

0.530018

0.530019

0.528406

0.528435

0.528409

0.528414

0.528421

0.528436

0.528392

0.529769

0.528366

0.528635

0.528387

0.528319

0.528453

0 ºC

0.529192

0.528201

0.527985

0.529806

0.529807

0.529918

0.529918

0.529918

0.529918

0.530029

0.530030

0.528579

0.528600

0.528587

0.528590

0.528592

0.528609

0.528584

0.529813

0.528559

0.528833

0.528578

0.528515

0.528649

25 ºC

qa–atoms

0.529509

0.528429

0.528366

0.529914

0.529915

0.529988

0.529988

0.529988

0.529988

0.530062

0.530063

0.529013

0.529009

0.529023

0.529022

0.529017

0.529036

0.529052

0.529912

0.529029

0.529277

0.529044

0.528992

0.529115

100 ºC

−32.0

−123.4

−156.2

16.1

16.1

−

13.3

−

12.9

0

0

−92.5

−85.1

−86.8

−88.4

−90.0

−88.0

−96.1

10.3

−97.9

−73.0

−96.3

−102.1

−90.6

0 ºC

−20.2

−104.8

−126.8

15.0

14.9

−

11.0

−

10.3

0

0

−68.7

−61.5

−61.4

−63.8

−66.5

−64.5

−71.2

9.9

−72.2

−50.8

−71.3

−75.2

−66.7

25 ºC

−3.1

−64.9

−68.4

11.3

11.2

6.6

−

6.1

0

0

−28.8

−22.1

−20.5

−23.7

−27.4

−25.7

−30.8

8.1

−30.5

−17.4

−30.8

−31.3

−28.8

100 ºC

D′17O vs. H2O vapor (per meg)

Mass Dependence of Equilibrium Oxygen Isotope Fractionation 155

1.01670E+14

−1.12366E+14

−6.18560E+14

Spinel (normal)

−4.39155E+15

−4.56891E+15

Xenotime YPO4

Xenotime LuPO4

4.57904E+15

−2.63255E+15

Glaucophane

Diaspore

7.27276E+14

−2.12065E+15

Phlogopite

Tremolite

7.73661E+15

6.51056E+15

Lizardite

Kaolinite

3.66292E+13

−1.88297E+15

Grossular

4.08989E+13

7.51877E+13

7.26398E+13

−7.03550E+13

1.71233E+13

4.51509E+13

3.79732E+13

−4.55563E+12

−9.35842E+13

5.63538E+13

−2.19103E+15

−3.23144E+15

Forsterite

7.31080E+13

6.16464E+13

7.71919E+13

Zircon

−3.62416E+15

−4.40482E+15

Diopside

Jadeite

−6.46928E+15

−4.67984E+15

Microcline (low)

Anorthite (ordered)

1.00579E+14

−6.38987E+15

Albite (low)

B 1.29277E+14

A

75.38

100 ºC

−8.57662E+15

109.86

25 ºC

a-quartz

126.57

0 ºC

Substance

H6Si2O7 vapor bridging O

Substance

1000 ln18/16b 25 ºC

−4.22893E+11

−4.11008E+11

4.54600E+11

−1.51621E+11

−2.37314E+11

−2.04889E+11

3.47214E+10

5.89200E+11

6.86921E+11

−2.47596E+11

−3.38586E+11

−2.65461E+11

−4.15958E+11

−3.60713E+11

−4.34289E+11

−5.38345E+11

−5.33809E+11

D

0.528935

100 ºC

1.52834E+08

1.51631E+08

−2.10919E+09

6.83972E+07

−4.08262E+08

−4.08901E+08

−9.73368E+08

−2.76100E+09

−2.81599E+09

1.14579E+08

1.45392E+08

1.19351E+08

1.52614E+08

1.44442E+08

1.57751E+08

1.56396E+08

1.54282E+08

1.13149E+08

0.528429

−6.47264E+11

C

0.528221

0 ºC

qa–atoms

1.04575E+07

1.02582E+07

1.21732E+07

8.26379E+06

1.12546E+07

1.07765E+07

1.09344E+07

1.40130E+07

1.26740E+07

8.94561E+06

9.50742E+06

8.92416E+06

1.06345E+07

9.72754E+06

1.04922E+07

1.15223E+07

1.15385E+07

1.27764E+07

E

−109.9

0 ºC

F

−27.0

100 ºC

1.53390E+01

1.59587E+01

−2.67567E+02

1.35275E+01

−6.21183E+00

−2.36835E+00

−1.45729E+01

−9.49342E+01

−8.49823E+01

1.92367E+01

2.04146E+01

1.89238E+01

1.60881E+01

1.80991E+01

1.60620E+01

6.38887E+00

6.24956E+00

−1.58089E+01

−78.1

25 ºC

D′17O vs. H2O vapor (per meg)

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

G

Table 5. Polynomial fits of the form 1000 ln18/16b = A/T6 + B/T5 + C/T4 + D/T3 + E/T2 + F/T for temperatures above 243.15 K (273.15 K for liquid water). A temperature independent term, “G”, is included in the fits for liquid water, taken directly from earlier liquid–vapor and supercritical fluid–vapor studies (Rosenbaum 1997; Horita and Wesolowski 1994).

156 Schauble & Young

8.58034E+13

Gypsum (sulfate O)

−6.95760E+13

−1.93531E+15

−6.23677E+15

1.00933E+14

−3.10907E+14

−4.14778E+14

−4.14442E+14

C

−5.54067E+11

1.88036E+12

1.31394E+12

2.68853E+11

2.75816E+12

2.75605E+12

3.94849E+12

3.88795E+12

−5.67548E+11

−2.20150E+11

−5.56075E+11

−5.50664E+11

−5.37818E+11

−5.39168E+11

−4.60322E+11

3.47959E+12

−4.68492E+11

8.53232E+11

−4.62533E+11

−4.97617E+11

−4.05288E+11

−3.90816E+11

D

1.87949E+08

−6.45554E+09

−8.38839E+09

−4.27840E+09

−9.82552E+09

−9.81791E+09

−1.27503E+10

−1.25885E+10

−1.04293E+08

−1.56554E+09

−2.53019E+08

−2.25445E+08

−2.40930E+08

−1.93699E+08

1.34434E+08

−1.16216E+10

1.13100E+08

−3.81657E+09

1.30922E+08

1.29805E+08

1.47629E+08

1.47530E+08

E

1.23447E+07

1.74651E+07

2.58267E+07

2.05286E+07

2.18670E+07

2.18496E+07

2.30136E+07

2.28002E+07

1.19529E+07

1.51029E+07

1.32925E+07

1.27776E+07

1.22970E+07

1.22391E+07

1.04159E+07

2.32601E+07

1.07298E+07

1.49278E+07

1.04920E+07

1.10175E+07

9.92196E+06

9.75493E+06

2.86501E+15

1.20346E+17

Liquid Water (anharm.) (273–403 K)

Liquid Water (anharm.) (403–647 K)

−6.66957E+12

−6.66957E+12

−1.98057E+12

−8.59748E+10

−1.15346E+08

−1.15346E+08

1.67523E+07

6.40332E+06

F

1.63985E+01

−1.60791E+02

−2.00113E+03

−1.32159E+03

−1.07882E+03

−1.07955E+03

−4.32931E+02

−1.24437E+03

−6.82541E+01

−3.28073E+02

−1.06063E+02

−9.88440E+01

−1.02204E+02

−8.98300E+01

6.62368E+00

−8.30661E+02

3.79932E+00

−2.81301E+02

5.27267E+00

2.01074E+00

1.50223E+01

1.62466E+01

−6.46500E+01

−6.46500E+01

Sums of 103 lnb H2O vapor and 103 ln a H2O liquid-vapor or 103 ln a H2O supercritical–vapor from Rosenbaum (1997)

H6Si2O7 vapor bridging O

H4SiO4 vapor

2.09683E+16

2.56214E+16

−6.27638E+15

Water Ice XI

CO2 vapor

CO vapor

4.56379E+13

2.55981E+16

Water Ice Ih

−6.37102E+14

4.15943E+16

−6.26044E+14

4.08073E+16

1.19422E+14

H2O vapor (harm.)

−8.18521E+15

Nitratine

7.90625E+13

1.21467E+14

1.19880E+14

1.18153E+14

1.16592E+14

8.48246E+13

−5.48078E+14

8.73493E+13

−1.25014E+14

H2O vapor (anharm.)

−8.52650E+15

−6.36640E+15

Magnesite

Nahcolite

−8.31575E+15

−8.39772E+15

Aragonite

−8.13464E+15

Calcite

Dolomite

−5.30560E+15

3.50923E+16

−5.50349E+15

NaClO4

Gypsum (H2O)

8.03873E+15

−5.39636E+15

Gypsum (all O)

Barite

9.37217E+13

−5.96338E+15

Anhydrite

7.20071E+13

−4.37161E+15

B 6.87433E+13

Fluorapatite

A

−4.13682E+15

Monazite LaPO4

Substance

−6.482

12.815

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

G

Mass Dependence of Equilibrium Oxygen Isotope Fractionation 157

−1.77280E+13 −2.77134E+08

−2.77134E+08

−2.77134E+08

−1.15346E+08

D

1.32097E+07

1.69657E+07

6.61672E+06

1.29963E+07

E

−6.26044E+14 −6.37102E+14

3.88795E+12 3.94849E+12

−1.22381E+10 −1.23999E+10

2.11338E+07 2.13472E+07

7.95388E+16

5.17439E+17

103 ln a H2O liquid–vapor (403-647K)

103 ln a H2O supercritical–vapor (≥ 647K) 6.19374E+14

6.19374E+14

6.19374E+14

−6.19374E+14

3.84852E+12

−6.66052E+12

−5.86852E+12

−3.97392E+12 1.24732E+10

1.24732E+10

1.24732E+10

−1.24732E+10

2.26339E+07

−9.80389E+06

−6.04789E+06

−1.63969E+07

1.17972E+03

1.17972E+03

1.17972E+03

−1.17972E+03

6.27937E+03

5.46793E+03

7.46789E+02

7.46789E+02

7.46789E+02

−6.46500E+01

F

−

−6.482

12.815

−

−7.685

−7.685

−

−6.482

12.815

−

G

−7.15131E+06 −7.07921E+06 −5.22563E+06 −3.43390E+06 −4.79241E+06 −1.70288E+06 −3.01991E+06

Albite (low)

Microcline (low)

Anorthite (ordered)

Diopside

Jadeite

Forsterite

Zircon

L −9.84260E+06

a−quartz

Substance

5.85699E+04

4.00637E+04

7.78984E+04

6.23164E+04

8.32484E+04

1.05174E+05

1.05390E+05

1.34471E+05

M

−3.33492E+02

−2.61182E+02

−3.95169E+02

−3.41450E+02

−4.11634E+02

−4.85387E+02

−4.84222E+02

−5.72152E+02

N

3.19019E−02

2.26548E−02

3.92213E−02

3.30828E−02

4.10861E−02

5.07437E−02

5.02774E−02

6.08257E−02

P

Table 6. Polynomial fits of the form qa–atoms = 0.530520 + L/T4 + M/T3 + N/T2 + P/T for temperaturesabove 243.15 K (273.15 K for liquid water).

−3.79422E+16

103 ln a H2O liquid–vapor (273-403K)

4.03612E+16

Fits to results of Rosenbaum (1997), used to estimate properties of liquid and supercritical water

4.08073E+16

4.15943E+16

Liquid Water (anharm.) (273–647 K)

Liquid Water (harm.) (273–647 K)

H2O vapor

−2.71204E+12

−1.92004E+12

−2.54358E+10

−2.77257E+12

C

Sums of 103 ln b H2O vapor and 103 ln a H2O liquid–vapor from Horita and Wesolowski (1994)

−1.77280E+13

1.21133E+17

5.59033E+17

Liquid Water (harm.) (403–647 K)

Supercritical Water (harm.) (≥ 647 K)

−6.66957E+12 −1.77280E+13

5.58246E+17

3.65207E+15

B

Supercritical Water (anharm.) (≥ 647 K)

A

Liquid Water (harm.) (273–403 K)

Substance

158 Schauble & Young

−1.82963E+06 −1.31818E+06 −3.26905E+06 −4.22525E+06

Kaolinite

Phlogopite

Tremolite

Glaucophane

7.30846E+04

−4.36909E+06 −4.56535E+06 −4.25029E+06 −4.45849E+06 −6.29166E+06 −5.82495E+06 −1.71512E+05 −5.87792E+06 −6.87656E+06 −5.49862E+06 −8.74242E+06 −9.24375E+06 −8.93017E+06 −8.88665E+06 −1.05391E+07 −8.48622E+06 −5.55222E+06

Xenotime YPO4

Xenotime LuPO4

Monazite LaPO4

Fluorapatite

Anhydrite

Barite

Gypsum (all O)

Gypsum (sulfate O)

Gypsum (H2O)

NaClO4

Calcite

Aragonite

Dolomite

Magnesite

Nahcolite

Nitratine

H2O vapor (anharm.)

4.16832E+04

1.11387E+05

1.24829E+05

1.12414E+05

1.13330E+05

1.16665E+05

1.11775E+05

8.53229E+04

5.60349E+04

8.89986E+04

1.82458E+04

8.81142E+04

9.36614E+04

7.38756E+04

7.16694E+04

7.53224E+04

3.77741E+04

−3.20897E+06

1.43521E+04

7.44971E+04

6.39611E+04

4.19366E+04

4.21814E+04

1.79214E+04

3.47731E+04

M

Diaspore

2.11190E+05

6.78135E+05

Spinel (normal)

−1.25214E+06

Lizardite

L

Grossular

Substance

−5.59908E+01

−4.63752E+02

−4.75553E+02

−4.60718E+02

−4.63424E+02

−4.71117E+02

−4.58694E+02

−4.09047E+02

−1.18337E+02

−4.19591E+02

−1.62159E+02

−4.15417E+02

−4.35133E+02

−3.75391E+02

−3.69102E+02

−3.83345E+02

−3.75570E+02

−1.87320E+02

−1.69555E+02

−3.92412E+02

−3.58080E+02

−2.82492E+02

−2.57960E+02

−1.91993E+02

−2.44601E+02

N

−2.15903E−01

4.37314E−02

1.61644E−02

3.95939E−02

4.06824E−02

4.15681E−02

4.10091E−02

4.19470E−02

−1.82943E−01

4.27316E−02

−1.57186E−01

4.24829E−02

4.48193E−02

3.78383E−02

3.70972E−02

3.85453E−02

3.76112E−02

−7.02837E−02

9.68832E−03

2.75325E−02

2.02277E−02

−1.24930E−02

−6.81728E−02

−7.41326E−02

2.01696E−02

P

Mass Dependence of Equilibrium Oxygen Isotope Fractionation 159

−5.84665E+06

H6Si2O7 vapor bridging O 3 

M

9.14111E+04

3.28910E+04

3.58154E+05

2.78083E+05

6.40300E+04

6.38621E+04

4.05846E+04

N

−4.40417E+02

−1.59882E+02

−9.25062E+02

−8.40698E+02

−1.51169E+02

−1.50800E+02

−5.21169E+01

P

4.54413E−02

−1.40973E−01

−1.27385E−01

−2.28591E−02

−1.38290E−01

−1.38100E−01

−2.20711E−01

−7.28054E+06 −8.79767E+06

Lesser of vapor vs. previous

50% ice model

6.73660E+04

5.94857E+04

4.63855E+05 −1.31127E+02

−1.22058E+02

−1.22371E+03

7.87587E−01 −1.62891E−01

−1.69771E−01

−7.26651E+06 −8.79767E+06

50% ice model

6.73660E+04

5.89854E+04

4.21352E+05

−1.31127E+02

−1.19406E+02

−1.10973E+03

6.92261E−01 −1.62891E−01

−1.71835E−01

−1.01415E+07 −1.24040E+06

Lesser of vapor vs. previous

50% ice model

6.01304E+03

8.71902E+04

1.08486E+05

2.66231E+01

−2.10441E+02

−2.70736E+02

−2.89380E−01

−7.78492E−02

−2.28243E−02

−1.18765E+07 −9.58417E+06 −1.24040E+06

qliquid–vapor = 0.529 (Barkan et al. 2005)

Lesser of vapor vs. previous

50% ice model

6.01304E+03

8.20815E+04

1.02119E+05

2.66231E+01

−1.95176E+02

−2.51906E+02

−2.89380E−01

−9.09826E−02

−3.92103E−02

Liquid Water (harm.; 273K ≤ T ≤ 647K) using 103 ln a H2O liquid–vapor from Horita and Wesolowski (1994)

−1.25778E+07

qliquid–vapor = 0.529 (Barkan et al. 2005)

Liquid Water (anharm.; 273K ≤ T ≤ 647K) using 10 ln a H2O liquid–vapor from Horita and Wesolowski (1994)

3 

−4.99105E+07

qliquid–vapor = 0.529 (Barkan et al. 2005)

Lesser of vapor vs. previous

Liquid and Supercritical Water (anharm.; ≥ 273K) using 103 ln a H2O liquid–vapor from Rosenbaum (1997)

−5.49858E+07

qliquid–vapor = 0.529 (Barkan et al. 2005)

Liquid and Supercritical Water (anharm.; ≥ 273K) using 10 ln a H2O liquid–vapor from Rosenbaum (1997)

−3.93502E+07 −2.33424E+06

H4SiO4 vapor

CO2 vapor

CO vapor

−7.57522E+06 −2.75388E+07

Water Ice XI

−7.55686E+06

Water Ice Ih

L −5.44629E+06

Substance

H2O vapor (harm.)

160 Schauble & Young

Mass Dependence of Equilibrium Oxygen Isotope Fractionation

161

to alternative calculations using separate, mineral specific or mineral-type specific scale factors, for instance applying a ~3% correction for carbonates, 4–5% for silicates, and ~5–6% for sulfates, phosphates, and perchlorates, based on correlations of subgroups of crystals with measured spectra reported in this study. As detailed by Meheut et al. (2007), the effects of such scale factor adjustments can be estimated using an effective power law scaling, e.g. ln β(SF1)/ln β(SF2) = (SF1/SF2) p, where β are predicted 18O/16O reduced partition function ratios calculated by applying two different scale factors (SF1 and SF2) to a given set of modeled vibrational frequencies for some substance. The exponent p is expected to be slightly less than 2 for typical oxygen-bearing compounds at geochemically relevant temperatures. Alternatively, one can simply scale the temperature, because frequency and temperature always appear as a ratio in the calculation of a reduced partition function ratio; i.e., ln β(SF1) at T = T1 is equal to ln β(SF2) at T = T1(SF2/SF1). Either way, one would expect that ~1% uncertainty or scatter in frequency scale factors will lead to ~2‰ scatter in 1000 ln18/16β, given typical values of ~80–110‰ for 1000 ln18/16β at 300 K for many of the crystals in this study. Errors will be correspondingly smaller at high temperatures. This uncertainty is much larger than typical 18 O/16O measurement precisions, and is likely to be a major source of potential error in the present calculations. However, the effect of scale factor uncertainty on calculated qa–atoms is much smaller. Test calculations with varying scale factors for α-quartz, diaspore, anhydrite, and calcite indicate a typical perturbation of ~2 × 10–5 on qa–atoms when the scale factor is varied by 1%, which is a precision well beyond current measurement capabilities. This result agrees with the scaling arguments presented by Cao and Liu (2011), suggesting that the mass law exponent will be a robust product of theoretical models in the absence of large errors in the electronic structure or major anharmonic effects. Uncertainties from residual random scatter in frequencies after scaling are expected to be even smaller due to partial cancellations of errors. Another approach to estimating uncertainties stemming from using the PBE functional to calculate vibrational frequencies is to compare models using different electronic structure methods, in the expectation that both systematic and random errors will change as well. Comparisons with molecule-based and cluster models using hybrid density functional theory (e.g., B3LYP; Becke 1993) and higher-order methods such as Møller-Plesset theory (MP2; Møller and Plesset 1934) provide the most robust tests of this sort. The qa–atoms results of Cao and Liu (2011) and Haynes et al. (2018) using such methods are thus of particular value, and are discussed in detail in a later section. As an additional check, we created models of a subset of crystals (α-quartz, diaspore, anhydrite, calcite) and molecules (water vapor and carbon dioxide) using two different density functionals: the Local Density Approximation functional (as parameterized by Perdew and Zunger 1981), here abbreviated LDA, and the PBEsol gradient corrected density functional optimized for accurately reproducing lattice constants of solids (Perdew et al. 2007). Frequency scale factors are determined independently for the models using each functional, these are 3.8% for PBE (slightly different from the 4.3% scaling fitted to the whole PBE model suite), 1.6% for the LDA models, and 2.7% for the PBEsol models. The residual scatter after fitting the scale factors for the PBE and PBEsol models for these six substances is similar (rms misfit of 17 cm–1 vs. 16 cm–1 respectively). The rms frequency over the correlated modes is 962 cm–1, suggesting slightly less than 2% relative scatter, which is similar to the larger set of correlated PBE models. The residual scatter for the LDA models is slightly larger (23 cm–1). Calculated reduced partition function ratios and qa–atoms are shown in Table 7. The two gradient-corrected functionals show typical mismatches of ~1–2‰ at 300 K, consistent with the crude scale-factor based estimate above, but this test may be overly optimistic given the close theoretical relationship between PBE and PBEsol. The LDA models are more variable, with mismatches of up to 4‰. qa–atoms is much less sensitive to the choice of functional, varying by less than 5 × 10–5 between PBE and PBEsol models, and by less than 1x10–4 between PBE and LDA models.

162

Schauble & Young

Effects of sampling the phonon density of states. The potential effects of incomplete phonon sampling on reduced partition function ratios and isotopic clumping have been discussed previously (e.g., Elcombe and Hulston 1975; Schauble et al. 2003, 2006; Méheut et al. 2007). As in prior work, these effects are estimated in the present study by comparing models of a subset of crystals (α-quartz, diaspore, anhydrite, calcite, and aragonite) using a coarser phonon wave vector sampling (with roughly half as many distinct wave vectors). The test results are shown in Table 8. They show a limited dependence of 18O/16O fractionation, with less than 0.2‰ variation at 298.15 K in all cases. qa–atoms varies by no more than 5 × 10–5 in all cases. The lack of sensitivity of qa–atoms to phonon wave vector sampling suggests that adequate results can often be obtained on a sampling grid containing only one distinct wave vector, so long as it is chosen with care. The variation in calculated reduced partition function ratios with fine vs. coarse phonon wave vector grids is notably smaller than the ~1‰ variation found in previous work on rhombohedral carbonates (Schauble et al. 2006) using phonon wave vector samples of similar size. An important difference in the earlier work is that in general only one atomic position per unit cell in each crystallographic site was included in the thermodynamic calculation, whereas the present study accounts for all oxygen atoms on each unit cell through a series of one-atom isotopic substitutions. This improves convergence because the crystallographic symmetries of a lattice are commonly split along the phonon wave vector, so that (for instance) 18O substitution on one of the O(2) atomic positions in aragonite will not necessarily generate the same frequency shifts for a particular phonon wave vector as 18O substitution on another O(2) atom. As it turns out, this asymmetric response has very little effect on qa–atoms. It also has little effect on the Keq of multiply substituted isotopologues in carbonate minerals, which is the main focus of the Schauble et al. (2006) study. A re-calculation of Keq[3866] in calcite using a grid with two distinct wave vectors from the present test models indicates that the asymmetry effect might be responsible for an up to 8 × 10–6 (i.e., 8 per meg) deviation for a particular C–O bond from the average over all bonds at 25 ºC, and the failure to account for this effect may be responsible for most of the difference in the Keq values calculated with 2 wave-vector vs. 5 wave-vector grids in that study (Table 9). In fact, the re-calculated result using a 2 wave-vector sample of phonon frequencies from this study, combined with the frequency scale factor of 1.0331 from Schauble et al. (2006) and averaging over all 6 C–O bonds in the primitive calcite unit cell, yields a Keq that is within 1 per meg of the Schauble et al. (2006) 5 wave-vector sample result, despite being based on models constructed using different pseudopotentials, electronic wave vector grids, and cutoff energies. This asymmetric substitution effect is smaller than other likely sources of error considered in the Schauble et al. (2006) study (such as anharmonicity and uncertainty in the frequency scale factor), and it does not change any of the significant conclusions reached in that work. Comparison with previous determinations of 18O/16O fractionation. Although the present work is primarily concerned with the estimation of the mass dependence of oxygen isotope fractionation qa–b, comparisons with measured or previously estimated 18O/16O fractionation factors are important for two reasons. 1. First-principles models that accurately reproduce 18O/16O fractionation factors can be reasonably be inferred to predict 17O/16O with similar accuracy, and thus yield realistic qa–b. They can also be inferred to predict 18O/16O fractionation factors for materials that have not yet been experimentally or empirically calibrated. 2. 18/16aa–b is itself an important term in the conversion between qa–atoms, qb–atoms, qa–b, and ∆′17Oa–b. Calibration of 18O/16O fractionation factors has been an ongoing project of stable isotope geochemistry for more than a half-century, and there is a large literature to provide a basis for comparisons. It is beyond the scope of the present chapter to provide a comprehensive evaluation of these calibrations, and excellent compilations are available in earlier volumes of this series, e.g., Chacko et al. (2001). However, it is worthwhile to examine a subset of materials spanning as much variability in crystal structure types and chemistries as is feasible.

Mass Dependence of Equilibrium Oxygen Isotope Fractionation

163

Table 7. Comparison of reduced partition function ratios and exponents calculated with different density functionals, using frequency scale factors determined just for these six species. The PBE results are thus slightly different from the results listed above. 298.15 K

1000 ln18/16b

Substance a-quartz

qa–atoms

PBE

PBEsol

LDA

PBE

PBEsol

LDA

107.87

108.52

109.99

0.528129

0.528154

0.528176

Diaspore

89.91

91.42

93.59

0.529202

0.529158

0.529118

Anhydrite

96.40

98.27

100.20

0.528525

0.528487

0.528457

Calcite

98.83

99.96

101.67

0.528623

0.528604

0.528584 0.530035

H2O vapor

64.45

63.57

62.73

0.530030

0.530033

CO2

114.84

113.89

114.07

0.527949

0.527951

0.527945

1.23

2.71

0.000027

0.000051

RMS Misfit vs. PBE:

Table 8. Comparison of reduced partition function ratios and exponents calculated with different phonon wave vector grids. The number of distinct phonon wave vectors for each species is given in parentheses. 298.15 K

1000 ln18/16b

qa–atoms

Substance

Fine grid

Coarse grid

a-quartz (4,2)

108.70

108.69

0.528118

0.528118

Diaspore (4,2)

90.65

90.65

0.529193

0.529193

Anhydrite (2,1)

97.16

97.32

0.528515

0.528511

Calcite (5,2)

99.75

99.59

0.528609

0.528614

Aragonite (2,1)

99.16

99.20

0.528592

RMS Misfit

Fine grid

0.10

Coarse grid

0.528591 0.000002

Table 9. Comparison of calculated 13C–18O–16O–16O clumping equilibrium constants in calcite. Results are given using both the carbonate-specific 1.0331 frequency scale factor used in Schauble et al. (2006), and the general 1.043 scale factor from the present study. Average Keq(3866) with a 2 q-point phonon grid 273.15 K

298.15 K

373.15 K

573.15 K

1273.15K

Schauble et al. (2006)

1.000482

1.000403

1.000241

1.000073

1.000004

Present Study (SF 1.0331)

1.000491

1.000411

1.000247

1.000075

1.000005

Present Study (SF 1.043)

1.000500

1.000419

1.000253

1.000078

1.000005

Schauble et al. (2006)

1.000490

Average Keq(3866) with a 5 q-point phonon grid 1.000410

1.000247

1.000075

1.000005

Here we focus on species with experimental calibrations and (ideally) ongoing interest for stable isotope studies, including calcite, the silicates quartz, albite, anorthite, diopside, forsterite, and zircon, and the rare-earth element phosphate mineral monazite. These are examined in terms of 18/16aquartz–x, the fractionation relative to quartz. The sulfate minerals barite and gypsum, the phosphate mineral fluorapatite, and the carbonate minerals calcite and dolomite are compared with liquid water, using the liquid–vapor model of Rosenbaum (1997) and our anharmonicitycorrected model for H2O vapor to estimate the properties of liquid H2O. This procedure likely introduces some error—and is clearly no longer ab initio. However, the systematics of model crystal fractionations vs. liquid water will still depend on the accuracies of the crystal models relative to each other. These comparisons are shown in Figure 5.

Schauble & Young

164 2

Prese nt study

Zhe ng e t a l. (1991) Kie ffe r (1982)

2

Chiba e t a l. (1989) Cla yton and Kie ffe r (1991)

Cla yton and Kie ffe r (1991)

1000 ln a qz-ab

1000 ln aqz-zr

3

Prese nt study

Chiba e t a l. (1989)

King et a l. (2001) T ra il et a l. (2009)

3

Prese nt study

Va lle y e t a l. (2003)

4

Zhe ng (1991) M ehe ut a nd Sc ha ubl e (2014)

1

1000 ln aqz-an

5

Zhe ng (1991)

2

1

1

a-quartz - zircon 800

100 0

a-quartz - albite

0

120 0

140 0

800

100 0

T (K) Prese nt study

7

Sha rp and Kirschner (2003)

Cla yton and Kie ffe r (1991) Zhe ng (1991)

4

a-quartz - calcite

3

Chiba e t a l. (1989) Cla yton and Kie ffe r (1991) Zhe ng (1991)

4

M ehe ut a nd Sc ha ubl e (2014)

3 2 1

1 0 132 3

800

100 0

T (K)

Chang and Bla ke (2015)

15 10

283

303

323

343

25

Ze e be (2010)

Anhydrite - liquid water or sulfate(aq) - liquid water

20 15 10

Prese nt study O 'Ne il e t a l. (1969)

473

Calcite - liquid water

15

5

273

373

Northrop a nd Clay ton (1966) She ppard and S chwarcz (1977)

2.5

Horita (2014)

2

Dolomite - calcite

1.5

Prese nt study Ice I h Prese nt study Ice XI

M ajoube (1970)

20 18 16

12

0

0

Ice - water vapor

10 773

T (K)

127 3

177 3

T (K) 50

240

250

260

270

280

T (K) Prese nt study

45

1000 ln a qz-liquid/supercrit. water

E lle hoj (2013)

22

14

273

673

24

0.5

873

573

26

5

673

473

T (K)

1

473

Barite - liquid water

10

10

273

Kusak abe and Robinson (1977)

15

873

Prese nt study

3

1000 ln adol-cc

1000 ln a cc-liquid water

4

25 20

673

3.5

Kim a nd O' Ne il (1997)

140 0

Prese nt study

T (K)

35

120 0

0 273

40

100 0

20

0

363

T (K)

30

800

25

5

Apatite - liquid water 263

a-quartz - monazite

Chiba e t a l. (1981)

1000 ln a ba-liquid water

Kolodny et a l. (1983)

0

3

600

Ha la s a nd Pluta (2000)

1000 ln a anh-liquid water

1000 ln a fap-liquid water

Pucéa t e t al. (2010)

5

4

0

140 0

Prese nt study

30

Longi ne lli and N uti (1973)

20

Ble ec ke r and S ha rp (2007)

5

T (K)

35

Ve nne ma n et a l. (2001)

25

Prese nt study

6

T (K) Prese nt study

30

120 0

1000 ln a ice-vap

35

140 0

7

1

a-quartz - forsterite

0 823

120 0

2

2

323

100 0

T (K) Prese nt study

5

1000 ln a qz-fo

1000 ln aqz-cc

6

Chiba e t a l. (1989)

5

a-quartz - K-feldspar 800

140 0

T (K)

8

6

0

120 0

1000 ln a qz-mo

0

Sha rp and Kirschner (1994)

40 35 30

a-quartz - liquid water

25 20 15 10 5 0 200

400

600

800

100 0

T (K)

Figure 5. Comparison of calculated 18O/16O fractionation factors with previous experimental and theoretical studies. The models for anhydrite and fluorapatite are also compared with previous calibrations of the dissolved sulfate–water fractionation (Zeebe et al. 2010; Halas and Pluta 2000) and the dissolved phosphate– water fractionation (Chang and Blake 2015).

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Experiments and empirical (field-based) calibrations of oxygen isotope fractionation between quartz and calcite give varying results—the empirical study of Sharp and Kirschner (1994) finds fractionation twice as large as a laboratory calibration (Clayton et al., 1989). The present models closely track the empirical calibration of Sharp and Kirschner (1994). It should be noted, however, that at least some other silicate–calcite fractionations show good agreement with direct exchange experiments, for instance phlogopite–calcite (−1.5‰ vs. −1.7‰ at 750 ºC; Hu and Clayton 2003), and it should also be noted that the quartz– calcite fractionation predicted by Hayles et al. (2018) is intermediate between the Sharp and Kirschner (1994) and Clayton et al. (1989) calibrations. Fractionations among silicate minerals show reasonably good consistency with experimental and empirical calibrations, particularly for quartz–albite, quartz–anorthite, quartz–forsterite, and quartz–diopside, which all remain within 0.2–0.3‰ of tabulated experimental calibrations (Chiba et al. 1989, Clayton and Kieffer 1991) above 600 ºC. Previous calibrations of the quartz–zircon fractionation are more variable, with theoretical estimates tending to predict larger fractionations than are observed. The present model behaves similarly, apparently overestimating the fractionation by 0.4–0.8‰ at 600 ºC—and is in fact remarkably similar to a much earlier theoretical prediction of Kieffer (1982). Qualitatively, the present model is reasonable even for this mineral pair, but it is conceivable that a slightly higher frequency scale factor would be appropriate to consider for zircon, as suggested by both the overestimated quartz–zircon fractionation and the Raman and IR correlations for zircon. Quartz–monazite fractionations measured by Breecker and Sharp (2007) are in good agreement with the present models. Mineral–water fractionations for phosphates, sulfates, and carbonates likewise generally show reasonable agreement with experiment, as has been found previously for similar types of models (e.g., Schauble et al. 2006; Meheut et al. 2007). The present models appear to underestimate sulfate–water and phosphate–water fractionations by up to 4‰ from 273–423 K. Interestingly, a model of meridianiite, Mg(H2O)6∙SO4∙5H2O, which contains fully solvated SO42– molecules, runs very close to previous calibrations of the aqueous sulfate–water fractionation (Halas and Pluta 2000; Zeebe 2010), falling within 1‰ of the both calibrations from 273–423 K. Our models closely match experimentally determined calcite–water and dolomite–water calibrations (e.g., O’Neil et al. 1969; Kim and O’Neil 1997; Horita 2014). The present results also match some previous dolomite–calcite fractionations well (e.g., Northrop and Clayton 1966; Sheppard and Schwarcz 1970) with greater disagreement with Horita (2014). Calculated fractionations between water ice and vapor (using the harmonic vapor model) are considerably larger than measurements (e.g., Majoube 1970; Ellehoj et al. 2013), by ~5‰ at 273 K. Note that using anharmonically corrected values for vapor would worsen the mismatch (by ~3–4‰ at 273 K). The present estimates are in reasonable agreement with a previous model using similar DFT parameters, however (Meheut et al. 2007), suggesting that this is a systematic error for the theoretical method. This misfit may in part be consistent with the underestimation of lattice constants for ice crystals by the PBE functional, in that both suggest that the hydrogen bonding network of ice is not reproduced as accurately as other bond types. Relatively poor descriptions of hydrogen-bonding interactions in water vapor clusters, liquid water, and ice are a well-known defect of DFT methods (e.g., Gillan et al. 2016), and it should perhaps not be surprising that this is one case where the methods used in the present chapter are less accurate. In contrast, the estimated fractionation between liquid water (using the harmonic model of water vapor and the liquid–vapor fractionation from either Rosenbaum 1997 or Horita and Wesolowski 1994) and the water of hydration of gypsum is within 1‰ of experiments and empirical calibrations (Gazquez et al. 2017; Herwartz et al. 2017), with ~4‰ higher 18O/16O in hydration water at ~20 ºC, and a temperature sensitivity of roughly −0.01‰/ ºC. This agrees with another recent theoretical result (Liu et al. 2019) using a similar type of model based on the PBEsol functional.

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Comparison with previous determinations of  qa–b and  qa–atoms. Much less is known about equilibrium deviations from the canonical mass-fractionation relationship than about 18O/16O fractionation factors. In this section the available theoretical, experimental, and empirical calibration data are compared to our present results. In general, comparison of qa–b with experimental data depends on qa–atoms, qb–atoms, and 103 ln18/16aa–b = 103 ln18/16ba − 103 ln18/16β b. The last term has just been discussed, with generally good agreement between model results and calibration, but suggesting some reason for concern that fractionations involving water will have modest systematic error. High-precision calibrations of θ have now been published for silica vs. liquid water, gypsum water vs. liquid water, and liquid water vs water vapor (Barkan and Luz 2005; Sharp et al. 2016; Gazquez et al. 2017; Herwartz et al. 2017). Theoretical calibrations for these and other systems have also been calculated recently by other authors (e.g., Cao and Liu 2011; Hayles et al. 2018). We compare these in turn (Fig. 6). In general, there is excellent agreement between the present results and those of Hayles et al. 2018, and reasonably good agreement with Cao and Liu (2011). This general agreement is consistent with the error analysis of Cao and Liu (2011), which demonstrated that theoretical estimates of qa–atoms, in particular, are relatively robust even for simplified models. The most extensive comparison sets come from Cao and Liu (2011) and Hayles et al. (2018). In the earlier work, qa–atoms (reported as κ, in their notation) is estimated for CO2, CO, H2O, and H6Si2O7, as well as for gas-phase CO32– and molecular clusters mimicking the structure of carbonate and silicate mineral structures. Cao and Liu (2011) mainly use hybrid density functional theory (B3LYP; Becke 1993) to estimate vibrational frequencies in their calculations. This method is closely related to the PBE functional used the present work—both are substantially based on gradient-corrected density functionals—but B3LYP incorporates a component of exact electron exchange. The exact exchange component of B3LYP is not as easily adapted to systems with periodic boundary conditions as pure density functionals such as PBE or BLYP, and so the calculations in Cao and Liu (2011) are limited to isolated atoms, molecules, and clusters, using atom-centered basis sets rather than the pseudopotential+plane wave basis set method applied here. However, a significant potential advantage for B3LYP is that it is typically observed to reproduce vibrational frequencies, molecular structures, and thermodynamic properties somewhat more accurately than PBE; for harmonic vibrational frequencies and zero point energies the scale factor for B3LYP is close to unity for typical molecular benchmark comparisons (e.g., Kesharwani et al. 2014; Alecu et al. 2010—updated at https://t1.chem.umn.edu/freqscale/index.html), and no scale factor is applied by Cao and Liu (2011) to their model calculations. However, the residual misfit after scaling, compared to harmonic frequencies inferred from spectroscopic measurements, is similar for both methods (e.g., Kesharwani et al. 2014). So cross-comparing results between the two studies is likely to give useful information about the reliability of both methods. Typical mismatches are ~5 × 10−5 or less for the small gas-phase molecules CO, CO2, and H2O, with somewhat larger mismatch of up to 2 × 10–4 for the bridging oxygen in vapor-phase disilicic acid H6Si2O7, and similar disagreements between calcite with CO32–(v), and anorthite with H6SiAlO7–. The relatively large mismatch between the present calcite model and the “calcite” result from Cao and Liu (2011) comes mainly from their proposed crystal–vapor correction to the gas-phase carbonate model. The close overall correspondence suggests that both model approaches are sufficiently accurate to be useful. The good match between molecules and crystals with similar bonding configurations around oxygen also suggests that a “building block” approach analogous to the methods developed for predicting 18O/16O fractionation by e.g. Garlick (1966) and Zheng (1991) will be even more well suited to predicting or rationalizing the mass dependence exponents, so that signatures in complex, incompletely characterized, and amorphous materials can likely be anticipated on the basis of simpler, better studied crystals and molecules.

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Figure 6. Comparison of calculated qa–b and ∆′17O with previous experimental and theoretical studies in the quartz–water (a) and calcite–water (b) systems. For each system, the first row of three panels shows the exponent as a function of temperature over a wide and narrow (low) range, and also a function of the equilibrium 18 16 O/ O fractionation. The irregular (hyperbolic) behavior of qcalcite–liquid water at ~700 K reflects a change in sign of the calcite–water fractionation factor. Three variant models for qliquid water–atoms from the present study are used, based on either qliquid water–water vapor=0.529 (Barkan l − v; Barkan and Luz 2005), the average of qwater vapor–atoms and qice-Ih–atoms (50% ice model), or the lesser of qwater vapor–atoms and the Barkan l − v exponent. Calibration references: Sharp et al. (2016), Cao and Liu (2011), and Hayles et al. (2018). The y-axis units are per meg.

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Hayles et al. (2018) focus on crystals and liquid water, mainly using a cluster-based method and hybrid density functional theory to estimate 18O/16O fractionation factors and qa–atoms. Many of the same crystals are modeled here, and in general the agreement is remarkably good, with a deviation in qquartz–atoms of about 1 × 10−4 (at 273–373 K, then converging at higher temperatures), and deviations < 2 × 10–5 for qcalcite–atoms, qdolomite–atoms, qfluorapatite–atoms, and θH2O vapor–atoms at 273 K and above. Calculated 18O/16O fractionations also generally agree, with the largest differences found for calcite and quartz at low temperatures. The present models predict ~1–1.5‰ higher ln18/16β for α-quartz over the 273–373 K temperature range, and 1.5–2.8‰ lower ln18/16β for calcite. Dolomite, fluorapatite, and water vapor models all agree within ~1‰ at temperatures ≥ 273 K. The overall magnitude of disagreement is similar to that observed between PBE and PBEsol-based models. There is at most a small systematic offset for the present PBE, periodic boundary condition models versus the Hayles et al. (2018) B3LYP, cluster models; the mean (signed) deviation in ln18/16β for the set of quartz, calcite, dolomite, fluorapatite, and water vapor is 0.1‰ or less above 273 K. The silica–water system has been studied empirically (Sharp et al. 2016), as well as with theoretical models, showing negative ∆′17O in SiO2 precipitates that is most pronounced in low temperature silica samples. All of the published theoretical models agree with the general trend of decreasing ∆′17OSiO2 and qSiO2–liquid water in low temperature samples. In detail, the models appear to underestimate the deviation from the 0.528 exponent somewhat, particularly at the lowest temperatures, only reaching as low as qSiO2–liquid water ≈ 0.524 vs. 0.523 and D′17OSiO2 ≈ –150 to –160 per meg vs.−180 to –190 per meg near 273 K. Note that the deviations in qSiO2–liquid water at high temperatures in some models may be misleading, because they are highly sensitive to small changes in the 18O/16O fractionation factor and θ liquid water–atoms that are difficult to resolve in measurements. The overall comparison suggests that these types of models will be useful guides to the behavior of ∆′17O and qmineral water as a function of temperature, potentially even in low temperature samples where it is not obvious that exchange equilibrium is obtained. The 17O systematics of the water of hydration of gypsum has become a focus of interest in hydrological studies in arid climates. Gazquez et al. (2017) recommend qgypsum water–parent brine = 0.5297 ± 0.0012. In a set of re-hydration experiments equilibrated at 21 ºC, Herwartz et al. (2017) find qgypsum water–parent brine = 0.5272 ± 0.0019, and they recommend a compromise value of 0.5286. Our models predict qgypsum water–liquid water ≈ 0.528 at 25 ºC, in good agreement with measurements. Our calculated qgypsum water–liquid water is consistently about 0.001 lower than the model calculations of Liu et al. (2019), though it is difficult to pinpoint the cause of the difference, and both results are consistent with measurements, given their uncertainties. A system of great potential interest in future work is CaCO3–liquid water, including both calcite and aragonite polymorphs of calcium carbonate. Although a number of measurements have been reported (e.g., Passey et al. 2014), it is difficult to convert these into a calibration vs. temperature. Initial results for calibration studies are beginning to appear in the literature (e.g., Wostbrock et al. in press; Voarintsoa et al. 2020; Bergel et al. 2020). The theoretical models of Hayles et al. (2018) and the present study are show excellent agreement; the adjusted, CO32–(v)-based model of Cao and Liu predicts lower qcarbonate–liquid water than the other two models, but their unadjusted CO32–-based model is closer to the more recent theoretical results. The overall trend vs. temperature in qcarbonate–liquid water is similar in all models. The models are also generally in agreement with low ∆′17O observed in carbonate minerals (e.g., Passey et al. 2014), and in reasonable agreement with the qcarbonate–liquid water results of Wostbrock et al. (2020) (0.525–0.526 at 0 ºC vs. 0.5251 in the present study, 0.5250 in Hayles et al. 2018, and 0.5253 in Guo and Zhou 2019). However, Voarinstsoa et al. (2020) and Bergel et al. (2020) measured a somewhat lower exponent (qcarbonate–liquid water ≈ 0.520–0.523 at 283–308 K).

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A final set of comparisons comes measurements of θ in higher-temperature systems, including tabulations aimed at finding a universally applicable mass fractionation exponent for silicate rocks (e.g., Rumble et al. 2007), including lunar samples (e.g., Young et al. 2016). As pointed out by Cao and Liu (2011), typical values in the range of 0.525–0.528 found in these compilations are broadly consistent with silicate–water fractionations at moderate–elevated temperatures, coinciding for instance with qquartz–water at temperatures from ~350–850 K. However, they are markedly at odds with the discovery of measurable ∆′17O of several per meg in feldspars and quartz from high-temperature rocks, including lunar and terrestrial anorthosites (Young et al. 2016). The characteristically low ∆′17O of feldspar-rich rocks, by ~10 per meg relative to related olivine and/or pyroxene-rich rocks, cannot be easily explained in the framework of the Urey (1947) harmonic oscillator theory of stable isotope fractionation, by nuclear field shift effects, or even by more exotic models such as the double-well potential. Taken together, these comparisons indicate that theoretical models, even highly simplified ones, provide a useful guide to actual 18O/16O fractionations and θ, though direct testing is still limited to a few materials. General properties of ∆′17O in crystals relative to water vapor. Cao and Liu (2011), Dauphas and Schauble (2016), and Hayles et al. (2018) have shown that the variation in qa–atoms with changing chemical structure is highly systematic, moving below the high-temperature harmonic limit of ~0.5305 most strongly at low temperatures in materials with high force constants and relatively high-mass bond partners for oxygen. High force constants and relatively high-mass bond partners also correlate strongly with preferential incorporation of oxygen with high 18O/16O, so it is not surprising to find correlation between 18O/16O fractionation factors and deviations in ∆′17O in systems approaching equilibrium. The present results are also consistent with these principles. For instance, the low mass of hydrogen means that the mass fractionation exponent qwater vapor–atoms stays close to the high-temperature limit even at Earth surface conditions, and this property largely carries over to liquid water and ice, which will have 0–20 per meg higher ∆′17O than vapor at temperatures from 243 K (−30 ºC) up to the critical point. This observation is important because many of the most promising geochemical applications of high-precision ∆′17O measurements are in mineral–water systems. Theoretical studies (e.g., Cao and Liu 2011; Hayles et al. 2018; and the present work) also find that the range of ∆′17O between different mineral/mineral and mineral/molecule pairs is predicted to decrease quickly at equilibrium as temperature increases towards hydrothermal, metamorphic, and igneous conditions. However, the choice of reference exponent becomes relatively important at elevated temperatures. At 773 K (500 ºC), the largest inter-phase ∆′17O will be less than 10 per meg (e.g., 9 per meg for the forsterite–water vapor pair), relative to a 0.528 reference exponent, but could be greater than 20 per meg if the high-temperature equilibrium limit exponent of 0.53052 is the reference (where CO is a fractionating phase). Using the 0.528 reference, the range only slightly decreases to ~8 per meg at 1273 K (1000 ºC), but the range is less than 5 per meg at this temperature if the 0.53052 high-temperature limiting exponent is used instead. To illustrate these systematic behaviors, we have plotted the difference in ∆′17O vs. 103 ln18/16aa–water vapor for a sample of the crystal types studied. Although there is substantial scatter, the systematic correlation in behavior of these two fractionation properties is clear (Fig. 7). Within the silicate mineral class (and especially for anhydrous silicates), strong 18 O/16O fractionation is strongly correlated with negative ∆′17O, becoming most pronounced in structures with the highest Si:O ratios, such as quartz and alkali feldspars. Interestingly, hydrous Mg–Si–O–H silicates follow a similar trend of ∆′17O vs. α. Among the anhydrous silicates studied, high Si:O corresponds to higher polymerization, whereas among the hydrous silicates high Si:O corresponds to lower polymerization because of Al:Si substitution into tetrahedral sites and increased OH concentrations in sheet silicates. The similar predicted ∆′17O of kaolinite and lizardite indicates that tetrahedrally coordinated cations in silicates mainly

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Figure 7. Calculated deviations of ∆′17O from water vapor at equilibrium from 243–1573 K. a) anhydrous silicate minerals and molecules. b) hydrous silicate minerals, diaspore, and spinel. c) carbonates and nitratine. d) phosphates. e) sulfates. f) CO2, CO, and sodium perchlorate. g) ice, liquid, and supercritical water. Unless otherwise specified, intermediate tick marks are given at 273 K, 373 K, 473 K, 573 K and 673 K on panels b–g. The same alpha-quartz data is shown in panels a–f, as a guide to the eye. The y-axis units are per meg.

control deviations from the reference fractionation exponent even though sites coordinated to octahedral Al3+ have a significantly higher affinity for 18O (and 17O) than sites coordinated to Mg2+. Divalent metal carbonates show the importance of strong, low-coordination cation-oxygen bonds in controlling ∆′17O even more strikingly, and it is possible to draw isothermal tie-lines at nearly constant ∆′17O from aragonite and calcite through magnesite, spanning 10‰ in 18O/16O but only a few per meg in ∆′17O at 273–373 K. In these crystals the strongest bonds are always internal to the carbonate group, and relative 18O/16O fractionation is controlled by weaker X2+–O bonds characterized by low vibrational frequencies that do not affect the exponent as strongly. This behavior suggests that details of cation chemistry in

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mixed-composition carbonates may not be very important for interpreting ∆′17O signatures. Nitratine, with a different trigonal oxyanion (NO3–) and even weaker inter-molecular Na+–O bonds, closely resembles its crystallographic cousin calcite. Phosphates show a similar nearinvariance of ∆′17O versus crystal chemistry, as do sulfates (excepting the water of hydration of gypsum). Silicate, phosphate, sulfate, and perchlorate crystals with the ZTetO4 structural formula, including zircon, monazite, xenotime, barite, anhydrite, and NaClO4, all show similar ∆′17O vs. water vapor at a given temperature, relative to the 0.528 reference line, echoing the similarity noted above for ZTriO3 carbonate and nitrate minerals. ∆′17O vs. 18O/16O fractionation relationships for silicates, sulfates, phosphates, carbonates, nitrates, and perchlorates relative to liquid (or supercritical) water and water vapor follow a characteristically concave-down trajectory as temperature decreases. This characteristic relationship suggests that ∆′17O relative to water could be crudely predicted even for crystals that have not be explicitly modeled, via comparison to other minerals of similar type. For silicates, in cases where ln18/16amineral–water can be reasonably well constrained, simply applying the ∆′17O vs 18/16aquartz–water relationship may be sufficient to give a useful approximation to the actual system of interest. There is no indication that the apparent ~10 per meg deviations between different silicate phases found in lunar and terrestrial igneous rocks can be explained by equilibrium inter-mineral fractionation (Fig. 8). As an illustration, we compare the results obtained here with the hightemperature rock data in Figure 1. While the trend of lower ∆′17O for quartz and feldspar relative to olivine and spinel is common to the data and the calculations, the magnitudes are entirely different. The calculations predict quartz and feldspar ~1 to 3 per meg lower in ∆′17O than olivine, at most, at magmatic temperatures while the data exhibit differences ten times larger. 7 973 K

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SUMMARY ln β and θ (and by extension ∆′17O relationships at equilibrium) have been estimated for a variety of silicate, phosphate, sulfate, and carbonate minerals, as well as for representative nitrate, perchlorate, oxide, hydroxide, and ice crystals using first-principles electronic structure models. The results are generally in good agreement with previous studies of fractionation factors and mass-fractionation exponents, including both theoretical work and measurements. The nuclear volume component of the field shift effect is shown have a minor 18/16

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or insignificant influence on fractionation and θ. A reconnaissance exploration of fractionation in an anharmonic, double-well potential does not find evidence for the generation of large ∆′17O effects, at least for the most chemically plausible potential shapes. None of the results provide a convincing explanation for ~10 per meg ∆′17O signatures observed in polymerized silicates in high-temperature terrestrial and lunar rock samples.

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Reviews in Mineralogy & Geochemistry Vol. 86 pp. 179–196, 2021 Copyright © Mineralogical Society of America

Standardization for the Triple Oxygen Isotope System: Waters, Silicates, Carbonates, Air, and Sulfates Zachary D. Sharp, Jordan A.G. Wostbrock Department of Earth and Planetary Sciences University of New Mexico Albuquerque, NM, 87131 USA [email protected]

INTRODUCTION Stable isotope analyses are a relative measurement. The precision is far higher than the accuracy, so that subtle isotopic differences must be made relative to a reference. Modern mass spectrometers can routinely measure the δ18O value of a gas with a precision of 0.01‰. This is 20 times more precise than the accuracy of the 18O/16O ratio of VSMOW (Baertschi 1976). It is for this reason that isotope analyses, like most analytical measurements, are reported relative to standards. The problem faced by the stable isotope community is that different materials are measured using different techniques, and direct comparison between them is difficult. Heroic efforts have been made to align the different types of analyses to the same scale, so that data collected on different materials in different laboratories can be directly compared. For traditional δ18O analyses, coalescence around common standards took decades. Triple oxygen isotope studies (δ18O and d17O) of terrestrial materials is a relatively new discipline, and agreement on standardization is only recently achieving a high level of conformity. In this chapter, we first consider the historical path towards standardization for the well-established 18 O/16O ratios. Then the extension to standardization to 17O/16O is discussed with a goal of presenting a uniform set of standard values for commonly used reference materials. There was a time when stable isotope standards didn’t exist. Consider the classic paper by Dole (1936), in which he determined the oxygen isotope composition of air relative to water. “The atomic weight of oxygen in air is 0.000108 atomic weight units heavier than Lake Michigan water”. This was a high precision analysis, considering that it was determined by density measurements, but it was far lower precision than what is achievable using modern extraction methods and modern mass spectrometers. Precise determinations of relative isotopic differences only began in earnest in the 1950s following the development of a dual inlet mass spectrometer (McKinney et al. 1950) under the direction of Harold Urey. Urey’s desire to develop a carbonate paleothermometer necessitated highly precise oxygen isotope analyses in order to obtain temperature estimates in the 1 °C range. This led to the University of Chicago group creating what is essentially the modern high precision mass spectrometer (McKinney et al. 1950). McKinney’s mass spectrometer measured the ratios of the voltages of 18O/16O of a sample gas relative to a reference gas using a set of changeover valves that allowed for rapid switching between the two gases. This reduced errors associated with the inevitable drift of the sensitive electronics. The 18O/16O ratios were presented by McKinney in what is now the ubiquitous delta notation in per mil units as R  18  O  sa  1 1000 R  std  1529-6466/21/0086-0005$05.00 (print) 1943-2666/21/0086-0005$05.00 (online)

(1) http://dx.doi.org/10.2138/rmg.2021.86.05

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In more general terms, delta is given by  18 O

Rsa 1 Rstd

(2)

and indeed, early hydrogen isotope measurements were given in % (e.g., Friedman 1953) rather than per mil and recent publications have presented Δ′17O values in parts per million (ppm or per meg). In this contribution, all additional equations (e.g., Eqn. 7) and delta values are given in terms of Equation (1). While it is generally assumed that the first measurements of oxygen isotope ratios were made on CO2 gas, interestingly, McKinney’s original mass spectrometer was used for measuring both the isotope ratios of CO2 (the ratio C16O18O/C16O2) and O2 (16O18O/16O2) gas. Today, O2 gas is the primary analyte for triple oxygen isotope analyses in order to be able to measure the d17O value. It is perhaps surprising to see that, from the very beginning, O2 gas was considered as a viable gas for the classic dual-inlet mass spectrometer. Some of the first high-precision measurements were made by Epstein et al. (1951, 1953) on natural waters and carbonates, which led to the carbonate–water oxygen isotope thermometer. Their paleotemperature equation is given as t ( °C) = 16.5 − 4.3 δ + 0.14 δ2

(3)

In this equation δ is the difference in the δ18O value of CO2 (in per mil) produced by reaction of carbonates with 100% phosphoric acid and the working standard CO2 gas. The reference gas was CO2 produced by the reaction of Belemnitella americana from the Peedee formation of South Carolina (Urey et al. 1951). They did not measure the δ18O values of either the water or the carbonate—only the small difference between the CO2 gases obtained by decarbonating the calcite and equilibrating CO2 with water, respectively. As long as their temperature equation was calibrated to their own internal reference gas, they would encounter no problems. Silverman (1951) measured the oxygen isotope composition of silicate rocks. The reference gas he used in all analyses was oxygen derived from quartz from the Randville pegmatite (Randville, Michigan, USA). In setting the standard for future measurements, he adjusted all of his silicate analyses to Hawaii seawater, with an arbitrary δ18O value of 0‰. (Hawaii seawater is 0.17‰ heavier than SMOW, Epstein and Mayeda 1953). Presumably Silverman fluorinated his water sample to quantitatively extract oxygen (Baertschi 1950). In those early years the different laboratories had good communication, and the standards were commonly exchanged for cross-comparison. At the Caltech laboratory, for example, Potsdam sandstone was the unofficial internal standard for years (Clayton 1959; Taylor and Epstein 1962) and was calibrated relative to Hawaiian water and, later, mean ocean water. As the number of stable isotope laboratories grew, it became increasingly imperative to develop a coordinated intercalibration so that the data from all labs could be compared with one another. Harmon Craig published a detailed presentation of stable isotope standards, combining existing standards from the University of Chicago laboratory with samples from the newly created National Bureau of Standards, NBS (Craig 1957). These included the NBS Solnhofen limestone and NBS 1 (water from the Potomac River, Maryland, Fig. 1). The oxygen isotope values of carbonates were reported relative to the PDB carbonate standard, whereas waters were reported relative to the NBS 1 water standard. Craig later defined the average ocean water (mean ocean water of Epstein and Mayeda 1953) in terms of NBS 1, giving the relationship  18 O   18 O   1.008   16   16   O SMOW Standard Mean Ocean Water   O  NBS1

(4)

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NBS 1 was distributed widely by the National Bureau of Standards and could be used for interlaboratory calibration. Later, Harmon Craig collected, distilled and adjusted ocean water at the request of the International Atomic Energy Agency (IAEA) to match the original SMOW so that it conformed to the definition in terms of NBS 1 (Craig 1961). The new reference material was called VSMOW (shortened from Vienna SMOW—Fig. 2) to distinguish it from the original SMOW (Gonfiantini 1978). At the same time, a second light water standard, SLAP (for Standard Light Antarctic Precipitation) was developed, allowing for laboratories to have two different water standards with δ18O and δD values that were far apart. The δ18O and δD values of VSMOW, by definition, are 0‰. Although not envisioned at the time, by analogy the δ17O value is also 0‰. SLAP has a δ18O value of −55.5‰ and a δD value of −428‰. There is some indication that the actual value of SMOW may be closer to −56.18‰ (Verkouteren and Klinedinst 2004). We will stick with the IAEA convention of −55.5‰ for SLAP and SLAP2 (IAEA 2006, 2017). An intermediate standard GISP (Greenland Ice Sheet Precipitation) has a δ18O value of −24.76‰ and a δD value of −189.5‰ (IAEA 2006). GISP is now discontinued and has been replaced with GRESP with a δ18O value of −33.39‰ and δD value of −257.8‰ (IAEA 2020) The absolute values for the 18O/16O and D/H ratios of VSMOW are 2005.20 ± 0.45×106 and 155.76 ± 0.05×10−6 (see compilation in Table 2.5 of Sharp 2013).  



 )LJXUH

Figure 1. Unopened sealed vial of NBS 1.

Figure 2.

Figure 2. The SMOW-1 standard (VSMOW). Why, if it is not to be moved, does it have handles? [USGS Public Domain].

Two formally adopted carbonate standards followed (Friedman et al. 2007). The first, NBS 19, essentially replaced PDB as the benchmark marine carbonate value, while the second, NBS 18, is a carbonate of igneous origin which has a lower δ18O value, much closer to that of the mantle. The δ18O and δ13C of NBS 19 are defined as δ18O ≡ −2.20‰ and δ13C ≡ +1.95‰ (where ≡ indicates that these values are exact by definition to the VPDB scale). NBS 19 is no longer available and has been replaced by IAEA 603 with δ18O ≡ −2.37‰ and δ13C ≡ +2.46‰ (Assonov et al. 2020). The relationship between VPDB and VSMOW is given by the equation (Kim et al. 2015) δ18OVSMOW = 1.03092 δ18OVPDB + 30.92

(5)

updated from the long-used equation (Coplen et al. 1983) δ18OVSMOW = 1.03091 δ18OVPDB + 30.91

(6)

As we will see, the difference between these two equations is significantly less than the total uncertainties in the fractionation factors necessary to construct them.

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Equation (5) allows a comparison of the δ18O values of waters reported to the VSMOW scale with carbonates reported to the VPDB scale. Silicates are also anchored to the VSMOW scale by the quartz sand reference material NBS 28, a sand donated by Corning Glass Co. Friedman and Gleason (1973) introduced this standard and determined its δ18O value relative to VSMOW by fluorinating both the quartz and VSMOW to quantitatively extract O2, which was then converted to CO2 for isotopic analysis. Their measured δ18O value for NBS 28 was 10.0‰ ± 0.12 (2σ). Friedman and O’Neil (1977) presented a range of published δ18O values for NBS 28 of 9.5 to 9.9‰ from different laboratories (the IAEA reference sheet for NBS 28 presents a literature range of 8.8 to 10.0‰). There is clearly uncertainty in the δ18O value of NBS 28 relative to VSMOW. This illustrates one of the most fundamental problems facing the triple oxygen isotope community with regards to standardization—intercalibrating reference samples that are traditionally measured using different methods tied to different standards.

INTERCALIBRATING WATERS, CARBONATES AND SILICATES FOR d18O In order to report the δ18O values of different materials relative to each other, it is critical to have all types of phases calibrated to the same standard. The problem is that the methods for analyzing carbonates, water, and silicates are completely different. Waters are generally analyzed by equilibration with CO2 gas which is then measured on the mass spectrometer (although laser spectroscopy methods are now commonly employed, e.g., Steig et al, 2014); carbonates are reacted with phosphoric acid to produce CO2; silicates are fluorinated to quantitatively produce O2. The results from these three methods are not directly comparable and require a correction factor to bring them into agreement. As explained below, the errors in these correction factors are far larger than the uncertainty of the analyses themselves.

Water The standard method for analyzing the δ18O value of water was developed by the biochemist and National Medal of Science recipient Mildred Cohn and Nobel laureate coauthor Harold Urey over 80 years ago (1938), and is used today virtually unchanged. A trace amount of CO2 is added to the water sample. The mixture is held at a constant temperature (generally 25 °C) for hours to days in order to allow the two phases to come into oxygen isotope equilibrium. The CO2 is removed from the reaction vessel, purified and measured on the mass spectrometer. Although there is a large fractionation between the water and CO2 gas, as long as there is a large excess of H2O and the equilibration process is performed using identical protocol at constant temperature, the isotope fractionation between the equilibrated water and CO2 gas should be constant. Epstein and Mayeda (1953) compared the δ18O values of many natural waters relative to the average of deep marine waters from the different oceans. All of their data were therefore relative to MOW (mean ocean water). This ultimately led to the formation of the SMOW and later VSMOW and still later VSMOW2 standards. The isotopic fractionation between CO2 and water is given by  CO2  water 

1000  18OCO2 1000  18O water

(7)

This is thought to be an equilibrium fractionation (unlike the acid digestion of carbonates—see below). It therefore can be determined theoretically as well as experimentally. Theoretical determinations give aCO2–water values of 1.042 (Urey and Greiff 1935), 1.039 (Urey 1947) and 1.0411 (Bottinga and Craig 1969). The difficulty in making this calculation is in the complexity of structure of liquid water in comparison to simple diatomic gaseous species from a statistical mechanical perspective (Cao and Liu 2011; Hayles et al. 2018).

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Experimental determinations of the alpha value for Equation (7) require a quantitative conversion of H2O to CO2 so that the δ18O value of the CO2 derived from the H2O can be compared directly to the CO2 equilibrated with the water. At least nine experimental determinations of the aCO2–water fractionation at 25 °C have been made using a variety of different methods based on carbon reduction or fluorination (see Brenninkmeijer et al. 1983 for a summary). The aCO2–water values range from 1.0407 to 1.0424 (Fig. 3) and have a standard deviation in the α values that corresponds to a 1σ uncertainty in the δ18O value of ~0.4‰. The general consensus is that aCO2–water = 1.0412 (Friedman and O’Neil 1977; Kim et al. 2015). 1.6‰

3 2

1.0425

1.0423

1.0421

1.0419

1.0417

1.0415

1.0411

1.0413

0

1.0409

1 1.0407

n

1000lna (CO2-water)

Figure 3. Published estimates of experimental αCO2–water. From (Friedman and O’Neil 1977; Brenninkmeijer et al. 1983).

Carbonates The method for analyzing carbonate, like water, is also an indirect measure. Developed by John McCrea (1950) as part of Urey’s project to develop a paleotemperature scale, calcite (and later other carbonates) is reacted with 100% phosphoric acid at a controlled temperature. The reaction liberates CO2 gas, which is purified and analyzed on the mass spectrometer. As is the case for CO2–water equilibration, the δ18O value of the evolved CO2 gas is not equal to that of the actual carbonate. It is offset by the acid-liberated CO2–calcite fractionation. By reacting all samples in controlled, repeatable conditions, the δ18O values of the CO2 from different samples can be compared relative to each other. Acid digestion of carbonates liberates only 2/3 of the total oxygen. The isotope fractionation during this process is the aCO2(ACID)–carbonate value. It is worth pointing out that the aCO2(ACID)–carbonate value is not the same as the aCO2–carbonate value. The latter is the equilibrium oxygen isotope fractionation between CO2 gas and the carbonate, while the former is not (Guo et al. 2009). The equilibrium α(18O/16O)CO2–calcite value is between 1.0014 and 1.0119 (O’Neil and Epstein 1966b; Bottinga 1968), over 1‰ greater than the average aCO2(ACID)–calcite value. The aCO2(ACID)–carbonate value is therefore determined experimentally, and can only be quantified and tied to the VSMOW scale if the δ18O value of the total carbonate is known. This is determined by quantitatively extracting 100% of the oxygen from a sample by high temperature fluorination (e.g., Sharma and Clayton 1965). The extracted O2 is then converted to CO2 by high temperature reaction with a graphite rod. Comparison of this CO2 gas with the CO2 liberated by reaction of the same carbonate by phosphoric acid gives the aCO2(ACID)–carbonate value. There have been five independent determinations of this value (see Kim et al. 2015 Table 2 for compilation). They range from aCO2(ACID)–calcite = 1.01015 to 1.01058 (average is 1.01036 ± 0.00017), corresponding to an uncertainty of 0.18‰ (1σ). The generally accepted aCO2(ACID)–calcite value at 25 °C is 1.01025 as determined by Sharma and Clayton (1965) and amended by Friedman and O’Neil (1977).

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Silicates Silicates were first analyzed with high precision using the method of fluorination (Baertschi and Silverman 1951; Silverman 1951). Unlike the techniques for carbonates and water, the fluorination method is quantitative in the sense that 100% of the oxygen in the silicate is released by the fluorination reaction. The early studies measured the 18O/16O ratios of the O2 gas produced by the fluorination (Baertschi and Silverman 1951). Most laboratories subsequently added a combustion step where O2 was quantitatively converted to CO2 by high temperature reaction with spectroscopic graphite in the presence of a Pt catalyst (Taylor and Epstein 1962). CO2 could be purified more easily and moved throughout a vacuum line by freezing with liquid nitrogen. It is ironic that, after more than a half a century of analyzing silicate oxygen in the mass spectrometer using CO2 as the analyte, we have returned to analyzing O2 gas in order to also obtain the 17O/16O ratios of samples. There are two IAEA silicate standards: NBS 28 (quartz) with a defined δ18O value of 9.57‰ and NBS 30 (biotite) with a δ18O value of 5.12‰ (https://nucleus.iaea.org/rpst/Documents/NBS28_NBS30.pdf). There are 16 tabulated δ18O values for NBS 28 in the abovementioned IAEA report with a standard deviation of 0.3‰ (1σ). Two recent studies have measured the δ18O values of both NBS 28 and VSMOW. The results are 9.56‰ (Tanaka and Nakamura 2013) and 9.58‰ (Wostbrock et al. 2020a) on the VSMOW scale, in excellent agreement with the recommended IAEA value. Note: NBS 30 is no longer distributed from IAEA.

Comparison of all data The crucial fractionation factors that are required to place waters, carbonates and silicates on the same scale are the equilibrium aCO2–water and kinetic aCO2(ACID)–calcite fractionation factors (Fig. 4). From the above discussion it is clear that there is a significant degree of uncertainty when comparing waters to carbonates to silicates. Only silicates (and air O2) are routinely determined quantitatively. The accuracy of carbonates and silicates on the VSMOW scale (relative to water) is dependent on the accuracy of the alpha factors and overall translates to an uncertainty as high as 0.5‰. This number may be slightly lower if we cull some of the experimental fractionation values that have been published. The most widely accepted values are aCO2–water = 1.0412 and for aCO2(ACID)–calcite =1.01025 (at 25 °C). These values may be refined by future researchers, but at present, the techniques available for analysis are essentially the same that were used in previous studies. Thus the ~0.5‰ uncertainty when comparing carbonates to waters to silicates remains.

CO2 equil. with SMOW (41.2±0.4)

Acid liberated CO2 from PDB (41.49±0.2) a=1.01025

a=1.0412

PDB (30.92)

a=1.03092

NBS 28 (9.6±>0.1)

SMOW (≡0)

Figure 4. Fractionation factors and relative effects for comparing waters to carbonates to silicates. Uncertainties discussed in text.

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STANDARDIZATION FOR d17O VALUES OF SELECTED REFERENCE MATERIALS All of the same problems and obstacles for calibrating standards for 18O/16O exist for O/16O as well, with several additional complications. Proper standardization for 17O/16O ratios is particularly critical because the differences that are measured in natural materials are so small. While the δ18O value of a material can be measured on either CO2, CO gas or O2 gas, δ17O values generally must be measured on O2 gas. Converting samples quantitatively to O2 gas can be extremely challenging, as in the case of carbonates.

17

The d17O and δ18O values of most terrestrial (Earth) materials co-vary, such that they follow the relationship d17O ≈ 0.52x × δ18O (see Miller and Pack 2021, this volume for a more detailed discussion). Plotting all Earth materials on a d17O–δ18O plot results in a linear trend that is often called the ‘Terrestrial Fractionation Line’ or TFL, especially in the meteoritic literature (e.g., McKeegan and Leshin 2001). The importance of measuring the d17O values of terrestrial materials becomes relevant only when we determine small deviations from some reference line that is representative of natural materials. This offset is the Δ′17O value, where Δ′17O = δ′17O – lRL δ′18O – γRL

(8)

Here lRL is the assigned slope of a reference line (hence the RL subscript) and γRL is the y intercept. l is commonly chosen to be 0.528 with γ = 0. The δ′ notation refers to the linearized form of δ, such that d′ = 1000 × ln(δ/1000+1) in per mil notation (Hulston and Thode 1965; Miller 2002). The advantage of the linearized notation is that the d′17O versus δ′18O relationship is close to linear, unlike d17O versus δ18O. The precision of Δ′17O measurements is on the order of ±0.005‰, when appropriate protocols are followed. These include extreme gas purification and long counting times on the mass spectrometer. This precision is significantly higher than what can be obtained for either the δ18O or δ17O value. The higher precision is obtained because the errors in the δ17O and δ18O values covary and therefore tend to cancel each other out (see appendix of Wostbrock et al. 2018 for details).

Method of measurement In conventional mass spectrometry, δ18O values can be measured on O2, CO2 or even CO gas. The δ17O value, however, must be determined using O2 as an analyte, where the [33]/[32] ratio (17O16O/16O16O) is measured. CO2 cannot be used because of the interference from 13C. Consider that 45/44 is both 12C17O16O/12C16O16O and 13C16O16O/12C16O16O. The mass resolution necessary to separate 12C17O16O from 13C16O16O is over 50,000, far above that attainable with any commercially available gas-source mass spectrometer. There are several other analytical options in place of the conventional mass spectrometer. The δ17O value of H2Ovapor is now routinely measured using cavity ringdown spectroscopy (Steig et al. 2014) with precision that rivals conventional mass spectrometry measurements. Promising preliminary data have also been made measuring the d17O value of CO2 gas in a laser spectroscopy system (Sakai et al. 2017; Stoltmann et al. 2017). A different approach is to measure the O+ fragment of CO2 produced in the source of an electron impact isotope ratio mass spectrometer (Adnew et al. 2019). Extremely high mass resolution (4700) is required to separate the 17O+ fragment (16.9991 amu) from the ubiquitous OH+ ion (17.0027 amu). This high mass resolution requires an expensive doubly focusing mass spectrometer (e.g. Thermo Fisher 253 Ultra) and has significantly reduced transmission, necessitating counting times in excess of 20 hours for high precision.

Water Ultimately all samples are related to VSMOW, using a stretching factor based on the difference between VSMOW and SLAP2. Therefore, it is critical to calibrate the working gas of a mass spectrometer and ultimately all materials to the VSMOW and SLAP2 scale. Water was first analyzed for the d17O value using electrolysis (Meijer and Li 1998) to produce

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the O2 from the water samples, which was then analyzed by conventional mass spectrometry. These authors recognized the relationship d17O = (1 + δ18O)l − 1 (l = 0.5281 ± 0.015) by analyzing waters of very different isotope compositions, but their precision for Δ′17O was far lower than what would be attainable with fluorination systems. Precise measurements for triple isotope analyses of water are made by either fluorination of water to O2, followed by analysis on a conventional dual inlet mass spectrometer, or, in recent years, by direct analysis of water vapor using either laser absorption cavity ringdown spectroscopy (Steig et al. 2014) or off-axis integrated cavity output spectroscopy (Tian et al. 2016). The latter gives precise analyses, but is not quantitative, and generally requires a correction due to the machine-related non-linearities. Fluorination methods are, in principle, quantitative, as 100% of the oxygen is converted to O2. Fluorination is accomplished either by passage of water through a CoF3 heated reaction chamber in a He flow (Barkan and Luz 2005; Schoenemann et al. 2013) or by reaction with BrF5 in a steel or nickel reaction vessel (O’Neil and Epstein 1966a; Jabeen and Kusakabe 1997; Pack et al. 2016; Wostbrock et al. 2020a). The data of Barkan and Luz (2005) may suffer from a slight D18O compression observed in the CoF3 method (Schoenemann et al. 2013; Passey et al. 2014). Figure 5 shows all published estimates for SLAP2 relative to VSMOW using the methods of fluorination. The vertical black line represents the accepted δ18O value of SLAP2 of −55.5‰. Three analyses are close to this value, with Δ′17O values averaging −0.011 ± 0.003‰ (1σ). All other studies report δ18O values that are higher than the accepted value. It has been shown that analysis of light waters suffers from a memory effect, and that the lightest (and presumably correct) values are only obtained after multiple injections (Barkan and Luz 2005; Schoenemann et al. 2013; Wostbrock et al. 2020a). While it has been suggested that the Δ′17O value of SLAP should be assigned a value of 0‰ because the measured value is close to 0‰ (Schoenemann et al. 2013), we argue that, while this may be a useful convention, accepting a 0‰ value is not necessarily correct. The clustering of data at δ18O = −55.5‰ and −0.011‰ implies that the Δ′17O value of SLAP2 is −0.011 ± 0.005‰. The Δ′17O value of −0.006‰ from Schoenemann et al. (2013) agrees with our suggested estimate for SLAP2 within error. One of the subtle complexities of accurately measuring Δ′17O values of samples with very different δ18O values is the possibility of scale distortion resulting from a pressure baseline effect (Yeung et al. 2018). Because the effect can be non-mass-dependent, it may lead to non-trivial errors in the measured Δ′17O value of SLAP2 relative to VSMOW. The magnitude

D'17O (‰ vs. VSMOW2, l=0.528 )

0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00

-0.02 -0.04

-56.5

-56.0

-55.5

-55.0

-54.5

-54.0

-53.5

-53.0

d18O (‰ vs. VSMOW2)

Figure 5. Published values for SLAP2 on the VSMOW2 scale. The accepted δ18O value is −55.5‰ (vertical line). We suggest a Δ′17O value of −0.011 ± 0.005‰. See Wostbrock et al. (2020a, Table 2) for sources.

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of this effect was evaluated by Wostbrock et al. (2020a), who reported a SLAP2 value of δ18OSLAP2/VSMOW2 = −55.55‰ and Δ′17O = −0.015 ± 0.005‰. They found no pressure-baseline effect in their mass spectrometer (Thermo Scientific™ 253 Plus). Two gases with δ18O values that differed by 25‰ were analyzed against each other at operating pressures of 3, 5 and 10 V [mass 32]. The measured Δ′17O values varied by no more than 0.002‰ over the entire pressure range. We therefore determine that the measured values are accurate and that the Δ′17O value of SLAP2 is between −0.015 and −0.010‰. The number is not very different from 0‰, and whether a Δ′17O value of −0.011 or 0.0‰ is used will have a negligible effect for most samples when adjusted to the VSMOW-SLAP2 scale. Nevertheless, it appears that the −0.011‰ is a closer fit to the true value of SLAP2 on the VSMOW scale relative to l = 0.528. Our best estimate for VSMOW and SLAP2 (and presumably the original SLAP, Lin et al. 2010) is given in Table 1. Table 1. Triple oxygen isotope values of various reference standards. Standard

Material

d17O (‰ relative to VSMOW-SLAP2)

d18O (‰ relative to VSMOW-SLAP2)

Δ′17O (l = 0.528)

VSMOW

water

≡0

≡0

≡0

SLAP & SLAP2

water

−29.709 ± 0.006

= −55.5a

−0.011 ± 0.006

San Carlos Olivine (SCO)

olivine

2.75 ± 0.08

5.32 ± 0.16

−0.052 ± 0.014

UWG garnet

garnet

2.94b

5.7c

−0.064b

NBS 28b

quartz

4.991b

9.57a

−0.050b

KRS

garnet

−13.34 ± 0.11

−24.95 ± 0.21

−0.091 ± 0.003

SKFSd

chert

17.57 ± 0.13

33.81 ± 0.26

−0.137 ± 0.004

O2 gas

12.09 ± 0.11

23.88 ± 0.21

−0.447 ± 0.034

a

d

air NBS 18

calcite

3.636 ± 0.009

6.99

−0.048 ± 0.009

NBS 19, 19A

calcite

14.92 ± 0.010

28.65a

−0.102 ± 0.010

IAEA603

calcite

14.83 ± 0.007

28.47a

−0.100 ± 0.007

a

0.003 ± 0.02

NBS 127

sulfate

4.57

8.67 ± 0.02

IAEA−SO−5

sulfate

6.14

12.07 ± 0.02a

−0.217 ± 0.02

IAEA−SO−6

sulfate

−6.21

−11.36 ± 0.02a

−0.204 ± 0.02

axOCO2(ACID)–calcite

acid fractionation factor @25 °C

−6

1.00535 ± (3.55 × 10 )

1.01025

a

Note: aIAEA defined value; bdetermined relative to SCO (see Fig. 6); cin relation to VSMOW-SLAP (see text); d developed by Miller et al. (2020), reporting new average of four labs (Table 3).

Silicates Determination of the d17O values of silicates is straightforward because O2 is produced during fluorination and the conversion from the silicate solid to O2 gas is quantitative (i.e., 100% of the silicate oxygen is converted to O2). The problem, of course, is calibration to VSMOW, and to a lesser extent, to the stretching factor VSMOW-SLAP2. That requires fluorination of water and silicate standards in the same extraction line and mass spectrometer, something that, until recently, has rarely been done. Early analyses calibrated their d17O value to SMOW by assuming that the d17O value of NBS-28 was equal to 0.52 × δ18O (Clayton and Mayeda 1983). Franchi et al. (1999) were perhaps the first to fluorinate both the NBS 28 standard and SMOW. Unfortunately, the errors

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in the analyses were high in comparison to more recent results. A number of more recent studies have been made in which the IAEA standard NBS 28 and two commonly used informal standards San Carlos olivine (SCO) and UWG garnet (Valley et al. 1995) have been analyzed relative to VSMOW and SLAP. One problem is that all researchers get their SCO from any one of a number of sources. It has been shown that there are at least two different populations of SCO with different d18O values (Macpherson et al. 2005; Starkey et al. 2016). Nevertheless, in general, the d17O and δ18O values from recent calibration papers give consistent values for SCO data, as shown in Table 2. The data in Table 2 are all corrected to the SLAP2 value in Table 1. The correction procedure involves the following standardization of each laboratories data: 1) The delta values for VSMOW, SLAP (or SLAP2) and SCO are converted to prime values where δ′ = 1000 × ln(δ/1000 + 1). 2) A constant given by δ′xOVSMOW-accepted − δ′xOVSMOW-measured is added to all data (δ′xOVSMOW-accepted = 0). 3) A stretching factor is applied such that all data are multiplied by 57.100  x OSMOW accepted   x OSLAP accepted , which reduces to 18  OSMOW measured  18OSLAP measured  x OSMOW measured   x OSLLAP measured 30.159 . and 17O 17 SMOW  measured   O SLAP  measured

The small differences seen in Table 2 may be due to slight differences in the oxygen isotope compositions of the olivine samples or slight miscalibrations to VSMOW-SLAP2. The San Carlos olivine measured in Wostbrock et al. (2020a) comes from a large aliquot of pure olivine and is available for others to calibrate their system. Samples of this standard can be obtained from the UNM CSI laboratory (csi.unm.edu) allowing for precise interlaboratory calibration. Widescale use of this particular batch of SCO could potentially reduce the interlaboratory discrepancies and result in further refinements of this value in the future. NBS 28 quartz and UWG garnet (Valley et al. 1995) are two other commonly measured reference silicates. There are only two direct comparisons of these two standards to VSMOW and SLAP (Tanaka and Nakamura 2013; Wostbrock et al. 2020a). Both obtain a δ18O value of 5.70 ( ± 0.01)‰ for UWG, in good agreement with the original published values of 5.74 to 5.8‰ (Valley et al. 1995). The reported Δ′17O values are −0.078‰ (Tanaka and Nakamura 2013) and −0.071‰ (Wostbrock et al. 2020a). For both studies, the δ18O values for NBS 28 are within 0.01‰ of the accepted IAEA value of 9.57‰, with Δ′17O values of −0.063‰ (Tanaka and Nakamura 2013) and −0.059‰ (Wostbrock et al. 2020a). Table 2. Triple isotope data for San Carlos Olivine. Data are corrected for δ18O and Δ′17O SLAP2 = −55.5 and −0.011‰. Laboratory/reference GZG, Goettingen

1

d17O

δ18O

Δ′17O

2.682

5.153

−0.036

ISIE, Okayama1

2.750

5.287

−0.038

2

2.717

5.294

−0.075

2.717

5.263

−0.058

ISIE, Okayama CSI, UNM3 CSI, UNM Average

4

2.892

5.588

−0.054

2.75 ± 0.08

5.32 ± 0.16

−0.052 ± 0.014

Note: 1 Pack et al. (2016), 2Tanaka and Nakamura (2013), 3Wostbrock et al. (2020a), 4Sharp et al. (2016).

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The Δ′17O values of UWG and NBS 28 can also be further refined by using additional published data. There are a large number of studies where UWG and NBS 28 are compared directly to SCO (see Fig. 6 caption for references). From Figure 6, we obtain a DΔ′17OUWG-SCO value of −0.012‰ and a DΔ′17ONBS 28-SCO value of 0.002‰ We use the IAEA-accepted δ18O value of 9.57‰ for NBS 28 and a δ18O value of 5.7‰ for UWG and the difference in the Δ′17O values between SCO and NBS 28 (Fig. 6) to determine the Δ′17O value and ultimately the d17O value of these two standards (Table 1). Two additional standards with extremely different δ18O values have recently been developed (Miller et al. 2020). The first is an extremely light garnet from Karelia, Russia (KRS) and the second is a heavy chert from Denmark (SKFS). The purpose of developing standards with such different δ18O values is to allow laboratories that are not set up to fluorinate waters to be able to determine a stretching factor based on two silicate samples with very different δ18O values. The standards were originally analyzed at Georg-August-Universität, Goettingen, Germany, and The Open University, UK and have subsequently been analyzed at The Center for Stable Isotopes, University of New Mexico, USA and The University of Oregon, USA (Table 3). All data were corrected to the common value of UWG given in Table 1. (This is because the SCO standard at Open University appears to have a different δ18O value from the other labs and what is seen in Table 2). Correcting all data to a common value of UWG (Table 1) allows for a common standardized value for these two light and heavy standards (Table 1).

DD'17O (‰ vs. SCO)

0.02 DD'17ONBS 28-SCO = 0.002

0.00 -0.02 -0.04 -0.06 -0.08

DD'17OUWG-SCO = -0.012

1

2

5

3

6

7

8

9

10

12 11

NBS 28 UWG

4

Figure 6. Published ΔΔ′17O values for UWG garnet and NBS 28 relative to San Carlos olivine values from Table 1. The average Δ′17O value of UWG is −0.012‰ less than SCO while the average Δ′17O value for NBS 28 is 0.002‰ heavier than SCO (pale horizontal lines). Data sources: 1 (Wostbrock et al. 2020a); 2 (Tanaka and Nakamura 2013); 3 (Pack and Herwartz 2014); 4 (Franchi et al. 1999); 5 (Starkey et al. 2016); 6 (Cowie and Johnston 2016); 7 (Miller et al. 2020); 8 (Kim et al. 2019); 9 (Ghoshmaulik et al. 2020); 10 (I. Bindeman, pers. comm.); 11 (Young et al. 2016); 12 (Yeung et al. 2018).

Air There are three direct comparisons between atmospheric oxygen (O2) and VSMOWSLAP (Barkan and Luz 2005; 2011; Wostbrock et al. 2020a) and three additional comparisons of O2 with secondary standards, either UWG or SCO (Young et al. 2014; Pack et al. 2017; Yeung et al. 2018). Accurate Δ′17O analyses of air require the separation of N2 and especially Ar from O2, which is done using a long gas chromatographic column chilled to ~ −80 °C. All studies removed Ar from the O2 gas except for two (Barkan and Luz 2005, 2011) in which an empirical correction was applied (Luz and Barkan 2005). All studies results were corrected to VSMOW-SLAP2 using the data for standards UWG, SCO and VSMOW-SLAP2 in Table 1. The newly normalized results are shown in Table 4.

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Table 3. Triple isotope data for light and heavy standards KRS and SKFS from four different laboratories. Data are corrected to UWG values given in Table 1. OU–Open University, UK; Goet–Georg-August-Universität Göttingen, Germany; CSI–Center for Stable Isotopes, U. New Mexico, USA; Or–University of Oregon, USA. Laboratory/ reference

Δ′17O

d18O

d17O KRS

OU

−13.50 ± 0.05

−25.25 ± 0.09

−0.088 ± 0.010

Goet

−13.34 ± 0.14

−24.95 ± 0.27

−0.091 ± 0.010

CSI

−13.31 ± 0.06

−24.87 ± 0.12

−0.096 ± 0.010

Or

−13.23 ± 0.05

−24.74 ± 0.03

−0.090 ± 0.015

Average

−13.34 ± 0.11

−24.95 ± 0.21

−0.091 ± 0.003

SKFS OU

17.61 ± 0.13

33.88 ± 0.24

−0.135 ± 0.009

Goet

17.38 ± 0.22

33.43 ± 0.41

−0.134 ± 0.009

CSI

17.68 ± 0.08

34.03 ± 0.11

−0.142 ± 0.005

Or

17.62 ± 0.12

33.90 ± 0.38

−0.136 ± 0.007

Average

17.57 ± 0.13

33.81 ± 0.26

−0.137 ± 0.004

Table 4. Compilation of published triple oxygen isotope analyses of Air corrected to VSMOW-SLAP2. d17O

d18O

Δ′17O

12.08 ± 0.01

23.88 ± 0.02

−0.453

Barkan and Luz 2011

12.03

23.88

−0.507

Young et al. 20143

11.94 ± 0.02

23.57 ± 0.05

−0.429 ± 0.01

Pack et al. 20171,5

12.25 ± 0.02

24.15 ± 0.05

−0.432 ± 0.019

Yeung et al. 2018

12.03 ± 0.01

23.73 ± 0.01

−0.429 ± 0.007

Wostbrock et al. 2020a1

12.18 ± 0.07

24.05 ± 0.11

−0.441 ± 0.012

Average

12.09 ± 0.11

23.88 ± 0.21

−0.447 ± 0.034

Reference Barkan and Luz 20051,2 1,2

3,4

Note: 1Measured directly to VSMOW-SLAP; 2Did not remove Ar from O2 sample; 3 Corrected to SCO; 4Includes pressure baseline correction; 5Corrected to SCO, A. Pack, pers. comm., (2020)

Carbonates The only way in which the δ17O of carbonates can be directly determined is by complete conversion to O2 by the method of fluorination. 100% oxygen retrieval requires high temperature fluorination in nickel reaction vessels. The difficulty with this method is that other intermediate oxygen-bearing compounds, such as CO, CO2 and COFx, are produced in the fluorination process and they are difficult to react completely to O2 (and CF4). In the one highprecision study of this type, Wostbrock et al. (2020a) fluorinated carbonates at 750 °C for four days with a large excess of BrF5. Yields approached 100%, but the δ18O values were often less than the accepted values determined by phosphoric acid digestion. It was found, however, that the lower δ18O also had proportionally lower d17O values, such that the measured l was 0.528, identical to our reference slope l. The measured Δ′17O values were therefore constant within ± 0.01‰ (Fig. 7). Wostbrock et al. (2020a) therefore used the conventionally accepted values for the δ18O values of IAEA carbonate standards and the measured Δ′17O values to

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Figure 7. Plot of Δ′17OFigure value7.of an individual analysis vs the difference in the accepted δ18O value and the measured δ18O value for carbonate samples. Extrapolation of 2‰ for the δ18O value will change the Δ′17O value by less than 0.006‰. The average of these three samples give a l = 0.528. Data from Wostbrock et al. (2020b).

back-calculate the d17O values of the samples. This same correction to the endmember Δ′17O values has been used for sulfates (Cowie and Johnston 2016) and CO2 gas (Farquhar et al. 1998). Results are given in Table 1. Wostbrock et al. (2020a) also fluorinated the CO2 released by phosphoric acid digestion from calcite at 25 °C. Their calculated θCO2(ACID)–calcite value is 0.5230 ± 0.0003, where θ = ln a17OCO2(ACID)–calcite / ln a18OCO2(ACID)–calcite. This corresponds to an a17OCO2(ACID)–calcite value of 1.00535 ± 3.55 × 10−6 relative to an a18OCO2(ACID)–calcite value of 1.01025. Using this fractionation factor, laboratories that measure the Δ′17O value of CO2 released from carbonates by phosphoric acid digestion (at 25 °C) can back-calculate to the original Δ′17O value of the carbonate. There are a number of indirect measurements of the δ18O and d17O values of carbonates obtained by measuring the CO2 gas liberated by phosphoric acid digestion. The CO2 is analyzed for the triple oxygen isotope composition using one of several methods: conversion to H2O followed by fluorination (Passey et al. 2014); equilibration with O2 in the presence of a Pt catalyst (Mahata et al. 2013; Barkan et al. 2015; Fosu et al. 2020); or by direct analysis of the O+ fragment of CO2 using a high resolution mass spectrometer (Adnew et al. 2019). With accurate determinations of the triple oxygen isotope composition of IAEA calcite standards, researchers who measure the CO2 released by phosphoric acid digestion can easily use the αCO2(ACID)–calcite values in Table 1 or determine an appropriate α value that brings their measurements into agreement with the δ17O and δ18O values of the carbonate standards. A compilation of Δ′17O values of IAEA standards and their relative values from different studies is given in Table 5. Although the measured Δ′17O values may be different depending on the analytical procedure used, the difference in the Δ′17O values between any two standards should be the same for all laboratories. The community is coming to consensus on the ΔΔ′17O of standards, although there are still large outliers, potentially due to issues with exchanging CO2–O2.

Sulfates The triple oxygen isotope composition of sulfates is measured by laser fluorination with either BrF5 (Bao and Thiemens 2000) or F2 with additional gas purification using a GC column (Cowie and Johnston 2016). The laser fluorination methods result in molar yields of 25–35% when using BrF5 and ~50% when using F2 as reaction reagents. Measured δ18O values can be as much as 15–20‰ below the accepted values. Due to the low yields, triple oxygen isotope compositions are corrected based on the measured Δ′17O value from fluorination and the δ18O value obtained by thermal conversion elemental analyzer (TC/EA) method (Kornexl et al. 1999;

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Table 5. Published Δ′17O values of carbonate and CO2 liberated from phosphoric acid digestion and DΔ′17ONBS 19– NBS 18 and DΔ′17OIAEA 603– NBS 18 values. Study

CO2

∆∆′17O

calcite

NBS 19

IAEA 603

NBS 18

NBS 19

IAEA 603

NBS 18

NBS 19 -NBS 18

IAEA 603 -NBS 18

Wostbrock et al. 2020aa

−0.155

−0.147

−0.100

−0.102

−0.100

−0.048

−0.055b −0.054c

−0.047b −0.052c

Barkan et al. 2019

−0.182

−0.194

−0.163

−0.019b

−0.023b

Passey et al. 2014

−0.135d

−0.098d

−0.037b

Fosu et al. 2020

−0.169

−0.119

−0.050b

Passey and Ji 2019

−0.143d

−0.088d

−0.055b

Barkan et al. 2015

−0.227e

+0.003e

−0.230b,e

Sha et al. 2020

−0.267

−0.225

−0.042b

Notes: afluorination; bCO2 gas extracted from carbonate; cdirect carbonate fluorination; dextracted at 90 °C. All others extracted at 25 °C; eBarkan et al. (2019) suggest that the analyzed samples may have been contaminated.

Savarino et al. 2001). Using a calculated θLF value (the fractionation associated with incomplete fluorination) of 0.5301, Cowie and Johnston (2016) were able to extrapolate their measured δ17O and δ18O to obtain the Δ′17O value of their sulfate standards NBS 127, IAEA-SO-5, and IAEA-SO-6. The δ18O values of these standards are tied to the VSMOW-SLAP scale using waters analyzed by CO2–H2O equilibration (Brand et al. 2009). The reported Δ′17O values in Cowie and Johnston (2016) are relative to their d17O values for the UWG standard. We recalculate the d17O and Δ′17O values of these standards using the difference between Cowie and Johnston’s Δ′17O values for UWG, San Carlos olivine and NBS 28 and those reported in the present communication (Table 1). The reported δ18O values are those given in Johnston et al. (2014). Results are presented in Table 1 calibrated to the VSMOW-SLAP scale based on the fluorination of VSMOW and SLAP2 .

CONCLUSION Mass dependent triple oxygen isotope geochemistry is a relatively new field. Until recently, laboratories generally measured variations in the Δ′17O values of materials without a proper interlaboratory calibration scheme. In some cases, the d17O values of their samples were estimated, with no direct ties to VSMOW and SLAP (SLAP2). While this did not affect the results from an ‘isolated’ publication, it made intercomparisons between laboratories extremely difficult. The problems in standardizing different materials to the same scale is related to the different methods employed for analysis. Silicates and waters are both fluorinated, but relatively few laboratories are set up to do both. More challenging is the total fluorination of carbonates, which requires high temperatures and long reaction times in order to approach 100% recovery.

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In this communication, we have attempted to calibrate all standards relative to VSMOW and SLAP2 as presented in Table 1. Standards include waters, silicates, carbonates, sulfates and air. We also provide the acid fractionation factor data for CO2–calcite as reported in Wostbrock et al. (2020a), so that laboratories that determine the triple isotope values of CO2 liberated by phosphoric acid digestion of calcite can back calculate the isotope values of the calcite relative to VSMOW-SLAP2. With this internally consistent standards table, practitioners can directly compare their data for different materials with different laboratories. Invariably, adjustments will be made to these suggested standard values. Nevertheless, the triple oxygen isotope geochemical community is reaching consensus on standards that makes possible direct comparison of the very subtle differences that are seen in natural materials.

ACKNOWLEDGEMENTS We would like to thank S.W. Schoenemann and M. Miller for their constructive reviews, and the editors I.N. Bindeman and A. Pack for their comments and support during this work. David Johnston provided us with unpublished sulfate data. Support for this study comes from the following grants: NSF-EAR 1551226 and NSF-EAR 1903852 to ZDS and NSF GRFP Grant DGE-1418062 to J.A.G.W.

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Rapid Commun Mass Spectrom 27:582–590 Sha L, Mahata S, Duan P, Luz B, Zhang P, Baker J, Zong B, Ning Y, Brahim YA, Zhang H, Edwards RL (2020) A novel application of triple oxygen isotope ratios of speleothems. Geochim Cosmochim Acta 270:360–378 Sharma T, Clayton RN (1965) Measurement of O18/O16 ratios of total oxygen of carbonates. Geochim Cosmochim Acta 29:1347–1353 Sharp ZD (2013) Principles of Stable Isotope Geochemistry, 2nd Edition. Open Educational Resources, Albuquerque, NM Sharp ZD, Gibbons JA, Maltsev O, Atudorei V, Pack A, Sengupta S, Shock EL, Knauth LP (2016) A calibration of the triple oxygen isotope fractionation in the SiO2–H2O system and applications to natural samples. Geochim Cosmochim Acta 186:105–119 Silverman SR (1951) The isotope geology of oxygen. Geochim Cosmochim Acta 2:26–42 Starkey NA, Jackson CRM, Greenwood RC, Parman S, Franchi IA, Jackson M, Fitton JG, Stuart FM, Kurz M, Larsen LM (2016) Triple oxygen isotopic composition of the high-3He/4He mantle. 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Reviews in Mineralogy & Geochemistry Vol. 86 pp. 197–216, 2021 Copyright © Mineralogical Society of America

Mass-Independent Fractionation of Oxygen Isotopes in the Atmosphere Marah Brinjikji and James R. Lyons School of Earth & Space Exploration Arizona State University 550 East Tyler Mall, PSF 686 Tempe, AZ 85287 USA [email protected] [email protected]

INTRODUCTION We review the O isotope modeling in the atmosphere below 100 km, which is a large and active area of research. Our review will not be exhaustive but instead will highlight some of the key papers on the topic over the past nearly 30 years. We focus our review on modeling the mass-independent fractionation signatures associated with O3 formation and other species that photochemically interact with O3. After a brief discussion of isotopic O3 formation, we present results from models of D17O in CO2, OH and H2O, nitrates, sulfates, and in pollution in urban environments. We then present new O isotope results for the atmosphere above 100 km. There are presently no oxygen isotope measurements for Earth’s atmosphere above about 60 km (Thiemens 1995). Here, we present model results for the oxygen isotope composition of Earth’s thermosphere and ionosphere using a 1-D photochemical model. This work was motivated by the NASA MAVEN mission, which is studying ion and neutral composition, and escape fluxes from, the thermosphere of Mars, and includes isotopic species (Jakosky 1994; Jakosky et al. 2017, 2018). The realization that comparable isotopic measurements for Earth’s thermosphere are lacking prompted our study.

PREVIOUS WORK IN THE LOWER ATMOSPHERE Early measurements Because our main interest here is in mass-independent fractionation (MIF) of O isotopes, or, as will be seen for the upper atmosphere, apparent MIF, we will not review the large literature on O and H isotopes of atmospheric water vapor, and the influence of exchange with soils, which has been a topic of ongoing research for many decades. We begin with the stratospheric work of Konrad Mauersberger. Using a balloon platform, Mauersberger (1981) performed in situ mass spectrometry of O3 in the stratosphere, discovering an enormous enrichment of ~ 400‰ in 16 16 18 O O O (mass 50). We now know that this value is too high, but, qualitatively, the discovery was made. In the laboratory the key discovery of mass-independent fractionation was made by Thiemens and Heidenreich (1983) by passing an electric discharge through O2 in a flask, and measuring the O isotope composition of the O3 produced and the residual O2. Instead of the usual mass-dependent isotope behavior (adhering to the slope of ~0.5 in 17O/16O vs. 18O/16O coordinates), they found that the O2 and O3 defined a line of nearly slope 1 on 3-isotope space, leading to the term ‘mass-independent’ fractionation. It is difficult to overstate the significance 1529-6466/21/0086-0006$05.00 (print) 1943-2666/21/0086-0006$05.00 (online)

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of this experiment on our understanding of atmospheric O isotopes. Ozone participates in a wide variety of oxygen chemical reactions, either directly as O3 or as a source of O(1D), which forms OH upon reaction with water vapor. In this manner, MIF inherited from O3 manifests itself in nearly all O-containing compounds in the atmosphere (Lyons 2001). Continued isotopic measurements in the laboratory and in the atmosphere confirmed the original discovery (Thiemens and Heidenreich 1983), and sought to clarify the mechanism responsible for the unusual isotopic behavior of O3. Analyses of O3 were made in both the troposphere and stratosphere (e.g., Krankowsky et al. 1995, 2000; Johnston et al. 1997). Laboratory studies focused on O3 formation reactions under a variety of conditions (e.g., Morton et al. 1990, Janssen et al. 1999), culminating in measured rate coefficients for formation of isotopic O3 (Mauersberger et al. 1999). Other studies discovered oxygen MIF effects in other relevant atmospheric reactions (Röckmann et al. 1998; Savarino and Thiemens 1999). Although much smaller in magnitude than the O3 MIF signature, these latter reactions are still informative from a chemical physics perspective.

Theory and photochemical modeling of O3 MIF signatures Photochemical models began exploring the implications of heavy ozone in the atmosphere, even though there was essentially no isotopic rate coefficient data available, and even the reaction responsible for O3 was debated. An early successful model looked at stratospheric CO2, and recognized that O(1D), produced from O3 photolysis, will form the metastable CO3 (Yung et al. 1991). Breakup of the CO3 imparts an O3-derived MIF signature to the CO2, diminished by the probability of 17O or 18O remaining in the CO2. This mechanism-based analysis of the transfer of O3 MIF to another molecule, namely stratospheric CO2, demonstrated both the significance and subtlety with which O3 can impart isotopic signatures to other molecules. With the measurement of isotopic rate coefficients by Mauersberger et al. (1999), it became possible to more quantitatively model O isotope exchange processes in the atmosphere. Lyons (2001) investigated transfer of O3 MIF signatures to about 10 other molecules, and provided some unification for the expected oxygen isotope composition of the troposphere and stratosphere. The measurement of the isotopic rate coefficients by Mauersberger et al. (1999) also made it possible for the physical chemists to quantitatively investigate the mechanism responsible for O3 MIF. A series of papers from Rudy Marcus’s group (Hathorn and Marcus 2000; Gao and Marcus 2002) provided a semi-empirical, and extremely useful, theory for understanding the role of zeropoint energy and symmetry in the wide range of isotopic rate coefficient values for O3 formation. The MIF signature derived from non-statistical behavior in the asymmetric O3 isotopomers, the exact physical origin of which is still being explored. Importantly for the photochemical modelers, the Marcus formulation allowed prediction of unmeasured rate coefficients. This is particularly important for the mixed-isotope O2 species, e.g., 16O17O and 16O18O, whose reactions with 16O are essential in the atmosphere but difficult to measure in the laboratory.

Applications of oxygen MIF Ozone MIF signatures (i.e., enhancements or depletions in 17O) have had a tremendous range of application in geochemistry, both for the modern and ancient Earth. We will not attempt to review all of these applications, but will mention a few that we think are especially notable, with the recognition that we are not without bias. Many of the most significant applications of oxygen MIF have been to measures of global primary productivity (GPP), as first pointed out by Bender et al. (1994). Accurate measurements of the MIF signature of O2 allowed Luz et al. (1999) to relate modern primary productivity to the cross-tropopause transport timescales for air. The small negative MIF signature in bulk tropospheric O2 with D17O ~ −0.2‰, results from the storage of a positive MIF signature in stratospheric CO2 via transfer from O3 by the excited state atom O(1D) (Yung et al. 1991). This powerful technique has also been applied to O2 collected from Antarctic ice and snow, extending productivity estimates back to the middle ages (Savarino et al. 2003).

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One of the most remarkable MIF-related discoveries is that of negative MIF signatures, D17O ~ −0.8 to −1.6‰ in sulfates from the Cryogenian period (Bao et al. 2008). Reconstructing the implied isotopic composition for O2 yields D17O ~ −2 to −6‰. By accounting for the efficiency of subaerial pyrite oxidation, the exact same mechanism invoked by Luz et al. (1999) may be applied to this much earlier geological period to place a constraint on atmospheric CO2. Given plausible assumptions about productivity at that time, greatly elevated levels of CO2 may be inferred (up to 30 times the modern value), just as predicted for the aftermath ‘hothouse’ following the end of a Snowball Earth glaciation (Bao et al. 2008). Most recently, Hodgkiss et al. (2019) used D17O values of sulfate (also ~ −0.8‰) to argue for the collapse of productivity at the end of the great oxidation event (GOE). Because the sulfate D17O values depend on pO2, pCO2, and GPP, different interpretations are possible for the Snowball Earth and the GOE. There are numerous other applications of O isotope MIF signatures, some of which are discussed in more detail below. These include atmospherically-derived nitrates such as those in the Atacama desert in Chile (Michalski et al. 2004), the origin of desert varnish on rocks (Bao et al. 2001), and an improved quantification of stratospheric volcanism (Gautier et al. 2019). Additionally, oxygen MIF signatures have been investigated for polar water vapor (Lin et al. 2013), stratospheric CO2 (Liang et al. 2007), and the sulfate formation mechanism in marine sea-salt aerosols (Alexander et al. 2005). The breadth of applications of O3 MIF signatures are a testament to the importance of the phenomenon.

MATERIALS AND METHODS VULCAN photochemical model VULCAN is a 1-D chemical kinetics model developed for high-temperature exoplanet atmospheres (Tsai et al. 2017). The original version of VULCAN utilized a reduced C–H–O chemical network consisting of about 300 gas-phase reactions valid in a 500−2500 K temperature range. However, the code is highly general, and is readily adapted to low-temperature atmospheres, as well as atmospheres with N and S-containing molecular species. We have adapted VULCAN to the Earth thermosphere and ionosphere, and with the inclusion of O isotopes. VULCAN solves a system of vertical 1-D continuity equations (Eqn. 1) using a Rosenbrock solver (Tsai et al. 2017). The Rosenbrock solver has been shown to be highly effective for systems of ‘stiff’ ordinary differential equations, such as occur in atmospheric chemical kinetics. Vertical transport due to both eddy and molecular diffusion is represented by a vertical diffusion equation. For high-temperature atmospheres, reverse reaction rate coefficients are computed from a measured forward rate, combined with the equilibrium constant for the reaction. The equilibrium constant is computed from the Gibbs free energy of the reaction, adjusted for pressures (Tsai et al. 2017). To model Earth’s atmosphere, we have turned off the reverse reactions. We have done this even for the thermosphere because the kinetics of the relevant neutral–neutral and ion–molecule reactions are well known from decades of laboratory work (e.g., Brasseur and Solomon 1984). The isotopic reactions are less well studied, but we assume that they do not differ greatly from the reactions of the dominant 16O isotope. For reactions involving O3 in the lower atmosphere, such an assumption is incorrect due to the non-statistical nature of O3 recombination reactions (Gao and Marcus 2002). In the thermosphere, O3 formation is unimportant, and we assume that the isotopic reaction rate coefficients are independent of isotope, apart from a mass-dependent reduced-mass factor discussed further below. The continuity equations solved in VULCAN are given by dni di  Pi  Li dt dt

(1)

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where ni and fi are the number density (cm−3) and vertical flux (cm−2 s−1) for species i in the model. Pi and Li are the production and loss rates (cm−3 s−1) for species i due to chemical and photodissociation reactions. The vertical flux satisfies a 1st-order diffusion equation,  dn  dn n  n  i   Di  i  i   K  i  i   dz H a   dz Hi 

(2)

where Di is the molecular diffusion coefficient for species i diffusing through the background atmosphere, and K is the vertical eddy diffusion coefficient applicable to all species. The scale height of species i is Hi 

kT mi g

(3)

Ha 

kT ma g

(3b)

and for the well-mixed atmosphere is

for mean molecular mass, ma. The homopause is defined as the height at which Di ~ K for most species. Above this height, which is about 100 km for Earth, molecular diffusion dominates over eddy diffusion. Here, eddy diffusion means mixing by eddies on the full range of size scales from the Kolmogorov microscale to the scale height of the bulk atmosphere, Ha. The occurrence of mi in Equation (3a), and not in Equation (3b), is the basis of diffusive separation in the thermosphere.

RESULTS FOR THE LOWER ATMOSPHERE We present a short synopsis of O isotopes in the lower atmosphere based on the photochemical equilibrium calculations in Lyons (2001), and then discuss more recent work on modeling MIF signatures in O3, CO2, H2O, nitrates, sulfates, and O-containing components of air pollution. The focus of Lyons (2001) was the transfer of O3 MIF signatures to other oxygen-containing molecules in the atmosphere. We summarize this work below, and present updated results for D17O of several lower atmosphere species. The relevant isotopic O3 formation reactions are the following: O + O2 M O3

k1

(R1)

Q + O2 M QOO

k2

(R2)

O + QO M QOO

k3  Q

(R3a)

k3 (1   Q )

(R3b)

P + O2 M POO

k4

(R4)

O + PO M POO

k5  P

(R5a)

k5 (1   P )

(R5b)

O + QO M OQO

O + PO M OPO

In these reactions k is the 3-body rate coefficient, γ is the branching ratio, Q = 18O and P = 17O, and M is a 3rd-body collision partner, usually O2 or N2. The primary loss for ozone is photodissociation. There are multiple photodissociation channels, but, for the purpose of illustration, we only consider the channel forming O(1D). We also assume the photodissocation rate constants are

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identical for all isotopomers of O3. This is not exactly correct, but it simplifies the resulting equations. The resulting photodissociation reactions are shown in reactions (R6–R10). O3  hv  O(1D)  O2

J1

(R6)

QOO + hv  O(1D)  QO

1 2

J1

(R7a)

QOO + hv  Q(1D)  O2

1 2

J1

(R7b)

OPO + hv  O(1D)  PO

J1

(R8)

POO + hv  O(1D)  PO

1 2

J1

(R9a)

POO + hv  P(1D)  O2

1 2

J1

(R9b)

J1

(R10)

Q + O2  QO + O

k6 f

(R11a)

O + QO  Q + O2

k6 r

(R11b)

P + O2  PO + O

k7 f

(R12a)

O + PO  P + O2

k7r

(R12b)

OPO + hv  O(1D)  PO

We must also include O exchange with O2:

Finally, we include quenching of the electronically excited O(1D) by collision with O2 and N2 to produce a ground state O atom. For the presentation here we will not include this reaction, but will simply assume that all O(1D) is rapidly quenched to O. This is, of course, not actually the case in the atmosphere, as O(1D) is involved in essential reactions with H2O (to form OH), CO2 (isotope exchange), and many other molecules. However, this assumption does not significantly affect the isotopic composition of O3. From the above set of reactions, and assuming O(1D) → O proceeds rapidly, we may derive expressions for the O3 isotopomer number densities and delta-values. We do this by setting production and loss rates equal to each other for a given species, and then solving for the species number densities. This will only be valid for short-lived species that are essentially not affected by transport, i.e., species in photochemical steady state. From reaction (R11) and (R12), we find [Q] 1 [QO]  Q [O] K eq [O2 ]

(4)

1 [ PO] [P]  P [O] K eq [O2 ]

(5)

/T .8 / T 1.9463e and , In Equations (4) and (5)  K eqQ =k / / k k66r 1.9463 e31.631.6/T  K eqP = kk / k7r7r = 11.9728e .9728 e1515.8/T 6kf 6f  r = 77f  f / k where T is atmospheric temperature. The equilibrium constants have been evaluated from statistical mechanics and are given in Yung et al. (1997). The forward rate constants are k6 k7 3.4  10 12 (300 / T )1.1 , neglecting reduced factors in the rate of reaction. f f

Again, assuming photochemical equilibrium, we derive approximate expressions for the O3 isotopomer number densities:

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[OQO] k3 [QO] (1   Q )  [ O3 ] [O2 ] k1

[QOO]  [ O3 ]

 k2 1  [QO] k  3  Q   Q k K k 1  1 eq  [O2 ]

[OPO] k5 [ PO] (1   P )  [ O3 ] [O2 ] k1

[ POO]  [ O3 ]

 k4 1  [ PO] k  5  P   P  k1 K eq k1  [O2 ]

(6)

(7)

(8)

(9)

The total isotopomer number densities are independent of branching ratio, [QOO]  [OQO]  [ O3 ]

 k2 1 k  [QO]  3   Q  k1 K eq k1  [O2 ]

(10)

[ POO]  [OPO]  [ O3 ]

 k4 1 k  [ PO]  5   P k K  1 eq k1  [O2 ]

(11)

Using the experimental results of Mauersberger et al. (1999) and Janssen et al. (1999), together with the semi-empirical model results of Hathorn and Marcus (2000) and Gao and Marcus (2002), we compile a table of relative rate coefficients is compiled for O3 isotopomer formation (Table 1). The values in the ‘theory’ column for η = 1.15 imply gQ = 0.594 and gP = 0.575. Lyons (2001) used gQ = gP = 0.57 based on the incomplete experimental values. These small differences in branching ratios produce dramatically different D17O values for the symmetric and asymmetric O3 isotopomers, i.e., OQO and QOO, respectively. We compute delta-values as  x O(O3s ) 

[O x OO]  O  1 [O3 ]  x O SMOW

(12)

 x O(O3a ) 

[ x OOO]  O  1 2[O3 ]  x O SMOW

(13)

[ x OOO]  [O x OO]  O  1  xO  3[O3 ]  SMOW

(14)

 x O(O3 ) 

Lyons (2001) assumed photochemical steady state for a system of reactions in the midlatitude atmosphere from 0 to 60 km, analogous to Equations (6−11), but yielding a coupled non-linear system. As noted by Zahn et al. (2006), Lyons assumed gQ = gP = 0.57 based on the experimental data available at the time, which resulted in D17O ~ −40 to −50‰ for symmetric O3 and too high a D17O value for asymmetric O3. Here, and below we define D17O as 17O  (17O  1)  (18O  1)

(15)

where λ =0.50–0.53, and where the reference is VSMOW. Updated results from Lyons (2001) are shown in Figure 1. The branching ratios used in Figure 1 are gQ = 0.594 and gP = 0.564, which yields a vertically-averaged symmetric O3 ~ 0‰. Temperature and pressure affect the formation rate of isotopic O3, and although these effects were included in Lyons (2001), they have not been updated here. A more precise treatment was given in Liang et al. (2006), which we discuss further below. The key point of Figure 1 is the illustration of how O3-derived MIF signatures are transferred to other photochemically active species.

Mass-Independent Fractionation of Oxygen Isotopes in the Atmosphere

203

Table 1. Relative rate coefficients for O3 isotopomer formation. Rate coefficient

Experiments1

Theory2 (η = 1.15)

Theory2 (η = 1.00)

Theory3 (η = 1.18)

k2/k1

0.93

0.95

0.83

0.93

k3/k1

1.27

1.28

1.18

1.25

k3gQ/k1

0.73

0.76

0.66

0.74

k3(1 − gQ)/k1

0.54

0.52

0.52

0.52

k4/k1

1.03

1.02

0.89

1.03

k5/k1

1.17

1.20

1.11

1.19

k5gP/k1

not measured

0.69

0.60

0.68

k5(1 − gP)/k1

not measured

0.51

0.51

0.51

Notes: 1  Mauersberger et al. (1999); Janssen et al. (1999). 2  Hathorn and Marcus (2000). The parameter η characterizes the magnitude of non-statistical behavior in the asymmetric ozone isotopomers. Nonstatistical behavior in a chemical reaction means a deviation from the usual Boltzmann distribution of energy levels in a microcanonical statistical mechanics description of a molecule (e.g., Gao and Marcus 2002). These values are for 140 K. 3  Gao and Marcus (2002).

60

Altitude (km)

O3

NO2

50

NO

40

Oa3 ClO

Os3

30

O(1D)

OH

20

HO2

10

0

-10

0

10

20

30

40

∆17O (permil)

50

60

70

80

Figure 1. Photochemical equilibrium model results. Calculations assume an O atom exchange rate coefficient of 1×10−19 cm3 s−1 between OH and O2, well below the upper limit value (Table 2). The hatched regions show the range of D17O measurements for stratospheric (Schueler et al. 1990; Krankowsky et al. 2000) and tropospheric (Krankowsky et al. 1995; Johnston and Thiemens 1997) O3. The narrow rectangle near the origin is the range of measurements in rainwater H2O2 (Savarino and Thiemens 1999). This figure closely follows Lyons (2001) but with an updated isotopic branching ratios (see text), with a non-zero exchange rate for OH and O2, and with the addition of symmetric ozone. Slope = 0.520

Figure 1 includes exchange reactions (X1–X7), and (X9) (Table 2), with the rate coefficient for X6 set arbitrarily to 1×10−19 cm3 s−1. If the rate coefficient for X6 is set to zero (as in Fig. 1 of Lyons 2001), the maximum D17O values for OH are about 27‰ from 28−32 km, several permil higher than shown here, but still about 20‰ lower than Figure 1 in Lyons (2001). Using the improved isotopic branching ratios has a quantitative impact on atmospheric D17O values, but does not change the qualitative picture of the prediction of an enrichment of 17O in many stratospheric species (Lyons 2001). It is also possible that additional O exchange reactions are present, which will further modify the D17O values shown in Figure 1. Exchange reactions for ClO have not been included here.

Brinjikji & Lyons

204

Table 2. O atom exchange rate coefficients (Lyons 2001). Rate coefficient cm3s-1

Reaction

Ref.

X1

O + O ↔ OO + O

2.9(‒12)

X2

Q + NO ↔ O + NQ

3.7 (‒11)

X3

QH + H2O ↔ OH + H2Q

2.3 (‒13)e

X4

QH + NO ↔ OH + NQ

1.8 (‒11)

c c

a a -2100/T

b

X5

QH + NO2 ↔ OH + NOQ

1.0 (‒11)

X6

QH + O2 ↔ OH + OQ

1000 m)

Kinetic fractionation

Mn-oxide (IV)

Mn-oxide (II)

Figure 4. Plot of Δ′17O vs. δ18O illustrating the oxygen pathways and sources of deep-sea ferromanganese nodules (brown filled circles, Sutherland et al. 2020). I assume that photosynthetic oxygen (red filled hexagon) is a mixture of marine (red filled pentagon) and terrestrial (green filled diamond; average composition of leaf water) photosynthesis. The seawater composition (light blue filled circles) is from Barkan and Luz (2011). The marine authigenic clay composition is from Sengupta and Pack (2018). The silica composition is from Sharp et al. (2016). The dark grey filled area outlines oxygen mixing between authigenic minerals (clay, silica) and seawater. The dissolved O2 isotope data (light gray filled circles, >1000 m: red filled crosses) are taken from Yeung et al.’s dataset https://www.bco-dmo.org/dataset/753594 as of 2020. “Mn oxides I” outlines the composition of Mn and Fe oxides in equilibrium with seawater. “Mn oxides II” have acquired the entire oxygen from deep-sea dissolved O2 without fractionation (Mandernack et al. 1995), whereas “Mn oxide IV” would have acquired the oxygen from air equilibrated dissolved O2. “Mn oxide III and V” would have formed from the respective dissolved O2 under participation of a 20‰ kinetic isotope fractionation (Mandernack et al. 1995). The light gray shaded area outlines the possible field for bulk ferromanganese nodules.

Isotopic Traces of Atmospheric O2 in Rocks, Minerals, and Melts

227

well-mixed with the atmosphere, and no fractionation would occur during the oxidation, Mn oxide would have a composition identical to that of dissolved and air equilibrated O2 (“Mn oxide IV”). This composition has been considered as one endmember by (Sutherland et al. 2020). If 20‰ fractionation is associated with the oxidation of Mn (Mandernack et al. 1995), one would get a Mn oxide endmember with a composition labeled “Mn oxide V”. This is the second endmember considered by Sutherland et al. (2020). Any of these pure endmembers are likely to exist. The experiments by Mandernack et al. (1995) show that during the oxidation, also equilibration with the surrounding water plays a role and only ~40% of the oxygen in the Mn oxides sources from O2. This means that the Mn oxides in ferromanganese crusts are expected to have compositions on the mixing trends between “Mn oxides II–V” and the water equilibrated “Mn oxide I”. Because the ferromanaganese nodules form in the deep sea, a mixture between “Mn oxide II” and “Mn oxide III” should be considered rather than “Mn oxide IV” and “Mn oxide V”. Bulk ferromanganese nodules are mixtures of Mn and Fe oxides, and silicates. The Fe oxides will have a composition close to that of seawater. Following the suggestion by Sutherland et al. (2020), the silicate fraction can be approximated by a mixture of silica (Sharp et al. 2016) and clay (from Sengupta and Pack 2018; orange filled region in Fig. 4). The composition of bulk ferromanganese nodules is expected to fall in the light gray shaded area, which is, indeed, the case (Fig. 4). Because of their deep-sea formation and considering 40% O2 in the Mn oxides, the data by Sutherland et al. (2020) can be explained by “Mn oxide III” as one endmember, mixed with seawater-equilibrated Fe and Mn oxides and various portions of silicates. In such a model, those deep-sea ferromanganese nodules with Δ′17O below the “Mn oxide II,III”–“Mn oxide I, Fe oxide” mixing trend would be explained by a lower Δ′17O of atmospheric O2. A lower Δ′17O of atmospheric O2 could be due to elevated pCO2 and/or decreased GPP (Bender et al. 1994; Luz et al. 1999; Young et al. 2014). As a quantitative paleo-CO2 and paleo-GPP proxy, more data are required to better understand the particular fractionation processes during the crust formation. Nevertheless, the deep-sea ferromanganese nodules are an interesting target for future triple oxygen isotope studies.

Tektites Air melt exchange. Urey (1955) discussed the origin of tektites and concluded that they are of extraterrestrial origin. He based his argument on the observation of tektite liquidus temperatures that are beyond temperatures known from magmatic processes and their (intergroup) chemical homogeneity that is unrelated to the local rock chemistry. He also noted that tektite occurrences are unrelated to the spatial distribution of terrestrial volcanism. Based on their distribution on Earth, Urey (1955) speculated that tektites may have arrived from the Moon. The chemical composition of tektites, however, is very similar to that of the Earth′s crust and makes a lunar origin less likely. Two decades earlier, Spencer (1933) had put forward the now-established idea that tektites formed during melting end ejection of target rock during a meteorite impact. He based his suggestion on the occurrence of tektites in the vicinity of impact craters and on the chemical similarity of tektites and the Earth surface material. A review on the origin of tektites on basis of geochemistry is given by Koeberl (1988, 1994). The first oxygen isotope data of tektites was published by Silverman (1951). He analyzed tektites from the Phillippines, which belong to the Australasian strew field, and from Bohemia (moldavites), which were ejected from the Ries crater in Southern Germany ~15 Ma ago. For both glasses, Silverman (1951) measured δ18O = 10.4‰. He noted that their composition is different from stony meteorites, but similar to terrestrial sedimentary rocks. He leaves the reader with the options that tektites are either of terrestrial origin or of extraterrestrial origin and that similar sedimentary processes that enrich rocks in 18O operate on other bodies of the Solar System. Taylor and Epstein (1962) analyzed a wider range of tektites and found δ18O in a narrow range between 9.6 and 10.4‰. They noted that the oxygen-isotope composition resembles that

Pack

228

of felsic igneous rocks, whereas their chemistry rather agrees with that of sedimentary rocks. Sedimentary rocks, however, typically have δ18O > 10‰. In conclusion, Taylor and Epstein (1962) suggested that tektites were of extraterrestrial origin. The total range of published tektite data is 7 ≤ δ18O ≤ 15‰ (see Zák et al. 2019, and references therein), i.e., covering the range typical of sedimentary rocks. The first triple oxygen isotope data for tektites were published by Clayton and Mayeda (1996). They reported data for 14 tektites of different origin. Their δ18O values range between 8.6 and 10.3‰, typical for continental surface rocks (e.g., Bindeman 2021, this volume). All tektite data are in the δ18O range typical for sedimentary rocks and are by 1600 °C. For two alumina materials used as refractory in steelmaking Pack et al. (2005), determined 18‰ ≤ δ18O ≤ 20‰. So far, no triple oxygen isotope analyses have been published on high-T refractories. A PostDoc from my group, Dr. Nina Albrecht, conducted first triple oxygen isotope measurements on technical alumina (Table 2). The material was a densely sintered alumina crucible for application in high-T furnace experiments. She obtained a δ18O of 16.5‰ and a Δ′17O as low as −0.270‰ (Fig. 7). The δ18O of the sintered alumina is close to the data reported by Pack et al. (2005) for alumina refractories. The Δ′17O of the sintered alumina is clearly much lower than what has been measured for natural rocks and minerals (Fig. 7). A simple mass balance indicates ~60% exchange with atmospheric O2 during sintering (Fig. 7). For comparison, Dr. Albrecht analyzed a set of natural corundum, ruby, and sapphire samples (Table 2). They range in δ18O from 12 to 26‰, but have Δ′17O values typical of sediments (Fig. 7). For comparison, Giuliani et al. (2005) reported similarly spreading δ18O values of 3 to 23‰ from various ruby and sapphire deposits.

Crustal rocks

Raw materials

Figure 7. Plot of Δ′17O vs. δ18O of natural (purple filled crosses, corundum, ruby sapphire) and sintered technical (yellow filled triangles) alumina. The range of typical terrestrial crustal rocks and data for San Carlos olivine (light green filled circles) and air O2 (gray filled star) are displayed (e.g., Pack and Herwartz 2014; Bindeman et al. 2018, 2019; Bindeman 2021, this volume). Data for synthetic corundum starting materials (pentagon, diamonds), and Czochralski grown ruby and sapphire crystal (red filled square) are displayed. The corresponding data are listed in Table 2.

Pack

234

Table 2. List with description and oxygen isotope data for the analyzed corundum samples. The materials were provided by Dr. Klaus Dupré of the Forschungsinstitut für Mineralogische und Metallische Werkstoffe Edelmetalle/Edelsteine (FEE) in Idar Oberstein and by Dr. Alexander Gehler from the collection of the Geoscience Center in Göttingen (GZG). The Δ′17O is reported relative to a slope − 0.528 reference line. δ17O

δ18O

Δ′17O

GZG Collection

9.336

17.873

–0.082

GZG Collection

13.558

25.993

–0.066

– “” –

– “” –

10.633

20.361

–0.082

– “” –

– “” –

– “” –

11.534

22.116

–0.061

Ruby (Slatoust)

Ural, Russia

GZG Collection

11.874

22.767

–0.082

Technical alumina

Commercial

Laboratory

8.44

16.58

–0.281

– “” –

– “” –

– “” –

Alumina microbeads

~ 50 µm spherulitic powder, oxyhydrogen flame fused

FEE Idar Oberstein

Crackle corundum

Coarse fraction, Verneuil

– “” – – “” –

Sample

Comment

Source

Sapphire (Ceylon)

Sri Lanka

Ruby (Ceylon)

Sri Lanka

– “” –

8.29

16.22

–0.239

11.548

22.637

–0.338

FEE Idar Oberstein

14.865

29.237

–0.460

Fine fraction, Verneuil

FEE Idar Oberstein

14.866

29.25

–0.466

– “” –

FEE Idar Oberstein

15.652

30.777

–0.475

– “” –

– “” –

FEE Idar Oberstein

16.71

32.925

–0.533

Sapphire FEE

Czochralski XX

FEE Idar Oberstein

14.258

27.995

–0.420

Ruby FEE

Czochralski XX

FEE Idar Oberstein

14.115

27.754

–0.438

San Carlos olivine

N = 20 (av.)

Arizona, USA

2.745

5.306

–0.052

The δ18O of magnesia refractories and first δ17O and δ18O data for technical alumina clearly show that during the high-T production processing of these materials, considerable exchange occurs between the atmosphere and the refractory product. The studied alumina refractory carries a triple oxygen isotope signature that suggests ~ 60% equilibration with the atmosphere.

Using Δ′17O as a new tool to distinguish synthetic and natural gems The most common technique of producing single crystals of alumina is growing them by continuously pulling the growing crystal out of a melt (Czochralski 1918). After his inventor, this technique is now called the Czochralski method (see Tomaszewski 2002, for some dispute on the name). An illustration of the process is given in (Fig. 8A). Earlier, Verneuil (1904) described a method for the production of single crystals of corundum, ruby or sapphire; a method now named after him as Verneuil process (Smith 1908). In that process, fine alumina powder is rinsed through an oxyhydrogen torch, in which the powder melts and coagulates to fine alumina droplets (Fig. 8B). The droplets of liquid alumina then fall onto a seed crystal, where they grow to form a single crystal of corundum, ruby, or sapphire. For high-quality and larger crystals, this technique is inferior compared to the Czochralski method. It is, however, used for the preparation of starting materials used in the Czochralski process. We have obtained three natural ruby and sapphire samples and five samples of synthetic corundum (Table 2). Sample “Alumina microbeads” consists of a granulate of ~50 µm large alumina spherules. No details about the production process are available. The alumina spherules were likely produced by oxyhydrogen flame fusion in an apparatus similar to that invented by Verneuil (1904), except that the molten droplets were not grown on a single crystal but quenched and

Isotopic Traces of Atmospheric O2 in Rocks, Minerals, and Melts

B

235

Hammer O2 Al2O3 powder Sieve

H2

Oxyhydrogen flame Al2O3 melt droplets Al2O3 crystal

Figure 8. Sketches illustrating the Czochralski method (A) and the Verneuil method (B, modified after Blumberg and Müller 1970). In the Czochralski method (A) a crystal is grown by continuously pulling out of an alumina melt. In the Verneuil process (B), alumina powder is melted to small droplets that fall onto the growing crystal, where they crystallize in the same lattice orientation as the underlying crystal substrate.

collected as small spherules. Data about the composition of the alumina starting material as well as about the oxygen isotope composition of the O2 used, however, are not known. The second sample is “Crackle corundum”, which is a granulate made by crushing of alumina crystals that were produced by the Verneuil process. As in the case of “Alumina microbeads”, not further details about the production process, e.g., the composition of the O2 gas used, are known. A mixture of “Alumina microbeads” and “Crackle” corundum was used as starting material for the Czochralski process. The pre-fused material is used because of its higher bulk density. Usage of powdered alumina from the Bayer process would require fusion, followed by refilling of the crucible before the growth can start. A Czochralski-grown ruby and a Czochralski-pulled sapphire (both FEE, Idar-Oberstein, Table 2) were also analyzed. The ruby and sapphire were pulled from an alumina melt at a temperature exceeding the melting point of alumina at 2072°C. The atmosphere during the crystal growth was a mixture of N2 with 0.5 vol.% of air, i.e., 0.105 vol.% O2. The melt mass was 6–8 kg and the crystal pulling took ~ 10 days. The apparatus was flushed at a rate of 0.5 m3 h–1. This translates to a total amount of oxygen of 10.3 mol O (in form of O2) that went through the apparatus. This number is small compared to the 208 mol O that is contained in 7 kg of well-mixed liquid alumina. This small mass balance calculation demonstrates that, under given growth conditions, as maximum, only 5% of the alumina can have equilibrated with air. In reality, this number may well be an order of magnitude lower as only a small fraction of the O2 contained in the N2 atmosphere ever will have touched the melt surface. The oxygen isotope compositions of the oxyhydrogen flame fused and the Verneuil alumina starting materials and the Czochralski grown ruby and sapphire are listed in Table 2 and illustrated in Fig. 7. The δ18O of the oxyhydrogen flame fused and Verneuil starting material (“Alumina microbeads” and “Crackle”) varies from 22 to 33‰. The variations among the different fragments of the “Crackle” (Table 2) are attributed to the rapid and likely incomplete exchange process between the alumina melt droplets and flame oxygen while the droplets fall through the flame. The data fall on a tight mixing trend of the raw materials with slope λ = 0.509.

236

Pack

Although air O2 does not fall on that trend, the low Δ′17O of the raw materials and the crystals made from them is clearly related to the influence technical O2 that was prepared by liquefaction from air O2. Pack et al. (2007) showed that technical O2 can vary in δ18O between 0 and 30‰, but, because of mass-dependent fractionation during the oxygen production (λ ≈ 0.524), that the anomaly in Δ′17O is preserved. The isotope compositions of the Czochralski grown ruby and sapphire plot on a mixing trend between “Alumina microbeads” and “Crackle” (Fig. 7), which is expected as these materials were used as starting materials. It was discussed that likely no isotope exchange had affected the isotope composition of the melt during the Czochralski process. The observation that the Δ′17O of the sapphire and ruby crystals is identical to that of air is a mere coincidence and results from the compositions and mixing ratios of the raw materials. The data presented here show that synthetic alumina (corundum, ruby, sapphire) can clearly be distinguished from natural corundum, ruby and sapphire in that the synthetic crystals have a much lower Δ′17O resembling that of air O2 and its technical derivatives. Hence, Δ′17O is a clear and difficult-to-manipulate indicator of the gemstone formation process. The studied Czochralski grown ruby and sapphire crystals largely reflect the Δ′17O of the modern atmosphere along with mass-dependent variation due to the liquefaction process. As such, they can be regarded a suitable proxy for the pCO2 · GPP. One can imagine that a centimeter to decimeter sized synthetic alumina crystal is highly resistant to any kind of isotopic modification by geological processes. In the far future (e.g., billions of years from now), such then fossil Czochralski-grown ruby and sapphire crystals buried in sedimentary rocks could serve an isotope geochemist as a unique tracer of anthropogenic activity and as an atmospheric proxy.

CONCLUSIONS It has been stated by Bao (2015) “[…] that sulfate, to this point, is the only compound from which direct atmospheric O2 and O3 signals from the distant past can be retrieved.” In this chapter, I highlight that not only sulfate, but a number of other solids carry information about the isotope anomaly of air O2. The processes are exchange at high temperatures and/or transfer of O2 during an oxidation process. Some of the materials are potential proxies for the Δ′17O of air O2.

ACKNOWLEDGEMENTS The constructive reviews by Laurence Y. Yeung and Huimin Bao helped improving the manuscript. Ilya Bindeman is thanked for initiating this volume, his comments and for the editorial handling. Dennis Kohl, Nina Albrecht, and the entire lab team is thanked for their various contributions. Klaus Dupré is thanked for providing alumina crystals ad background information. Christian Stübler is thanks for allowing me to use his data from his BSc theses.

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PhD thesis, Rheinische Friedrich Wilhelms Universität, Bonn, 164 pp Pack A, Herwartz D (2014) The triple oxygen isotope composition of the Earth mantle and understanding Δ17O variations in terrestrial rocks and minerals. Earth Planet Sci Lett 390:138–145 Pack A, Hoernes S, Göbbels M, Broß R, Buhr A (2005) Stable oxygen isotopes—a new approach for tracing the origin of oxide inclusions in steel. Euro J Mineral 17:483–493 Pack A, Toulouse C, Przybilla R (2007) Determination of oxygen triple isotope ratios of silicates without cryogenic separation of NF3—technique with application to analyses of technical O2 gas and meteorite classification. Rapid Commun Mass Spectrom 21:3721–3728 Pack A, Gehler A, Süssenberger A (2013) Exploring the usability of isotopically anomalous oxygen in bones and teeth as paleo-CO2-barometer, Geochim Cosmochim Acta 102: 306–317 Pack A, Tanaka R, Hering M, Sengupta S, Peters S, Nakamura E (2016) The oxygen isotope composition of San Carlos olivine on VSMOW2-SLAP2 scale. Rapid Commun Mass Spectrom 30:1495–1504 Pack A, Höweling A, Hezel DC, Stefanak M, Beck AK, Peters ST M, Sengupta S, Herwartz D, Folco L (2017) Tracing the oxygen isotope composition of the upper Earth atmosphere using cosmic spherules. Nat Commun 8:15702 Payne RC, Brownlee D, Kasting JF (2020) Oxidized micrometeorites suggest either high pCO2 or low pN2 during the Neoarchean, PNAS 117:1360 Passey BH, Levin NE (2021) Triple oxygen isotopes in meteoric waters, carbonates, and biological apatites: implications for continental paleoclimate reconstruction. Rev Mineral Geochemistry 86:429–462 Peters ST, Alibabaie N, Pack A, McKibbin SJ, Raeisi D, Nayebi N, Torab F, Ireland T, Lehmann B (2020) Triple oxygen isotope variations in magnetite from iron-oxide deposits, central Iran, record magmatic fluid interaction with evaporite and carbonate host rocks. Geology 48:211–215 Sengupta S, Pack A (2018) Triple oxygen isotope mass balance for the Earth’s oceans with application to Archean cherts. Chem Geol 495:18–26 Sharp ZD, Wostbrock J (2021) Standardization for the triple oxygen isotope system: Waters, silicates, carbonates, air, and sulfates. Rev Mineral Geochem 86: 179–196 Sharp ZD, Gibbons JA, Atudorei V, Pack A, Sengupta S, Shock EL, Knauth LP (2016) A calibration of the triple oxygen isotope fractionation in the SiO2–H2O system and applications to natural samples. Geochim Cosmochim Acta 186:105–119 Sharp Z, Wostbrock J, Pack A (2018) Mass-dependent triple oxygen isotope variations in terrestrial materials. 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Reviews in Mineralogy & Geochemistry Vol. 86 pp. 241–290, 2021 Copyright © Mineralogical Society of America

Triple Oxygen Isotopes in Evolving Continental Crust, Granites, and Clastic Sediments Ilya N. Bindeman Department of Earth Sciences University of Oregon Eugene OR 97403-1272 USA [email protected]

INTRODUCTION This Chapter considers triple oxygen isotope variations and their 4 Gyr temporal evolution in bulk siliciclastic sedimentary rocks and in granites. The d18O and ∆′17O values provide new insights into weathering in the modern and ancient hydrosphere and coeval crustal petrogenesis. We make use of the known geological events and processes that affect the rock cycle: supercontinent assembly and breakup that influence continent-scale and global climate, the fraction of the exposed crust undergoing weathering, and isotopic values of precipitation. New data from a 5000 m Texas drillhole into the Oligocene Frio Formation demonstrate minimal isotopic shifts from mudrocks to shales during diagenesis, mostly related to expulsion of water from smectite-rich loosely cemented sediment and its conversion to illite-rich shale. Inversion of triple oxygen isotope fractionations return isotopic values and temperatures along the hole depth that are more consistent with weathering conditions in the Oligocene and modern North America (d18O = −7 to −15‰, and T of +15 to +45 °C) rather than d18O from 8 to 10‰ diagenetic water in the drill hole at 175–195 °C. More precise T and d18Owater are obtained where the chemical index of alteration (CIA) based detrital contribution is subtracted from these sediments. Triple oxygen isotopes from suspended sediments in major world rivers record conditions (T and d18Ow) of their watersheds, and not the composition of bedrock because weathering is water-dominated. In parallel, the Chapter presents new analyses of 100 granites, orthogneisses, migmatites, tonalite-trondhjemite-granodiorite (TTG), and large-volume ignimbrites from around the world that range in age from 4 Ga to modern. Most studied granites are orogenic and anatectic in origin and represent large volume remelting/assimilation of shales and other metasediments; the most crustal and high-d18O of these are thus reflect and record the average composition of evolving continental crust. Granites also develop a significant progressive increase in d18O values from 6–7‰ (4–2.5 Ga) to 10–13‰ (~1.8–1.2 Ga) after which d18O stays constant or even decreases. More importantly, we observe a moderate −0.03‰ step-wise decrease in ∆′17O between 2.1 and 2.5 Ga, which is about half of the step-wise decrease observed in shales over this time interval. We suggest that granites, as well as shales, record the significant advent and greater volumetric appearance of low-∆′17O, high-d18O weathering products (shales) altered by meteoric waters upon rapid emergence of large land masses at ~2.4 Ga, although consider alternative interpretations. These weathering products were incorporated into abundant 2.0–1.8 Ga orogens around the world, where upon remelting, they passed their isotopic signature to the granites. We further observe the dichotomy of high-∆′17O Archean shales, and unusually low-∆′17O Archean granites. We attribute this to greater contribution from shallow crustal hydrothermal contribution to shales in greenstone belts, while granites in the earliest 3.0–4.0 Ga crust and TTGs require involvement of hydrothermal products with lower-∆′17O signatures at moderately high-d18O, which we attribute to secondary silicification of their protoliths before partial melting. 1529-6466/21/0086-0008$500 (print) 1943-2666/21/0086-0008$5.00 (online)

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The Chapter further discusses evolution of the shale record through geologic history and discusses the step-wise change in d18O and ∆′17O values at Archean–Proterozoic transition. Denser coverage for shales in the past 1 billion years permits investigation of the rocks and their weathering in the last supercontinent cycle, with observed lighter d18O values, characteristic for the mid-Phanerozoic at the initiation of Gondwana breakup. The continuing increase in d18O values of the shales since 4 Ga is interpreted to reflect accumulation of weathering products via shale accretion to continents, as low-density and buoyant shales tend to not subduct back into the mantle. The rock cycle passes triple oxygen isotopic signatures from precipitation to sedimentary, metasedimentary, and finally to anatectic igneous rocks. Continental crust became progressively heavier in d18O, lighter in ∆′17O due to incremental accumulation of high-d18O sediments in accretionary wedges. Second-order trends in d18O and ∆′17O are due to supercontinent cycles and glacial episodes. The evolution of continental crust since its formation in the early Archean has been a major theme of petrologic investigation for many decades (Goldschmidt 1933; Taylor and MacLennan 1995; Wedepohl 1995; Rudnick and Gao 2003; Greber et al. 2017; Spencer et al. 2017; Bucholz et al. 2018). The appearance of each new chemical analytical method or a new isotopic system, as well as improving geological and geochronologic investigation and recognition of ancient geologic formations adds greater understanding of Earth and the early processes of its evolution. It is reasonable to assume that weathering conditions on Earth have evolved as conditions (such as solar luminosity and CO2 and O2 concentrations) changed, and thus both uniformitarian and non-uniformitarian approaches can apply, especially to the Archean. As the Archean and Proterozoic eons capture ~88‰ of Earth′s history, most events occurring in Earth′s crust are rooted there: the timing and rate of plate tectonics, the appearance of first continents, their composition (mafic vs. silicic); their emergence from water as subaerial land masses, the evolution of the atmosphere and the causes of the Great Oxidation Event at 2.3 Ga, Snowball Earth glaciations in early and late Proterozoic, and the appearance of microbial and multicellular life (Holland 1984; Buick et al. 1998; Bekker and Holland 2012; Hoffman 2013).

Shales, what do they reflect? Mudrocks constitute 50 to 80% of total sedimentary rock mass (Pettijohn 1957, Ronov and Yaroshevsky 1969), and shales have been traditionally used to deduce the role of continental weathering and sediment recycling through geologic time, and to constrain the average chemical composition of the exposed and eroding continental crust (Goldschmidt 1933; Wedepohl 1995; Rudnick and Gao 2003). Their chemical and isotopic compositions have been used since the early days of geochemistry to address weathering conditions and sediment provenance, and address fundamental questions of elemental and isotopic fluxes from and into the mantle and the hydrosphere, and element and isotope recycling in the framework of plate tectonics, after the acceptance of that theory (Holland 1984). Unmetamorphosed clay-rich shales are known to exist since 3.4–3.5 Ga, and they are relevant to the study of conditions under which organic matter becomes incorporated into weathering products throughout geologic history (Buick et al. 1998; Hayes et al. 1999; Retallack 2001; Sageman and Lyons 2004; Kump 2014). Like many other sedimentary rocks, shales and mudrocks represent a mixture of detrital and authigenic (equilibrated with weathering fluid at a specific temperature and water, and less pronounced exchange during transport and post-depositional diagenesis) components (Sageman and Lyons 2004). The authigenic component is important for recording environmental factors. Silverman (1951), Savin and Epstein (1970a,b) and Bindeman et al. (2019) demonstrated that oxygen isotopic values of recent sediments and authigenic shale samples reflect exclusively isotopic values of meteoric water at respective values of temperature, since weathering proceeds with a great excess of water over rocks.

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Other isotopic systems in sediments such as Sr, Nd, Hf, Mg, Li, Ti, and Si, whose dissolved concentration in weathering water is low, reflect provenance (exposed bedrock) of the crust undergoing weathering (Goldstein and Jacobsen 1988; Bayon et al. 2015, 2018, 2020; Li et al. 2016; Dellinger et al. 2017; Greber et al. 2017). Therefore shales and their constituent detrital and secondary minerals are a valuable resource for the investigation of the detrital portion of crustal maturation. In their oxygen and hydrogen isotopes they additionally record evolving weathering conditions: d18O and temperature on the Earth′s surface (Fig. 1), which themselves are related to watershed latitude, and global climate as well as the concurrent (and hotly debated!) d18O value of seawater. This complexity creates both significant opportunities and challenges in the application of isotope geochemistry to sedimentary environments. Shales remained the “most studied but poorly understood rock” (Shaw and Weather 1965), but recent advances in isotopic analysis of multiple elements in shales and sediments will solve many of the puzzles stored in shales. Prior efforts to characterize stable isotopes in shales, mudrocks, soil weathering profiles, and marine sediments date back to the early 1970s (Savin and Epstein 1970a,b) using conventional methods and relying on 30 mg of material. The d18O and dD isotopic investigation of shales and the details of their partitioning among their constituent minerals (clay minerals and secondary quartz) has been performed in the past in great detail by Taylor and Epstein (1962), Savin and Epstein (1970a,b), Yeh and Savin (1976), Yeh and Epstein (1978), and others (Churchman et al. 1976; Savin and Lee 1988; Sheppard and Gilg 1996). Their results showed that: 1) The clay and quartz components in shales are isotopically heavy, and d18O is shifted during weathering by a few to +25‰ with respect to the the mantle or the igneous protolith, with meteoric waters diverse in d18O, and at different temperatures. 2) Upon formation of secondary minerals and their accumulation in sedimentary basins, rates of isotope exchange with ambient water are slow, and thus shales show little isotope exchange with lacustrine or sea waters after deposition (Land and Lynch 1996). 3) Diagenesis occurs in a narrow temperature window of 80 to 120 °C (Eberl 1993) and leads to a profound change in clay mineralogy and morphology (e.g., smectite and kaolinite are transformed into illite

Mackenzie

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Figure 1. The isotopic composition of precipitation in the modern world, and river basins that were sam)LJ&RORU pled for triple oxygen isotope analysis of suspended sediments. The sampled river basins cover most of the modern environments of weathering from tropical to Arctic, and from wet to arid. XRD-determined clay proportions for selected rivers and global average are shown. Predominant watershed bedrock types are also shown, but isotopic values of clays are not influenced by the bedrock, and reflect predominantly the temperature of weathering and d18OMW. [Used by permission of Elsevier, from Bindeman et al. (2019), EPSL, Vol. 528:115851, Fig. 1]

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and chlorite, developing shistosity (Fig. 2). However, these changes may cause only 1–2 permil d18O increases due to loss of porewaters (Wilkinson et al. 1992), and they do not erase the multi-permil isotopic differences between shales formed in diverse environments. 4) Low post-diagenetic Darcy permeability of fine-grained shales leads to the preservation of both O and H isotopic signatures in the geologic record, far better than in cherts or carbonates (Land and Lynch 1996; Sheppard and Gilg 1996). 5) After diagenetic reactions are complete, finegrained shales become virtually impermeable to secondary waters (Fig. 2, Pettijohn 1957). Of the many chemical and isotopic proxies targeting these diagenetic processes, oxygen isotopes serve as the boundary between evolving lithosphere and hydrosphere, as oxygen makes up 49–53 wt% of rocks and 89 wt% of waters. Upon weathering, oxygen (and hydrogen) isotopic values of weathering products reflect that of the water, due to the great quantitative excess of water over rock (Silverman 1951; Savin and Epstein 1970a,b). Likewise, chemical precipitates from sea or meteoric water reflect the oxygen isotopic value of that water. If unaltered by subsequent isotopically different waters, these chemical sediments (carbonates, cherts, phosphates, etc.) should reflect the original oxygen isotopic values. It is also important to stress that shales record d18O and d17O values of precipitated water, while cherts, carbonates and phosphates for the most part provide a record of seawater. A

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Figure 2. Shales and their isotopic values. These figures demonstrate the utility of using bulk shale as a proxy for weathering conditions, and that more tedious analysis of fine clay fractions shows equal scatter in the results. A) An unaltered shale with fine-grained texture, and a shale core sample that underwent secondary alteration, visible in disruption of thinly laminated schistosity, and recrystallization into coarser texture. Wells 6 and 1 Pleasant Bayou, Brazoria County Texas. B) Comparison of bulk shale analysis with that of the fine clay 80 wt.% quartz are shown for cherts from Liljestrand et al. (2020). The inset in the upper right corner shows our data normalized using a two-point calibration using UWG−2 and SKFS standards (Miller et al. 2020; updated values in Sharp and Wosbrock 2021, this volume), demonstrating the negligible effect of scale compression issues. The red points depict ‘stretched’ values, while black points are normalized using the single-point normalization (same as in the large plot).

values ranging between 19 and 25‰. Their Δ′17O values are varying within −0.08 ± 0.01‰, significantly lower than that of the Mendon and Dresser Formations. The two samples of the Reykjanes geothermal scale have δ′18O of +14.2 and +14.6‰, accompanied by a Δ′17O of −0.03‰. The results of triple oxygen isotope analyses are reported in Supplementary Table 1. The new SIMS values are reported for 2 samples from Schreiber Beach and Frustration Bay (Gunflint Formation) and one sample PPRG193 (from the Kromberg Formation) in Supplementary Table 2. The results of previous investigations by Marin-Carbonne et al. (2012) are compiled in Supplementary Table 2 as well. PPRG193 returned the range of δ′18O values between +14.2 and +15.2‰, with an average of +14.8 ± 0.3‰ (n = 23). The δ′18O values range between +18 and +26‰, with an average value of +23.7 ± 1.8‰ (mean ± σ; n = 90) for the two Gunflint samples, Schreiber Beach and Frustration Bay. We found that in the Schreiber Beach sample the δ′18O values vary on a scale of ~100 μm by 8‰ (Fig. 4). The megaquartz segregations are particularly low in δ′18O, as low as 18‰, while microquartz and chalcedony reach values of +26‰. These are shown in Figure 4B. The δ30Si in Schreiber Beach varies between +0.8 and +2.5‰ with an average value of +1.9 ± 0.4‰ relative to NBS28. The linear regression (Fig. 8) constructed based on the δ′18O bulk vs. mean δ′18O SIMS values yields a slope of 0.8 ± 0.1 and a y-intercept of 4 ± 2‰ (mean ± 1se). It is worth noting that the previous SIMS

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measurements were specifically designed to preferentially target microcrystalline δ′18O quartz resulting in somewhat higher (1−2‰) mean δ18O values compared to the measurements by bulk laser fluorination (Fig. 8). This suggests that bulk fluorination analyses inevitably contain fragments of altered and recrystallized cherts with δ′18O values lower than that of microquartz. The overall δ′18O range of the samples is consistent with the values determined in previous studies (Hayles et al. 2019; Liljestrand et al. 2020). However, the Δ′17O are mostly slightly elevated compared to previous analyses of triple oxygen isotope values in Archean and early Paleoproterozoic cherts produced by Liljestrand et al. (2020), but agree better with the values determined by Hayles et al. (2019). To further improve the comparison, we only plotted samples from Liljestrand et al. (2020) that contain > 80 % quartz. The previously measured cherts from Hayles et al. (2019) shown in Figure 9 are from the Gunflint Formation and Onverwacht group that makes comparison even more accurate. Further, we attempted to re-normalize the previously published analyses to the single scale defined by UWG−2 (see Figs. 5 and 9). Despite these procedures, we cannot explain these differences in the datasets as purely related to calibration. We thus suggest that these differences in Δ′17O measured here and in previous studies are at least partly a result of natural variations between samples. This is suggested by the excellent agreement between the samples that come from the same well-preserved Gunflint Formation from this study and from the study of Hayles et al. (2019). The samples from the Kromberg Formation reported here and in Liljestrand et al. (2020) are more difficult to compare because the formation includes multiple chert layers with variable δ18O values (Knauth and Lowe 2003). Further, we observe a positive correlation between the δ′18O values determined in bulk samples and the average of the δ30Si values determined by SIMS (Fig. 8). Consequently, the Δ′17O values correlate negatively with δ30Si. This relationship between the triple oxygen isotope and silicon isotope values (Fig. 8) has not been identified in the previous studies. We suggest that the δ′18O–Δ′17O–δ30Si correlation documents preservation of distinct differences between samples that, in turn, can be used to decipher the processes recorded in isotope signals. The δD values and water content. The hydrogen isotope values range between −110 and −60‰ with water contents between 0.1 and 1.2 wt. % (Fig. 10). The Mendon and Dresser cherts have the lowest water contents, below 0.2 wt. %, and δD ranging from −100 to −60‰. The early Paleoproterozoic Gunflint cherts contain 0.3−1.2 wt. % water and δD values between −110 and −90‰. Within each group of samples there is no significant relationship between hydrogen and oxygen isotope ratios or the water contents (Fig. 10). We observe no systematic difference between the duplicated analysis of the same chert samples using 3−4 mg or 7−9 mg of analyte. The δD values are variable within ~10‰ between the replicates with the exception of two samples where the difference is close to 20‰, likely reflecting natural variability as the analytical precision of this method is ±1‒3‰ (Fig. 10). The water content of the duplicated measurements varies within  60 °C; see Fig. 1). However, given that carbonates are even more soluble than quartz, the complexity of diagenetic interactions with fluids must bear a significant impact on the isotope signature of ancient sediments. Moreover, recent clumped isotope studies of early Phanerozoic carbonates show that many samples experienced diagenetic alteration (Cummins et al. 2014; Bergmann et al. 2018; Ryb and Eiler 2018), and that the preserved samples do not bear evidence for exceptionally high oceanic temperatures or for drastically low seawater δ18O. Similarly to microanalytical investigations of cherts, ancient (postCenozoic) carbonates require detailed imaging and trace elemental measurements to define the best preserved domains (Grossman 2012). Bergmann et al. (2018) provided estimates for Ordovician and Cambrian seawater that range between −2.5 and + 3‰ in δ18O and with temperatures between 26 and 38 °C. However, the recent iron oxide sedimentary record (Galili et al. 2019) presents yet another challenging evidence for the change in oxygen isotope

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values of seawater through time, where Cambrian and Precambrian time was characterized by seawater with δ18O at least 5‰ lower than today, inconsistent with the clumped isotope studies of the early Phanerozoic and with the model presented in Figure 13. Though the iron oxide record has not been explored in detailed by in situ methods, it presents an interesting low-solubility archive of both the redox and isotope evolution of terrestrial oceans. In our suite of samples, the oxygen isotope variations do not require a significantly different triple oxygen isotope composition of seawater outside the realm of variable fluxes (Fig. 13). Recrystallization during late diagenesis or metamorphism is likely to disturb the primary signal shifting the triple oxygen isotope composition downward in terms of Δ′17O, towards the composition of fluids that reacted with crustal rocks.

FUTURE DIRECTION AND CONCLUSIONS Fractionation of triple oxygen isotopes between fluids and minerals is a powerful tool recently added to the arsenal of geochemists studying ancient marine record. Theoretically, the δ′18O–Δ′17O values measured in a pristine microquartz that formed during the last silica transformation within the subseafloor setting should reflect the temperature of the transition and the isotope signature of marine pore water fluids. In the realm of Precambrian chert deposits that underwent multiple episodes of recrystallization induced by diagenesis and metamorphism, the measured δ′18O–Δ′17O values likely represent a mixture of equilibrium compositions generated asynchronously. This is evident from the SIMS analyses that reveal several-‰ spatial heterogeneity in δ′18O values within each sample. Sometimes, but not always, the heterogeneities are accompanied by petrographic distinction, e.g., low δ′18O veins in high δ′18O microquartz. The distance between several-‰ heterogeneities varies on the scale of 10−100 μm. Consequently, the currently available triple oxygen isotope values of cherts produced by bulk laser fluorination GS-IRMS measurements of ~1 mm3 samples are unlikely to give completely accurate reflections of the original marine pore fluids and equilibrium temperatures. The question then is, which composition measured by SIMS corresponds to the seafloor-deposited silica that underwent just the early stage of marine diagenesis? Is it possible to reconstruct the δ′18O–Δ′17O values of this phase? We suggest that future triple oxygen isotope endeavors should include careful investigation of chert samples with identification of multiple generations of silica. Then, selection of the best-preserved domains could be assessed by trace element measurements, CL-imaging, and δ′18O and δ30Si values measured in situ. Following that, the triple oxygen isotope composition should be measured on these distinct generations of quartz, perhaps using micro-drilling of the samples or partial fluorination. Additional triple oxygen isotope measurements of modern silica sediments carried out across the phase transitions, aided by measurements of local geothermal gradient and pore water fluids (see example in Yanchilina et al. 2020) would greatly assist our understanding of the ancient silica cycle. In this study we examined the triple oxygen isotope compositions of Precambrian cherts accompanied by SIMS measurements. We provided an attempt to disentangle triple oxygen isotope signals of early and late quartz generations in the Precambrian cherts of the wellstudied Dresser, Kromberg, Mendon and Gunflint Formations using SIMS-determined δ′18O and δ30Si values that span several ‰ within the samples. Aided by measurements of Al and Ti concentrations, δ30Si values, and Raman spectroscopy, we provide estimates for the triple oxygen isotope signature of the early microquartz and late-stage recrystallized quartz on a case-by-case basis. Using the Raman spectroscopy of organic matter hosted in these samples, we derived the maximum possible temperature at which recrystallization might have occurred. Further, by using δD values measured in the same samples we tested for the involvement of meteoric water during the recrystallization of the cherts. We found that the data set is best explained by the following:

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The Archean 3.5 Ga Dresser, 3.4 Ga Kromberg and 3.2 Ga Mendon cherts contain low-Al microquartz that was likely the earliest generation of silica precipitated in an environment with mixed hydrothermal and seawater input. The triple oxygen isotope signature of samples with negative δ30Si values is consistent with precipitation of microquartz at 150−170 °C and some contributions from vent fluids. The extrapolation of vent fluids towards pristine seawater does not require a hydrosphere significantly different from the modern-day and ice-free world values. This interpretation applies to the samples studied here, which does not mean that all Archean cherts formed from mixed hydrothermal solutions. However, each chert deposit needs to be evaluated for the influence of marine vs hydrothermal contributions to its isotope composition.

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The triple oxygen isotope signature of modern amorphous silica scale precipitated in pipelines of the seawater-dominated hydrothermal system at Reykjanes, Iceland is used here as a possible analogue of Archean chert deposits that resulted from reaction between seawater and basalt. The Reykjanes silica formed at ~188 °C due to high-temperature reaction between basalt and seawater. The δ′18O−Δ′17O values of such silica are is in good agreement with this temperature and previous measurements of the Reykjanes well fluids. Based on the triple oxygen isotopes, we suggest that at least some of the Archean chert deposits might reflect a similar regime of silica precipitation. Such cherts would have δ′18O−Δ′17O values defined by high-temperature exchange reactions with basaltic rocks at different water–rock ratios. At decreasing water–rock ratios, the silica acquires Δ′17O values lower than that of silica in equilibrium with pristine seawater.

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The Paleoproterozoic Gunflint chert contains a high-δ′18O generation of microquartz that is thought to originally crystallized from marine siliceous sediment based on trace element concentrations and silicon isotope measurements. We interpret the triple oxygen isotope signature of such microquartz as a record of marine pore fluids. The δ′18O­−Δ′17O of such quartz is consistent with an equilibrium temperature of 60−80 °C, given that the pore fluid values had δ′18O of around −2‰.

•

Triple oxygen isotope values of secondary quartz resulting from dissolution– reprecipitation of original material indicates involvement of crustal fluids, akin to modern basinal brines. The temperature of the imposed signature is estimated from Raman-spectroscopy at 330 ± 30 °C and 160 ± 30 °C for the Archean and Paleoproterozoic formations, respectively. These estimates help to assess the preservation state of the original microquartz. They do not necessarily indicate that oxygen isotope exchange occurred at these temperatures, however in the case of Onverwacht group cherts, these temperatures are close to the homogenization temperatures measured in chert-hosted fluid inclusions (Marin-Carbonne et al. 2011). These temperatures also allow us to suggest that the fluids altering primary signals might have ranged between +2 and +5‰, and that their Δ′17O values are low, close to −0.1‰, characteristic of crustal origin. Such fluids would cause cherts to become low in Δ′17O, between −0.06 and −0.1‰, offering a generalized explanation for some of the low-Δ′17O cherts present in the global dataset (Fig. 12).

Triple oxygen isotope investigation of Precambrian cherts, even in combination with highresolution methods, demonstrates their polygenic nature and limited utility to directly read isotopic values of the seawater and the Earth’s surface temperatures. Despite the complexity of chert deposition and its cycle through diagenetic and metamorphic transformations, the recorded secular isotope trend is still best explained by the temperature control, but not in a straightforward way as a reflection of ocean temperatures. The high-temperature early diagenetic and hydrothermal processes fueled by circulation of seawater within seafloor sediments can account for the signature of some Archean cherts without the need to invoke a significantly different oxygen isotope value of the terrestrial hydrosphere. Future triple oxygen isotope investigations of cherts should involve samples that underwent careful examination in the context of geological setting, trace elemental and mineralogical composition, as well as microscale isotope variations.

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ACKNOWLEDGEMENTS We are thankful to Stanley Awramcik, Bill Schopf, François Robert for donating their samples to this study and previous studies, and Mike Hudak for measuring the δD values in cherts. We also thank Vigdís Hardardóttir for granting the samples of Reykjanes silica scales for triple oxygen isotope analyses and Mark Reed for facilitating the access to the samples. JMC and JA thank the European Research Council (ERC) under the European Union’s Horizon program (STROMATA, grant agreement 759289). INB and DOZ thank the NSF grant EAR #1833420. We are grateful to the reviewers Daniel Herwartz and Zach Sharp for their input, comments and suggestions that helped to improve the manuscript. We also greatly appreciate Dylan Colón’s help proofreading the manuscript.

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Astrobiology 10:381–395 Wacey D, Menon S, Green L, Gerstmann D, Kong C, Mcloughlin N, Saunders M, Brasier M (2012) Taphonomy of very ancient microfossils from the 3400 Ma Strelley Pool Formation and 1900 Ma Gunflint Formation: New insights using a focused ion beam. Precambrian Res 220:234–250 Walker JC, Lohmann KC (1989) Why the oxygen isotopic composition of sea water changes with time. Geophys Res Lett 16:323–326 Watkins JM, Hunt JD (2015) A process-based model for non-equilibrium clumped isotope effects in carbonates. Earth Planet Sci Lett 432:152–165 Wenner DB, Taylor HP (1973) Oxygen and hydrogen isotope studies of the serpentinization of ultramafic rocks in oceanic environments and continental ophiolite complexes. Am J Sci 273:207–239 Whitehouse MJ, Fedo CM (2007) Microscale heterogeneity of Fe isotopes in > 3.71 Ga banded iron formation from the Isua Greenstone Belt, southwest Greenland. Geology 35:719–722 Whitehouse MJ, Nemchin AA (2009) High precision, high accuracy measurement of oxygen isotopes in a large lunar zircon by SIMSChem Geol 261:32–42 Wilkinson JJ, Jenkin GRT, Fallick AE, Foster RP (1995) Oxygen and hydrogen isotopic evolution of Variscan crustal fluids, south Cornwall, UK. Chem Geol 123:239–254 Williams LB, Hervig RL, Bjørlykke K (1997) New evidence for the origin of quartz cements in hydrocarbon reservoirs revealed by oxygen isotope microanalyses. Geochim Cosmochim Acta 61:2529–2538 Williford KH, Ushikubo T, Schopf JW, Lepot K, Kitajima K, Valley JW (2013) Preservation and detection of microstructural and taxonomic correlations in the carbon isotopic compositions of individual Precambrian microfossils. Geochim Cosmochim Acta 104:165–182 Winter BL, Knauth PL (1992) Stable isotope geochemistry of cherts and carbonates from the 2.0 Ga Gunflint Iron Formation: implications for the depositional setting, and the effects of diagenesis and metamorphism. Precambrian Res 59:283–313 Wopenka B, Pasteris JD (1993) Structural characterization of kerogens to granulite-facies graphite: applicability of Raman microprobe spectroscopy. Am Mineral 78:533–557 Wostbrock JAG, Sharp ZD (2021) Triple oxygen isotopes in silica–water and carbonate–water systems. Rev Mineral Geochem 86:367–400 Wostbrock JAG, Sharp ZD, Sanchez-Yanez C, Reich M, van den Heuvel DB, Benning LG (2018) Calibration and application of silica–water triple oxygen isotope thermometry to geothermal systems in Iceland and Chile. Geochim Cosmochim Acta 234:84–97 Wostbrock JAG, Cano EJ, Sharp ZD (2020) An internally consistent triple oxygen isotope calibration of standards for silicates, carbonates and air relative to VSMOW2 and SLAP2. Chem Geol 533:119432 Xie X, Byerly GR, Ferrell Jr RE (1997) IIb trioctahedral chlorite from the Barberton greenstone belt: crystal structure and rock composition constraints with implications to geothermometry. Contrib Mineral Petrol 126:275–291 Yanchilina AG, Yam R, Kolodny Y, Shemesh A (2020) From diatom opal-A δ18O to chert δ18O in deep sea sediments. Geochim Cosmochim Acta 268:368–382 Yui T-F, Huang E, Xu J (1996) Raman spectrum of carbonaceous material: A possible metamorphic grade indicator for low-grade metamorphic rocks. J Metamorph Geol 14:115–124 Zakharov DO, Bindeman IN (2019) Triple oxygen and hydrogen isotopic study of hydrothermally altered rocks from the 2.43–2.41 Ga Vetreny belt, Russia: An insight into the early Paleoproterozoic seawater. Geochim Cosmochim Acta 248:185–209 Zakharov DO, Bindeman IN, Slabunov AI, Ovtcharova M, Coble MA, Serebryakov NS, Schaltegger U (2017) Dating the Paleoproterozoic snowball Earth glaciations using contemporaneous subglacial hydrothermal systems. Geology 45:667–670 Zakharov DO, Bindeman IN, Serebryakov NS, Prave AR, Azimov PY, Babarina II (2019a) Low δ18O rocks in the Belomorian belt, NW Russia, and Scourie dikes, NW Scotland: A record of ancient meteoric water captured by the early Paleoproterozoic global mafic magmatism. Precambrian Res 333:105431 Zakharov DO, Bindeman IN, Tanaka R, Friðleifsson GÓ, Reed MH, Hampton RL (2019b) Triple oxygen isotope systematics as a tracer of fluids in the crust: A study from modern geothermal systems of Iceland. Chemical Geology 530:119312 Zheng Y-F (1993) Calculation of oxygen isotope fractionation in anhydrous silicate minerals. Geochim Cosmochim Acta 57:1079–1091

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Reviews in Mineralogy & Geochemistry Vol. 86 pp. 367–400, 2021 Copyright © Mineralogical Society of America

Triple Oxygen Isotopes in Silica–Water and Carbonate–Water Systems Jordan A.G. Wostbrock* and Zachary D. Sharp Department of Earth and Planetary Sciences University of New Mexico Albuquerque, NM 87131 USA [email protected] [email protected]

INTRODUCTION The field of stable isotope geochemistry began with the recognition that the oxygen isotope composition of ancient carbonates could be used as a paleothermometer (Urey 1947; Urey et al. 1951). As stated by Urey (1947), “Accurate determinations of the Ol8 content of carbonate rocks could be used to determine the temperature at which they were formed”. This concept was based on the temperature dependence for the oxygen isotope fractionation between calcite and water. Urey realized that if a mass spectrometer with sufficient precision could be built, a method of reproducibly extracting oxygen from solid carbonate could be developed, and the isotope fractionations between calcite and water could be quantified, then the oxygen isotope composition of ancient carbonates could be used to determine the temperature of their formation. This idea led to the carbonate–water temperature scale (McCrea 1950; Epstein et al. 1951, 1953; Urey et al. 1951). The oxygen isotope compositions of marine carbonates are sensitive to temperature (increase with decreasing formation temperature), so that ancient seawater temperatures could be determined by measuring the oxygen isotope composition of the carbonate. Urey et al. (1951) recognized a number of potential problems with the carbonate thermometer, including: 1) the possibility that organisms form out of oxygen isotope equilibrium, a term he called the ‘vital effect’; 2) the possibility that shells might not preserve their oxygen isotope composition over geological time and undergo some sort of post-mortem diagenesis; and 3) the uncertainty in the estimate of the oxygen isotope composition of the formation water. To this last point, the oxygen isotope composition of the ancient seawater is estimated and not measured directly. What is the possibility that the ocean has changed its oxygen isotope composition through time? Urey et al. (1951) concluded that any significant changes would have occurred before the Cambrian, although he states that ‘it is a conclusion based on little more than prejudice’. In spite of these caveats, the carbonate paleothermometer has been immensely successful and applied in many thousands of studies. It also led to the development of other mineral–water thermometers such as silica–water thermometry. However, the concerns raised by Urey remain, despite numerous efforts to ascertain diagenesis and quantify any changes in the ocean oxygen isotope composition through time. Recently, the rare 17O/16O ratio has begun to be measured and included in geologic studies. The addition of this new variable has allowed researchers to discern equilibrium vs. disequilibrium processes governing precipitation of a mineral and determine whether alteration occurred in a sample after its initial precipitation. 1529-6466/21/0086-0011$05.00 (print) 1943-2666/21/0086-0011$05.00 (online)

http://dx.doi.org/10.2138/rmg.2021.86.11

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While triple oxygen isotope measurements (measuring both the 17O/16O and 18O/16O ratios) have been performed on a variety of materials, this chapter reviews the current literature on the triple oxygen isotope fractionation between silica–water and carbonate–water. An overview of both equilibrium and disequilibrium fractionation is given through theory, empirical calibrations, and laboratory experiments. We then apply these different fractionation regimes to geologic samples. We also give a brief overview of how the silica–water and calcite–water triple oxygen isotope fractionation curves can be used to reconstruct past seawater oxygen isotope values. We conclude the chapter by calculating and discussing potential uses of a quartz–calcite fractionation curve.

MINERAL–WATER OXYGEN ISOTOPE THERMOMETERS 18

O/16O fractionation

Oxygen isotope paleothermometers are based on the temperature dependent fractionation between authigenic minerals and their formation water. For marine sediments, we generally assume that the formation water is seawater and that the oxygen isotope composition of the seawater has not varied through time. Obviously, this is a critical assumption that has been questioned and evaluated extensively and is discussed later in this chapter. Oxygen isotope paleothermometers have been developed for carbonates, silicates, phosphates and sulfates. In this communication, we address only the silica–water and carbonate–water paleotemperature equations. We begin with an overview of the generic 18O/16O thermometer. One of the first calibrations of the calcite–water oxygen isotope thermometer took the form (Epstein et al. 1951, 1953) t (°C) = 16.5 – 4.3 d + 0.14 d2

(1)

In this equation δ is the isotopic composition of the CO2 evolved from the carbonate relative to the δ value of CO2 evolved from a reference carbonate (Peedee belemnite or PDB). The δ18O value is defined, in per mil (‰) notation, as  Rsa   1   1000 d18O =  R  std 

(2)

where R is the 18O/16O ratio of the sample (sa) and standard (std). A similar equation can be written for the d17O value, in which case R is the 17O/16O value. Equation (1) is simply a quadratic best fit to empirical data and is not based on any theoretical considerations. Bigeleisen and Goeppert Mayer (1947) showed that the log of the equilibrium fractionation between diatomic molecules should be proportional to T −1 and T −2 (in Kelvin) at low and high temperatures, respectively. The system becomes more complicated with more complex phases, especially when water is considered (Criss 1991). Empirical data are often fit to 1/T, 1/T 2 or a combination of these two. In mineral–water fractionation equations, a constant is often included as a consequence of the high vibrational frequencies of water (Bottinga and Javoy 1973). An appropriate fit to the temperature dependence of fractionation between phase i and water is given by: a  106 (3) c T2 1000  i R Here i H2O  i and in delta notation i H2O  . An alternative form for 1000  H2O RH2O mineral–water fractionation is to add a 1/T term to the equation (e.g., Zheng 1991): 1000 ln i H2O 

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a  106 b  103 (4)  c T2 T The constant in Equations (3) and (4) lead to equations that are not valid at high temperatures because 1000 ln α values approach zero, and not c, at infinite temperatures. An alternative expression is to fit the data to a polynomial of 1/T, such as 1000 ln i H2O 

1000 ln i H2O 

a  106 b  103  T2 T

(5)

The justification of using the form of Equation (3) is apparent when we consider actual data. Figure 1 shows experimental and empirical fractionation data for quartz–water and carbonate–water as a function of 1/T2. The data are approximated by a linear fit and a y intercept (the c term in Eqn. 3) of 3.4‰ (quartz) and 2.95‰ (calcite) (Fig. 1A). Obviously, this relationship fails at very high temperatures, where the 1000 lnα must approach zero. A better fit is expected if we use a polynomial of 1/T and 1/T 2 as predicted from theory (Clayton and Kieffer 1991). A polynomial fit for quartz–water and carbonate–water is shown in Figure 1B. The constant is zero in these fits so that 1000 ln α goes to infinity at infinite temperatures. Both curves have the same general sigmoidal form, indicating that the constant in Equation (3), which is likely valid at lower temperatures (e.g., Bottinga and Javoy 1973) must decrease with increasing temperature. The quartz–water system has been experimentally and empirically studied over a uniquely wide temperature range. Quartz–water exchange experiments have been made between 250 °C and 800 °C (see Sharp et al. 2016 for a compilation). Low temperature empirical fractionation of diatoms and abiogenic silica have been measured over the temperature range of 0 to almost 100 °C (Kita et al. 1985; Leclerc and Labeyrie 1987; Shemesh et al. 1995; Brandriss et al. 1998; Schmidt et al. 2001; Dodd and Sharp 2010). All low- and high-temperature quartz–water fractionation data can be fit to Equation (5), where a = 4.28 ± 0.07 and b = −3.5 ± 0.2 (R2 = 0.9978) (Sharp et al. 2016). Eliminating the c constant allows for the fractionation equation to be extrapolated to infinite temperature. In contrast, carbonate–water experimental and empirical data are better fit to the form of Equation (3) up to ~1000 K (O′Neil et al. 1969; Wostbrock et al. 2020b). Equation (5) does not adequately fit both the high temperature experimental results and low temperature synthesis and empirical data. In this paper we use the general form of Equation (4). Based only on fitting published fractionation data, we set the c term to zero for quartz–water, and the b term to zero for carbonate–water. )LJXUH

Figure 1. Quartz–water (green diamond) and calcite–water (blue circle) oxygen isotope fractionation. A) Best fit using Equation (3) (a × 106/T2 + c) with a negative y-intercept. B) Best fit using Equation (5) (a × 106/T2 + b × 103/T) and a y-intercept of zero. The quartz–water data are better approximated by Equation (5) (Fig. 1B), whereas the carbonate–water data is better fit by Equation (3). Higher order polynomial fits are not warranted, as the errors in the coefficients become very large.

)LJXUH

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Triple oxygen isotope fractionation The equilibrium fractionation of 17O/16O relative to 18O/16O between two phases A and B is given by the equation



17O A  B  18O A  B





(6)

In a linearized format, where δ′ = 1000 ln (δ/1000 + 1) (Hulston and Thode 1965; Miller 2002), δ′A − δ′B = 1000 ln αA–B and Equation (6) can be recast as d′17OA − d′17OB = θ(d′18OA − d′18OB)

(7)

The θ value varies with temperature ranging from 0.5305 at T = ∞ to 0.526, 0.524, and 0.518 − 0.52 at T = 298 K for calcite–water (Wostbrock et al. 2020b), quartz–water (Cao and Liu 2011; Sharp et al. 2016; Hayles et al. 2018), and quartz–calcite (Hayles et al. 2018 and this chapter), respectively. To a first approximation, the temperature dependence of θ for phases A and B is given by (Sharp et al. 2016)  (8) T where ε is a constant, although higher order polynomials are indicated from theory (Cao and Liu 2011; Hayles et al. 2018; Guo and Zhou 2019). Combining Equations (4), (7) and (8) gives the equilibrium d17O fractionation equation between phases A and B:

θΑ−Β = 0.5305 

17

1000 ln  A O/B

16

O

 a  106 b  103    17O A  17O B     c   0.5305   2 T T T    

(9)

For all terrestrial samples not affected by mass independent fractionation processes (e.g., Thiemens 2006), δ′17O varies with δ′18O by the empirical equation known as the Terrestrial Fractionation Line or TFL d′17O = ld′18O + g

(10)

In Equation (10), λ is an empirical best fit to natural data and not tied to any thermodynamic relationship and γ is the y intercept that is generally assumed to be zero. Similar to other chapters in this volume, throughout this work we use a λ value of 0.528. Departures from the linear relationship given in Equation (10) are subtle and expressed using the ∆′17O value, given by the equation D′17O = d′17O – λ d′18O

(11)

The equations governing the mineral–water isotope fractionation for the three oxygen isotopes are the following:

18Omineral  18O water 

a  106 b  103  c T2 T

(12)

 a  106 b  103   17Omineral  17O water     c   0.5305   2 T T T    

(13)

 a  106 b  103    17Omineral  17O water    18O water     c   0.5305     2 T T   T 

(14)

and

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For minerals in equilibrium with seawater similar to Standard Mean Ocean Water (SMOW, δ17O = δ18O = 0), Equation (14) reduces to

 a  106 b  103    (15) 17Omineral     c   0.5305     2 T T   T  Combining Equations (12) and (13) allows us to calculate the relationship between the Δ′17O and δ′18O values of a mineral (subscript r) in equilibrium with water (subscript w). The solution is the following:





17O r  17O w  18O r  18O w 

)LJXUH

 c  18O r  18O w    0.5305  500 b  b 2  4 a c  18O r  18O w  











      18O w    

(16)

Equilibrium triple oxygen isotope fractionation—the Δ′17O–δ′18O plot The benefit of the triple oxygen isotope system is apparent when we plot the Δ′17O value of a mineral against the δ′18O value using Equation (16) (Fig. 2). The triple oxygen isotope plot (Δ′17O vs. δ′18O) allows us to clearly distinguish equilibrium or disequilibrium precipitation for a given sample. Figure 2 is constructed for quartz in equilibrium with ocean water, but an equally relevant figure could be generated for calcite or any other low temperature phase for which triple oxygen isotope fractionation data are available. The solid black curve represents the locus of δ′18O and Δ′17O values of silica in equilibrium with seawater equal to SMOW (yellow star). All silica samples in oxygen isotope equilibrium with SMOW must plot on the solid black curve. Note, that seawater with a δ18O value of 0‰ and Δ′17O value of −0.005‰ can also be used to represent seawater based on Luz and Barkan (2010). In this chapter, we clearly state whether we are using seawater with a Δ′17O value of 0 or −0.005‰. Equilibrium temperatures (in °C) decrease along the curve with increasing δ′18O values and decreasing Δ′17O values. )LJXUH

Figure 2. Δ′17O–δ′18O plot for silica–water. The solid black curve shows the combined Δ′17O–δ′18O values of silica in equilibrium with SMOW (Standard Mean Ocean Water, δ18O = Δ′17O = 0). The position along the line is determined by the temperature of equilibration. The grey line is for a seawater with a δ′18O value of –1‰ (ice free conditions). The dashed curves are the same as the equilibrium fractionation curve (black solid curve) only inverted. The curve′s origin is placed at the silica triple oxygen isotope value and the dashed lines represent the water in equilibrium with the silica. The red and green circles represent two hypothetical samples. The dashed line emanating from the green circle passes through the seawater composition with a 20 °C temperature. The dashed line from the red circle does not intersect seawater. Therefore, the sample represented by the red circle cannot be in equilibrium with seawater at any temperature. It could be in equilibrium with a different water composition, such as the pink square.

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The triple oxygen isotope values of two hypothetical samples are shown in Figure 2 by the red and green circles. Both have δ′18O values of 37.9‰. With δ′18O values alone, the two samples are indistinguishable and correspond to a formation temperature of 20 °C. The addition of the Δ′17O value clearly provides more information. The green circle lies on the equilibrium curve, suggesting that the sample is indeed in equilibrium with seawater at 20 °C. The red circle does not plot on the seawater equilibrium curve. Therefore, this sample cannot be in equilibrium with seawater (δ18O and Δ′17O = 0) at any temperature. Adding the 17O isotope unambiguously demonstrates disequilibrium precipitation with modern seawater and/or equilibrium precipitation with a different water oxygen isotope composition. Lowering the δ18O value of the ocean by ~1‰ during interglacial periods is shown by the grey equilibrium curve (Fig. 2). The Δ′17O value of an ice-free ocean should be close to 0, so the curve moves to −1‰ and does not explain the position of the red circle. As described later in this chapter, the region where the red circle plots in Figure 2 is diagnostic of diagenesis. The quartz-seawater equilibrium curve (solid grey and black curves; Fig. 2) can be inverted such that the origin of the curve is placed on the measured δ′18O–Δ′17O value of the sample (dashed lines; Fig. 2). In this case, the dashed line defines the water composition in equilibrium with that sample. For the green circle, the intersection of the dashed line with SMOW occurs at 20 °C, the apparent equilibrium temperature. The dashed line emanating from the red circle does not pass through SMOW, again indicating that there is no temperature at which this sample can be in equilibrium with seawater. The red circle could be in equilibrium with a water having a δ18O value of –5‰ and δ′17O value of 0‰ (pink square; Fig. 2) or any water with a triple oxygen isotope value the plots on the dashed line emanating from the red circle.

KINETIC EFFECTS RESULTING IN OXYGEN ISOTOPE DISEQUILIBRIUM Rapid precipitation of a mineral at low temperature may result in kinetic effects that lead to disequilibrium oxygen isotope fractionations. The effect was recognized in the first synthesis study of calcite for the purpose of determining the a18OCaCO3–H2O fractionation (McCrea 1950). He found that the δ18O value of rapidly precipitated calcite approached that of the carbonate ion in solution. Disequilibrium has been seen in many natural samples as well. Cave calcite (speleothems) and travertines can precipitate out of oxygen isotope equilibrium due to rapid CO2 degassing (Gonfiantini et al. 1968; Mickler et al. 2006; Carlson et al. 2020). Biogenic calcite can precipitate out of oxygen isotope equilibrium due to the rapid precipitation of calcite resulting in incomplete equilibration between the carbonate ion CO32 and water (McConnaughey 1989), or by changing the relative concentrations of the dissolved carbonate species by changing pH (Spero et al. 1997; Zeebe 1999). On the basis of clumped carbonate isotope measurements (∆47), it has been suggested that most natural calcites are out of oxygen isotope equilibrium (Daëron et al. 2019). The problem appears to be minimal for the silica–water system. Silica–water fractionations are mostly insensitive to biogenic vs. abiogenic conditions (Shemesh et al. 1992; Wostbrock et al. 2018), although there is clear evidence that diatoms precipitate out of equilibrium with water (Schmidt et al. 1997, 2001; Dodd et al. 2012). However, diatoms appear to re-equilibrate with water within a year post-mortem (Dodd et al. 2012; Tyler et al. 2017). The general insensitivity of silica precipitation to kinetic isotope effects is probably related to the simple chemistry of precipitation. Silica forms from H4SiO4 with an intermediate SiOOH+ ion (Crundwell 2017). Solubilities of quartz are extremely low at pH below 9 with H4SiO4 being the principle dissolved species (Krauskopf 1956). Precipitation is generally slow, so that there is minimal disequilibrium between the dissolved species and crystallizing silica.

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Disequilibrium effects with dissolved inorganic carbon Carbonates, on the other hand, have been shown on numerous occasions to precipitate out of thermodynamic equilibrium (Gonfiantini et al. 1968; Shackleton et al. 1973; McConnaughey 1989; Kim and O′Neil 1997; Spero et al. 1997; Zeebe 1999, 2014; Mickler et al. 2004, 2006; Beck et al. 2005; Dietzel et al. 2009; Tremaine et al. 2011; Watkins et al. 2013; Devriendt et al. 2017; Bajnai et al. 2018; Daëron et al. 2019; Carlson et al. 2020). The primary complication that exists for carbonates is that the oxygen isotope fractionation is not simply controlled by the water oxygen isotope composition, but rather by the fractionation between calcite and all dissolved inorganic carbon (DIC) species: CO2(aq), H2CO3, HCO3 , and CO32 . The relevant proportions of these DIC species are strongly controlled by pH, and there is a large oxygen isotope fractionation between them. The 1000 ln a18Ο values (at 25 °C) range from 31.1‰ for HCO3 –H2O to 24.2‰ for CO32–H2O (Beck et al. 2005). Combining these results with the acalcite–water demonstrates that HCO3 has a higher δ18O value than coexisting calcite, whereas CO32 has a much lower δ18O value than calcite. Dissolved inorganic carbon is mainly present as HCO3 at intermediate pH, but CO32 at high pH. When all species are in oxygen isotope equilibrium, pH has no effect on fractionation between calcite and water. Calcite precipitation is governed by the reaction (Garrels and Christ 1965) (17)

Ca 2+ + CO32 = CaCO3 2 3

and, as long as the CO ion is in equilibrium with water, and calcite precipitates in equilibrium with all DIC species, then the calcite is also in equilibrium with water. The equilibrium δ18O value of all dissolved carbonate species is determined by the δ18O value of water, which is overwhelmingly the predominant oxygen reservoir. Several phenomena lead to disequilibrium oxygen isotope values during calcite precipitation. First, a transient disequilibrium between the dissolved carbonate species and water will occur if the pH of the system is rapidly changed. This happens for example, when CO2 is added to or lost from the system. When subterranean CO2-saturated waters reach the surface, they rapidly degas CO2, pH increases and calcite (travertine) precipitates. Second, kinetic effects at the surface of a growing calcite crystal may lead to non-equilibrium if the rates of incorporation and detachment of the HCO3 and CO32 ions into the carbonate lattice are different (Watkins et al. 2013). Because the relative proportions of DIC species are strongly controlled by pH, the δ18O values of some shell-secreting organisms are affected by the pH of the solution (Spero et al. 1997; Zeebe 1999; Adkins et al. 2003). For the reaction HCO3 ↔ H+ + CO32   (18)   2 isotopic equilibrium is reached almost instantaneously because the protonation of CO3 and deprotonation of HCO3 are extremely rapid. Equilibration between the bicarbonate ion and water and dissolved CO2 (or H2CO3) occurs far more slowly. Equilibrium between H2O and DIC will occur via CO2 hydration and hydroxylation by the reactions

and

CO2 + H2O ↔ H2CO3 ↔ H+ + HCO3 

CO2 + OH− ↔ HCO3

(19) (20)

Equation (19) controls equilibration rates at moderate pH, Equation (20) becomes important at high pH with higher OH− concentrations. Oxygen isotope equilibration between H2O and DIC requires hours to days, depending on temperature and pH (Mills and Urey 1940; McConnaughey 1989; Beck et al. 2005; Uchikawa and Zeebe 2012; Watkins et al. 2013)1. 1

Mills and Urey (1940) found very similar rates for DIC–water equilibration as later work.

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The δ18O value of the sum of the hydrated DIC species is given by

 

18

 O( DIC ) 18











OH2CO3 H 2 CO3   18OHCO3 HCO3   18OCO32 CO32   H 2 CO3   HCO3   CO32  

(21)

where the square brackets are the concentration of the dissolved species (Zeebe 1999). Note that dissolved CO2 is not considered in our computation of the δ18OΣ(DIC) value. If all dissolved species are in equilibrium with water, then the δ18OΣ(DIC) value will change with pH (Fig. 3). At low pH (below about 6.5), the δ18OΣ(DIC) value will be equal to that of H2CO3 (δ18O = 39.5‰), which makes up the vast majority of the total DIC. At very high pH (above about 9), the δ18OΣ(DIC) value will be equal to the CO32 ion (δ18O = 18.4‰), which is the predominant DIC species. If the relative incorporation of the DIC species into the carbonate lattice is kinetically controlled, then the oxygen isotope composition of the precipitating calcite will be affected by pH. If all DIC were to be incorporated into a fast-growing calcite, then the δ18O value of the calcite would simply equal the δ18OΣ(DIC). In Figure 3, the δ18O value of the calcite would track along the δ18OΣ(DIC) curve (thick black line). Spero et al. (1997) and Bijma et al. (1999) found a clear linear relationship between pH and the δ18O values of foraminifera, independent of symbiont activity and temperature. There is a well-established kinetic-based pH–δ18O relationship for carbonates that is controlled by non-equilibrium fractionation during hydration and hydroxylation of CO2 or by rate-dependent incorporation of different DIC components. Oxygen isotope disequilibrium can occur due to rapid CO2 degassing or ingassing, such as production or consumption of CO2 within the cell membranes by respiration (McConnaughey 1989). Some researchers suggest that slowly precipitated calcites in caves closer represent thermodynamic calcite–water equilibrium, represented by the higher 1000 ln acalcite–water values than that of most biogenic calcite and laboratory precipitation experiments (Coplen 2007; Tremaine et al. 2011; Daëron et al. 2019). )LJXUH

Figure 3. Effect of pH on the relative abundance of DIC species and on the δ18O value of total dissolved inorganic carbon. At low pH the δ18OΣ(DIC) is nearly identical to that of the H2CO3 species (δ18O = 39.5‰), whereas at very high pH, it is equal to that of theCO32 ion (δ18O = 18.4‰). The above diagram is calcu)LJXUH lated assuming oxygen isotope equilibrium and the total DIC concentration Σ[DIC] = [H2CO3] + [HCO3 ] + [ CO32]. For this example, δ18Owater = 0‰, T = 25 °C, isotope fractionation data from Zeebe (1999).

Application to the triple oxygen isotope system Guo and Zhou (2019) estimated both equilibrium and kinetic triple oxygen isotope fractionations in the H2O–DIC–CO2 system using ln a18Oeq values between dissolved carbonate species from earlier theoretical estimates (Hill et al. 2014). The triple oxygen isotope exponent, κ, is similar for all dissolved carbonate species and calcite, but different for CO2 (κ = ln17β/ln18β,

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and is equivalent to the θ value between the phase and monoatomic oxygen; Cao and Liu 2011). They considered three processes that would disturb the equilibrium conditions of a system and modelled how the triple oxygen isotope system evolved as it returned to equilibrium. The three processes are: 1) a sudden change in DIC oxygen isotope composition due to dissolution of a water-soluble carbonate, 2) a rapid loss of CO2 by degassing, and 3) an increase in CO2 concentration (AKA ingassing or absorption) as might occur inside a cell during CO2 respiration. When the system is perturbed, the δ18O and δ17O values of all DIC species initially change and, over time, return to oxygen isotope equilibrium with the water. However, the rates of exchange are different for 17O and 18O, so that there are subtle variations in the θ and Δ′17O values of the dissolved carbonate species during the perturbation (Fig. 4). The pathways shown in Figure 4 illustrate the transient changes in the δ18O and Δ′17O values of HCO3 . We can consider the HCO3 ion to control the δ18O value of the carbonate triple oxygen isotope composition during one of )LJXUH at moderate pH (6.5–9) and temperature (20–30 °C). Rapid loss of these perturbation episodes CO2 increases the θ, Δ′17O, and δ18O values (Fig. 4), which then return to equilibrium over a period of several hours. Absorption of CO2 has the opposite effect, lowering the θ, Δ′17O and δ18O values (Fig. 4) which again return to equilibrium in several hours. Changing the DIC concentration and oxygen isotope composition (by addition of sodium bicarbonate in the example) results in a curved trajectory in Δ′17O–δ18O space (Fig. 4) where the θ and Δ′17O values initially increase, and then decrease while the δ18O values continuously decreases and whole system approaches equilibrium over a period of several hours to days (depending on pH and temperature). As an example, rapid surface degassing of a subterranean fluid with high p(CO2) will raise the pH of the fluid and cause rapid deposition of carbonates (travertines). The red curve in Figure 4 shows that under such a degassing process, we might expect the δ18O and Δ′17O values to increase. Preliminary results of the triple oxygen isotope composition of travertines from actively precipitating 10–20 °C springs in Tierra Amarilla, NM have higher Δ′17O and δ′18O values, 0.05‰ and 2–5‰, respectively, than expected from equilibrium precipitation from its formation fluid (unpublished results from a senior thesis at the University of New Mexico). )LJXUH

   18 17 Figure 4. Changes in the δ O and Δ′ O values of dissolved HCO3 during degassing of CO2 (red curve), absorption of CO2 (yellow curve) and introduction of a disequilibrium source of DIC (such as dissolution 

of Na2CO3–blue dashed curves). The starting point of the equilibration path following introduction of DIC (blue curves) is controlled by the δ18O and Δ′17O of the starting DIC, as illustrated by three different starting points. Figure is reformatted after modelling data in Guo and Zhou (2019). Temperature, pH and isotopic composition of the water also have an effect.

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Fosu et al (2020) measured the triple oxygen isotope composition of a large variety of carbonates and found a surprisingly wide range of Δ′17O values. For example, they measured two cold seep carbonates with Δ′17O values that differed by 0.13‰ between each other. This is more than double the Δ′17O range of carbonate samples thought to be in equilibrium with seawater (see Fig. 13 later in this chapter). Cold seep carbonates have been shown to be out of clumped isotope equilibrium (Loyd et al. 2016). One cold seep sample has a Δ′17O value that is about 0.05‰ higher than the Δ′17O equilibrium value expected with seawater while the other sample has a Δ′17O value that is 0.10‰ lower than expected for equilibrium formation with seawater (δ17O = δ18O = Δ′17O = 0). Perhaps the triple oxygen isotope compositions are also showing disequilibrium values. Research addressing how disequilibrium processes affect the triple oxygen isotope values of the precipitating mineral is clearly an area of future research.

SILICA–WATER FRACTIONATION Calibration of the triple oxygen isotope silica–water thermometer The 18O/16O fractionation between silica and water and its temperature dependence is extremely well studied. There are at least 7 experimental fractionation studies of quartz–water at high temperatures (see Sharp et al. 2016 for a compilation) and a number of empirical studies of naturally-formed abiogenic and biogenic amorphous silica at low to moderate temperatures (Kita et al. 1985; Leclerc and Labeyrie 1987; Shemesh et al. 1995; Brandriss et al. 1998; Schmidt et al. 2001; Dodd and Sharp 2010). Low temperature diatom silica initially form out of equilibrium with their host water (Brandriss et al. 1998; Dodd and Sharp 2010), but then undergo an early maturation phase, such that the silica reaches oxygen isotope equilibrium within the first year or two post-mortem (Schmidt et al. 2001; Dodd et al. 2012; Tyler et al. 2017). Wostbrock et al. (2018) compared the triple oxygen isotope values of abiogenic and biogenic silica as well as amorphous and microcrystalline silica and found no measurable differences in the δ18O fractionation. Therefore, we include both the high temperature equilibration experiments and the low temperature empirical fractionation data from biogenic and abiogenic silica to derive an SiO2–H2O oxygen isotope fractionation equation valid at temperatures above 273 K, given by 1000 ln 18OSiO2 H2 O 

4.28  106 3500  T2 T

(22)

The low temperature anchor on Equation (22) is primarily controlled by Antarctic diatom data. Shemesh et al. (1992) recommended only using Antarctic diatoms for the empirical silica–water fractionation to avoid complications of upwelling effects seen in other regions. Equation (22) fits the published low temperature diatom data well (Fig. 5), suggesting that the equation is valid down to 0 °C. The temperature dependent 17O/16O fractionation for quartz–water has been determined empirically by measuring the triple oxygen isotope compositions of quartz and abiogenic and biogenic amorphous silica (coexisting water was also measured when possible) over a temperature range of 0 to over 100 °C (Sharp et al. 2016; Wostbrock et al. 2018). The θ–T relationship can be calculated using Equation (8) with the best fit given by 1.85 (23) T The θ–T results are shown in Figure 6 along with two theoretical calibrations (Cao and Liu 2011; Hayles et al. 2018). There is generally good agreement between the empirical and theoretical estimates, with the latter having slightly higher θ values at low temperatures.  qz – wt 0.5305 

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)LJXUH

Figure 5. Comparison of the quartz–water fractionation equation (solid curve) with low temperature diatom data (Leclerc and Labeyrie 1987; Sharp et al. 2016). All analyses fit the equation to within 4 °C. )LJXUH )LJXUH

Figure 6. Measured θ values for natural samples and best fit for a θ vs. 1/T relationship. Data from Sharp et al. (2016) and Wostbrock et al. (2018). Also shown are the theoretical curves of Cao and Liu (2011) and Hayles et al. (2018).

The ΔΔ′17O fractionations (Δ′17Osilica − Δ′17Owater) as a function of temperature are governed by Equation (14). For silica–water, we have  4.28  106 3.5  103   1.85  17Osilica  17O water    18O water       0.5305  2 T T T   

(24)

where λ is assigned a value of 0.528 in this chapter. Equation (24) allows us to construct the Δ′17O–δ′18O equilibrium curves for silica–water (Fig. 2).

Silica in the terrestrial environment Figure 7 shows the quartz–water triple oxygen isotope plot with the equilibrium curves inverted (dashed lines) so that the origin is placed at the silica oxygen isotope composition for three silica samples. This allows us to estimate the oxygen isotope compositions of the formation waters in a terrestrial (non-marine) setting in equilibrium with a given silica sample. The green diamond is a modern sinter (amorphous silica) from Yellowstone National Park, Wyoming. Both the neoform silica and coexisting water (green circle) were sampled. A water temperature of 47 °C was measured at the time of collection. The silica and water appear to be in triple oxygen isotope equilibrium. They both lie on the same equilibrium curve with a

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)LJXUH Figure 7. Triple isotope compositions of low-T terrestrial silica samples. Data from Sharp et al. (2016). The Yellowstone sinter and Keokuk geode have oxygen isotope data for the coexisting waters and correspond to formation temperatures of 40–50 °C. The Moroccan geode has a similar oxygen isotope composition to the )LJXUH other two samples suggesting similar conditions of formation. Meteoric water field from Sharp et al. (2018).

corresponding temperature of 42 °C. The measured water is ~10‰ higher than local meteoric water, suggesting the sampled water has undergone some degree of evaporation and/or hydrothermal exchange with the host rock. The blue diamond is microcrystalline quartz from a Keokuk geode that retained fossil water in its core (blue circle). We do not know if the core water represents the formation water. However, the triple oxygen isotope values for the quartz and the water do in fact suggest equilibrium at a temperature of ~45 °C, suggesting the core water could be representative of the initial formation water. The purple diamond is microcrystalline quartz found in a stalactitic geode from Morocco (Sharp et al. 2016). We do not have coexisting water for this sample, but recognizing the Δ′17O value of the sample is slightly lower than the other two samples, we estimate a formation temperature of ~40 °C. Data from all the samples suggest that crystalline quartz can form at temperatures as low as 40 to 50 °C.

CARBONATE–WATER FRACTIONATION Analytical method The standard method for determining the δ18O value of carbonates was derived in 1950 (McCrea 1950). Carbonates are reacted with 100% phosphoric acid at a constant temperature, producing CO2 gas from the breakdown of the carbonate. Only 2/3 of the oxygen in the carbonate is liberated as CO2 gas. However, if the decarbonation is performed at a constant temperature, then the fractionation (δ18OCO2 (ACID)–δ18Ocarbonate or αCO2 (ACID)–carbonate) should be constant, although there are subtle second order effects that should be considered (Sharp 2017). In order to calculate the actual δ18O value of the carbonate on the VSMOW-SLAP scale, it is necessary to know the αCO2 (ACID)–carbonate fractionation factor (Sharp and Wostbrock 2021, this volume). This value is determined by liberating 100% of the oxygen from the carbonate either through complete fluorination of the carbonate (Sharma and Clayton 1965) or decarbonation of the carbonate as CO2 followed by fluorination of the remaining CaO (Kim and O′Neil 1997; Kim et al. 2007). In these carbonate studies, CO2 and/or a combination of CO2 and O2 gas were produced. The O2 was converted to CO2 by reaction with a heated graphite rod and all CO2 was recombined for the measurement of the δ18O value of the total carbonate. The difference between the δ18O values of the CO2 produced by reaction with phosphoric acid and of the total carbonate gives us the a18OCO2 (ACID)–carbonate value.

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These procedures cannot be used to determine the δ17O value of carbonates. There is an isobaric interference at mass 45 (12C16O17O) by 13C (13C16O16O). The d17O value must be measured on O2 gas unless an ultra-high precision mass spectrometer is being used that can measure the O+ fragment of CO2 (Adnew et al. 2019). The problem with extracting O2 gas from carbonates by fluorination is that intermediate compounds, such as CO and COF2, are produced and they are very resistant to fluorination. Wostbrock et al. (2020a) modified the Sharma and Clayton (1965) procedure of carbonate fluorination to quantitatively extract O2. The method involves conventional fluorination in Ni reaction tubes heated to 750 °C for four days. Wostbrock et al. (2020a) measured the triple oxygen isotope values of international standards as well as the CO2 liberated by phosphoric acid digestion. These data provide us with the a17OCO2 (ACID)–carbonate value of 1.00535 when using the a18OCO2 (ACID)–carbonate value of 1.01025 (Wostbrock et al. 2020a) . With these data, other laboratories that indirectly measure the δ17O value of CO2 generated by phosphoric acid digestion can calculate the δ17O value of the total carbonate. Alternative methods that start with the CO2 gas released by phosphoric acid digestion include the following: converting CO2 to H2O followed by fluorination (Passey et al. 2014), equilibrating CO2 gas with O2 using a hot Pt catalyst (Mahata et al. 2013; Barkan et al. 2015; Fosu et al. 2020), and analyzing the O+ fragment of CO2 generated in the ion source using a high resolution mass spectrometer (Adnew et al. 2019). Laser spectroscopy that measures the δ17O value of CO2 is a promising new technology that has yet to be adapted to wide-scale use (Sakai et al. 2017). We refer readers to Passey and Levin (2021, this volume) and Sharp and Wostbrock (2021, this volume) for more information about procedures used to measure the triple oxygen isotope values of carbonates.

Triple oxygen isotope fractionation in the calcite (aragonite)–water system Debate is ongoing regarding which type of carbonate (synthetic, biogenic, or abiogenic) best represents equilibrium oxygen isotope fractionation (Coplen 2007; Bajnai et al. 2018; Brand et al. 2019) or if naturally forming carbonates even reach equilibrium with the waters in which they form (Daëron et al. 2019). Wostbrock et al. (2020b) examined each category of carbonates (biogenic marine carbonate, biogenic and abiogenic marine aragonite, abiogenic Devils Hole calcite, synthesized calcite with and without carbonic anhydrase) to determine differences in triple oxygen isotope fractionation using the carbonate fluorination method. The synthesis experiments consisted of slowly precipitating calcite at a constant temperature following the method of Kim and O′Neil (1997) either with or without carbonic anhydrase (CA) as a catalyst (Silverman 1973; Uchikawa and Zeebe 2012; Watkins et al. 2013). The natural samples included marine biogenic calcite and marine abiogenic and biogenic aragonite that had known water δ18O values and growth temperatures. They found no statistically significant difference in the 1000 ln α18Occ-wt between synthetic, biogenic, and abiogenic calcite or aragonite but the 1000 ln α18Occ-wt values were at the higher end of that in reported literature (1000 ln α18Ocarb-wt = 29.0 at 25 °C). Wostbrock et al. (2020b) used all the samples from each category, combined with high temperature experimental data from O′Neil et al. (1969) to derive the 1000 ln α18Ocarb-wt portion of the triple oxygen isotope fractionation (Eqn. 14) given by 18

16

O 1000 ln  carbO / water 

2.84  106  2.96 T2

(25)

A difference was seen in the 1000 ln α17O values between calcite–water and aragonite–water (Wostbrock et al. 2020b). Calcite–water has higher θ values and smaller ΔΔ′17Ocarb–wt (Δ′17Ocarbonate − Δ′17Owater) values than aragonite–water (Fig. 8). However, these conclusions are based on aragonite samples from a very narrow range of temperatures (25–26 °C) and should be considered preliminary until a wider temperature range is measured. The calcite–water triple oxygen isotope fractionation equation from Wostbrock et al. (2020b) is:

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 2.84  106  –1.39  17Ocarb – 17O wt    0.5305 –   – 2.96  2 T T   

(26)

It is unclear whether any of the carbonates presented in Wostbrock et al. (2020b) represents true thermodynamic equilibrium. Isotopic equilibrium will not be reached in a natural setting if there is disequilibrium between the dissolved carbonate species (see earlier section “Effects of dissolved inorganic carbon”). If one of the dissolved species is out of equilibrium with the others and with the water, then the precipitated carbonate may reflect that disequilibrium (Guo and Zhou 2019). Regardless of whether Equation (26) represents ‘true’ thermodynamic equilibrium or not, it does show a correlation between ΔΔ′17Ocarb–wt and temperature that should be applicable any naturally formed carbonates. The triple oxygen isotope fractionation equations for calcite have also been calculated from theory (Cao and Liu 2011; Hayles et al. 2018; Guo and Zhou 2019). There is a systematic increase in the ΔΔ′17Ocarb–wt value as a function of decreasing temperature, similar to what is seen for quartz and what is predicted from theory (Fig. 8; Hayles et al. 2018; Guo and Zhou 2019). As noted earlier, there was no statistical difference in the ΔΔ′17Ocarb–wt values between the different calcite groups presented in Wostbrock et al. (2020b). There was a statistical difference between the calcite samples (blue circles and squares, Fig. 8) and the aragonite samples (brown circles, Fig. 8) where the best fit of the aragonite samples (brown line, Fig. 8) is lower at all temperatures, compared to the best fit of the calcite samples (blue line, Fig. 8). The calcite results agree well with theoretical estimates (black line, Fig. 8; Hayles et al. 2018; Guo and Zhou 2019). However, theoretical calculations predict there to be little to no difference between the Δ′17O values of aragonite and calcite (Guo and Zhou 2019; Schauble and Young 2021, this volume). Two other studies (Bergel et al. 2020; Voarintsoa et al. 2020) also derived θ values using freshwater aragonitic mollusks (green diamonds, Fig. 8) and synthetic calcite/aragonite (orange crosses, Fig. 8), respectively, using the Pt catalyzed CO2–O2 equilibration method. In Figure 8, data from both studies, measured on O2 derived from CO2, were converted to the total carbonate using the published a 17OCO2 (ACID)–carbonate of 1.00535 (Wostbrock et al. 2020a). The ΔΔ′17Ocarb–wt values from both studies are significantly larger and both studies do not report a significant variation with temperature (Fig. 8). Although the reason for the differences between the studies is unknown and warrants further investigation, one possible )LJXUH explanation could be a kinetic fractionation effect during the CO2–O2 equilibration method (Fosu et al. 2020; Passey and Levin 2021, this volume) used in both the Bergel et al. (2020) )LJXUH

Figure 8. The ΔΔ′17Ocarb-wt as a function of temperature from published studies. Symbols are the average of multiple measurements of a particular sample and error bars are ±1 s.d of average of the reported data in the study. Theoretical ΔΔ′17Ocarb-wt–T relationship (thick black line) from two studies overlap.

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and Voarintsoa et al. (2020) studies. Also, the synthesized calcite and calcite/aragonite mixture studies from Wostbrock et al. (2020b) and Voarintsoa et al. (2020), respectively, noted different times before the first crystals appeared during the experiment (3 days vs. 15–30 min (at 35 °C) to 1–2 days (at 10 °C), respectively). The rapid precipitation at 35 °C may have resulted in some kinetic effect where the precipitating carbonate incorporated the oxygen isotope values of the DIC, instead of precipitating in equilibrium with the water. The DIC species were most likely in equilibrium with the water since they waited 24 hours before adding the sodium bicarbonate and calcium chloride solution (Voarintsoa et al. 2020). Nevertheless, this explanation does not explain the differing results between Bergel et al. (2020) which used freshwater aragonitic mollusks and Wostbrock et al. (2020b) who use measured marine calcite shells and aragonite coral, shells, ooids and sediment. Perhaps freshwater aragonitic mollusks tend to form further out of equilibrium with its formation water than marine calcite and aragonite. Again, more research is necessary to better address these differences.

Applications to natural marine samples Triple oxygen isotope values have also been measured in carbonates found in soil (Passey et al. 2014), tooth enamel and egg shells (Passey et al. 2014), lakes (Passey and Ji 2019) and metamorphic settings (Fosu et al. 2020) and more information can be found in various chapters in this book (e.g., Passey and Levin 2021, this volume). In this chapter, we will focus on calcite and aragonite that formed in a marine setting. Figure 9 shows the triple oxygen isotope compositions of various marine carbonates from published data (Passey et al. 2014; Fosu et al. 2020; Wostbrock et al. 2020b). Note, Passey et al. (2014) measures the triple oxygen isotope composition of CO2 evolved from phosphoric acid digestion at 90 °C. Only an a17OCO2 (ACID)–carbonate at 25 °C is known (Wostbrock et al. 2020a). Therefore, we use the published a17OCO2 (ACID)–carbonate of 1.00535 to correct the CO2 triple oxygen isotope values to total carbonate, but this correction may not be completely accurate. In this communication we add two additional triple oxygen isotope analyses of Early Triassic ammonites from the Western Interior Seaway of North America (University of New Mexico, Earth and Planetary Sciences collections, donation by Jim Jenks). The Smithian ammonoid (Anasibirites sp.) comes from the Crittenden Springs (NE Nevada) locality (Jenks and Brayard 2018). The shell preservation of the ammonoids from this locality is believed to be exceptional, as many specimens have original color patterns preserved. The Spathian ammonoids were collected from the Hot Springs locality from SE Idaho (Guex et al. 2010) and are assigned to the Columbites biozone. These ammonoids are commonly found in carbonate concretions. The triple oxygen isotope values of the Smithian ammonite (blue rhombohedron, Fig. 9) are 12.624, 24.227, and −0.094‰ for d17O, d18O, and Δ′17O, respectively. The triple oxygen isotope values of the Spathian ammonite (blue pentagon, Fig. 9) are 13.490, 25.867, and −0.084‰ for d17O, d18O, and Δ′17O, respectively. Modern carbonates, six aragonite coral samples (red circle, yellow diamond, and four green squares), four modern brachiopod shells comprised of calcite (green diamonds) and one calcitic oyster (red diamond) are shown in Figure 9. The calcitic oyster appears to be in equilibrium with modern seawater, within reported error, and suggests a formation temperature of ~20 °C, similar to the measured water temperature of 24 °C (Passey et al. 2014). The calcitic brachiopod shells (green diamonds) also plot in equilibrium with the seawater–calcite fractionation curve (Note, these brachiopod samples were among the samples used to derive the fractionation curve in Wostbrock et al. 2020b). Two aragonitic coral samples (red circle and yellow diamond) have triple oxygen isotope values that plot below the calcite–seawater fractionation curve, suggesting a larger aragonite–water fractionation for Δ′17O than that of calcite–water. This is similar to the conclusions between the Δ′17O fractionation of calcite–water and aragonite–water presented in Wostbrock et al. (2020b).

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Figure 9. The Δ′17O values vs. the δ′18O values of marine carbonates in relation to the equilibrium triple oxygen isotope fractionation curve for calcite (black curve) in equilibrium with modern seawater (yellow star, δ18O = 0 and Δ′17O = −0.005‰; Luz and Barkan, 2010). Equilibration temperatures are marked along the black curve. The seawater curve is bracketed by the modern range (–2 to +2‰) of seawater oxygen isotope compositions for equatorial and mid-latitude oceans (grey lines; Schmidt et al. 1999). The range of modern brachiopod δ18O values (26.5 to 35.5‰) is represented by the light grey box (Brand et al. 2019). Data from Wostbrock et al. (2020b) are green symbols: modern marine brachiopods (diamonds), modern marine aragonite samples (squares) and blue symbols: Cretaceous belemnite (diamond); brachiopods: Mid Ordovician, (X), Silurian (square), Mid Devonian (circle), Late Pennsylvanian (triangle), and Mid Maastrichtian (Late Cretaceous; cross); ammonites: Smithian (rhombohedron) and Spathian (pentagon). Data from Passey et al. (2014) are red symbols: Permian brachiopod (square), modern estuarine oyster normalized to seawater (diamond), modern coral (Porites porites, circle). Data from Fosu et al. (2020) are yellow symbols: modern aragonitic deep sea coral (diamond), late Cretaceous chalk comprised of coccoliths (circle), modern cold seep high Mg calcite (square). An additional cold seep calcite plots off the chart and has a Δ′17O value of −0.18‰.

Of the fossil carbonate samples shown, only two, a Silurian brachiopod (blue square) and a Cretaceous belemnite from the Peedee formation (PDB, blue diamond), plot close to the seawater fractionation curve (Fig. 9). These samples are consistent with having precipitated in equilibrium with seawater with a δ18O value of 0 and Δ′17O value of −0.005‰ (Luz and Barkan 2010). The PDB sample corresponds with a formation temperature of 12 °C while the Silurian brachiopod corresponds to 28 °C. All other samples plot to the left of the seawater–calcite fractionation curve and, therefore, cannot be in equilibrium with 0‰ seawater. Assuming that the Phanerozoic seawater value was similar to today (−1 to 0‰), as suggested by the triple oxygen isotope values of the Silurian brachiopod sample and the Cretaceous belemnite, then all of the triple oxygen isotope values of these samples are best explained by diagenesis. Discussion of what these altered samples tell us about the ancient ocean is presented in “Application to carbonate and silica sediments”.

CONSIDERATIONS NECESSARY TO INTERPRET ANCIENT SEDIMENTS Traditional oxygen isotope studies have used the oxygen isotope composition of ancient carbonates and silicates to reconstruct the temperature of the seawater over time, as well as other proxies such as phosphates and shales (see Sharp 2017; Bindeman 2021, this volume, for more information on additional proxies). The accuracy of oxygen isotope paleothermometry is critically dependent on the assumed δ18O value of the ancient ocean. While it is generally agreed upon that the ocean is buffered to its present value by a complex interplay of plate tectonics and erosion (Muehlenbachs and Clayton 1976; Muehlenbachs 1986), the δ18O value of past seawater is still debated. There is a secular trend seen in the carbonate and silica (chert) record

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with decreasing δ18O values with increasing age (Lowenstam 1961; Degens and Epstein 1962; Keith and Weber 1964; Perry 1967; Knauth and Epstein 1976; Veizer and Hoefs 1976; Knauth and Lowe 1978, 2003; Perry et al. 1978; Popp et al. 1986; Veizer et al. 1986, 1989, 1997, 1999; Lohmann and Walker 1989; Brand 2004; Knauth 2005; Prokoph et al. 2008; Veizer and Prokoph 2015; Ryb and Eiler 2018). See Figure 1 in Zakharov et al. (2021, this volume). For example, the δ18O value of Archean cherts are generally 15‰ lower than modern (Knauth and Epstein 1976; Knauth and Lowe 1978, 2003; Perry et al. 1978; Winter and Knauth 1992). The explanation for the secular trend falls under three main hypotheses (Degens and Epstein 1962) and a fourth, less talked about hypothesis: 1. The ocean was warmer in the Archean than it is today (Knauth and Epstein 1976, 1986; Knauth and Lowe 1978, 2003; Winter and Knauth 1992; Perry and Lefticariu 2007). This hypothesis implies the d18O value of seawater remains constant (~0‰) over time and the temperature of Archean seawater was 50–80 °C and cooled over time. Assuming a linear cooling, the warm ocean theory would imply that the Cambrian seawater was about 40–60 °C warmer than modern seawater during the explosion of life, a direct contradiction to reasonable temperature estimates of survivability of most prokaryotes (Brock 1985). Additionally, when applied to the Archean, this hypothesis complicates the faint sun paradox (Sagan and Mullen 1972), although the faint sun paradox itself has been recently called into question (Rosing et al. 2010). Seawater modelling studies based on the oxygen isotope values of altered oceanic crust support this idea that seawater has been buffered to 0‰ for most of Earth′s history (Muehlenbachs and Clayton 1976; Gregory and Taylor 1981; Muehlenbachs 1986; Gregory 1991; Holmden and Muehlenbachs 1993, 1998; Zakharov and Bindeman 2019). Various studies using carbonate clumped isotope (Δ47) values also suggest the ocean was buffered to 0‰, albeit with varying temperature estimates (20–70 °C), since at least the Cambrian (Eiler 2011; Finnegan et al. 2011; Cummins et al. 2014; Ryb and Eiler 2018; Price et al. 2020). 2. The d18O value of seawater was lower in the past (Perry 1967; Perry and Tan 1972; Veizer and Hoefs 1976; Veizer et al. 1997, 1999; Hren et al. 2009; Veizer and Prokoph 2015). This hypothesis implies the d18O value of Archean seawater was as low as −15‰. Models to explain the low d18O value of the ancient ocean have been developed by assuming very different ratios of high to low temperature alteration flux rates compared to the modern (Wallmann 2001; Kasting et al. 2006; Jaffrés et al. 2007; Kanzaki 2020). Ocean temperatures would be similar to modern over the geologic rock record. The idea of an ocean with lower d18O values than modern seawater is contradicted by oxygen isotope studies of ancient ophiolites, where the oxygen isotope values of the altered rocks is governed by the oxygen isotope value of the hydrothermal water (initially seawater) at an assumed constant temperature over time (Muehlenbachs and Clayton 1976; Gregory and Taylor 1981; Muehlenbachs 1986, 1998; Gregory 1991). Recent seawater oxygen isotope compositional modelling by Sengupta and Pack (2018) suggest that a 100-fold increase of the continental weathering flux rate would be required to lower the ocean to −8‰. The authors could not reconstruct a seawater with the a d18O value of −15‰ using any feasible changing scenario of known or estimated flux rates. 3. Ancient samples have been overprinted by diagenesis (Gao and Land 1991; Wenzel et al. 2000; Brand 2004; Marin-Carbonne et al. 2012, 2014; Sengupta and Pack 2018; Liljestrand et al. 2020). Diagenetic alteration generally occurs at elevated temperatures and/or in the presence of waters with a lower d18O value of seawater (Popp et al. 1986; Lohmann and Walker 1989; Banner and Hanson 1990; Gao and Land 1991; Marshall 1992; Wadleigh and Veizer 1992; Kah 2000; Swart 2015; Ahm et al. 2018). However, there are rare instances where the d18O value of the diagenetic fluid may be higher than modern seawater (Grossman et al. 1991), particularly in evaporative basinal porewaters (Swart 2015).

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4. Hydrothermal systems formed much of the Archean chert record (De Ronde et al. 1997; Sengupta et al. 2020; Zakharov et al. 2021, this volume). The triple oxygen isotope data are explained by this idea, but some geologic and petrographic evidence does not support high temperature, hydrothermal deposition. For example, some stratigraphic evidence of laterally continuous chert beds and low temperature facies preservation such as rip-up clasts suggest that at least some of the ancient chert was deposited in shallow, near surface settings during the Archean (Knauth 1979; Lowe 1983; Maliva et al. 1989, 2005; Tice et al. 2004; Tice and Lowe 2006; Perry and Lefticariu 2007). To complicate things further, there are some studies where the δ18O of seawater is proposed to have been up to 3‰ higher in the past (Longinelli et al. 2002, 2003; Johnson and Wing 2020). In summary, the δ18O value of seawater over the geologic record is still an open question. Triple oxygen isotope measurements help constrain the fluid in which the silicate or carbonate formed or can help determine if the sample is preserving primary depositional information because samples must fall on a unique curve in Δ′17O–δ′18O space for a given composition of water (Fig. 2). Departures from this line are explained by changes in the triple oxygen isotope composition of the ocean and/or diagenesis, explained in further detail below. Samples that lie to the left of the seawater equilibrium curve have been altered by a diagenetic fluid of meteoric origin. Samples that lie above the modern seawater equilibration curve have either formed in an ocean with a lower δ′18O–higher Δ′17O value or, rarely, undergone alteration with a fluid with a higher δ18O value than seawater. The triple oxygen isotope composition of ancient materials should therefore shed light on which processes might explain their low δ18O values.

Modelling changing ocean composition in the past Sengupta and Pack (2018) modeled how the Δ′17O and δ′18O values of seawater would change in response to changing rates high- to low-temperature alteration. Similar to Muehlenbachs (1998), they determined that continental weathering and high temperature hydrothermal alteration during seafloor spreading were the two principal fluxes that drive the seawater oxygen isotope change. They obtained a λ value of 0.51 for changing the continental weathering and high temperature seafloor alteration fluxes. Liljestrand et al. (2020) suggested that at least 90% of the total alteration must come from low temperature continental weathering in order to have Archean seawater with a δ18O value of −15‰. They propose a λ of 0.524 for low temperature seafloor alteration (Liljestrand et al. 2020), slightly higher than the combined high- and low-temperature alteration λ proposed in Sengupta and Pack (2018). Bindeman (2021, this volume) measured the triple oxygen isotope composition of shales and proposes an intermediate λ value of 0.521. For simplicity, we use the λ value of 0.51 in Figure 10 to show how the seawater equilibrium fractionation curve would change over time if low temperature alteration governed Archean seawater oxygen isotope composition. Sediments that formed in equilibrium with a seawater composition plotting on the λ = 0.51 line would then plot above the modern equilibrium curve (shaded grey region, Fig. 10). Hypothetical triple oxygen isotope values of samples are shown as circles in Figure 10. The green circle can be interpreted as being in equilibrium with modern seawater. The blue circle could be in equilibrium with seawater with a δ′18O value of −4‰ and a Δ′17O value of 0.075‰. The red circle in Figure 5 could only be in equilibrium with the ocean if the δ′18O value was significantly higher than today as suggested by Johnson and Wing (2020). It is not unreasonable that continental erosion would have been lower in the Archean due to a low abundance of continental crust (Bindeman et al. 2018), in which case the ocean would move

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)LJXUH Figure 10. Δ′17O–δ′18O plot of changing seawater composition. The line labeled λ = 0.51 is the trajectory of seawater composition for changing high- to low-temperature alteration ratios (Sengupta and Pack 2018). All circles represent hypothetical data. The green circle is in equilibrium with modern water at 70°C. The blue circle is the Δ′17O–δ′18O value of silica in equilibrium with a modelled lower δ′18Oseawater value of −4‰ at 70 °C.)LJXUH The red circle is the Δ′17O–δ′18O value of silica in equilibrium with a modelled higher δ′18Oseawater value of +2‰ at 70 °C (Johnson and Wing 2020). For similar temperatures of formation, triple oxygen isotope values of silica should have higher Δ′17O values and lower δ18O values than modern silica if the δ18O value of seawater was lower in the past and lower Δ′17O values and higher δ18O values than modern silica if the δ18O value of seawater was higher in the past.

along the λ = 0.51 line towards higher δ18O values (Johnson and Wing 2020) and lower Δ′17O values As discussed below, a shift to higher δ18O values for the ancient ocean then leads to higher temperature estimates based on the mineral–water fractionations. It is therefore argued that ancient cherts may have formed in high temperature hydrothermal system (De Ronde et al. 1997; Sengupta et al. 2020; Zakharov et al. 2021, this volume). Alternatively, the red circle in Figure 5 may be the result of diagenesis, as explained in the following section.

Modelling triple oxygen isotope trends during diagenesis Low temperature diagenesis of marine sediments generally drives the d18O values lower and ∆′17O values higher (Sharp et al. 2018). Several variables control the oxygen isotope composition during diagenetic alteration including, temperature, initial rock and fluid oxygen isotope compositions, and the fluid/rock (F/R) ratio. Nevertheless, the δ′18O–∆′17O field of most diagenetically altered rock is surprisingly limited (Fig. 11; Sharp et al. 2018). The effect of alteration can be determined using a simple mass-balance mixing model. A fraction of water is allowed to equilibrate with a rock at a given temperature following Taylor (1978). The bulk composition is given by the equation dxObulk = Xwater (dxOwater initial) + (1−Xwater) (dxOrock initial)

(27a)

dxObulk = Xwater (dxOwater final) + (1−Xwater) (dxOrock final)

(27b)

and dxO can be either δ18O or d17O. The final dxO value of the rock is determined by the additional equation

x 

1000   x Ofinal rock 1000   x Ofinal water

(28)

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Figure 11. Alteration trajectories in Δ′17O–δ′18O space. The rock starts at δrinit (black circle) and moves along the solid curve with increasing fluid/rock ratio. The infiltrating fluid has a composition at δMW (white star), equilibrates with rock and has a composition δwinit (white circle). The re-equilibrated water follows the dotted curved path from δwinit towards lower δ′18O and higher D′17O values as the F/R ratio increases. The final rock and water compositions in this example correspond to an Xwater value of 0.6, resulting in the δwfinal (white diamond) and δrfinal (black diamond) The equilibrium oxygen isotope fractionations at 100 °C are shown by the doubled arrow lines.

Combining Equations (27a), (27b), and (28) leads to the relationship between the initial rock and water oxygen isotope compositions, the fluid/rock ratio and the final isotopic composition of the rock:  x O rock final 



1000 X   X   x O rock initial  X   x O water initial   x O rock initial  1000X



(29)

X    X

A typical alteration pathway at 100 °C is shown in Figure 11. The fractionation between the water and rock is shown by the arrows δ′r–δ′w and Δ′r–∆′w. As long as temperature is held constant, these fractionations will not change. The initial rock is silica in equilibrium with seawater water at 20 °C (black circle and δrinit). The meteoric water that infiltrates the rock has initial δ18O and Δ′17O values of –6 and +0.03‰ (white star and δMW). The infiltrating meteoric water always has a constant composition (δMW) and equilibrates with the rock as it enters the system. When the alteration process first begins, an infinitely small amount of water enters the system and equilibrates with the rock. The fraction of oxygen from the water relative to the total water–rock oxygen reservoir is near zero. In the model, this first ‘aliquot’ of water will equilibrate with the overwhelmingly large oxygen reservoir of rock and have a composition given by δwinit (white circle, Fig. 11). This is the oxygen isotope composition of the equilibrated water when the fluid–rock interaction process first begins to take place. As more fluid enters the system, the F/R ratio increases and the oxygen isotope composition of the fluid and rock track up the solid (rock) and dotted (water) curves. As the F/R ratio approaches an infinite value, the oxygen isotope composition of the fluid is equal to that of infiltrating meteoric water (δMW). The infiltrating water ‘overwhelms’ the buffering capacity of the rock. The δ′18O and Δ′17O values the rock will be in equilibrium at 100 °C with the δMW (white star, Fig. 11). The final oxygen isotope composition of the rock at the end of the alteration process is a function of the F/R ratio. In Figure 11, the white and black diamonds illustrate an intermediate condition corresponding to an Xwater = 0.6 or a fluid–rock ratio of 1.5 (Xwater/Xrock = 0.6/0.4). The variables that control the alteration pathways are the temperature of alteration, the δ18O and Δ′17O values of the infiltrating water, and the initial oxygen isotope

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composition of the rock (which is a function of its formation temperature). Figure 12 shows various alteration trajectories for different water compositions and temperatures. In general, we expect to see altered marine rocks lying to the left of the seawater equilibrium curve, shown by the lavender region in Figure 13. This field is generated by considering a wide range of reasonable infiltrating fluid triple oxygen isotope compositions, alteration temperatures, and initial rock triple oxygen isotope (black curves, Fig. 13). For case studies see )LJXUH Herwartz et al. (2015), Zakharov and Bindeman (2019), Chamberlain et al. (2020), and Herwartz (2021, this volume). The alteration field is mostly distinct from the ‘changing seawater’ field generated by lowering the δ18O value of ancient seawater by changing high- to low-temperature alteration ratios (shaded grey region, Fig. 13). These two fields—alteration in lavender and )LJXUH

Figure 12. Alteration trajectories for a rock starting with a δ′18O–Δ′17O of δrinit. Dashed and solid lines are for interaction with an infiltrating meteoric water (δMW) with δ′18O values of −10‰ and −6‰, respectively )LJXUH and Δ′17O values of 0.03‰. The rock trajectories are thick curves, fluids are thin curves.

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Figure 13. Generalized fields for sedimentary silica. The lavender field represents the general region expected for alteration based on numerous trajectories for different water compositions and temperatures (black curved lines). The grey region is calculated for lower oxygen isotope compositions of seawater predicted if high- to low-temperature alteration ratios changed dramatically in the past.

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lowering ocean values in grey—represent the generalized regions where we can expect most sediment phases to plot. Overall, samples that lie below and to the left of the equilibrium line are explained by diagenesis. There are alteration scenarios that would result in a positive shift for both the δ18O and Δ′17O values. This may be seen in hot buoyant fluids that infiltrate a cooler overlying sedimentary pile (see final section of this chapter).

Application to carbonate and silica sediments Phanerozoic calcite. Wostbrock et al. (2020b) reported the triple oxygen isotope values of five ancient brachiopods and one belemnite from the Phanerozoic. Only two samples, a Silurian brachiopod (formation temperature ~28 °C) and a Cretaceous belemnite (formation temperature ~12 °C), have triple oxygen isotope values that can be in equilibrium with seawater similar to a modern ocean oxygen isotope composition (Fig. 9). The remaining brachiopods from that study and the two ammonites presented in this manuscript all have δ18O and Δ′17O values that plot to the left of the modern seawater triple oxygen isotope fractionation curve, suggesting alteration by a meteoric water. It is only with the addition of the Δ′17O value that we are able to conclude that these ancient brachiopods do not preserve triple oxygen isotope compositions and could not have formed in seawater similar to modern oceans (grey box, Fig. 9). We can use the fluid/rock alteration model to ‘see through’ the alteration and calculate the original triple oxygen isotope composition of the samples, prior to alteration (Fig. 14). For the Ordovician brachiopod, Wostbrock et al. (2020b) were able to fit the measured triple oxygen isotope data using a meteoric fluid as the alteration fluid with a δ18O value between −15 and −10‰, a Δ′17O value of +0.03‰, and an alteration temperature between 35 and 100 °C. Under these conditions, the back-calculated initial δ18O value of the brachiopod was between 30 and 32.5‰, corresponding to a formation temperature of 10 to 20 °C, assuming the seawater had a similar triple oxygen isotope composition as modern oceans. Using the same fluid–rock mixing model, we calculated the primary composition of the other altered brachiopod and ammonite samples (Fig. 14). All the brachiopod shells formed in water ranging between 10 and 20 °C, similar to the 0–30 °C water temperature range of modern brachiopods (Brand et al. 2019). For the Smithian and Spathian (Early Triassic) ammonites, we find that both ammonites are altered in spite of the high visual preservation quality of the fossil shell. Nevertheless, we can back-calculate formation temperatures of 10 and 20 °C for the Spathian and Smithian age samples, respectively. These agree well with the 10 °C difference suggested using the δ18O values of conodonts (Sun et al. 2012). Overall, we do not see evidence of lower δ18O values of the ocean, nor higher temperatures in the Phanerozoic, although the number of samples measured to date is still small. Ancient silica. Sedimentary bulk silica is found throughout the rock record from 3.5 Ga through to the present day (Knauth 2005). Chert is inherently the product of a diagenetic process where dissolved silica is reprecipitated and evolves from Opal-A to Opal-CT to microcrystalline quartz. Generally, the term “chert” refers to microcrystalline quartz. The amount of time it takes for Opal-A to transform to microcrystalline quartz is still an active area of research (Yanchilina et al. 2020). The ocean has been undersaturated with respect to silica since the appearance of silica-secreting radiolarians and siliceous sponges in the Phanerozoic and later diatoms in the Jurassic. Most Phanerozoic silica deposits originated as biogenic Opal-A, which later transformed to microcrystalline quartz generally in an offshore environment (Maliva et al. 1989; Perry and Lefticariu 2007). Prior to the Phanerozoic, the ocean may have been close to or at silica saturation, and marine silica is thought to have mostly precipitated through abiogenic (or inorganic) processes. Preservation of sedimentary features in Precambrian and earlier outcrops gives credence to the idea that some transformations can occur in the near subsurface not long after deposition (Knauth 1973; Knauth and Lowe 1978; Lowe 1983; Maliva et al. 1989, 2005; Tice et al. 2004; Tice and Lowe 2006; Perry and Lefticariu 2007). The ubiquitous presence of chert throughout geologic time and the assumed lower susceptibility to diagenesis than carbonate has made the oxygen isotope composition of chert an attractive sample to use as a paleo-indicator of ancient seawater.

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 Figure 14. Back-calculated initial triple oxygen isotope compositions of altered brachiopod and ammonite  samples. Alteration fluid triple oxygen isotope value are written on each graph and pathways were mod elled for alteration temperatures of 35 (blue lines), 50 (orange lines), and 100 (red lines) °C. A) The Mid Ordovician brachiopod formed between 10 and 20 °C. To demonstrate the fact that the fluid–rock interaction model is under constrained, Wostbrock et al. (2020b) used two different alteration fluids to calculate  two different potential primary calcite triple oxygen isotope values and show the range of results the model  can produce. For B–E, we only show one potential solution for the fluid–rock mixing model for the sake of simplicity. B) The Mid Devonian brachiopod calculated primary calcite triple oxygen isotope composition )LJXUH suggests an initial precipitation temperature of ~18 °C. C) The Late Pennsylvanian brachiopod calculated primary calcite triple oxygen isotope composition suggests an initial precipitation temperature of ~15 °C. D) The Mid Maastrichtian (Late Cretaceous) brachiopod calculated primary calcite triple oxygen isotope composition suggests an initial precipitation temperature of ~10 °C. E) The Smithian ammonite (rhombohedron) calculated primary calcite triple oxygen isotope composition suggests an initial precipitation temperature of ~20 °C. The Spathian ammonite (pentagon) calculated primary calcite triple oxygen isotope composition suggests an initial precipitation temperature of ~10 °C.



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Four studies have published values on the triple oxygen isotope composition of cherts from the Archean through the Phanerozoic (Levin et al. 2014; Liljestrand et al. 2020; Sengupta et al. 2020; Zakharov et al. 2021, this volume) and the results are presented in Figure 15. First, the vast majority of all chert samples that have been measured for triple oxygen isotope analysis plot to the left of the modern silica-seawater equilibrium fractionation line. Perhaps most importantly, all chert samples from the Archean (dark blue icons in Fig. 15) plot at far lower δ18O values than other samples and to the left of the modern silica–seawater equilibrium fractionation line. The fact that they do not plot above the equilibrium line indicates that their unique δ18O–Δ′17O values are not due to lower δ18O seawater compositions related to changing high- to low-temperature alteration ratios (Figs. 12 and 13). Therefore, the secular trend seen in the δ18O values of chert is not compatible with an Archean seawater δ18O value of −8 to −15‰ unless the alteration trend of λ = 0.51 (Sengupta and Pack 2018) is not correct. Other studies suggest higher λ values of 0.521 (Bindeman 2021, this volume) and 0.524 (Liljestrand et al. 2020). Using a λ value of 0.524 and a δ18O value of −8‰ for the ocean can explain only a few of the Proterozoic chert data (solid red line, Fig. 16) with a formation water temperature of 30 to 40 °C. However, even this high λ value cannot reconcile any Archean chert or the majority of the published chert dataset (Fig. 16). Almost none of the chert data can be explained by equilibration with a modern seawater oxygen isotope composition. Chert samples from the Phanerozoic presented in Sengupta et al. (2020), represented by the yellow diamonds in Figure 15, are explained by dissolution and equilibrium re-precipitation with a meteoric–marine fluid mixture with a δ18O value of −3‰ and a Δ′17O value of +0.010‰ (dashed purple line with purple star, Fig. 15; Sengupta et al. 2020). This implies the samples are preserving a precipitation temperature between 20 and 30 °C, suggesting near-surface dissolution and re-precipitation. Similarly, Zakharov et al. (2021, this volume) suggest the first generation of microcrystalline quartz in a Proterozoic chert sample (light blue crosses in Fig. 14) formed in equilibrium with

Figure 15. Published Δ′17O and δ′18O values of ancient chert from the Archean through Phanerozoic from )LJXUH Levin et al. (2014, squares) Liljestrand et al. (2020, circles), Sengupta et al. (2020, diamonds), Zakharov et al. (2021, this volume, crosses). Yellow colors are younger cherts while blue colors represent older cherts. One interpretation for the chert data suggest alteration by a fluid with a lower triple oxygen isotope value than the modern ocean (SMOW, yellow star). Using a fluid–rock mixing model, the precipitation temperature of the primary chert was calculated as 30 °C (Liljestrand et al. 2020; orange line and triangle) and 10 °C (Sengupta and Pack 2018; pink lines and hexagon). Sengupta et al. (2020) proposed that Phanerozoic chert (yellow icons) generally form by dissolution and equilibrium re-precipitation after burial in a meteoric-marine water mixture (purple star and dashed lines). The initial formation temperatures are then 30 and 40 °C. Zakharov et al. (2021, this volume) suggests a similar precipitation scenario with pore fluid during the Proterozoic (light blue icons) and formation temperatures greater than 60 °C.

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)LJXUH

Figure 16. Various seawater triple oxygen isotope compositions can describe published Δ′17O and δ′18O values of ancient chert from the Archean through Phanerozoic from Levin et al. (2014, squares) Liljestrand et al. (2020, circles), Sengupta et al. (2020, diamonds), Zakharov et al. (2021, this volume, crosses). Yellow colors are younger cherts while blue colors represent older cherts. The triple oxygen isotope val ues of chert are not consistent with seawater having had a lower δ18O value in the past (red stars) if cor responding change in δ18O and Δ′17O following either the trend with the lowest λ value of 0.51 modelled  by Sengupta and Pack (2018; dashed red line) or the trend with the highest λ value of 0.524 suggested by )LJXUH Liljestrand et al. (2020; solid red line). A possible explanation is that the δ18O value of seawater was higher in the Archean compared to modern or that Precambrian chert tended to form in a hydrothermal system with a higher δ18O value than modern seawater. The fluid could have a δ18O value of +1‰ (purple star and dashed purple line) as proposed in Sengupta et al. (2020) and Zakharov et al. (2021, this volume) or have a δ18O value as high as +3‰ as proposed in Johnson and Wing (2020; green star and dashed line). Either seawater δ18O scenario suggests high formation temperatures between 150 and 300 °C for Archean chert (orange circle) and 70 to 150 °C for Proterozoic chert (purple circle).

interstitial pore fluid that is similar to slightly lower than the modern seawater oxygen isotope composition at a temperature between 50 and 80 °C, representative of the temperature of early diagenesis. Alteration of Phanerozoic cherts has long been known to commonly occur and are actually probably the norm (Knauth and Epstein 1976). It is not surprising, therefore, to expect alteration by meteoric waters to have occurred in older samples. All current triple oxygen isotope studies of chert suggest alteration by secondary fluids. Sengupta and Pack (2018) and Liljestrand et al. (2020) suggest the initial precipitation of the silica occurred in seawater with a δ18O value similar to modern seawater and at temperatures below 30 °C. Both studies used fluid–rock interaction models (Figs. 11 and 12) to calculate primary chert compositions. Liljestrand et al. (2020) constrained the initial silica formation to have occurred at 30 °C, with a subsequent diagenetic alteration at 200 °C with a fluid of −16.5‰. Sengupta and Pack (2018) (using renormalized data from Levin et al. 2014) concluded that alteration by a fluid with a δ18O value of −6‰ at 50 °C generally explains the Phanerozoic chert data. In contrast, an alteration fluid of 10‰ at 180 °C explains the Archean cherts and a chert precipitation temperature of −10 °C. Sengupta et al. (2020) used a Bayesian model to calculate two different alteration scenarios for their Archean and Proterozoic chert data. For the Archean samples they separated samples

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into two groups, one with δ18O values between 13 and 16‰ and one group with δ18O values between 18.7 and 19.3‰. For the first Archean group, they concluded that the silica precipitated in seawater with an oxygen isotope composition similar to modern seawater, and was subsequently altered by a fluid with a δ18O value of −16.5‰ at an alteration temperature of 50 °C and W/R ratio of 1. Their Bayesian model was inconclusive on initial silica precipitation temperature. For the second group of Archean chert, the Bayesian model again predicted initial precipitation in seawater with an oxygen isotope composition similar to modern at 80 °C and was subsequently altered with a fluid with a δ18O value of –14‰ at either 50 or 150 °C. The Bayesian model was ambiguous as to the W/R ratio. Proterozoic cherts fit within both Archean diagenetic models. Sensitivity in the Bayesian model allows for the initial silica from either the Archean or Proterozoic samples to have formed in temperatures as low as 10 °C (Sengupta et al. 2020). Although diagenesis can explain the above data, Sengupta et al. (2020) also consider the hypothesis that the Archean and Proterozoic samples are retaining primary oxygen isotope values in which the chert equilibrated with a fluid that had a higher δ18O value than modern seawater (Fig. 16). This idea is also favored by Zakharov et al. (2021, this volume). Sengupta et al. (2020) acknowledge that they cannot distinguish between whether the samples formed in seawater with higher δ18O and lower Δ′17O values than modern seawater (Johnson and Wing 2020) due to higher hydrothermal water flux in the Archean (Isley 1995; Lowell and Keller 2003) or whether the samples formed in high temperature hydrothermal vent fluids with ambient seawater similar to modern (Bindeman et al. 2018; Zakharov and Bindeman 2019; Peters et al. 2020). Zakharov et al. (2021, this volume) use a modern hydrothermal vent in Iceland as an analog to an Archean vent-like setting with fluids having a δ18O value of 0.9 to 1.6‰ (De Ronde et al. 1997; Farber et al. 2015) and temperatures between 150 and 300 °C. Sengupta et al. (2020) suggest a similar fluid (either vent or ambient seawater) oxygen isotope composition with a δ18O value of +1‰ and Δ′17O value of −0.040‰, corresponding to a temperature of formation for the Archean cherts of 150 to 220 °C and 75–150 °C for Proterozoic cherts (purple star and dashed line, Fig. 16). They explain the lower Proterozoic fluid temperatures result from a lowering of the geothermal gradient. Johnson and Wing (2020) argue that, due to the absence of continents, the Archean ocean could have a δ18O value as high as +3‰ (green star and dashed line, Fig. 16). Following a λ ≈ 0.51 for the changing seawater trend presented in Sengupta and Pack (2018), an Archean seawater with a δ18O value of +3‰ would then have a Δ′17O value of about −0.05‰. Seawater with a δ18O value of +3‰ also fits the Archean and Proterozoic chert samples (blue symbols in Fig. 16) at similar temperatures proposed by Sengupta et al. (2020) and Zakharov et al. (2021, this volume). Interestingly, seawater with a δ18O value of +3‰ does not fit the majority of the Phanerozoic chert samples. If the hypothesis that most Precambrian chert formed in seawater with a higher δ18O value than modern, perhaps chert formation processes in the Phanerozoic were different, due to the presence of marine silica-secreting organisms (Maliva et al. 1989, 2005; Perry and Lefticariu 2007). Overall, most Archean and Proterozoic chert that has currently been measured for triple oxygen isotope values could have formed or been altered by high-temperature vent fluids with δ18O values higher than modern seawater. Alternatively, the data can be explained by having initial silica precipitation at less than 30 °C in marine water with a modern oxygen isotope composition, and subsequent diagenetic alteration by meteoric waters (Sengupta and Pack 2018; Liljestrand et al. 2020). This latter interpretation agrees with the classic δ18O–δD study of Knauth and Epstein (1976) where altered samples have a δD/δ18O slope similar to the meteoric water line. Examining Archean and Proterozoic chert that preserve sedimentary facies, such as draping and rip up clasts, indicating formation in a near-shore marine setting at or near the seafloor would provide additional information. Based on the data published thus far, however, we conclude that the data do not suggest Archean or Proterozoic seawater with a lower δ18O value than modern.

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TRIPLE OXYGEN ISOTOPES OF COEXISTING QUARTZ AND CALCITE We can combine the ΔΔ′17O fractionation equations (Eqns. 24 and 26) for quartz–water and calcite–water to derive the equilibrium oxygen isotope fractionation between quartz and calcite (Fig. 17). The qqz–cc values are less than those of quartz–water or calcite–water. At 0°C, our calculated qqz–cc of 0.518 compares well with the theoretical estimate of 0.520 (Hayles et al. 2018).

Figure 17. Δ′17O–δ′18O plot for quartz and calcite and the equilibrium qqz–cc values from 0 to 70 °C.

)LJXUH

We consider three carbonate lithologies that contain authigenic quartz: the well-known Herkimer Diamond quartz crystals hosted in carbonate (New York, USA), doubly terminated quartz crystals in early–middle transition Triassic marine pelagic limestone (North Dobrogea, Romania), and chert nodules from a Cretaceous limestone (Étretat, France). The Herkimer Diamond and marine pelagic limestone from North Dobrogea, Romania both contain glassy, optically clear quartz crystals. The Romanian samples do not contain sponge spicules, although they are found elsewhere in the section, suggesting that the quartz crystals are the product of dissolution and reprecipitation of the sponge spicules. The Étretat, France sample is not glassy quartz, but rather fine-grained chert (data from Pack and Herwartz 2014). The other two samples are data from Sharp et al. (2016) and all data are normalized to the same San Carlos olivine scale (see Sharp and Wostbrock 2021, this volume). The two authigenic quartz samples can be explained by dissolution of amorphous silica and recrystallization as quartz during a period of meteoric water infiltration (Fig. 18). If a small amount of meteoric water entered the system, it could dissolve the reactive, metastable amorphous silica and cause it to reprecipitate without appreciably interacting with the host calcite. Using a simple mass balance model following Equation (29), we can calculate the initial Δ′17O and δ′18O values of the amorphous silica for both the Romanian and New York samples with differing F/R ratios and reaction temperatures. For the Romanian samples, the δ18O value of the calcite is ~33.3‰ (not shown in Fig. 18), corresponding to a formation temperature of ~10 °C. Two reactions paths are illustrated at diagenesis temperatures of 45 and 70 °C using a starting quartz value in equilibrium with seawater at 10 °C. For the Herkimer samples, alteration temperatures approaching 100 °C are expected (not shown in Fig. 18). Calculated F/R ratios for both samples are high, but it is important to recognize that this is the effective F/R ratio. If the calcite had only minimal interaction with the infiltrating fluid, then the ratio of oxygen in the fluid to quartz could be high even if there was only a small amount of fluid.

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Figure 18. Isotopic compositions of authigenic euhedral quartz crystals hosted in carbonates. The isotope data suggest some degree of alteration by meteoric fluids. Pathways for interaction between a sample formed at ~10 °C (as evidenced by carbonate δ18O values and a meteoric fluid (δ18O = −6‰, Δ′17O = 0.03‰. Alteration paths shown for temperatures of 45 °C and 70 °C.

The French chert samples plot above the equilibrium curve for quartz and seawater (Fig. 19). It is not possible to explain this sample in terms of equilibrium with ocean water or diagenesis with meteoric water. Instead, we suggest a scenario of fluids migrating from deeper hotter sections into overlying sediments. The overall process shown in Figure 19 is the following: First, a carbonate is precipitated at 35 °C in equilibrium with seawater at composition  illustrated by the red diamond. The sample is buried and heated to 100 °C. Interstitial fluid in equilibrium with the heated carbonate re-equilibrates to an oxygen isotope composition at  (red pentagon). The curve between  and  is the oxygen isotope equilibrium curve for carbonates with the origin at the carbonate value (position ; blue solid line). This fluid then buoyantly infiltrates the overlying sediment at a lower temperature and precipitates quartz at  (red hexagon). The black curve between  and  is the oxygen isotope equilibrium curve for quartz with a fluid at . The geological scenario is reasonable and provides an explanation for how samples can plot above the mineral–seawater equilibrium curve. )LJXUH

Figure 19. Possible reaction sequence to explain the high Δ′17O value (red circle) of carbonate-hosted chert from Étretat, France (data from Pack and Herwartz 2014). 1) Carbonates form with an isotopic composition at . 2) The sample is heated and the pore fluid buffered by the carbonate is shown at . 3) The fluid infiltrates the cooler overlying sediment and precipitates quartz at . The grey curve shows the equilibrium quartz–water fractionation with seawater.

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CONCLUSION Recent studies have clearly demonstrated the usefulness in making triple oxygen isotope measurements compared to measuring the δ18O value alone. Triple oxygen isotope measurements serve as a unique tool that can determine equilibrium vs. non-equilibrium vs. alteration processes. Triple oxygen isotope compositions allow for a definitive test for diagenesis. If a sample does not lie on the equilibrium curve, it is not in equilibrium with modern seawater. The silica–water triple oxygen isotope fractionation system appears to be well constrained. Inconsistencies remain in published carbonate–water triple oxygen isotope fractionation values, probably due to the different methods used to obtain the triple oxygen isotope values. Nevertheless, application of the calcite–water or quartz–water triple oxygen isotope fractionation curves to samples where the formation water is no longer present allows us to constrain the temperatures of formation and conditions of diagenesis. A fluid–rock mixing model can be used to ‘see through’ alteration and calculate the primary oxygen isotope compositions of silicate and carbonate rocks. Applying this model to silicates and carbonates from the geologic record shows that the low δ18O values of the ancient samples do not appear to be related to changing ocean temperatures and/or ocean isotope values. Instead, Phanerozoic carbonate and chert samples are better explained by diagenesis and Proterozoic and older chert can be explained by either diagenesis or precipitation in hydrothermal fluid.

ACKNOWLEDGEMENTS J.A.G.W and Z.S acknowledges support from NSF GRFP grant DGE-1418062, NSF EAR 1551226, and NSF EAR 1747703. We thank Jim Jenks, Viorel Atudorei, and UNM EPS collections for the Smithian and Spathian ammonite samples. The authors also thank constructive reviews by Weifu Guo and Page Chamberlain and the patience of editors Ilya Bindeman and Andreas Pack.

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Tyler JJ, Sloane HJ, Rickaby REM, Cox EJ, Leng MJ (2017) Post-mortem oxygen isotope exchange within cultured diatom silica. Rapid Commun Mass Spectrom 31:1749–1760 Uchikawa J, Zeebe RE (2012) The effect of carbonic anhydrase on the kinetics and equilibrium of the oxygen isotope exchange in the CO2–H2O system: Implications for δ18O vital effects in biogenic carbonates. Geochim Cosmochim Acta 95:15–34 Urey HC (1947) The thermodynamic properties of isotopic substances. J Chem Soc:562–581 Urey HC, Epstein S, McKinney CR (1951) Measurement of paleotemperatures and temperatures of the Upper Cretaceous of England, Denmark, and the southeastern United States. Geol Soc Am Bull 62:399–416 Veizer J, Hoefs J (1976) The nature of O18/O16 and C13/C12 secular trends in sedimentary carbonate rocks. Geochim Cosmochim Acta 40:1387–1395 Veizer J, Prokoph A (2015) Temperatures and oxygen isotopic composition of Phanerozoic oceans. Earth Sci Rev 146:92–104 Veizer J, Fritz P, Jones B (1986) Geochemistry of brachiopods: Oxygen and carbon isotopic records of Paleozoic oceans. Geochim Cosmochim Acta 50:1679–1696 Veizer J, Hoefs J, Lowe DR, Thurston PC (1989) Geochemistry of Precambrian carbonates: II. Archean greenstone belts and Archean sea water. Geochim Cosmochim Acta 53:859–871 Veizer J, Bruckschen P, Pawellek F, Diener A, Podlaha OG, Carden GA, Jasper T, Korte C, Strauss H, Azmy K, Ala D (1997) Oxygen isotope evolution of Phanerozoic seawater. Palaeogeogr Palaeoclimatol Palaeoecol 132:159–172 Veizer J, Ala D, Azmy K, Bruckschen P, Buhl D, Bruhn F, Carden GA, Diener A, Ebneth S, Godderis Y, Jasper T (1999) 87 Sr/86Sr, δ13C and δ18O evolution of Phanerozoic seawater. Chem Geol 161:59–88 Voarintsoa NRG, Barkan E, Bergel S, Vieten R, Affek HP (2020) Triple oxygen isotope fractionation between CaCO3 and H2O in inorganically precipitated calcite and aragonite. Chem Geol 539:119500 Wadleigh MA, Veizer J (1992) 18O16O and 13C12C in lower Paleozoic articulate brachiopods: Implications for the isotopic composition of seawater. Geochim Cosmochim Acta 56:431–443 Wallmann K (2001) The geological water cycle and the evolution of marine δ18O values. Geochim Cosmochim Acta 65:2469–2485 Watkins JM, Nielsen LC, Ryerson FJ, DePaolo DJ (2013) The influence of kinetics on the oxygen isotope composition of calcium carbonate. Earth Planet Sci Lett 375:349–360 Wenzel B, Lécuyer C, Joachimski MM (2000) Comparing oxygen isotope records of silurian calcite and phosphate— δ18O compositions of brachiopods and conodonts. Geochim Cosmochim Acta 64:1859–1872 Winter BL, Knauth LP (1992) Stable isotope geochemistry of cherts and carbonates from the 2.0 Ga gunflint iron formation: implications for the depositional setting, and the effects of diagenesis and metamorphism. Precambrian Res 59:283–313 Wostbrock JAG, Sharp ZD, Sanchez-Yanez C, Reich M, van den Heuvel DB, Benning LG (2018) Calibration and application of silica–water triple oxygen isotope thermometry to geothermal systems in Iceland and Chile. Geochim Cosmochim Acta 234:84–97 Wostbrock JAG, Cano EJ, Sharp ZD (2020a) An internally consistent triple oxygen isotope calibration of standards for silicates, carbonates and air relative to VSMOW2 and SLAP2. Chem Geol 533:119432 Wostbrock JAG, Brand U, Coplen TB, Swart PK, Carlson SJ, Sharp ZD (2020b) Calibration of carbonate–water triple oxygen isotope fractionation: seeing through diagenesis in ancient carbonates. Geochim Cosmochim Acta 288:369–388 Yanchilina AG, Yam R, Kolodny Y, Shemesh A (2020) From diatom opal-A δ18O to chert δ18O in deep sea sediments. Geochim Cosmochim Acta 268:368–382 Zakharov DO, Bindeman IN (2019) Triple oxygen and hydrogen isotopic study of hydrothermally altered rocks from the 2.43–2.41 Ga Vetreny belt, Russia: An insight into the early Paleoproterozoic seawater. Geochim Cosmochim Acta 248:185–209 Zakharov DO, Marin-Carbonne J, Alleon J, Bindeman IN (2021)Triple oxygen isotope trend recorded by Precambrian cherts: a perspective from combined bulk and in situ secondary ion probe measurements. Rev Mineral Geochem 86:323–365 Zeebe RE (1999) An explanation of the effect of seawater carbonate concentration on foraminiferal oxygen isotopes. Geochim Cosmochim Acta 63:2001–2007 Zeebe RE (2014) Kinetic fractionation of carbon and oxygen isotopes during hydration of carbon dioxide. Geochim Cosmochim Acta 139:540–552 Zheng Y-F (1991) Calculation of oxygen isotope fractionation in metal oxides. Geochim Cosmochim Acta 55:2299–2307

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Reviews in Mineralogy & Geochemistry Vol. 86 pp. 401–428, 2021 Copyright © Mineralogical Society of America

Triple Oxygen Isotope Systematics in the Hydrologic Cycle Jakub Surma Institute of Geology and Mineralogy University of Cologne Zülpicher Straße 49b Cologne, 50674 Germany [email protected]

presently at: Geoscience Center Georg August University Goldschmidtstraße 1 Göttingen, 37077 Germany

Sergey Assonov formerly at: Institute of Geology and Mineralogy University of Cologne Zülpicher Straße 49b Cologne, 50674 Germany

Michael Staubwasser

Institute of Geology and Mineralogy University of Cologne Zülpicher Straße 49b Cologne, 50674 Germany INTRODUCTION The analysis of hydrogen (δD) and oxygen (δ18O) isotope ratios of H2O are widely used tools for studies of the hydrological cycle (Friedman 1953; Dansgaard 1954; Gonfiantini 1986; Gat 1996; Araguás-Araguás et al. 2000; Gat et al. 2000) and climate reconstruction (Dansgaard 1964; Johnsen et al. 1989; Petit et al. 1999). Natural variations of δD and δ18O in precipitation are well correlated and fall on a common global trend, the Global Meteoric Water Line (GMWL, Craig 1961):

D  8   18 O 10‰

(1)

The slope (  2GMWL ) of 8 in this equation is defined by mass-dependent equilibrium fractionation during condensation of atmospheric vapor (Dansgaard 1964; Horita and Wesolowski 1994). 1529-6466/21/0086-0012$05.00 (print) 1943-2666/21/0086-0012$05.00 (online)

http://dx.doi.org/10.2138/rmg.2021.86.12

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The 10‰ positive offset in δD results from kinetic (diffusive) isotope fractionation during the initial formation of atmospheric vapor over the ocean which follows a slightly lower δD/δ18O slope than the GWML (Craig and Gordon 1965; Merlivat 1978). Typically, any evaporation process in the hydrologic cycle results in waters that deviate from the average global  2GMWL. This deviation is expressed with the d-excess parameter (e.g., Gat 1996): d-excess D  8   18 O

(2)

The process of isotopic fractionation during vapor formation is explained by the evaporation model of Craig and Gordon (1965) (Fig. 1). The model describes the total isotopic fractionation (*aL–V–evap) resulting from evaporation from a water body (*RW), which is controlled by relative humidity (h), fractionation factors for equilibrium and diffusion, and the isotopic composition of free atmospheric vapor (*RA). At lower h, the vapor concentration gradient between the interface layer (vapor saturation) and the free atmosphere increases and amplifies diffusivity. Hence, the magnitude of d-excess is mostly controlled by relative humidity (h) and becomes larger when h decreases (Craig and Gordon 1965; Cappa et al. 2003; Steen-Larsen et al. 2014). Therefore, d-excess is traditionally used to reconstruct evaporation conditions at vapor source regions and to quantify evaporation of continental water bodies (Gat and Bowser 1991; Gat 1996; Masson-Delmotte et al. 2005; Pfahl and Wernli 2008).

Figure 1. The Craig and Gordon Model for evaporation of surface water (modified from Gat 1996).

However, the d-excess parameter is not exclusively controlled by h but also by the different temperature sensitivity of equilibrium fractionation factors for D/H (2aL–V–eq) and 18O/16O (18aL–V–eq). This prevents a unique interpretation by introducing uncertainty to h estimates (Horita and Wesolowski 1994; Luz et al. 2009). Also, the diffusivity fractionation factors (2adiff and 18adiff, respectively) of both isotope systems underlie a temperature dependent relationship (Luz et al. 2009): 2

 diff  1.25  0.02  T  



18



 diff  1  1

(3)

Due to the different temperature relationships of D/H and 18O/16O fractionation factors for liquid–vapor and solid–vapor equilibrium (2aS–V–eq and 18aS–V–eq, respectively), d-excess is additionally affected by precipitation temperature (Merlivat and Nief 1967; Majoube 1971; Ellehoj et al. 2013). The additional combined analysis of 17O/16O and 18O/16O of H2O was suggested to be a promising complement to reconstruct relative humidity at the vapor source (Angert et al. 2004).

Analysis Due to methodical limitations and analytical uncertainties, the use of triple oxygen isotopes in hydrological applications was impractical in the past. However, the temperature dependency

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of d-excess created the need for another second order parameter of water isotopologues. In parallel, methodical advances over the past two decades provided the necessary analytical resolution to identify mass-dependent anomalies in the 16O–17O–18O distribution in natural waters (Meijer and Li, 1998; Baker et al. 2002). The latter method was greatly advanced by Barkan and Luz (2005). An analytical uncertainty of ±0.005‰ for 17O-excess was achieved based on liberation of oxygen gas from H2O by means of fluorination with a CoF3 reagent, providing an adequate precision to resolve small variations in the hydrosphere and to determine H217O/H216O equilibrium and diffusivity fractionation factors (17aL–V–eq and 17adiff, respectively) with a sufficient accuracy (Barkan and Luz 2005, 2007). Over the past decade, laser absorption instruments have been developed and also proven to achieve sufficiently high precision to resolve 17O-excess variations in natural waters (Berman et al. 2013; Steig et al. 2014; Affolter et al. 2015; Schauer et al. 2016; Tian et al. 2016). Analytical requirements: Two-point calibration. Reported d18O in natural waters so far ranges from −69.6‰ (East Antarctic snow) to 29.2‰ (Sistan Desert, Iran) and, thus, covers a total range of approximately 100‰ (Surma et al. 2015; Touzeau et al. 2016). In order to account for inter-laboratory scaling differences, a two-point calibration based on certified reference materials is essential (e.g., Kaiser 2008; Kusakabe and Matsuhisa 2008). A commonly used normalization in triple oxygen isotope studies is the one suggested by Schoenemann et al. (2013):  * O smp   * Osmp_VSMOW  _ VSMOW  SLAP

nom  * OSLAP/VSMOW * meas  OSLAP/VSMOW

(4)

where d*Osmp_VSMOW is the measured value of a sample expressed against VSMOW, meas nom is the assigned distance between SLAP−2 and VSMOW−2, and  * OSLAP/VSMOW  * OSLAP/VSMOW is the difference between SLAP−2 and VSMOW−2 in the respective laboratory. Assigned nom values for SLAP−2 (vs. VSMOW−2) are  17 OSLAP/VSMOW  = −29.6986‰ and 18 nom 17  OSLAP/VSMOW  = −55.5‰ ( O-excess = 0 per meg).

New data presented in this work This review is supplemented with new samples and data from one case study in the highaltitude environment of the Southern German Alps. Sampling was carried out at Mt. Zugspitze (2962 m above sea level, m a.s.l.), 10 km SW of Garmisch-Partenkirchen (720 m a.s.l.). The temperate regional climate is characterized by a mean annual temperature of −4.3 °C. Samples were collected from February to May 2016 in the local surrounding of Mt. Zugspitze— at the Schneefernerhaus Research Station (UFS, 2,650 m a.s.l.) and the nearby Zugspitze plateau (Zugspitzplatt, N 10.99°, E 47.41°; ~2,450 m a.s.l.). The sample set comprises 25 atmospheric vapor samples (Table S1) that were collected in February and May 2016 by means of cryogenic extraction at UFS station in LN2 at low pressure in a modified version of a high efficiency trap (Brenninkmeijer and Röckmann 1996). We also obtained a total number of 25 precipitation/snow samples and a larger number of samples from the seasonal local snow cover (Tables S2 and S3). Isotope analysis. All samples were analyzed for their triple oxygen isotope and hydrogen isotope composition at the Institute for Geology and Mineralogy, University of Cologne. 17 O/16O and 18O/16O analysis is performed with modified method based on Barkan and Luz (2005). Details on the analytical procedure are given in Surma et al. (2015, 2018). Long-term external reproducibility of standard waters and selected samples is approx. ±0.06‰ (δ17O), ±0.1‰ (δ18O), and ±8 per meg (17O-excess). D/H ratios were determined by continuous flow analysis of H2 gas liberated by TC/EA carbon reduction of H2O at 1550 °C (also see Surma et al. 2018). The average long-term external reproducibility is approximately ±0.3‰ for δD and ± 2.1‰ for d-excess. Laboratory reference waters were analyzed between every 5 to 10 samples. All isotope data were normalized to the SMOW-SLAP scale following the procedure suggested by Schoenemann et al. (2013) and standard-sample bracketing (Table S4).

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TRIPLE OXYGEN ISOTOPES IN WATER Triple oxygen isotope fractionation The triple oxygen isotope fractionation exponent for equilibrium liquid–vapor fractionation (qL–V–eq) was determined by Barkan and Luz (2005), giving a constant qL–V–eq of 0.529 for the entire experimental T range from 11.4 to 41.5 °C. Therefore, 17O-excess can be considered temperature-independent for equilibrium fractionation of evaporation from water surfaces and formation of rain. A difficulty arises from the fact that no experimental data are available for triple oxygen isotope fractionation at solid–vapor equilibrium of H2O. Theoretical predictions suggest qS–V–eq ≈ 0.528 (Van Hook 1968). Landais et al. (2012b) confirm this value with a set of vapor and snowfall samples from Greenland. Molecular diffusion of water vapor in air is characterized by a somewhat lower qdiff of 0.5185 ± 0.0002 (Barkan and Luz 2007). However, the experiment has shown a small temperature dependence in the range from 0.5183 ± 0.0001 (25 °C) to 0.5187 ± 0.0001 (40 °C). It is unclear whether this qdiff/T trend is linear and whether a lower qdiff would apply for diffusive fractionation at low temperatures (e.g., 0.5172 at −50 °C if the trend is extrapolated linearly; Bao et al. 2016). 17

O-excess during the formation of vapor

In the field of hydrology 17O-excess is the commonly used term to describe deviations 17 of 17O/16O ratios from a reference slope with  GMWL  = 0.528 and typically reported in per meg with respect to VSMOW (Meijer and Li, 1998; Luz and Barkan 2010): 17

O-excess (per meg)  ( 17 O  0.528   18 O)  106

(5)

with δ′*O = ln(δ*O+1).  here is defined by the slope of average global precipitation— represented by the Global Meteoric Water Line—in the δ′17O vs. δ′18O space. The GMWL itself shows a positive offset of ~33 per meg with respect to seawater (Luz and Barkan 2010). 17 GMWL

The exact magnitude—or slope (Fig. 2)—of *aL–V–evap is determined by h, respective equilibrium and diffusion fractionation factors, and the isotopic composition of vapor in the free atmosphere (cf. Fig. 1; Craig and Gordon 1965; Ehhalt and Knott 1965; Criss 1999; Cappa et al. 2003): * *

 L-V_evap 

 diff  *  L-V_eq  1  h 



1  *  L-Veq  h  * RA / * RW

(6)



For a single moisture source (e.g., open ocean) and absence of vapor admixture, all atmospheric vapor is generated from the evaporating water itself and *RV =*RV (closure assumption). In that case Equation (6) reduces to: *

 L-V_evap 

*



 L-V_eq  *  diff  1  h   h



(7)

The temperature of ambient air may deviate from the temperature of the water surface in natural settings. Here, normalized humidity (hn) should be used in Equations (6) and (7) instead of h. hn is calculated by: hn  h 

qsat_a qsat_s

(8)

where qsat_a is the vapor concentration in the free air and qsat_s is the saturated vapor concentration at water temperature (Barkan and Luz 2007; Uemura et al. 2010).

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Figure 2. Fractionation of triple oxygen isotopes in the atmosphere (modified from Barkan and Luz 2007). Initial atmospheric vapor (white diamond) forms from sea water (black diamond) at non-equilibrium conditions. Evaporation results in positive lower δ′17O and δ′18O, and higher 17O-excess of vapor with respect to the reference slope (blue). Transport, cooling, and rainout leads to steady isotopic depletion of the residual vapor reservoir.

In addition, air turbulence—or wind—reduce the magnitude of diffusive isotope fractionation during the evaporation process. In the Craig and Gordon Model, this effect is described by the turbulently mixed sublayer, in which actual mixing of air with different vapor concentration balances the h gradient without molecular diffusion (Fig. 1). However, the derivation of a clear relationship between wind speed and lowering of molecular diffusion is complex (Merlivat and Jouzel 1979). A recent study demonstrates that, we cite: ‘for isotope water balance studies where winds are frequently above 2 m/s, the C–G model may be inadequate without appropriate corrections for spray vaporization, or the introduction of appropriate kinetic isotope fractionation factors’ (Gonfiantini et al. 2020). This would be strongest felt over water bodies deep enough to sustain breaking waves. In order to account for boundary layer turbulence, the effect is usually parametrized in the Craig and Gordon model by correcting *adiff with the exponent n: *

 diff  corr  



*

 diff



n

(9)

n is determined empirically and ranges from 1 (pure molecular diffusion) to 0.5 (rough continental regime) (Dongmann et al. 1974; Mathieu and Bariac 1996; Haese et al. 2013). Reduction of diffusive fractionation with n < 0.5 is observed for wind tunnel experiments and evaporation above the ocean surface (Merlivat and Jouzel 1979; Uemura et al. 2010).

NATURAL VARIATIONS OF 17O-EXCESS IN WATER Meaning and purpose of the Global Meteoric Water Line δD and δ18O in meteoric waters around the world are tightly correlated and follow the δD/δ18O trend (l2) with a slope of 8 (Eqn. 1), i.e., the GMWL (Craig 1961; Dansgaard 1964). The +10‰ offset (d-excess) results from diffusive, non-equilibrium fractionation during formation of pristine vapor above the ocean (Eqn. 6), resulting in relative preferential enrichment of deuterium with respect to 18O in the vapor phase. Precipitation that forms from that vapor follows the GMWL towards more depleted values with increasing distance from the coast, higher latitude, and increasing altitude, whereby the underlying process is approximated by Rayleigh distillation (Dansgaard 1964; Horita et al. 2008). The GMWL concept provides an empirical reference frame for the field of stable isotope hydrology, but is in general agreement with Rayleigh fractionation (Dansgaard 1964; Criss 1999).

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Meijer and Li (1998) analyzed a set of natural waters yielding  17 GMWL  = 0.528, thus providing an analogous reference frame for 17O/16O and 18O/16O. Including standard measurements of GISP, SLAP, and Antarctic snow data (Barkan and Luz 2005; Landais et al. 2008) to their larger dataset of natural waters (n = 52), Luz and Barkan (2010) confirmed this slope for the GMWL with a positive offset of 0.033‰ with respect to VSMOW−2: ´ 17 O  0.528  ´ 18 O  0.033‰

(10)

Similar to d-excess, the deviation from this line is reported as 17O-excess (cf. Eqn. 5). 17 The value of  GMWL  = 0.528 is close to θL–V_eq = 0.529, thus confirming Rayleigh equilibrium condensation as the controlling mechanism of precipitate formation (Passey and Levin 2021, this volume). Figure 3 shows a compilation of reported triple oxygen isotope data of global precipitation, surface water bodies, hydrothermal waters, and seawater, that cover a total range of ≈ 100‰ in δ18O. In the case of closure ( * RV0  * RA0 , cf. Eqn. 7), vapor isotopic composition ( * RV0 ) is calculated by (Craig and Gordon 1965):  RV0

*

*

RW0  *



1



 L-V_eq   diff  h  1  *  diff *



(11)

where * RW0 is the isotopic composition of ocean surface water. When the air parcel is advected and cooled after initial vapor formation, first condensate forms in equilibrium with * RV0 : *

R P0

*

RV0  *  L-V_eq

(12)

The residual fraction (fres) of initial oceanic vapor decreases with increasing distance from the source. The isotopic composition of residual vapor is calculated by the Rayleigh equation:

 RA

*

*

*



RV0  fres L-V_eq

1

(13)

Precipitating water in equilibrium results in observed  2GMWL= 8 and 17 GMWL = 0.528. For the triple oxygen isotope space this slope is valid for δ18O ranges between −40‰ and −5‰ (Fig. 3), thus providing a reasonable reference frame for global precipitation that is mostly provided by Rayleigh distillation of oceanic vapor (e.g., Trenberth et al. 2007). The bell-shaped distribution of 17O-excess vs. δ18O indicates that water samples found in the lower range of the δ18O scale (polar snow) as well as in highly enriched samples (surface waters from arid regions) are systematically lower in 17O-excess with respect to the GMWL (Fig. 3). We note that the apparent bell-shape to some degree may also result from a bias towards samples that are studied precisely because of their inherent kinetic fractionation effects found in polar and hyper-arid regions. The vast majority of continental waters not too far removed from the ocean source will likely fall in the δ18O range from −30‰ to −5‰. In the case of polar snow, the systematic deviation from the GMWL leads to pronounced Local Meteoric Water Lines (LMWL) >  0.528—i.e., showing positive correlation of 17O-excess and δ18O—that result from snow formation at vapor supersaturation, and thus kinetic fractionation, at temperatures below −20 °C (Landais et al. 2012a,b; Casado et al. 2016). Miller (2018) states that this pattern of snow with δ18O below −40‰ is also a result of ‘diamond dust’ (open-sky precipitation) contribution to central Antarctic snow cover, which is characterized by a fractionation slope of l17 = 0.531 in this study. It is also suggested that the LMWL in remote polar regions may be additionally affected by incorporation of massindependently, fractionated, largely 17O-enriched stratospheric oxygen in precipitation (Winkler et al. 2013; Miller 2018). Evidence for stratospheric water intrusions is suggested by negative correlation of 17O-excess and δ18O found in the study which contradict the general synoptic

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Figure 3. Compilation of 17O-excess vs. δ18O in global waters. The gray horizontal line depicts the GMWL as reported by Luz and Barkan (2010). Precipitation in polar regions (diamonds) show values below −24‰ in δ18O. 17O-excess ranges from 30 to 70 per meg in snow from Greenland and Alert, Canada, and shows correlation with decreasing δ18O (below −40‰) for Antarctic precipitation (Landais et al. 2008, 2012a,b; Lin et al. 2013a; Winkler et al. 2013; Pang et al. 2015, 2019; Touzeau et al. 2016). Fresh waters (gray circles) comprise snowfall, rain, cave drip water, tap water, lakes, springs, and rivers (Landais et al. 2010; Luz and Barkan 2010; Lin et al. 2013a; Affolter et al. 2015; Li et al. 2015, 2017; Gázquez et al. 2018; Tian et al. 2018; Alexandre et al. 2019; Passey and Ji, 2019; Tian et al. 2019; Uechi and Uemura 2019; Bergel et al. 2020; Bershaw et al. 2020; Sha et al. 2020; Voigt et al. 2020; this study). In general, those waters range from −22‰ to ~0‰ in δ18O and show a large variability in 17O-excess, ranging from −40 to 120 per meg. Water bodies from arid, evaporative environments (yellow crosses) generally show δ18O values higher than −8‰ and progressively lower 17O-excess with increasing δ18O. Lowest 17O-excess values are found in highly evaporated water bodies from the Sistan Desert, Iran, the Atacama Desert, Chile, and Lake Chichancanab, Mexico (Surma et al. 2015, 2018; Evans et al. 2018; Voigt et al. 2020). Hydrothermal waters (blue triangles) are in good agreement with freshwaters and show a narrow range in δ18O from −12‰ to −6‰ and from −20 to 45 per meg in 17O-excess (Sharp et al. 2016; Wostbrock et al. 2018; Zakharov et al. 2019b). Seawater measurements are indicated with asterisks (Luz awnd Barkan 2010).

positive correlation in Antarctic precipitation. We note that such effects at mid-latitudes, which is the major focus of this review, are much less likely. First, stratospheric air is brought to the troposphere mostly by the polar vortex. The stratosphere-troposphere exchange flux at midlatitudes is very limited. Second, the troposphere in the mid-latitudes has a much higher water content than the polar troposphere, so the mass-balance may be too unfavorable to observe stratospheric downdraft. Third, 17O-excess found in snow at polar regions demonstrates only limited deviations, if any, from the range expected (Landais et al. 2012a; Touzeau et al. 2016). Isotopically enriched samples from arid regions do not reflect fractionation effects during precipitate formation but a systematic decrease of 17O-excess during intensive evaporation of continental waters (Surma et al. 2015, 2018; Voigt et al. 2020). Here the negative correlation of 17O-excess and δ18O in those waters is the result of excessive evaporation, where total fractionation integrated over the course of a day is controlled by relative humidity, evaporation degree, and evaporative loss with respect to recharge. Resulting trajectories in the δ′17O vs. 17 δ′18O space are flatter than  GMWL and analog to local evaporation lines (LEL) known in the 18 traditional δD vs. δ O system (Fontes and Gonfiantini 1967; Gat 1984; Gat and Bowser 1991). However, it should be noted that triple oxygen isotopes in natural evaporative systems do not depict straight lines but typically form curved trajectories.

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17 O-excess in polar snow precipitation. Ice cores from Greenland and Antarctica are important records of past climate over glacial-interglacial cycles (e.g., Petit et al. 1999; NorthGRIP members 2004). The d-excess parameter is widely used to reconstruct variations in temperature and relative humidity at oceanic moisture sources (e.g., Vimeux et al. 1999; Steen-Larsen et al. 2011). However, the use of 17O-excess shows promise as a novel and more robust temperature independent tracer that provides additional constraints on source region humidity (Uemura et al. 2010).

Landais et al. (2012b) investigated seasonal triple oxygen isotope variations in surface snow at the NEEM drilling site, Greenland, where a slight anticorrelation of δ18O and 17 O-excess in snow is found. Maximum 17O-excess is present in samples with lowest δ18O values. Measurements of 17O-excess and δ18O in atmospheric vapor and concomitant snow at NEEM site show similar values in both phases that were also found to be in equilibrium based on previous δ18O and δD measurements (Steen-Larsen et al. 2011; Landais et al. 2012b). Modeling of air temperature and relative humidity in moisture source regions also reveals that 17 O-excess reflects h conditions at the vapor source. Triple oxygen isotope studies on Greenland ice cores further provide valuable information on the coupling between high-latitude and lowto mid-latitude climate variations in the northern hemisphere during abrupt climatic changes over the course of the last glaciation (Guillevic et al. 2014; Landais et al. 2018). For the case of Antarctica, Winkler et al. (2012) demonstrate that moisture source humidity can be reliably reconstructed from coastal ice core records, whereas the isotopic composition of snow in continental areas is dominated by local temperature effects. This is also confirmed by a spatial gradient which is observed for 17O-excess in precipitation across Antarctica (Fig. 3), showing elevated values in coastal areas that are dominated by marine conditions and low 17O-excess in the Antarctic interior (Landais et al. 2012a; Schoenemann et al. 2014; Touzeau et al. 2016). Low 17O-excess in continental Antarctic precipitation is attributed to seasonal variations, variability in sea ice extent, and supersaturation of vapor over ice at low temperatures (Risi et al. 2013; Schoenemann et al. 2014). Supersaturation of vapor over ice. In order to interpret polar precipitation records, one needs to account for the supersaturation effect at cloud temperatures  3000 ppbv above tropospheric ozone background. Therefore, the isotopic balance of atmospheric vapor at mid-latitudes is likely dominated by synoptic processes (i.e., Rayleigh distillation and potential continental recycling). Rayleigh distillation. Several studies have demonstrated that 17O-excess in vapor and precipitation reflects evaporation conditions at the initial moisture source (Uemura et al. 2010; Landais et al. 2012b; Uechi and Uemura 2019). However, as summarized above in the discussion of mid-latitude rainfall data, there is some indication of subsequent modification by evaporative recycling of continental moisture. With the Mt. Zugspitze data at hand, we may test the respective primary and subsequent controls of water vapor isotopic composition. *  RA in the troposphere at high altitude and—by inference—the continental interior. Rozanski et al. (1982) have demonstrated that formation of condensate from vapor in westerly air masses may be well approximated by a Rayleigh approach. δDA and d-excessA analyses by Dütsch et al. (2018) demonstrate that the occurrence of mixed phase clouds is negligible for westerly moisture pathways, thus, excluding complexity of vapor, water, and ice coexistence during cloud formation (Ciais and Jouzel 1994). This is also supported by the liquid–vapor precipitate formation in rapidly advected air masses at Mt. Zugspitze. Based on the analysis of 11 snow and vapor samples that were collected simultaneously (Table S2, Roman numerals), we determined to overlying fractionation process for snow formation at Mt. Zugspitze. Observed deviation of actual samples (18eA–P_meas from predicted fractionation (18eA–P_cal) is calculated by Δ18εA–P (18eA–P_meas −18eA–P_cal), with 18eA–P_meas ≈ 18Op − 18OA and: 18

 ( 18 S-V_eq  1)  1000 A-P_cal

(23)

where aS–V_eq is the solid–vapor equilibrium fractionation factor (Majoube 1971). Δ εA–P based on this calculation averages −4.4 ± 2.0‰ (Fig. 9). Replacing 18 aS–V_eq in Equation (23) with 18 aL–V_eq to account for the occurrence of supercooled water droplets provides a better approximation for 18eA–P_meas (Δ18εA–P = 1.9 ± 0.9‰) (Ciais and Jouzel 1994; Bolot et al. 2013), thus confirming that liquid orographic clouds are the prevalent cloud species in strong updraft regimes at temperatures between 0 and −15 °C, such as Mt. Zugspitze (Kneifel et al. 2014; Lohmann et al. 2016; Lowenthal et al. 2016). Respective 17O-excessP_cal and d-excessP_cal deviate by 19 ± 19 per meg and 11.1 ± 4.3‰. Due to their large scatter, these values are also reasonably well reproduced at given uncertainty, even though d-excessP is systematically lower, presumably due to the different T dependencies of 2 aL–V_eq and 18 aL–V_eq. Typically, the orographic cloud basis is located either below or at the altitude of Mt. Zugspitze, hence we assume that pairs of vapor–precipitation samples are closely related. However, vapor samples may potentially not represent free atmospheric vapor but a mixture of atmospheric and snow surface vapor. We also note that the determination of *αL–V_eq does not cover T  below 0 °C and is therefore extrapolated for ambient conditions at Mt. Zugspitze (Horita and Wesolowski 1994). 18 

18

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Figure 9. Difference between measurement data of precipitation samples and predicted isotopic composition of precipitation (Δ18εA–P). Values are calculated with 18αL–V_eq (solid black squares and line, Horita and Wesolowski 1994) and 18αS–V_eq (solid red squares and line, Majoube 1971).

The evolution of * RA (Fig. 10) is based on Monte Carlo simulations (n = 500) for Equations (11) and (13), using a * RW0 of ocean surface with dDW0 = 0‰, d17OW0= –0.005‰, and d18OW0 = 0‰. Modeling parameters (source h, Ta, * adiff, *αL–V_eq) were approximated from HYSPLIT air trajectory reanalysis (see Table S8 for details). * adiff is corrected for air turbulence by Equation (9) with an average n = 0.26 (Merlivat and Jouzel 1979; Luz and Barkan 2010). The range of observed δ18OA is well reproduced for fres between 0.5 (days of relatively warm Ta) and 0.15 (days of lower Ta). Higher δ18OA is found in vapor from warmer air masses and lower δ18OA in vapor provided by cold air (Fig. 8), indicating a distillation effect that is also in agreement with the HYSPLIT output for specific humidity. This observation is also confirmed by regression analysis of δ18OA vs. Ta (Table 1). A change from a warmer (25 °C) to a cooler (10 °C) vapor source would shift δ18OA according to the change in equilibrium fractionation during vapor formation (Fig. 10, blue arrows), which is only a minor effect compared to that of relative condensation loss from the air parcel. The variability in 17O-excessA is controlled by ambient h and wind turbulence (n) at the moisture source (e.g., Uemura et al. (2010); Uechi and Uemura (2019)). The magnitude of initial d-excessA is, in contrast, additionally controlled by surface temperature at the source, resulting from the different T dependency of 2αL–V_eq Table 1. Regression analysis (slope, standard error (SE), and coefficient of determination (R2) of δ18O, 17O-excess, and d-excess in vapor and precipitation samples vs. meteorological parameters (left column): Air temperature (Ta) and relative humidity (h). δ18O

Parameter  

slope

17

SE

R2

slope

O-excess SE

d-excess R2

slope

SE

R2

Vapor (total) Ta

0.52

0.11

0.47

h

−1.46

4.36

0.00

−0.81

0.48

0.11

−0.01

0.20

0.00

14.53

13.79

0.05

−12.14

4.82

0.22

Vapor (February) Ta

0.70

0.18

0.51

h

5.27

5.31

0.07

−1.50

0.70

0.25

0.05

0.40

0.00

2.66

5.31

0.00

−20.80

6.17

0.45

Vapor (May) Ta h

0.51

0.24

0.40

−1.78

0.98

0.32

−0.04

0.19

0.01

−12.49

5.90

0.39

44.65

24.06

0.33

4.36

4.33

0.13

Precipitation (total) Ta

0.21

0.17

0.06

0.03

0.50

0.00

−0.51

0.31

0.18

h

4.70

5.69

0.03

−27.08

15.23

0.12

−12.26

11.02

0.09

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Figure 10. Rayleigh fractionation model for initial atmospheric vapor at given source condition for 17OexcessA vs. δ18OA (a), and for d-excessA vs. δ18OA (b). Simple Rayleigh distillation of initial oceanic vapor (solid frame, fres = 1) at hs = 0.8 (white) and at hs = 0.6 (gray) results in steady isotopic depletion of * RA. Numbers represent respective fres. Blue arrows indicate a change in Ts from 25 to 10 °C, red arrows the change if a wind correction exponent of n = 0.29 instead of n = 0.23 is used. Ellipsoids represent probability density functions for a 0.95 quantile of the Monte Carlo simulation. Black and red open symbols represent atmospheric vapor sampled in February and May at Mt. Zugspitze, respectively. 2  diff and 18αL–V_eq, and 18 (Horita and Wesolowski 1994; Luz et al. 2009). Although the range  diff of δ18OA may be successfully modeled by continuous vapor distillation to a reasonable degree, high 17O-excessA and d-excessA values are not reproduced. Variation of from n = 0.26 to n = 0.33 do not sufficiently increase 17O-excessA and d-excessA values (Fig. 10, red arrows). Lower h over the ocean might also elevate initial 17O-excessA and d-excessA, but h < 0.6 is unlikely for given oceanic moisture sources (Pfahl and Sodemann 2014). Consequently, Rayleigh distillation alone may not explain the observation.

Moisture pathways and air trajectory modeling. Reanalysis of air trajectories provides important information on atmospheric pathways and potential moisture sources (Pfahl and Wernli 2008; Vogelmann et al. 2015; Yu et al. 2015; Uechi and Uemura 2019). Atmospheric transport to Mt. Zugspitze is determined by three patterns: (i) Long-range transport from North America, (ii) long-range transport from Northern Africa, and (iii) stratospheric deep intrusions (Hausmann et al. 2017). We modeled 240 h back-trajectories (including Ta and specific humidity) using the NOAA HYSPLIT software package and GDAS reanalysis data sets (available at ftp://arlftp.arlhq.noaa.gov/pub/archives/gdas1) (Stein et al. 2015). Since the higher resolution record (0.5° grid) is incomplete, we use datasets of 1.0° spatial resolution for modeling. According to previous studies we use altitudes of 1,900 to 2,200 m above ground level (m a.g.l.) to approximate the low-level troposphere (3,000 m a.s.l.) at Mt. Zugspitze (Trickl et al. 2010; Vogelmann et al. 2015) and identify two source patterns: The Central Atlantic, between N 30° and N 50° for warmer air, and the Nordic Sea providing cold air (Fig. 11). These patterns are also in agreement with general moisture pathways that were determined for the Northern Alps by Sodemann and Zubler (2010). Analysis of specific humidity indicates low continental evaporation rates in winter with the Central Atlantic being identified as the predominant moisture source in February, whereas moisture uptake above Western and Central Europe contributes to the moisture balance in late spring. Continental moisture recycling. Triple oxygen isotope studies of mid-latitude waters suggest that continental recycling may be an important local effect (Li et al. 2015; Tian et al. 2018; Tian et al. 2019) but a rigorous demonstration has not been provided yet. It is also known from δD and δ18O analyses that moisture recycling plays an important role in the continental moisture balance (Bastrikov et al. 2014; Wei and Lee 2019). The continental vapor budget (* RA) is therefore balanced by the isotopic composition of initial vapor (* RA0) and the surface vapor flux (* RV) with qR being the relative quantity of local, recycled moisture (Aemisegger et al. 2014):

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Figure 11. HYSPLIT 240 h back trajectories (modelled for 2,200 m a.g.l. and 3 h resolution) of air masses arriving at Mt. Zugspitze (asterisk). Modeling is performed for both field campaigns in February (a) and May (b). Trajectories of warmer air masses (red) suggest moisture uptake above the Central Atlantic Ocean, colder air masses (black) cross the Northern Atlantic and the Nordic Sea.

*

1  qR   * RA

 qR  * RV

(24)

RV  qT  * RVT  1  qT   * RVE

(25)

RA 

0

The surface vapor flux is defined as: *

where qR is the relative quantity of recycled vapor being contributed by plant transpiration and RVT the corresponding isotopic ratio which is approximated by quantitative, non-fractionating transfer from surface water (* RW) to vapor, so that * RVT = * RW (Wang and Yakir 2000; Peng et al. 2005). It has been shown that moisture of the continental boundary layer is significantly balanced by recycling of surface water (He and Smith 1999; Welp et al. 2012; Jasechko et al. 2013). * RVEis the isotopic ratio of the evaporative flux from surface waters and saturated soil (* RWi). Figure 12 outlines the process of initial vapor formation and continental recycling. *

Figure 12. Schematic representation showing isotopic fluxes during Rayleigh distillation with continental recycling: I. Initial vapor forms above the ocean surface. II. First condensate formation and precipitation. III (a and b). Evaporation of continental surface water, admixture of vapor, and subsequent precipitation. Solid, black arrows indicate H2O fluxes, gray arrows indicate mixing of residual vapor with secondary vapor.

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The results from HYSPLIT air trajectory reanalysis (see above) and previous studies suggest that moisture recycling above Western and Central Europe affects the balance of * RA0 (van der Ent et al. 2010; Sodemann and Zubler 2010). Based on the 1D-model (Fig. 12), we here use Equations (11), (13), (24), and (25) to calculate the evolution of atmospheric vapor, * RAi* (Fig. 13 a and b). Average qT = 0.7 is suggested by different previous studies for Central Europe (Lawrence et al. 2007; Aemisegger et al. 2014; Christner et al. 2017). Wind-induced turbulence (Eqn. 9) for continental evaporation is parametrized with n = 0.5 (Dongmann et al. 1974; Gat 1996; Haese et al. 2013). * RWiis approximated with mean regional * Rp (February: δ17O ≈ –5.525‰, δ18O ≈ –10.5‰, δD ≈ –74.0‰; May: δ17O ≈ –4.199‰, δ18O ≈ –8.0‰, δD ≈ –54.0‰), using average precipitation over Western to Central Europe from the Online Isotopes in Precipitation Calculator (OIPC) (Bowen and Revenaugh 2003; Bowen 2018) with 17 O-excess being expected to be close to the average GMWL value (≈ 33 per meg). Continental recycling shows a small increase of 17O-excessA for higher qR (Fig. 13 a), whereas no significant effect is visible for d-excessA (Fig. 13 b). Changing * RW of surface water to lower values (February) results in an according shift in δ18OA which is visibly larger for qR = 0.5 but does not affect both excess parameters. This may be explained by the fact that average surface water’s d-excessW ≈ 10‰ and, thus, lower than d-excessA of arriving moisture (≈ 10‰). Evaporation from surface water will elevate d-excessV in the local vapor flux to a degree which is not significantly different from arriving d-excessA. 17O-excessW in surface water, on the other hand, is already comparably high to 17O-excessA in the arriving air parcel. Re-evaporation elevates 17O-excessV in the vapor flux and induces a positive shift in the resulting mixed vapor. Since typical qR is below 0.2 during winter and spring in Western and Central Europe, the uncertainty in * RW may be neglected here (Trenberth 1999; van der Ent et al. 2010). However, an accurate estimate will be more critical when recycling is balanced for summer months and intensive evaporation elevates qR and significantly alters * RW. Vapor contribution from a local evaporation. Considering the above findings, recycling over continental Europe may probably explain some increase in 17O-excessA and should be accounted for in the total balance but is not sufficient to explain high 17O-excessA and d-excessA found in atmospheric vapor at Mt. Zugspitze. Even at low continental h = 0.6 and qR = 0.5—as used in this model—only a minor increase in 17O-excessA would result from this process. The effect on d-excessA is even smaller. This is mainly due to the fact that transpiration by vegetation (qT = 0.7) effectively diminishes fractionation of surface water during continental vapor formation. Much larger effects may be expected when vapor is formed from open water surfaces or saturated soil. However, the range of 17O-excessA modeled with low qR is in good agreement with 17O-excess ranging from 14 to 27 per meg in natural water data reported for low altitudes in Western and Central Europe (Luz and Barkan 2010; Affolter et al. 2015; Alexandre et al. 2019). Our results also show that modeling with qR = 0.5 provides sufficiently high 17O-excess (~40 per meg) to explain elevated values in precipitation as reported for Northwestern U.S. (Li et al. 2015) or inland China (Tian et al. 2019). Even though the recycling ratio (qR) is relatively small for Western and Central Europe at lower altitudes, evaporative loss from local snow cover provides significant vapor quantities in Alpine hydrological balances (Froehlich et al. 2008; van der Ent et al. 2010; Schlaepfer et al. 2014). Evaporation may account for up to 90% of total mass loss from snow cover and is especially high when turbulent transport of snow is effective, i.e., at wind-exposed locations and high-altitude mountain ridges (Strasser et al. 2008). Ambient conditions at Mt. Zugspitze are characterized by high snow accumulation and wind-induced re-deposition, providing a constant source of fresh snow surfaces, that i) lower a potential fractionation limitation by self-diffusion in stagnant snow cover (Friedman et al. 1991; Schlaepfer et al. 2014), and ii) can supply a significant quantity of moisture from local snow cover (Kaiser et al. 2002; Froehlich et al. 2008).

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Figure 13. Distillation model as shown in Figure 10 but accounting for moisture recycling over Central Europe for 17O-excessA vs. δ18OA (a), and for d-excessA vs. δ18OA (b). Bold ellipsoids were modeled with average surface * RW for May. Atmospheric vapor evolves along a Rayleigh condensation path (cf. Fig. 10) and mixes with hypothetical quantities of qR = 0.1 (green) and qR = 0.5 (yellow) of recycled moisture that evaporates from surface water (* RW). Light ellipsoids indicate same vapor trends but with average * RW for February. Rayleigh fractionation model for atmospheric vapor including continental moisture recycling with qR = 0.2 at given fres (gray ellipsoids, numbers) for for 17O-excessA vs. δ18OA (c) and d-excessA vs. δ18OA (d). Solid black circles represent the average isotopic composition of local snow cover. The isotopic compositions of local vapor fluxes at Mt. Zugspitze (* RV) for February (blue) and May (red) vary with changes in h and Ta. Gray ellipsoids and open symbols represent the same Monte Carlo simulation and data as described in Figure 10, respectively.

Local * RW input values for calculating the isotopic composition of the vapor flux are obtained from the average composition of the local snow cover (δ17O = –8.729‰, δ18O = –16.555‰, δD = –122.3‰). Both * RW calculated for February and May are identical within analytical uncertainty. Turbulence in the diffusive boundary layer is parametrized with n = 0.5. A slightly higher value of n = 0.58 is suggested for water droplets and snow particles suspended in air (Stewart 1975; Froehlich et al. 2008). However, it is more likely that prevailing winds induce steady turnover of surface snow but do not necessarily keep it in suspension. Isotopic fluxes that were calculated for snow evaporation (* RV_Feb and * RV_May) only show a small difference (Fig. 13 c and d) that can be attributed to the different average h and Ta used in the calculation (February: h = 0.73 ± 0.05, Ta = −5.9 ± 3 °C; May: h = 0.67 ± 0.05, Ta = 1.0 ± 3 °C). The isotopic composition of local evaporation, * RV, represents the isotopic end-member in the local atmospheric vapor balance. Actual * RA of the free atmosphere results from mixing of * RV and the isotopic composition of vapor in the arriving air mass (Fig. 13 c and d, gray ellipsoids). A higher recycling ratio will shift * RA towards the composition of * RV, whereas low qR will not change the isotopic composition of arriving vapor significantly. This explains why peak values of 17O-excessA and d-excessA coincide with low Ta and δ18OA, while minimum 17O-excessA and d-excessA are associated with higher Ta and δ18OA (Fig. 8).

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Cold air generally holds lower H2O concentrations which would, in turn, decrease the contribution of arriving vapor in the local vapor balance, elevating local qR and, thus, the imprint of the local vapor flux. Some uncertainty may arise from the fact that vapor samples were extracted at ~2.5 m above ground and may—due to insufficient mixing of the diffusive boundary layer—reflect the isotopic composition of the evaporative flux rather than free atmospheric vapor.

FUTURE WORK AND CONCLUSION Future work Analytical challenges. It was demonstrated that fluorination of H2O using a CoF3 reagent combined with dual-inlet mass spectrometry provides a reasonably good reproducibility (±5 per meg) in 17O-excess to identify small natural variations (Barkan and Luz 2005). Analytical errors (seen as data scatter) in δ17O and δ18O are well correlated, thus not affecting the precision for 17O-excess (Landais et al. 2006). A sample memory effect occurring in CoF3 lines is evident but well corrigible (i.e., by four blind injections between samples with a 55‰ difference in δ18O (Barkan and Luz 2005)). Mass spectrometric analysis may be affected by unrecognized blanks, leaks, and scale compression. So far, two-point data normalization using VSMOW-2 and SLAP-2 provides an adequate correction (Schoenemann et al. 2013). Still, this normalization has to be extrapolated for samples exceeding δ18O = 0‰ (e.g., waters from arid regions), hence an isotopically enriched standard with a commonly accepted triple oxygen isotope composition would improve inter-laboratory comparison. In the past years, it has been shown that cavity ring-down spectroscopy provides sufficiently low uncertainty for measuring natural variations in 17O-excess (Berman et al. 2013; Schoenemann et al. 2014; Affolter et al. 2015; Tian et al. 2018). However, water mixing by the autosampler syringe and water adhesion to internal surfaces of the instrument were identified as causes for considerably high memory effects (Berman et al. 2013 and references therein). Three approaches are suggested to minimize these effects: i) preconditioning with blind injections, ii) a mathematical memory correction, and iii) avoiding large differences in isotopic composition of adjacent samples (Schauer et al. 2016). In contrast to mass spectrometric analysis, data scatter in δ17O and δ18O is not correlated, thus increasing the uncertainty for 17O-excess (Berman et al. 2013). Still, the improvement of analytical protocols has demonstrated that optical isotope analysis may reach ± 10 per meg uncertainty providing a sample throughput comparable to that of isotope laboratories using the fluorination method (Schauer et al. 2016). In the future, these developments will be crucial for the expansion of spatial coverage and automated long-term observations that will be needed for a global monitoring network of triple oxygen isotopes in precipitation and vapor. Precise knowledge of 17O-excess in atmospheric vapor would e.g., be essential to constrain the evaporative fractionation in lake balance models (Gázquez et al. 2018; Surma et al. 2018; Voigt et al. 2020) and to improve the performance of general circulation models (Steen-Larsen et al. 2016). Modeling of cloud processes and global transport. In order to improve the understanding of 17O-excess distribution in precipitation and vapor across the globe, adequate prediction using isotope-enabled general circulation models (GCM) is inevitable. The fractionation of water isotopologues (including H217O) was implemented into the LMDZ GCM and extensively tested for variations along latitudinal gradients and seasonal variations (Risi et al. 2013). Accounting for evaporative conditions, Rayleigh distillation, tropospheric vapor mixing, and rain reevaporation the authors have shown that the sensitivity of 17O-excess to evaporative conditions is apparently underestimated by the model. Schoenemann and Steig (2016) also demonstrated that intermediate complexity modeling (ICM) which accounts for seasonal climatological cycles

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(i.e., relative humidity, sea surface temperature, sea ice extent, evaporation, precipitation rate) and diffusivity during low temperature precipitation, captures 17O-excess variations observed in Antarctic precipitation. The authors show that variable moisture source conditions alone cannot explain large seasonal at Vostok/East Antarctica, stressing the importance of local temperature effects on snow formation. It is suggested to apply additional corrections for snow sublimation and ‘diamond dust’ (clear-sky precipitation) input in interior Antarctica (Casado et al. 2018; Miller 2018; Pang et al. 2019). Improving these parametrizations and the understanding of advection processes during poleward transport of moisture will be critical for triple oxygen isotope based GCM simulations of past climate (e.g., Cauquoin et al. 2019a,b). In order to improve GCM estimates on spatio-temporal 17O-excess distribution in vapor and precipitation, the coverage of measurements should be drastically improved to provide a profound basis for GCM vs. observation evaluations (Risi et al. 2013; Steen-Larsen et al. 2016). Better knowledge of equilibrium and diffusive solid–vapor fractionation at low temperatures will be necessary to improve GCM capabilities in polar regions. Adequate integration of evaporation from soils and plants will be essential to provide robust estimates on continental moisture recycling (Gat and Matsui 1991; Aemisegger et al. 2014). Mineral–water systems. 17O-excess studies of ice core records have shown that 17O-excess is a valuable tracer for paleoclimate reconstruction (Guillevic et al. 2014; Landais et al. 2018). However, ice records are mostly restricted to polar areas, emphasizing the need of other triple oxygen isotope records in low- and mid-latitude regions. Recent publications demonstrate a several mineral–water systems that show the capability to capture triple oxygen isotope compositions of ambient water by direct equilibration with mineral-bound oxygen or in hydration water and fluid inclusions. Speleothems provide a unique climate archive with high temporal resolution for low- and mid-latitudes since they are known to reflect the isotopic composition of regional precipitation (e.g., Bar-Matthews et al. 1996). 17O-excess in meteoric water that was reconstructed from speleothem carbonates is in good agreement with actual precipitation measurements and show significant regional differences between sampling sites (South American and Asian monsoon regions, eastern Mediterranean, China, and Central Asia). The authors explain these variations to different moisture source conditions of regional precipitation (Sha et al. 2020). However, reconstructed moisture source humidity remains mostly constant in those records during glacial-interglacial transitions. Affolter et al. (2015) also present a method for direct 17O-excess measurements on fluid inclusions in speleothem samples, providing a more direct estimate of paleo precipitation without requiring accurate constraints on the isotopic fractionation between water and calcite (Bergel et al. 2020; Fosu et al. 2020; Voarintsoa et al. 2020). However, this approach requires larger sample amounts (0.5–1.5 g of carbonate). Authigenic lake minerals that form in equilibrium with ambient waters provide another valuable tracer for 17O-excess reconstruction. It was shown shown that isotopic compositions of parent water bodies (i.e., lakes and ponds) can be precisely reconstructed by liberation and analysis of gypsum hydration water, and accurate knowledge of triple oxygen fractionation between the structurally bonded and the ambient water (Gázquez et al. 2015, 2017; Herwartz et al. 2017). Quantitative estimates on local relative humidity changes were made by combining this approach with d-excess measurements to natural samples from lakes in arid regions (Evans et al. 2018; Gázquez et al. 2018). Recent studies also reveal that 17O-excess in lake carbonates reflects the isotopic composition of parent water bodies and primary catchment precipitation (Passey et al. 2014; Passey and Ji 2019; Passey and Levin 2021, this volume). It is also suggested that additional analysis of ‘clumped isotopes’ (Δ47) is valuable to improve back-projection modeling of parent waters by adding constraints on the carbonate formation temperature (Ghosh et al. 2006; Passey and Ji 2019).

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Analysis of triple oxygen isotopes in fine-grained and clay-rich sediments by Bindeman et al. (2019) has also shown that integrated isotope signals of regional precipitation are captured in weathering products of bedrock. Using appropriate fractionation factors for water–clay equilibrium (Bindeman et al. (2019) and references therein) and a model for back-projection of water, mean annual temperatures can be reconstructed. Another application of this approach is the reconstruction of a paleo-GMWL based on the analysis of shales and clay minerals (Bindeman 2021, this volume). Landais et al. (2006) have demonstrated that δ17O–δ18O variations in plant leaf water follow a transpiration fractionation trend (λtransp) which is distinctively lower than equilibrium fractionation of water and that λtransp is controlled by ambient relative humidity. Recent studies have shown that phytoliths (amorphous silica microstructures in plants) reflect the triple oxygen isotope composition of leaf water (Alexandre et al. 2018; Alexandre et al. 2019).Assuming constant triple oxygen isotope fractionation between silica and leaf water (θPhyto–LW = 0.521), this approach may provide a unique tracer for paleo-humidity. However, it has yet to be proven that θPhyto–LW is climate independent and can thus be applied for reconstructing paleo-leaf water. If so, reconstructed leaf water could provide e.g., insights into humidity conditions and the triple oxygen isotopic composition of plant CO2 (Alexandre et al. 2019). Water–rock interaction and bedrock re-equilibration also provide valuable hydrological information for geological periods (i.e., the Precambrian) where other records are rare (Herwartz 2021, this volume). Zakharov et al. (2019b) show that regional meteoric water can be reconstructed from triple oxygen isotope mixing patterns found in Icelandic metamorphic rocks. In studies this approach was used to reconstruct the average δ18O continental ice during Paleoproterozoic global glaciations (Herwartz et al. 2015; Zakharov et al. 2019a). Modeling the isotopic balance for water–rock interaction of Precambrian cherts provides key information on the isotopic composition of the ancient ocean (Sengupta and Pack 2018; Liljestrand et al. 2020; Zakharov et al. 2021, this volume).

Conclusion Significant improvement of analytical techniques during the last two decades has triggered the use of triple oxygen isotopes in the hydrological cycle, the investigation of underlying fractionation mechanisms, triple-O-based climate reconstructions, and the comprehension of hydrological processes. A major achievement is understanding the global distribution of triple oxygen isotopes which is described by δ′17O = 0.528 ⋅ δ′18O + 0.033‰ and referred to as the GMWL. Essential isotope fractionation processes operating on the global scale include equilibrium evaporation, diffusion of water vapor, and vapor condensation. Though, diffusion and the Craig and Gordon model are well established for δD and δ18O, the accurate determination of triple oxygen isotope fractionation factors describing the 17O/16O and 18O/16O distribution for dominating processes marks a major breakthrough. Processes that involve diffusive fractionation, such as evaporation or snow formation at low temperatures produce trends that deviate from this relationship and which are found in extreme environments like remote polar regions (low δ18O) or hyper-arid deserts (high δ18O). However, also waters that fall in the range of intermediate δ18O values (e.g., mid-latitude precipitation) form local δ′17O–δ′18O trends that deviate from overall 17 GMWL = 0.528 and reflect re-evaporation of rain droplets or continental moisture recycling. The temperature independent 17O-excess parameter is a useful, complementary tool in addition to traditional d-excess for the stable isotope-based assessment of hydrological processes, paleoclimatology and paleohydrology. Its sensitivity to diffusive fractionation makes it a valuable tracer for (paleo-)humidity conditions and locations of moisture source regions. However, it has been demonstrated that second order effects such as distillation at low temperatures and reevaporation of rain droplets may systematically lower the 17O-excess in the final precipitate.

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Similar to the use of d-excess in arid regions, 17O-excess is used for hydrological balancing of evaporative water bodies. Combining both parameters results in a better understanding and parametrization of environmental conditions. The use of lake balance models and adequate constraints of boundary conditions (isotopic composition of inflowing water and atmospheric vapor, wind regime) provides valuable estimates on humidity conditions in arid regions. Analysis of authigenic minerals from lake bodies also demonstrates the potential of 17O-excess for paleoclimate applications. Studies of precipitation in mid-latitudes suggest that elevated 17O-excess in continental interior cannot be explained by the above-mentioned effects and result from moisture recycling along air trajectories. In this work we demonstrate that 17O-excess of atmospheric vapor provides valuable information on continental moisture recycling. However, no data on triple oxygen isotopes in continental vapor from mid-latitudes were available so far to obtain systematic constraints on this effect. The investigation of moisture recycling would be greatly improved with larger datasets on both, precipitation records and atmospheric vapor. Measurements of 17O-excess in atmospheric vapor in a high temporal resolution will be necessary to improve the understanding of local meteorological effects on local evaporative fluxes and, thus, the isotopic balance of H2O in the atmosphere. Triple oxygen isotope analysis holds large potential to constrain isotopic estimates for land-locked water reservoirs that are balanced by local evaporation and sublimation to a large extent.

ACKNOWLEDGEMENTS The project was funded by the German Research Foundation (DFG, grant no. STA 936/8−1).

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Tellus 34:142–150 Schauer AJ, Schoenemann SW, Steig EJ (2016) Routine high-precision analysis of triple water-isotope ratios using cavity ring-down spectroscopy. Rapid Commun Mass Spectrom 30:2059–2069 Schlaepfer DR, Ewers BE, Shuman BN, Williams DG, Frank JM, Massman WJ, Lauenroth WK (2014) Terrestrial water fluxes dominated by transpiration: Comment. Ecosphere 5:61 Schoenemann SW, Steig EJ (2016) Seasonal and spatial variations of 17Oexcess and dexcess in Antarctic precipitation: Insights from an intermediate complexity isotope model. J Geophys Res Atmos 121:11,215–11,247 Schoenemann SW, Schauer AJ, Steig EJ (2013) Measurement of SLAP2 and GISP δ17O and proposed VSMOWSLAP normalization for δ17O and 17Oexcess. Rapid Commun Mass Spectrom 27:582–590 Schoenemann SW, Steig EJ, Ding Q, Markle BR, Schauer AJ (2014) Triple water-isotopologue record from WAIS Divide, Antarctica: Controls on glacial-interglacial changes in 17Oexcess of precipitation. J Geophys Res Atmos 119:8741–8763 Sengupta S, Pack A (2018) Triple oxygen isotope mass balance for the Earth’s oceans with application to Archean cherts. Chem Geol 495:18–26 Sha L, Mahata S, Duan P, Luz B, Zhang P, Baker J, Zong B, Ning Y, Brahim YA, Zhang H, Edwards RL, Cheng H (2020) A novel application of triple oxygen isotope ratios of speleothems. Geochim Cosmochim Acta 270:360–378 Sharp ZD, Gibbons JA, Maltsev O, Atudorei V, Pack A, Sengupta S, Shock EL, Knauth LP (2016) A calibration of the triple oxygen isotope fractionation in the SiO2–H2O system and applications to natural samples. Geochim Cosmochim Acta 186:105–119 Sodemann H, Zubler E (2010) Seasonal and inter-annual variability of the moisture sources for Alpine precipitation during 1995–2002. Int J Climatol 30:947–961 Steen-Larsen HC, Masson-Delmotte V, Sjolte J, Johnsen SJ, Vinther BM, Bréon FM, Clausen HB, Dahl-Jensen D, Falourd S, Fettweis X, Gallée H, Jouzel J, Kageyama M, Lerche H, Minster B, Picard G, Punge HJ, Risi C, Salas D, Schwander J, Steffen K, Sveinbjörnsdóttir AE, Svensson A, White J (2011) Understanding the climatic signal in the water stable isotope records from the NEEM shallow firn/ice cores in northwest Greenland. J Geophys Res Atmos 116:D06108 Steen-Larsen HC, Risi C, Werner M, Yoshimura K, Masson-Delmotte V (2016) Evaluating the skills of isotope-enabled general circulation models against in situ atmospheric water vapor isotope observations. J Geophys Res 122:246–263 Steen-Larsen HC, Sveinbjörnsdottir AE, Peters AJ, Masson-Delmotte V, Guishard MP, Hsiao G, Jouzel J, Noone D, Warren JK, White JWC (2014) Climatic controls on water vapor deuterium excess in the marine boundary layer of the North Atlantic based on 500 days of in situ, continuous measurements. Atmos Chem Phys 14:7741–7756 Steig EJ, Gkinis V, Schauer AJ, Schoenemann SW, Samek K, Hoffnagle J, Dennis KJ, Tan SM (2014) Calibrated high-precision 17O-excess measurements using cavity ring-down spectroscopy with laser-current-tuned cavity resonance. Atmos Meas Tech 7:2421–2435 Stein AF, Draxler RR, Rolph GD, Stunder BJB, Cohen MD, Ngan F (2015) NOAA’s HYSPLIT Atmospheric Transport and Dispersion Modeling System. Bull Am Meteorol Soc 90:2059–2077 Stewart MK (1975) Stable Isotope Fractionation Due to Evaporation and Isotopic Exchange of Falling Waterdrops: Applications to Atmospheric Processes and Evaporation of Lakes. J Geophys Res 80:1133–1146 Strasser U, Bernhardt M, Weber M, Liston GE, Mauser W (2008) Is snow sublimation important in the alpine water balance? Cryosphere 2:53–66 Stumpp C, Klaus J, Stichler W (2014) Analysis of long-term stable isotopic composition in German precipitation. J Hydrol 517:351–361 Surma J, Assonov S, Bolourchi MJ, Staubwasser M (2015) Triple oxygen isotope signatures in evaporated water bodies from the Sistan Oasis, Iran. Geophys Res Lett 42:8456–8462 Surma J, Assonov S, Herwartz D, Voigt C, Staubwasser M (2018) The evolution of 17O-excess in surface water of the arid environment during recharge and evaporation. Sci Rep 8:4972 Tian C, Wang L, Novick KA (2016) Water vapor δ2H, δ18O and δ17O measurements using an off-axis integrated cavity output spectrometer—sensitivity to water vapor concentration, delta value and averaging-time. Rapid Commun Mass Spectrom 30:2077–2086 Tian C, Wang L, Kaseke KF, Bird BW (2018) Stable isotope compositions (δ2H, δ18O and δ17O) of rainfall and snowfall in the central United States. Sci Rep 8:6712 Tian C, Wang L, Tian F, Zhao S, Jiao W (2019) Spatial and temporal variations of tap water 17O-excess in China. Geochim Cosmochim Acta 260:1–14

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Touzeau A, Landais A, Stenni B, Uemura R, Fukui K, Fujita S, Guilbaud S, Ekaykin A, Casado M, Barkan E, Luz B, Magand O, Teste G, Le Meur E, Baroni M, Savarino J, Bourgeois I, Risi C (2016) Acquisition of isotopic composition for surface snow in East Antarctica and the links to climatic parameters. Cryosphere 10:837–852 Trenberth KE (1999) Atmospheric moisture recycling: role of advection and local evaporation. J Clim 12:1368–1381 Trenberth KE, Smith L, Qian T, Dai A, Fasullo J (2007) Estimates of the global water budget and its annual cycle using observational and model data. J Hydrometeorol 8:758–769 Trickl T, Feldmann H, Kanter H-J, Scheel H-E, Sprenger M, Stohl A, Wernli H (2010) Forecasted deep stratospheric intrusions over Central Europe: Case studies and climatologies. Atmos Chem Phys 10:499–524 Uechi Y, Uemura R (2019) Dominant influence of the humidity in the moisture source region on the 17O-excess in precipitation on a subtropical island. Earth Planet Sci Lett 513:20–28 Uemura R, Barkan E, Abe O, Luz B (2010) Triple isotope composition of oxygen in atmospheric water vapor. Geophys Res Lett 37:L04402 van der Ent RJ, Savenije HHG, Schaefli B, Steele-Dunne SC (2010) Origin and fate of atmospheric moisture over continents. Water Resour Res 46:W09525 Van Hook WA (1968) Vapor pressures of the isotopic waters and ices. J Phys Chem 72:1234–1244 Vimeux F, Masson V, Jouzel J, Stievenard M, Petit JR (1999) Glacial–interglacial changes in ocean surface conditions in the Southern Hemisphere. Nature 398:410–413 Voarintsoa NRG, Barkan E, Bergel S, Vieten R, Affek HP (2020) Triple oxygen isotope fractionation between CaCO3 and H2O in inorganically precipitated calcite and aragonite. Chem Geol 539:119500 Vogelmann H, Sussmann R, Trickl T, Reichert A (2015) Spatiotemporal variability of water vapor investigated using lidar and FTIR vertical soundings above the Zugspitze. Atmos Chem Phys 15:3135–3148 Voigt C, Herwartz D, Dorador C, Staubwasser M (2020) Triple oxygen isotope systematics of evaporation and mixing processes in a dynamic desert lake system. Hydrol Earth Syst Sci Discuss in review Wang XF, Yakir D (2000) Using stable isotopes of water in evapotranspiration studies. Hydrol Process 14:1407–1421 Wei Z, Lee X (2019) The utility of near-surface water vapor deuterium excess as an indicator of atmospheric moisture source. J Hydrol 577:123923 Welp LR, Lee X, Griffis TJ, Wen X-F, Xiao W, Li S, Sun X, Hu Z, Val Martin M, Huang J (2012) A meta-analysis of water vapor deuterium-excess in the midlatitude atmospheric surface layer. Global Biogeochem Cycles 26:GB3021 Winkler R, Landais A, Risi C, Baroni M, Ekaykin A, Jouzel J, Petit JR, Prie F, Minster B, Falourd S (2013) Interannual variation of water isotopologues at Vostok indicates a contribution from stratospheric water vapor. PNAS 110:17674–17679 Winkler R, Landais A, Sodemann H, Dümbgen L, Prié F, Masson-Delmotte V, Stenni B, Jouzel J (2012) Deglaciation records of 17O-excess in East Antarctica: reliable reconstruction of oceanic normalized relative humidity from coastal sites. Clim Past 8:1–16 Wostbrock JAG, Sharp ZD, Sanchez-Yanez C, Reich M, van den Heuvel DB, Benning LG (2018) Calibration and application of silica-water triple oxygen isotope thermometry to geothermal systems in Iceland and Chile. Geochim Cosmochim Acta 234:84–97 Yu W, Tian L, Ma Y, Xu B, Qu D (2015) Simultaneous monitoring of stable oxygen isotope composition in water vapour and precipitation over the central Tibetan Plateau. Atmos Chem Phys 15:10,251–10,262 Zakharov DO, Bindeman IN, Serebryakov NS, Prave AR, Azimov PY, Babarina II (2019a) Low δ18O rocks in the Belomorian belt, NW Russia, and Scourie dikes, NW Scotland: A record of ancient meteoric water captured by the early Paleoproterozoic global mafic magmatism. Precambrian Res 333:105431 Zakharov DO, Bindeman IN, Tanaka R, Friðleifsson GÓ, Reed MH, Hampton RL (2019b) Triple oxygen isotope systematics as a tracer of fluids in the crust: A study from modern geothermal systems of Iceland. Chem Geol 530:119312 Zakharov DO, Marin-Carbonne J, Alleon J, Bindeman, IN (2021) Temporal triple oxygen isotope trend recorded by Precambrian cherts: A perspective from combined bulk and in situ secondary ion probe measurements. Rev Mineral Geochem 86:323–365

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Reviews in Mineralogy & Geochemistry Vol. 86 pp. 429–462, 2021 Copyright © Mineralogical Society of America

Triple Oxygen Isotopes in Meteoric Waters, Carbonates, and Biological Apatites: Implications for Continental Paleoclimate Reconstruction Benjamin H. Passey and Naomi E. Levin Department of Earth and Environmental Sciences University of Michigan 1100 North University Avenue Ann Arbor, MI, 48103 USA [email protected] [email protected]

INTRODUCTION The usefulness of triple isotope studies of natural systems is contingent on the existence of resolvable differences in mass-dependent fractionation exponents θ [where θ = ln(17/16α)/ln(18/16α)] among processes that are prevalent in the system(s) of interest, or on the existence of resolvable non-mass-dependent fractionation in the system. Both such contingencies are satisfied in continental hydroclimate systems. The process of evaporation of water involves molecular diffusion of water vapor through air, which carries a θ value of 0.5185 (Barkan and Luz 2007) that differs strongly from the value of 0.529 for equilibrium exchange between water vapor and liquid water (Barkan and Luz 2005). This means that waters that have been isotopically modified by evaporation can, in many cases, be clearly identified on the basis of triple oxygen isotope analysis (Landais et al. 2006; Surma et al. 2015, 2018; Gázquez et al. 2018), and that it may even be possible to reconstruct the isotopic composition of the unevaporated source waters (Passey and Ji 2019). Leaf waters are highly evaporated and have distinctive triple oxygen isotope compositions (Landais et al. 2006; Li et al. 2017), which has implications for the triple oxygen isotope compositions of atmospheric CO2 and O2 (Liang et al. 2017), plant materials such as cellulose and phytoliths (Alexandre et al. 2018), and animals that ingest significant amounts of leaf water (Pack et al. 2013; Passey et al. 2014). Molecular oxygen in the atmosphere is strongly fractionated in a non-mass-dependent way due to photochemically-driven isotopic exchange in the stratosphere (Luz et al. 1999; Bao et al. 2008; Pack 2021, this volume), with the degree of fractionation dependent on pCO2, pO2, and global gross primary productivity (GPP) (Cao and Bao 2013; Young et al. 2014). Through the process of respiration, this oxygen with ∆′17O of approximately −430 per meg (Barkan and Luz 2005; Pack et al. 2017; Wostbrock et al. 2020) can become part of body water and hence biominerals (Pack et al. 2013). Note that in this chapter, we calculate ∆′17O as: ∆′17O = δ′17O – 0.528 δ′18O, where δ′1xO = ln(x/16Rsample / x/16Rstandard), where x is 17 or 18. We report all δ and δ′ values in per mil (×103), and all ∆′17O values in per meg (×106). This definition of ∆′17O is equivalent to the ‘17O-excess’ parameter commonly used in the hydrological literature. Recently, Guo and Zhou (2019a,b) have predicted from theory that kinetic fractionation may impart materials like speleothems and corals with distinct triple oxygen isotope compositions that testify to the extent of isotopic disequilibrium during mineralization. 1529-6466/21/0086-0013$05.00 (print) 1943-2666/21/0086-0013$05.00 (online)

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As such, the continents are emerging as a particularly fruitful area of application for triple oxygen isotope studies, with ∆′17O values strongly influenced by evaporation, possibly influenced by kinetic fractionation during mineralization, and, for organisms with waters of respiration comprising a large fraction of their overall water budget, by the unique ∆′17O values of atmospheric O2. Triple oxygen isotopes are potentially useful in systems ranging from lakes to soils to caves to plants to animals. At the time of this writing, very little information exists for soils and caves, so we focus our review on lakes, animal body waters, plant waters, and on the isotopic compositions of carbonates and bioapatites forming in natural waters and animals, respectively. Precipitation (rain, snow) is the source of water on the continents, and thus is the triple oxygen isotope ‘starting point’ for all of these systems. The triple oxygen isotope compositions of continental carbonates and biological apatites are, to first-order, controlled by the isotopic compositions of their parent waters (e.g., lake water, animal body water). Therefore, much of this chapter focuses on the triple oxygen isotope compositions of natural waters and body water. The format for this discussion is to model the triple oxygen isotope evolution of water beginning with evaporation from the oceans, followed by Rayleigh distillation and production of continental precipitation, evaporative modification of this precipitation on the continents, and the triple oxygen isotope compositions of animals and plants that are sustained by this precipitation. All along this journey, we present the basic governing equations for modeling isotopic compositions, and we present observed triple oxygen isotope data in the context of these models. As much as possible, we present the model predictions and data in the form of ∆′17O versus d18O bivariate plots, keeping the axis ranges uniform to give the reader a better context for the comparative absolute values and variability from one system to another. Useful application of triple oxygen isotopes in paleoclimate depends on the ability to determine the triple oxygen isotope compositions of common minerals such as carbonates and apatites to high precision and accuracy. Following our discussion of natural and biological waters, we review the exciting developments of the past decade with respect to the analysis of carbonates and apatites and summarize the current state of inter-laboratory reproducibility. We examine the existing knowledge of key fractionation exponents for carbonate–water fractionation and fractionation during acid digestion. We conclude the chapter by highlighting gaps in knowledge and opportunities for future research. Throughout this chapter, we use isotopic nomenclature as described in Miller and Pack (2021, this volume).

METEORIC WATERS Evaporation from the oceans The oceans are the dominant source of water vapor to the atmosphere. The triple oxygen isotope composition of the oceans is d18O ~ 0‰, ∆′17O = −5 per meg (Luz and Barkan 2010), From this point of origin, there are four principle factors that determine the isotopic composition RE of the evaporation flux reaching the free atmosphere: 1) the (temperaturedependent) equilibrium isotope fractionation between liquid and vapor, aeq; 2) the relative humidity of air, normalized to the surface temperature of the water, hn; 3) the relative contributions of molecular diffusion and turbulence in transporting water vapor to the free atmosphere (embodied in the adiff parameter), and 4) the isotopic composition of ambient atmospheric water vapor, Ra. The isotopic composition of the evaporative flux is given by: Rw  hRa  eq RE   diff 1  hn 

(1)

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For adaptation to triple oxygen isotopes, equations such as Equation (1) are used twice: first in the 18O/16O space to determine 18/16RE, and then in the 17O/16O space to determine 17/16RE. For the latter, 17/16α values are computed from 18/16α values using appropriate fractionation exponents θ and the relation θ = ln(17/16α)/ln(18/16α). Then, d17O and d18O values are calculated from the R values using the appropriate R values for VSMOW, and from these the ∆′17O value is calculated after converting d1xO values to δ′1xO values. As pointed out by Luz and Barkan (2010), the basic form of Equation (1) has been obtained from the standpoints of diffusion theory (Ehhalt and Knott 1965), kinetic theory (Criss 1999), and from a steady-state evaporation model (Cappa et al. 2003). We note that Equation (1) is a key equation for describing the isotopic evolution of evaporating bodies of water on land, as discussed in the next section. Equation (1) also arises from the Craig–Gordon linearresistance model (Craig and Gordon 1965; see also Gat 1996, and Horita et al. 2008), which envisions an equilibrium vapor layer immediately overlying the liquid water surface, with further fractionation resulting from transport of this equilibrium vapor to the free atmosphere via a combination of molecular diffusion and turbulence. Pure molecular diffusion carries fractionations of 18/16α = 1.028 and θ = 0.5185 (as determined experimentally by Merlivat 1978 and Barkan and Luz 2007, respectively; see discussion in the latter and also Horita et al. (2008) and Cappa et al. (2003) regarding discrepancies between experimentally-derived 18/16α values and the theoretical value, 1.032, and possible explanations for these discrepancies). Thus, in the λ = 0.528 reference frame, diffusion-dominated evaporation involves a substantially higher ∆′17O value for the vapor, and, by mass balance, a corresponding lowering of ∆′17O of the residual liquid (Fig. 1), while turbulence-dominated evaporation will result in less elevated ∆′17Ο of vapors and more modest lowering of ∆′17O in the residual liquid. To firstorder, turbulence scales with windiness: in stagnant air, which occurs inside of leaves and soils, and can be achieved in laboratory experiments, 18/16adiff approaches the 1.028 limit for A c

ion

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Figure 1. Schematic depiction of triple oxygen isotope fractionation during evaporation. A. In the Craig–Gordon model, an equilibrium layer of water vapor (b) with hn = 1 lies in contact with the water surface (a). From here, vapor is transported to the atmosphere via a combination of turbulent transport, which is non-fractionating, and molecular diffusion, which is fractionating. The vapor produced by each process are noted by (c) and (d) in the figure. Note that the Craig–Gordon model, these two processes are linked in series and not in parallel as this simplified endmember schematic might imply. The schematic also does not depict isotopic exchange with ambient water vapor. B, C. Evaporation in triple oxygen isotope space, showing the relative trajectories for vapor and residual liquid in the turbulent transport endmember (c and double arrow, respectively), and for vapor and residual liquid in the diffusion endmember (d, hand pointer, respectively). Liquid a and vapor b are linked by the equilibrium fractionation exponent qeq = 0.529 (Barkan and Luz 2005), and molecular diffusion (b to d) has a θ value of 0.5185 (Barkan and Luz 2007).

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molecular diffusion. Combined with the qdiff value of 0.5185, this leads to highly-modified ∆′17O values of vapor and residual liquid. In windy conditions, turbulence develops, 18/16adiff values become substantially smaller, and ∆′17O values are less extreme even though the qdiff value is unchanged. This is because deviations in ∆′17O are dependent both on the magnitude of isotopic fraction (18/16α) and the numerical difference between the θ value of the fractionation and the reference frame slope (here 0.528) (Guo and Zhou 2019a): 17O AB

 A B  0.528   ln  18/16  A B 

(2)

where ∆∆′17ΟA–B is the difference in ∆′17O between two phases that exchange isotopes, θA–B is the fractionation exponent between these two phases, and 18/16αA–B is the fractionation factor between these phases. A simplifying assumption when treating evaporation of seawater is the ‘closure assumption’ (Merlivat and Jouzel 1979), which assumes that the only source of water vapor in the atmosphere is evaporation from the oceans, so that RE = Ra. Inserting this equivalency into Equation (1) gives:  RE Rw  eq   diff 1  hn   hn 

(3)

Uemura et al. (2010) determined a value of 18/16adiff = 1.008 for evaporation from the South Indian and Southern Oceans, meaning that the fractionation during vapor transport is closer to the turbulence endmember (18/16adiff = 1) than it is to the molecular diffusion endmember (18/16adiff = 1.028). Using 18/16adiff = 1.008, we use Equation (3) to model the isotopic compositions of marine vapors and the theoretical initial condensates of those vapors for hn of 0.5, 0.7 and 0.9 (Fig. 2). As can be seen, lower relative humidity results in higher ∆′17O values of the water vapor flux, which ultimately will lead to higher ∆′17O values of condensates, including precipitation on the continents. This arises from a combination of enhanced diffusion due to the greater water vapor concentration gradient between the boundary layer and free atmosphere, as well as the decreased influence of ambient atmospheric water vapor at lower relative humidity, in terms of isotopic exchange. In general, the positive ∆′17O values of global precipitation can be attributed to (1) the influence of molecular diffusion during evaporation from the oceans, and (2) the fact that condensation has a θ value of 0.529, slightly steeper than the 0.528 reference slope, which imparts condensates with a slightly higher ∆′17O value than the parent vapors (Fig. 2B).

Rayleigh distillation and the triple oxygen isotope meteoric water line Rayleigh distillation theory has stood the test of time as the explanation for the first-order features of the δD – d18O global meteoric water line (GMWL) (Craig 1961; Dansgaard 1964), and Rayleigh theory also accurately predicts the general features of the triple oxygen isotope GMWL (Luz and Barkan 2010). The Rayleigh equation for water vapor in a condensing parcel of air can be given as: R f  R0 f

(  eq 1)

(4)

where f is fraction of water vapor that remains in a parcel of air relative to the initial amount of water vapor, R0 is the initial isotopic composition of water vapor in the parcel, Rf is the instantaneous isotopic composition of vapor when fraction f remains, and aeq is the equilibrium fractionation between liquid water and water vapor. The adiff parameter does not appear in Equation (4) because the condensation of liquid requires that relative humidity is 100%; hence there is no concentration gradient in water vapor, and therefore no net transport by molecular diffusion. The only isotopic fractionation at play is equilibrium between liquid water and water vapor, which carries a fractionation exponent of 0.529 (Barkan and Luz 2005).

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free atmosphere δ18O = –9.3‰ Δʹ17O = –14 p.m. h = 0.7

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boundary layer h hn > adiff > Ra > RI > F)), so a lack of direct constraints on e.g., RI and F may not greatly hinder interpretations in certain cases. Here we discuss some additional considerations, not mutually exclusive, for sound interpretation of triple oxygen isotope data, and do so in the context of published results where appropriate. Qualitative indicator of evaporation. Authigenic minerals are commonly used to reconstruct past climates or past surface elevation in tectonic settings (e.g. Rowley and Garzione 2007), and both approaches generally assume that the reconstructed d18O values are reflective of primary precipitation, with recognition that evaporation can throw interpretations into serious error. Despite the large number of variables in Equation (17), all scenarios of evaporation lead to lowering of ∆′17O of surface waters, save perhaps for cases where ∆′17O of atmospheric vapor is unusually high. ∆′17O values lower than 0 per meg are uncommon for unevaporated precipitation (Fig. 4), whereas values lower than 0 per meg are common for evaporated waters (Surma et al. 2015, 2018; Gázquez et al. 2018; Passey and Ji 2019). Therefore, at the most basic level, triple oxygen isotope analysis will reveal whether the mineral parent waters are likely to have been modified by evaporation (∆′17O < ~ 0 per meg), and thus are unsuitable for interpretation in terms of d18O of pristine precipitation. Low ∆′17O values will also qualitatively indicate hydrological and climatic conditions conducive for appreciable evaporation (high XE, low hn). Directional constraints. As ∆′17O values of lake water becomes lower, the parameter space that can account for the values diminishes. For example, ∆′17O values of ~ 0 per meg are consistent with very low relative humidity but little net evaporation (Figs. 5B, F), as well as high relative humidity and appreciable evaporation (Figs. 5D, E). On the other hand, ∆′17O values of lower than ~ –50 per meg only occur when net evaporation is > 50 %, and relative humidity is ~0.6 or lower (Figs. 5B, D, E). Therefore, although ∆′17O data may not permit precise reconstruction of parameters such as hn or XE, they can be used to rule out portions of the parameter space. Independently-constrained variables. Gázquez et al. (2018) presented the first application of lacustrine triple oxygen isotope systematics to the paleoclimate record. Following methods described by Gázquez et al. (2017), they analyzed triple oxygen isotopes and hydrogen isotopes in waters of hydration of lacustrine gypsum extending back ~15 kyr at Lake Estanya in Spain. Given that gypsum formation requires closed-basin or nearly closed basin settings, gypsumbased studies are able isolate XE to values near 1. Gázquez et al. (2018) then used a MonteCarlo approach to randomly vary the other parameters in an equation similar to Equation (17), and then selected only the parameter sets that correctly predicted the measured triple oxygen and deuterium isotopic compositions of the gypsum hydration waters. This approach allowed them to constrain changes in normalized atmospheric relative humidity over this time interval, and to robustly conclude that hn during the Younger Dryas was substantially lower than during the late Holocene (by ~20% or more on the 0–100% hn scale; see their Fig. 5). Their inferred absolute values of hn for the Younger Dryas and late Holocene are more dependent on assumptions made about the 18/16adiff parameter (see their Fig. 5c). Passey and Ji (2019) sought to examine the predictions of Equation (17) by studying modern lakes where many of the free parameters in Equation (17) could be constrained. They examined three closed-basin lakes (XE = 1) (Great Salt Lake, Mono Lake, Pyramid Lake), each having three or fewer major inflowing rivers that account for the vast majority of water input into the lake, hence allowing RI to be constrained. Additionally, detailed climatologies exist for this region, including monthly relative humidity and potential evapotranspiration, which together allow for estimates of the effective relative humidity weighted to the months with highest evaporation (here, the summer months). For Great Salt Lake, Pyramid Lake, and Mono Lake, the evaporation-weighted relative humidities are 43%, 42%, and 44%, respectively, based on data from New et al. (2002). A compilation of monthly lake water and air temperature data from 88 lakes globally in Hren and Sheldon (2012) shows that summer water temperatures are generally

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similar or slightly warmer (by a few degrees) than summer air temperature; thus the water surface temperature normalized relative humidities (hn) are likely similar to, or lower than, the free air relative humidities reported above. Consequently, the major unconstrained parameters for the closed-basin lakes was 18/16adiff and Ra. 18/16adiff is commonly assumed to be ~ 1.014 for continental lakes (e.g., Gat 1996; Horita et al. 2008; Jasechko et al. 2013; Gibson et al. 2016). Figure 7 shows the results for these lakes in the context of models where 18/16adiff = 1.0142 and 1.0086. For the 18/16adiff = 1.0142 models, the relative humidities required to explain the observed lake water compositions are unrealistically high, whereas the 18/16adiff = 1.0086 models achieve a much better fit to the known relative humidities and isotopic compositions. Alternatively, models where 18/16adiff = 1.0142, but Ra is higher (60 per meg instead of 12 per meg) also better predict the observed data within the constraints of known hn and XE.

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There is good evidence that both Ra and 18/16adiff may depart from commonly assumed values. For example, Surma et al. (2021, this volume) show that continental vapors in the European Alps have substantially higher ∆′17O than water vapors in equilibrium with local surface waters. The parameter 18/16adiff can theoretially range by 28‰ (!) (1 to 1.028), and 100 50 initial waters h = 0.8 0.6 0.3

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Figure 7. Western United States closed-basin lakes and inflow rivers (Mono Lake, Pyramid Lake, and Great Salt Lake). A. Inflow rivers (triangles) and lake waters (gray circles), plotted in the context of the model (Eqn. 16) from Figure 5D, where 18/16adiff = 1.0142. Solid lines connect waters with initial (unevaporated) isotopic compositions shown in Figure 3b for hn = 0.7. B. As (A), but plotted in the context of models for 18/16adiff = 1.0086. The latter models are more realistic, given that potential evapotranspiration-weighted relative humidity for these lakes is ~40 – 45%. C. As (A), but with Ra = 60 per meg instead of 12 per meg. The significance of the value of 60 per meg is that it is in the upper ~1/3 of the range of values reported for the European Alps by Surma et al. (2021, this volume). Data are from Passey and Ji (2019).

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the wide range of values observed in experimental studies (see Fig. 6), and the closed-basin results from Passey and Ji (2019) suggest that variation for natural lakes may be greater than commonly assumed. Moving forward, there is a need better characterization of Ra and 18/16adiff parameter across the range of continental evaporation scenarios. Exploiting parameter-insensitive trajectories. Surma et al. (2018) explored evaporation trajectories in triple oxygen isotope space using a combination of modeling and observational results from the Atacama Desert, Chile. They suggest that in many cases, the shape of the evaporation trajectory for flow-through lakes in ∆′17O versus d18O is insensitive to parameters such as hn, adiff, and temperature (their Figs. 4a–e), whereas the extent to which samples evolve along the trajectory is highly sensitive to XE and hn. However, variation in Ra can cause these trajectories to differ significantly (their Figs. 4f–h), and in cases of transient evaporation, the shape of the trajectory is strongly dependent on hn (Fig. 5B of this chapter). Alternatively, Passey and Ji (2019) used a Monte-Carlo approach to show that the evaporation slope llake between unevaporated inflow waters and evaporated lake waters is relatively conservative despite the large number of variables in Equation (17). Thus, this slope is predictable and can be used to ‘back-project’ the composition of the evaporated lake water to the intersection with an assumed unevaporated triple oxygen isotope MWL. In other words, while the reconstructed triple oxygen isotope composition cannot be used to uniquely reconstruct individual parameters such as XE and hn, the data can be used to estimate the d18O value of unevaporated precipitation, which is an important goal in the isotopic reconstruction of past climates. The uncertainty is not insubstantial (generally a few per mil), but given that closed basin lakes can be elevated in d18O by 10–15‰ relative to unevaporated catchment precipitation, this level of error may be acceptable in many applications.

ANIMAL AND PLANT WATERS Carbon and oxygen isotope analysis of vertebrate bioapatites is a cornerstone of reconstructing continental climate and paleoecology (Koch 1998; Kohn and Cerling 2002), but the unequivocal interpretation of oxygen isotope data has been hampered by the numerous competing factors that influence animal body water d18O, and hence animal bioapatite d18O (e.g., Luz and Kolodny 1985; Ayliffe and Chivas 1990; Bryant and Froelich 1995; Kohn 1996; Levin et al. 2006; Blumenthal 2017). Evaporation is a key part of the water balance of many animals, in terms of the intake of evaporated waters (e.g., leaf waters, evaporated surface waters), and in terms of evaporation of water from the animal. Furthermore, in many animals, a substantial fraction of the O in body water comes from atmospheric O2 via basic metabolic respiration (i.e., CH2O + O2 → CO2 + H2O). Atmospheric O2 has a highly distinctive ∆′17O value of –434 ± 22 per meg (this is the average and standard deviation from studies analyzing tropospheric O2 directly against the VSMOW2-SLAP scale: Barkan and Luz 2005, Pack et al. 2017; Wostbrock et al. 2020; cf., Pack 2021, this volume). Therefore, triple oxygen isotopes are uniquely suited for application to terrestrial vertebrates. Andreas Pack’s group at Georg August University of Göttingen have pioneered this emerging field (Gehler et al. 2011), focusing in particular on the prospect of reconstructing past carbon dioxide levels (Pack et al. 2013; Gehler et al. 2016), following on the sensitivity of the ∆′17O of atmospheric O2 to pCO2 (Luz et al. 1999; Bao et al. 2008; Cao and Bao 2013; Young et al. 2014; Brinjikji and Lyons 2021, this volume; Pack 2021, this volume). O2-derived oxygen in body water is diluted by other sources of oxygen to animals, and the isotopic composition of body water is further modified by isotopic fractionations associated with both inputs and outputs of oxygen-bearing species. Therefore, accurate isotope mass balance body water models are necessary for meaningful interpretation of triple oxygen isotope data in terms of reconstructing the ∆′17O of atmospheric O2, and also of reconstructing

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the paleoclimatic and paleoecological significance of data. Pack et al. (2013) developed a triple oxygen isotope model based on the d18O model of Bryant and Froelich (1995), where the input and output fluxes are scaled to body mass. In the model, the relative proportion of O2-derived oxygen decreases as body mass increases, which follows the observation that smaller animals are often more independent of water (i.e., require less drinking water) than larger animals. Whiteman et al. (2019) developed a model that similarly ties the relative proportion of O2-derived oxygen to metabolic rate and hence body mass. Figure 8 shows the currently available triple oxygen isotope data for modern vertebrates, plotted as a function of body mass (Pack et al. 2013; Passey et al. 2014; Whiteman et al. 2019). The data support a general trend with body mass, with smaller animals having lower ∆′17O values, which is consistent with a higher fraction of O2-derived oxygen, given that the ∆′17O of O2 is ~ –0.43‰. However, Figure 8 also shows that there is a large degree of variation in ∆′17O that is independent of body mass, and that the degree of variation at a fixed body mass can rival or exceed the difference in ∆′17O between the low and high ends of the regression lines. This is not surprising, given that previous studies have shown that d18O may vary greatly according to factors unrelated to body mass, such as relative humidity (Ayliffe and Chivas 1990; Luz et al. 1990) and leaf-water intake (Levin et al. 2006; Blumenthal et al. 2017). Here we explore such “mass independent” influences on the triple oxygen isotope compositions of animals. We make use of a triple oxygen isotope version (Hu 2016) of the d18O model developed by Kohn (1996), which allows for detailed adjustments in fluxes such as plant leaf water (fractionated by evaporation), stem/root water (unfractionated relative to soil water), the carbohydrate / protein / fat composition of diet (as each has a different stoichiometric demand for O2 during respiration), and the relative effluxes of urinary, fecal, and sweat water (unfractionated relative to body water) and breath / panting vapor / transcutaneous vapor (fractionated relative to body water). The Kohn model, converted to the form of isotope ratios and fractionation factors, is given by: 50 0

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Figure 8. Mammal and bird body water ∆′ O values and water economy index (WEI) as a function of body mass. A. Body water ∆′17O versus body mass. Squares are data from Pack et al. (2013), circles from Passey et al. (2014), and diamonds from Whiteman et al. (2019). The apatite phosphate data from Pack et al. (2013) were converted to the λ = 0.528 reference frame, and equivalent body water compositions were calculated using 18/16aap-bw = 1.0173 and qap-bw = 0.523 (Pack et al. 2013). The apatite carbonate acid-digestion CO2 data from Passey et al. (2014) were converted to body water using 18/16aap,carb-bw = 1.0332 and qap,carb-bw = 0.5245. The eggshell carbonate data from Passey et al. (2014) were converted to body water using 18/16acarb-bw = 1.0380 and qcarb-bw = 0.5245 (see Passey et al. 2014; Table 3 footnotes for details). The Whiteman et al. (2019) data were reported as body water, so no conversion was necessary. B. WEI versus body mass for birds, eutherian mammals, marsupial mammals, and reptiles. Data are from Nagy and Petersen 1988. 17

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where fi and fo are the fractional inputs and outputs of oxygen from each source, ai-mw are the fractionations of the oxygen inputs relative to meteoric water (Rmw), ao–bw are the fractionations of oxygen outputs relative to body water (Rbw), fO2 and RO2 are the fractional contribution and isotopic composition of atmospheric oxygen, and ain–O2 is the fractionation of oxygen during uptake in the lungs. Figure 9 shows the different fluxes considered in the Kohn model, and the associated isotopic fractionations. A central aspect of the Kohn model is the use of taxon-specific water economy index values (WEI): this is the water use efficiency of the animal, measured in terms of volume of liquid water per unit metabolic energy (e.g., ml/kJ). In essence, WEI is the water usage “per unit of living” (Nagy and Petersen 1998), and relates to adaptations for water conservation such as the urea-concentrating abilities of the kidneys, the ability of animals to tolerate changes in body temperature (and thus reduce the need for evaporative cooling, an adaptation termed ‘adaptive heterothermy’), and the ability to avoid heat (e.g., burrowing).

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Figure 9. Triple oxygen isotope body water model (Eqn. 18) based on the Kohn (1996) model. A. Graphical depiction of the isotopic inputs and outputs considered in the model. For uniformity, all fluxes have an assigned fractionation factor (α), but those marked with an asterisk are unity (i.e., α = 1, no isotopic fractionation). 18/16α values are as reported by Kohn (1996), except for leaf water, for which we use a modified version of the Flanagan et al. (1991) model (Roden et al. 2000). θ values are as follows: leaf water: θ = −0.008h + 0.522 (Landais et al. 2006, where h is relative humidity); atmospheric O2: θ = 0.5179 (Pack et al. 2013; Luz and Barkan 2005); atmospheric water vapor: θ = 0.529 (Barkan and Luz 2005); food bound O: 0.5275 (best guess by Pack et al. 2013; no data are available); carbon dioxide: θ = 0.5248 (Cao and Liu 2011, a theoretical prediction in close agreement with our unpublished experimental value of 0.5243); transcutaneous water: θ = 0.5235 (no data available; this value is intermediate between molecular diffusion of water vapor in air (0.5185) and equilibrium liquid–vapor exchange (0.529); nasal water vapor and breath water vapor: θ = 0.529 (Barkan and Luz 2005). B. Evaluation of the model for max water, max evap, and max ox physiologies (see text), modeled with ∆′17O(O2) = −410 per meg (the value for modern atmosphere measured by Pack et al. 2017). C. As (B), but modeled with ∆′17O(O2) = −1000 per meg, which corresponds to pCO2 = 940 ppm in the Cao and Bao (2013) model under present-day global gross primary productivity (GPP) and pO2.

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Compilations of WEI for different animals show only weak correlation with body mass (Fig. 8B). Contrary to common expectations, animals with high metabolic rates (and hence high absolute rates of O2 intake) do not consistently have higher relative intakes of O2 compared to other sources of oxygen (e.g., drinking water, plant water). For isotopic mass balance, it is the relative sizes of different fluxes (i.e., fractional contributions) that are important. The WEI value becomes important in the Kohn model because it determines the amount of liquid drinking water that the animal must consume. The total energy requirement of the animal is determined based on body mass using allometric scaling equations, and this value along with WEI determines the water requirement of the animal. If other sources of water to the animal (plant water, metabolic water) are less than this requirement, then the drinking water influx is used to make up the difference. If other sources of water are in excess of the animal’s water requirement, then no drinking water is consumed, and the excess water exits the animal via nonfractionating mechanisms (e.g., urinary and fecal water). Figure 9 shows predictions of the Kohn model for three endmember animal physiologies. In the ‘maximum water’ (max water) scenario, the animal is highly dependent on drinking water (WEI = 0.6 ml/kJ), consumes very little leaf water (which is strongly modified by evaporation; see Fig. 12), has relatively low digestibility and high fecal water content (more fecal water means more water loss per unit of energy metabolized) and has non-fractionating water effluxes (e.g., sweat versus panting). The hippopotamus is an example of a ‘max water’ physiology. In the ‘maximum evaporation’ (max evap) scenario, the animal obtains most of its water in the form of leaf water, which is strongly modified by evaporation). The animal is extremely water-efficient (WEI = 0.05 ml/kJ) and hence drinks little or no water, has high digestibility and low fecal water content, and loses water via fractionating mechanisms (panting versus sweating). Selective browsers such as giraffe, deer, and ostrich are examples of ‘max evap’ physiologies. Finally, in the ‘max oxygen’ (max ox) scenario, the degree of O2-sourced oxygen is maximized by imparting the animal with low WEI (0.05 ml/kJ), a diet high in fats and low in free watercontent (which increases the fraction of metabolic water and hence usage of O2), high digestibility, and low fecal water content. Kangaroo rats and other highly-waterindependent desert animals are examples of max ox physiologies. Figure 10 shows the published data in the context of these model predictions. There is general agreement between models and data. For example, highly water-dependent species such as river otters, elephants, hippos, and humans tend to have high ∆′17O values. Of special interest are domestic birds (Fig. 10B), including ostrich, which is normally a water-independent species. The domestic birds all have high ∆′17O, consistent with a dry pellet diet that necessitates substantial drinking, which ties the triple isotope composition of these animals close to the composition of meteoric waters. Animals known to be selective leaf consumers (browsers) generally have low ∆′17O, reflective of the signature of leaf water; this includes giraffe, deer, and ostrich. Finally, most of the rodents plot in the direction of the max ox and max evap models. The most conspicuous inconsistency between the model predictions and observations is for the desert rodents in the dataset of Whiteman et al. (2019): many of these data are 50 to 100 per meg lower in ∆′17O than predicted by the model! It is unclear at this point why the data / model discrepancy exists. In terms of the modeling, a major uncertainty is the fractionation between atmospheric oxygen and the oxygen that is absorbed by the lungs. It is known that the lungs discriminate against 18O by several per mil (Epstein and Zeiri 1988), with values for free-ranging animals poorly known (Kohn 1996). No measurements of θ values for this process have been made, and if the true value is substantially higher than the estimate by Pack et al. (2013) used here (θ = 0.5179; Luz and Barkan 2005), then modeled body water values would be lower in ∆′17O. Furthermore, there may be aspects of the burrow enviroment of these desert rodents that influence isotopic compositions (i.e., the composition of soil water vapor,

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Figure 10. Measured triple oxygen isotope compositions of animals. All datasets are presented in the context of the max water, max evap, and max ox models shown in Figure 9B. A. Dataset of Pack et al. (2013). B. Dataset of Passey et al. 2014, with the addition of three new data points: a modern giraffe from Tsavo National Park, Kenya (d18O = 13.5‰, ∆′17O = −122 per meg), a modern deer from Parowan, Utah, USA (d18O = 1.9‰, ∆′17O = −142 per meg), and a modern bison from Antelope Island, Utah, USA (d18O = −1.6‰, ∆′17O = −64 per meg). C. Dataset of Whiteman et al. (2019). See Figure 8 caption for explanation of how the bioapatite phosphate data of Pack et al. (2013) and the bioapatite carbonate and eggshell carbonate data of Passey et al. (2014) were converted into equivalent body water values.

and even O2, which may be isotopically fractionated by respiration in soils), and the soil water available to plants (and hence food) may be modified by evaporation. These discrepancies highlight the need for ongoing research both in terms of collecting data from modern animals and environments, determining key fractionation exponents, and refining models. Stepping back, the results presented in Figure 10 are very encouraging for application of triple oxygen isotopes to animals: The observed ranges in ∆′17O are the largest out of any system discussed in this chapter, and there is clear ecological patterning that makes sense

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in the context of the current state of modeling. As yet published datasets developed by our group for modern mammals (Lehmann 2016) and dinosaurs (Hu 2016) point to clear signals of aridity and changes in ∆′17O of past atmospheric O2, respectively. A such, studies of triple oxygen isotopes in animals promise to reveal information not only about past climates, but also about paleoecology and past global biogeochemical cycles.

Prospects for reconstructing ∆′17O of past atmospheric O2 The wide variation in ∆′17O of extant animals—and therefore certainly for extinct animals as well—may appear to portend badly for the prospects of precisely reconstructing ∆′17O of past atmospheric O2 based on analyses of fossil teeth, bones, and eggshell. However, this variability can potentially be embraced and used to good effect towards reconstructing both ∆′17O(O2) and aspects of paleoecology and paleoclimate. As Figure 9B predicts, animal communities living in times of high pCO2 and hence anomalously-low ∆′17O(O2) (here, −1000 per meg) will be shifted downwards in ∆′17O and will have a greater range in ∆′17O. Therefore, in an approach where data are generated for specimens from multiple taxa, the utility of the ∆′17O(O2) signal lies not in the absolute value of any particular specimen, but in the ∆′17O values of the upper and lower limits of the population (i.e., position and range in ∆′17O space). Figure 11 shows the max water, max evap, and max ox models calculated as a function of ∆′17O(O2), evaluated for a relative humidity of 0.2 (i.e., an extreme low limit). Figure 11 also shows the highest 10 and lowest 10 ∆′17O values observed for modern animals, plotted as horizontal bars, corresponding on the vertical axis to the observed ∆′17O value of each sample, and on the x-axis to range in ∆′17O(O2) that is permissible for the sample. Note that this approach requires no information about the water balance physiology of specific animals. For the community as a whole, there should be a limited, concordant range in ∆′17O(O2) values that can explain all of the data. We term this the environmental physiology isotope concordance (EPIC) approach (Hu 2016): If the body water endmember models are appropriate for extinct organisms, and if all animals analyzed in an assemblage existed under a uniform value of ∆′17O(O2), and if diagenesis is not a factor, then there should be a concordant range in ∆′17O(O2) values that can explain all of the data. Clearly, reliable implementation of this EPIC approach will be a challenging task. It will require highly-vetted body water models that reliably bracket the range of common water balance physiologies for terrestrial animals. The data in Figure 8B suggests that this may be tractable: water economy relative to metabolic demand for O2 falls within fairly narrow limits, for the vast majority of organisms, with no systematic differences among reptiles, birds, marsupial mammals, and eutherian mammals. Given that the present-day manifestation of the extant range of water balance physiologies is the product of more than 400 million years of evolution of separate lineages animals on the continents, it is probably safe to assume that ranges were not hugely dissimilar during e.g., the reign of the dinosaurs in the Mesozoic, or during radiation of mammals in the Cenozoic. The EPIC approach will require the analysis of a wide range of species that existed more or less at the same time (from contemporaneous fossil assemblages), which is challenging both in terms of finding suitable assemblages, and in the laboratory challenge of analyzing often very small fossils that make up the majority of the diversity (e.g., rodents, early mammals, dinosaur teeth with extremely thin tooth enamel). Diagenesis will need to be addressed through both microanalytical methods and stable isotope approaches. All of these challenges are considerable, but the scientific products—records of pCO2, paleoecology of extinct species, and paleoclimate—are also considerable, and will make the effort worthwhile.

Plant waters Actively transpiring leaves are evaporatively-enriched in 18O (Gonfiantini et al. 1965), whereas there is no measurable fractionation during soil water uptake by the roots, nor during transport in the xylem (White 1989; Ehleringer and Dawson 1992). Although more recent

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Figure 11. Illustration of the environmental physiology isotopic concordance (EPIC) approach for determining the ∆′17O of atmospheric O2 (∆′17O(O2)) based on triple oxygen isotope analysis of vertebrate biogenic carbonates. Bold dashed lines show the max water, max evap, and max ox body water models evaluated as a function of ∆′17O(O2). Thin horizontal lines mark the ∆′17O values (y-axis) of the highest 10 and lowest 10 observed values in the combined datasets of Pack et al. (2013), Passey et al. (2014), and Whiteman et al. (2019). The horizontal extent of each line is bounded by the intersections with the body water model lines. In other words, the extent of each horizontal line shows the range of ∆′17O(O2) values that could give rise to the measured body water ∆′17O value. Omitted for clarity are horizontal lines for the 76 additional samples that fall between the highest 10 and lowest 10. The gray field shows the range of ∆′17O(O2) values that are concordant with all of the observed 96 data points, excluding the highest five and lowest five values as a measure of outlier removal. The resulting field overlaps the present-day ∆′17O(O2) of −430 per meg, and is consistent with the pre-industrial CO2 level of 280 ppm. Note that because the residence time of atmospheric O2 is of order 103 years, the ∆′17O(O2) value has not changed substantially during the past 150 years, and therefore reflects an atmosphere with ~280 ppm CO2. The relationship between pCO2 (top axis) and ∆′17O(O2) is from the model of Cao and Bao (2013).

and detailed models exist (see the review by Cernusak et al. 2016), the leaf water evaporation model presented by Flanagan et al. (1991) is a straightforward steady-state model based on the Craig–Gordon evaporation model, and a good entry point for understanding isotopic enrichment in leaves:

  e e   e e   e  (19) Rleaf   eq   k Rs  i s    kb Rs  s a   Ra  a    ei   ei   ei    where Rleaf, Rs, and Ra are the isotope ratios of leaf water, soil water, and atmospheric water vapor, respectively, ak is the fraction factor for molecular diffusion of water vapor in air, akb is the effective fractionation factor for water vapor transport through the boundary layer adjacent to the

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leaf surface (analogous to adiff), and ei, es, and ea are the water vapor pressures in the intercellular air spaces inside the leaf, at surface of the leaf, and in the free atmosphere, respectively. For adaptation to 17O, the following θ values are used: qk = qkb = 0.5185, qeq = 0.529.

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B

Δʹ17O (per meg, SMOW-SLAP, λ = 0.528)

Figure 12 shows the predictions of this model for a range of relative humidities, along with measured values for leaves, stems/roots, and soil water presented by Landais et al. (2006; for plants from Israel and some locations in Europe) and Li et al. (2017; for plants from Kenya). We omit growth-chamber data from Alexandre et al. (2018), which show similar trends. Why do leaf waters have such low ∆′17O values compared to e.g., evaporating pans of water and closed-basin lakes? The answer lies in the stagnant environment of the intercellular air spaces inside of the leaf, which allows for full expression of the isotope fractionation associated with molecular diffusion of water vapor down the concentration gradient from 100% rh inside of the leaf to 700 °C) and very long reaction times (~4 days) for quantitative conversion to O2. Wostbrock et al. (2020) have recently revived this method and adapted it for high-precision triple oxygen isotope analysis. A key aspect of their method, and indeed one that is common amongst most of the successful methods achieving high precision in ∆′17O, is the careful post-fluorination clean-up of O2 using a molecular sieve GC column (e.g., Pack and Herwartz 2014). Following fluorination of CaCO3 or CO2 for 96 hours at 750 °C, Wostbrock et al. (2020) pass the O2 gas over two lN2-temperature traps, through a 100 °C NaCl trap to remove traces of F2, through an additional lN2 temperature trap, and then absorb the gas onto a 5Å molecular sieve. The O2 is then released into a helium stream that carries it through a 6’ long, 1/8” diameter molecular sieve gas chromatography column held at room temperature. The O2 is then recollected on molecular sieve, and finally introduced into the mass spectrometer. All of this clean-up is to ensure that the O2 gas is free of isobars, including NF3, which can be fragmented into the m/z 33 NF+ ion in the ion source of the mass spectrometer.

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Although the method of Wostbrock et al. (2020) is the ‘newest kid on the block’ with respect to the modern era of triple oxygen isotope analysis of carbonates, we are of the opinion that their method is currently the best available for accurate and relatively assumption-free determination of ∆′17O values of carbonates. This is because the method features verifiable 100% conversion of CaCO3 oxygen to O2 oxygen, and hence there can be no isotope fractionation, barring exchange with O inside of the extraction apparatus, the possibility of which can be monitored using d18O values, and mitigated by running several replicates in series. As described below, other methods involve measurable blank and fractionation effects, and oftentimes require bespoke calculations to arrive at the final ∆′17O value of the carbonate. No such steps are required for the fluorination analysis aside from standardization within the SMOW-SLAP reference frame: the ∆′17O of the O2 gas measured by the mass spectrometer is the ∆′17O of the CaCO3 (or CO2), with no calculations or corrections required. Additionally, water (including VSMOW and SLAP) are analyzed on the same extraction line using nearly identical procedures, and furthermore the silicate oxygen isotope scale is calibrated using the same methods. For these reasons, we suggest that direct fluorination, when conducted properly, be considered as the ‘gold standard’ method that is used to standardize the ∆′17O values of carbonate minerals in the VSMOW-SLAP reference frame. These standardized ∆′17O values can then be used to normalize data from other methods into a common reference frame. Direct laser fluorination is used by Gehler et al. (2011, 2016) and Pack et al. (2013) to analyze the phosphate component of bioapatite (primarily tooth enamel). The methods are similar to those developed for laser fluorination of silicates, except that the bioapatite sample is first fused under argon at 1000 °C to drive off organic matter and oxygen from the carbonate and hydroxide components of bioapatite. Acid digestion–reduction–fluorination. Passey et al. (2014) developed a method similar to that conceived by Brenninkmeijer and Röckmann (1998), whereby carbon dioxide generated by phosphoric acid digestion of carbonate or bioapatite is reduced in the presence of excess molecular hydrogen and Fe catalyst to produce H2O, with the carbon exiting as methane. The water is then fluorinated over CoF3 to produce O2, largely following the methods of Barkan and Luz (2005). The sluggish reaction kinetics of the reduction reaction (CO2 + 4H2 → CH4 + 2H2O) are addressed by using a closed circulating loop reactor design, which ensures that unreacted CO2 can pass through the reactor multiple times for complete conversion to CH4 + H2O. The reaction takes place at 560 °C inside of a glassy carbon tube, which is essential to minimize exchange with O that might occur inside of a fused silica reactor, and to avoid unwanted catalytic activity and exchange with oxides that might occur inside of an iron- or nickel- based reactor tube. Observations using a Thermo ISQ7000 quadrupole mass spectrometer in our laboratory at Michigan have verified that CO is an intermediate product of the reaction. During several passes through the reactor, the CO is converted to CH4 + H2O. It also appears likely that C is deposited onto the Fe catalyst, and subsequently reduced to CH4 by reaction with the excess H2. At any rate, the product of interest in the reaction is H2O, which is trapped from the circulating loop at −78 °C (dry ice temperature), and is then purged through a CoF3 reactor via a helium stream, according to the basic procedures of Barkan and Luz (2005). The produced O2 is cleaned-up by passage through a multi-loop open nickel tube immersed in liquid nitrogen (to remove HF produced in the fluorination reaction), and then through a ~1.2 m, 1/8” o.d. 5Å molecular sieve GC held at −78 °C. The O2 leaving the GC is trapped onto a 5Å molecular sieve held at liquid-N2 temperature, then expanded at 90 °C for 10 minutes, and finally admitted into the mass spectrometer. The precision for this analysis is ~10 per meg. The method achieves nominally 100% yield, but has clear exchange and fractionation effects, which are revealed by comparing known d18O values of the carbonates (measured as CO2) to the d18O of O2 generated by the method (Passey et al. 2014). Slopes of this regression over a range of ~30‰ in d18O are typically ~0.95, meaning that the exchange effect is about 5%. Fractionation effects result in mediocre precision in d17O

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and d18O values (~0.2‰ and 0.4‰ 1σ, respectively), but these errors are correlated and massdependent with a slope near 0.528, which means that ∆′17O values are virtually unaffected. In our new system at Michigan, we have observed drift in ∆′17O values within some of our analytical sessions. This drift can have a magnitude of ~10–30 per meg, and is systematic across the ~ 4–5 different carbonate reference materials (NBS−18, NBS−19 / IAEA 603, and some in-house standards) that we regularly analyze throughout our sessions. Therefore, the drift is correctable by normalizing to long-term mean values for our standards (or, ideally in the future, to community consensus ∆′17O values for standards such as NBS−18 and IAEA 603), in the manner that is common for e.g., continuous flow methods. Because of the blank, fractionation, and drift effects, the method is less appropriate than direct fluorination for defining absolute ∆′17Ο values. Merits of the method are that it is relatively safe, that the entire procedure takes only ~2.5 hours per sample (i.e., from dropping the sample in phosphoric acid to admitting the final O2 product in the mass spectrometer), and, compared to exchange methods, that it requires only one kind of mass spectrometric determination (i.e., analysis of sample O2).

Exchange methods Several methods have been developed based on isotopic exchange between CO2 and another phase that is more amenable to analysis. These include analyzing CO2 before and after exchange with excess CeO2 or CuO with known oxygen isotopic composition, which permits backcalculation of the ∆′17O of the CO2 (Assonov and Brenninkmeijer 2001; Kawagucci et al. 2005; Mahata et al. 2012; Mrozek et al. 2015), exchange of an excess of CO2 with CeO2, which is then fluorinated to produce O2 (Hoffman and Pack 2010), exchange of subequal amounts of CO2 and H2O, fluorination of the H2O to produce O2, and back-calculation of the CO2 composition (Barkan and Luz 2012), and Pt-catalyzed exchange between subequal amounts CO2 and O2, analysis of the O2, and back-calculation of the CO2 composition (Mahata et al. 2013, 2016). Of these methods, only the latter has become widely-adopted for high-precision analysis (e.g., Barkan et al. 2015, 2019; Liang et al. 2017; Prasanna et al. 2016; Sha et al. 2020; Fosu et al. 2020; Bergel et al. 2020; Voarintsoa et al. 2020), so we will focus our discussion on this method. Pt-catalyzed CO2–O2 exchange. In this method, subequal quantities of CO2 and O2 are exchanged over a hot platinum wire or sponge (~750 °C) for ~ 1 h. The isotopic compositions of both gases are analyzed before the exchange. Following the exchange, the CO2 and O2 are separated, collected, and reanalyzed separately (either using two mass spectrometers, or by analyzing them in series after switching the configuration of a single mass spectrometer). The d17O value of the CO2 can then be calculated according to (Barkan and Luz 2015): 17O in  CO2  

1  17  Of  O2   1 1  17  Pt    17O in  O2   1  11 





 



(20)

where 

 18 O in  O2    18 Of  O2   18 Of  CO2    18 O in  CO2 

(21)

and where d18Of(CO2) can be calculated as:





18Of  CO2   18  Pt 18Of  O2   1

(22)

In Equations (20–22), the subscript ‘in’ refers to the initial (pre-equilibration) isotopic composition, the subscript ‘f’ refers to the final (post-equilibration) composition, and 17/16aPt and 18/16aPt are the isotopic fractionations between CO2 and O2 when the exchange reaction has reached steady-state.

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Of key importance for this method are knowledge of 17/16aPt and 18/16aPt values, and awareness of potential variation in these values. The 18/16aPt and qPt values [where qPt = ln(17/16aPt)/ln(18/16aPt)] values can only be determined using pairs of CO2 and O2 with known D17O. This presents a challenge, because the ∆′17O of CO2 cannot be measured directly, which is the reason for the development of these methods in the first place. In most laboratories, this problem has been addressed by reacting O2 with known ∆′17Ο over hot graphite wound with Pt wire to produce CO2 (Barkan and Luz 1996). Here it is assumed that if there is no exchangeable oxygen in the system, and if 100% of the O2 is converted to CO2, then the ∆′17O value of the product CO2 must be the same as that of the O2. This assumption can be evaluated by measuring the d18O of the CO2 and comparing this to the d18O of the O2 (they should be identical), but it cannot be strictly evaluated in the case of d17O. Based on results from different laboratories, there is no single set of 18/16aPt and qPt values that characterize the exchange reaction. 18/16aPt values are typically 0.998–1.002 (i.e., ± ~2 per mil or smaller d18O difference between exchanged CO2 and O2), and qPt values are typically ~0.55–0.62. These θ values are well beyond the theoretical high-temperature limit for mass dependent fractionation (0.5305; Young et al. 2002), implying kinetic fraction during the exchange reaction. 18/16aPt and qPt values apparently depend on the precise physical configuration of the exchange reactor, and must be determined for each system (Fosu et al. 2020). These findings underscore the need for (1) agreed upon ∆′17O values for widely-available carbonate standards that can be used to develop 18/16aPt and qPt values for each system, thus obviating the need for each laboratory to develop its own CO2 gas of ‘known’ ∆′17O based on combustion of O2, given potential errors in this approach, and (2) the routine analysis of (ideally) carbonate standards with known ∆′17O to monitor for systematic changes in in analytical results. Of course, (2) applies for any analytical method, whereas (1) is uniquely necessary to exchange methods that depend on accurate knowledge of exchange fractionation factors. We suggest that the ∆′17O values for NBS−19, NBS−18, and IAEA 603 reported by Wostbrock et al. (2020) be provisionally used for these purposes, as these values were determined by the direct fluorination method and normalized to analyses of VSMOW2-SLAP made using the same analytical procedures and equipment. These calibration issues notwithstanding, it appears that several different laboratories are able to produce internally consistent data with high precision, and are able to resolve clear environmental signals when analyzing natural materials (e.g., Liang et al. 2017; Sha et al. 2020; Bergel et al. 2020; Voarintsoa et al. 2020; Fosu et al. 2020).

Other methods Adnew et al. (2019) explored the measurement of O+ ion fragments produced from electron bombardment of CO2 in the ion source of the Thermo 253 Ultra mass spectrometer. The benefit of such a method is the ability to measure CO2 directly, sidestepping the need for lengthy chemical conversion or exchange procedures. Of particular challenge with this method is the relatively inefficient production of these ions, and the interferences of 16OH+ and 16OH2+ on the 17 + O and 18O+ signals, respectively. The high mass resolving power of the 253 Ultra, however, permits clear resolution of these ions on the low-mass shoulders of the larger 16OH+ and 16OH2+ peaks. Precisions for ∆′17O of 14 ppm (SEM) can be achieved with counting times of 20 hours. Tunable Infrared Laser Direct Absorption Spectroscopy (TILDAS) shows great promise for high precision analysis of ∆′17O in CO2 (Sakai et al. 2017; Prokhorov et al. 2019). In the region of wavenumber 2310 cm−1, the four most abundant isotopologues of CO2 are clearly resolved, with only minor overlap between 12C17O16O at 2309.98 cm−1, and 12C16O2 at 2310.00 cm−1. Sakai et al. (2017) report standard errors of less than 0.04‰ and 0.03‰ for 18O/16O and 17 O/16O, respectively, on CO2 released from sub-100 mg CaCO3 samples (i.e., about 50× less material than is required for most of the methods described above). Both Sakai et al. (2017) and Prokhorov et al. (2019) show tight correlations between d17O and d18O measured for

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suites of samples spanning a large range in isotopic composition. These papers stop short of presenting ∆′17O values. However, Wang et al. 2020, achieved precisions of 10 per meg on the 13 18 16 C O O ‘clumped’ isotopologue using a similar instrument from the same manufacturer as the TILDAS used in Sakai et al. (2017; Aerodyne Research, Inc.). Given that this isotopologue is 16 times less abundant than 12C17O16O, it seems likely that TILDAS will eventually achieve the 10 per meg precision benchmark for ∆′17O.

Interlaboratory reproducibility Several labs have reported ∆′17O values for the carbonate reference materials NBS18, NBS19, and IAEA 603 (Table 1). Most groups report values for CO2 released from acid digestion of these materials at 25 °C, while the Johns Hopkins / Michigan labs report values for 90 °C acid digestion, and Wostbrock et al. (2020) report values for the both the carbonate mineral and for the CO2 liberated by 25 °C acid digestion. For calculation of the equivalent CaCO3 composition from CO2 values, we use the qacid value of 0.5230 determined by Wostbrock et al. (2020). This value was determined for 25 °C acid digestion. Guo et al. (2009) predict very little temperature dependence in qacid (0.00003) between 25 °C and 90 °C, so we provisionally use Wostbrock’s value for 90 °C acid digestion data given a lack of qacid values at this temperature. In Table 1, we present new data from the Michigan lab for all of the carbonate standards that have been analyzed since the measurement was established in May 2008, uncorrected for the intra-session drift noted above. Note that the Michigan lab is effectively a ‘different’ lab compared to the Johns Hopkins lab (Passey et al. 2014, Passey and Ji 2019), given that the extraction line and mass spectrometer are different. Table 1 shows that there is very close agreement in ∆′17O(CaCO3) values amongst the labs using conversion methods, with standard deviations of 5 per meg or less for the populations of ∆′17O values for each material. Part of this agreement could be fortuitous given our lack of knowledge of qacid at 90 °C. Alternatively, it is possible that qacid has very little temperature sensitivity, as predicted by Guo et al. (2009), in which case the interlaboratory agreement is real. Another measure of methodological agreement is the magnitude of ∆′17O difference between different materials. The final column in Table 1 shows the difference in ∆′17O between NBS18 and NBS19. The magnitude of this difference (~50 per meg) is essentially the same across the three labs from which conversion data are reported, with the value from Passey et al. (2014; 37 per meg) showing the most departure from the mean. This agreement lends confidence to these methods. The results from the exchange methods are more variable. Barkan et al. (2019) attributed part of the difference in their values compared to those reported in Barkan et al. (2015) to the possibility of inhomogeneity between different bottles of reference material. The Sha et al. (2020) values appear to be systematically shifted downward, but the difference between NBS18 and IAEA 603 (which is identical within error to NBS19) is 42 per meg, which is similar to the values derived by conversion methods and the value reported by Fosu et al. (2020). The values of Fosu et al. (2020) are within 20 per meg of the values reported by Wostbrock et al. (2020). Note that Fosu et al. (2020) also used NBS18-CO2 and NBS19-CO2 to derive 18/16aPt and qPt values, although the ∆′17O values they report for NBS18 and NBS19 are independent of those determinations. Fosu et al. (2020) to-date have presented the most thorough exploration of variation in 18/16aPt and qPt in a single extraction line. Overall, the results in Table 1 are both encouraging and concerning. It is not clear precisely why the considerable lack of agreement exists for the Pt-exchange method, but the variability in 18/16aPt and qPt values observed across different laboratories, the exotic absolute values of qPt, and the fact that 18/16aPt values deviate from the value expected for CO2–O2 equilibrium at 700−800 °C by several per mil (Fosu et al. 2020), collectively suggest that there are important processes at play that are not fully understood, and that uncharacterized variability in these parameters may be a factor. Additionally, these values are generally determined using CO2 prepared by Pt-catalyzed combustion of graphite with O2 of known ∆′17O. If unusual isotope

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Table 1. Interlaboratory reproducibility for D′17O of carbonate reference materials. Source

NBS19

NBS18

IAEA 603

DD′17O

D′17O

D′17O

D′17O

D′17O

D′17O

D′17O

CO2

CaCO3

CO2

CaCO3

CO2

CaCO3

NBS18 – NBS19

Conversion Methods a

Passey et al. (2014)

−135

−95

−98

−58

−

−

37

Passey and Ji (2019)a

−143

−103

−88

−48

−

−

55

Wostbrock et al. (2020)b

−155

−102

−100

−48

−147

−100

54

−142

−102

−91

−51

−148

−108

51

Avg.

−100

Avg.

−51

Avg.

−104

49

Std.

4

Std.

5

Std.

5

8

Michigan IsoPaleoLab

a

Exchange Methods Barkan et al. (2015)c

−227

−176

3

54

c

Barkan et al. (2019)

−

−

230

−182

−131

−163

−112

−187

−136

19

Sha et al. (2020) c

−

−

−225

−174

−267

−216

42d

Fosu et al. (2020)c

−169

−118

−119

−67

−

−

50

Avg.

−141

Avg.

−75

Avg.

−176

100

Std.

30

Std.

96

Std.

57

114

Notes: D′17O values are reported in per meg relative to the VSMOW-SLAP scale, l = 0.528. CaCO3 values are calculated based on CO2 values using qacid = 0.5230 (Wostbrock et al. 2020), 18aacid = 1.0103 (25 °C reactions) and 18aacid = 1.00812 (90 °C reactions; Kim et al. 2007), except for the CaCO3 values for Wostbrock et al. (2020), which are directly measured. a . Reduction of CO2 produced by 90 °C acid digestion, and CoF3 fluorination of the resulting water. b . Direct BrF5 fluorination carbonate, and of CO2 produced by 25 °C acid digestion. c . Pt-catalyzed exchange with O2 of CO2 produced by 25 °C acid digestion. d . D′17O difference between NBS18 and IAEA 603.

effects characterize this reaction in the same way they have been demonstrated to characterize the Pt-catalyzed CO2–O2 exchange reaction, then the ∆′17O values of the produced CO2 may deviate from those of the combustion O2. For all of these reasons, a logical first step would be to use NBS18-CO2, NBS19-CO2, and IAEA 603-CO2 (or other materials calibrated by direct fluorination methods) to develop or validate 18/16aPt and qPt values (e.g., Fosu et al. 2020).

Fractionation exponents for carbonate–water equilibrium, and acid digestion Calculation of the triple oxygen isotope composition of carbonate and apatite parent waters requires knowledge of the fractionation exponents for mineral–water equilibrium, and for acid digestion. Theoretical predictions by Cao and Liu (2011) for qcc–H2O are 0.5235 at 25 °C, and they predict weak temperature dependence over the range 0–100 °C (0.5233–0.5239). More recently, Hayles et al. (2018) calculated a value of 0.5257 at 25 °C, and, Guo and Zhou (2019a) predicted values of 0.5253 to 0.5263 over the 0–100 °C temperature range, with a value of 0.5256 at 25 °C. Using an empirical approach and the reduction–fluorination conversion method, Passey et al. (2014) reported a value of θ = 0.5245 for combined mineral–water fractionation and acid digestion (90 °C). This value is based on analysis of fresh avian eggshell carbonate and water extracted from the same eggs (egg whites), and from analysis of an estuarine oyster and a marine coral and the waters they were found in at the time of sampling. Unpublished data from slow calcite precipitations in our laboratory (passive degassing) over a temperature range of 0–60 °C give a mean value of θ = 0.5242 for combined mineral–water fractionation and acid

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digestion, with no resolvable relationship with temperature. More recently, Sha et al. (2020) studied cave dripwater / speleothem pairs and obtained a value of 0.5235 combined mineral– water fractionation and acid digestion at 25 °C using the Pt-exchange method. Bergel et al. (2020) used the Pt-exchange method to derive a value of θ = 0.5231 for combined mineral– water fractionation and acid digestion at 25 °C, based on analyses of freshwater mollusks from well-constrained spring environments. Voarintsoa et al. (2020) of the same laboratory observed a value of θ = 0.5225 for laboratory-precipitated carbonates in the temperature range 10 to 35 °C. Neither study observed clear temperature dependence of the θ value, although the 35 °C values were distinctly lower (θ = 0.5220), which may reflect disequilibrium during very rapid precipitation of this material. Voarintsoa et al. (2020) observe no clear influence of carbonate polymorph (calcite vs. aragonite) or parent solution concentration on θ values. The only direct measurement of the qacid value is that of Wostbrock et al. (2020), who report a value of 0.5230 for 25 °C reactions, which is substantially lower than an early theoretical prediction of 0.5283 by Guo et al. (2009). The variability in θ values described above probably arises from a combination of methodological differences, differences in the exact nature of the θ value (i.e., mineral–water, or acid-digestion-produced CO2–water, with two different acid digestion temperatures used). Even if more reliable experimental estimates are obtained (i.e., from direct fluorination of laboratory-precipitated carbonates), it may still be the case that each laboratory would be better to use its own laboratory-derived θ values, given that these are influenced by the same analytical artifacts as samples processed in those laboratories.

FUTURE DIRECTIONS AND CONCLUDING REMARKS We have summarized the considerable progress that has been made during the past 15 years in the exploration and application of triple oxygen isotopes to continental hydroclimate, and have hopefully imbued the reader with an appreciation of the great potential for using triple oxygen isotopes in mineral records to unravel aspects of past climate and ecology. Despite the progress that has been made, the number of detailed studies into many systems such as lakes, plants, and animals can still be counted on one hand (or maybe two!), and many systems are just beginning to be studied or remain unstudied. Soil carbonates. Triple oxygen isotope studies of soil carbonates promise to reveal the extent to which soil waters from which the carbonates precipitated were evaporatively enriched in heavy isotopes, as well as changes in the ∆′17O of precipitation that may result from changes in regional atmospheric moisture sources. To our knowledge, the only published data for soil carbonates are the handful of data points in Passey et al. (2014) for modern soils in Inner Mongolia, California, and Ethiopia. Based on that dataset, and emerging data from our lab (Ji 2016; Emily Beverly, Julia Kelson, and Tyler Huth, pers. comm.), ∆′17O values for soil carbonate parent waters typically fall somewhere between values typical of meteoric waters, and values typical of closed-basin lakes. In other words, many samples show signs of evaporative modification, but the degree of lowering of ∆′17O is typically less than that observed for closed basin lakes. As was the case in the study of clumped isotopes in soil carbonates, it is becoming clear that triple oxygen isotopes will tell us as much about the seasonal timing and circumstances of soil carbonate formation as they will about prevailing climatic conditions. Speleothems. Sha et al. (2020) have presented the first triple oxygen isotope data for speleothems, studying a variety of samples from several caves around the world. Based on the present knowledge of triple oxygen isotope systematics, we can expect that cave drip water triple oxygen isotope compositions will vary with: (1) precipitation compositions, which are sensitive both to the effective relative humidity and turbulence over the oceans during the production of

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atmospheric vapor bodies (e.g., Fig. 2), and (2) evaporative modification of precipitation before it infiltrates into the subsurface or, in the case of rh < 1 caves, within the cave environments (Fig. 5). The speleothem mineral will record these factors, as well as (3) any kinetic effects that characterize the mineral growth process. Guo and Zhou (2019a,b) have explored the triple oxygen isotope systematics of the system DIC–H2O–CaCO3, and have developed a reaction– diffusion model to incorporate their predictions of triple isotope fractionation exponents into the transient process of mineralization. They predict kinetically-driven isotope trajectories with initial slopes of ~0.535, meaning that an array of kinetically-influenced sample would plot with a positive slope on a plot of ∆′17O (λ = 0.528) versus d18O. This is a distinctive slope compared to the universally negative slopes for the different systems that we have described in this review. All of the expected effects for ∆′17O in speleothems (moisture source effect, evaporation effect, kinetic effect) are subtle (Sha et al. 2020; Tyler Huth, pers. comm.), ranging by a few tens of per meg at most, so improving analytical precision beyond the 10 per meg level will be expedient. Tree rings and other organics. As far as we are aware, triple oxygen isotopes have not been measured to high precision in organic molecules. This should be possible using direct fluorination or high-temperature reduction to produce CO that could then be reduced to water and fluorinated using the approach of Passey et al. (2014). As shown in Figure 12, leaf water ∆′17O shows high sensitivity to relative humidity. Plant cellulose derives ~40% (Roden et al. 2000) of its oxygen from xylem water (which is not fractionated relative to soil water), meaning that the evaporation signal will be damped, but that it will still be highly resolvable. Thus, application to tree-ring records could help disentangle variations in d18O that are caused by changes in the isotopic composition of precipitation, from those that are caused by changes in evaporative enrichment. Biosynthesis of organic molecules involves isotopic fractionation, the mechanisms of which could possibly be probed using triple oxygen isotopes. Oxygencontaining molecules formed in waters of respiration should carry some of the anomalous triple oxygen isotope composition of atmospheric oxygen. As for the more ‘well studied’ systems (precipitation, lakes, plants, animals), the existing datasets are only a beginning. Most of the precipitation data are based on opportunistic sampling, and only the studies of Tian et al. (2018) and Uechi and Uemura (2019) involve the kind of continuous, systematic sampling that will reveal the mechanisms of e.g., seasonal variation in ∆′17O, and allow for determination of amount-weighted ∆′17Ο of precipitation. The ∆′17Ο of atmospheric water vapor is a fundamental parameter for evaporation, but only a handful of studies have conducted measurements (Uemura et al. 2010; Landais et al. 2012; Lin et al. 2013; Surma et al. 2021, this volume), and of these only the Surma et al. study is from a non-polar continental setting. Lake systems are tremendously understudied, especially in more humid settings that may be less ‘exciting’ in terms of large evaporative ∆′17Ο signals, but that are nonetheless important for understanding the full scope of the system. Back-calculation of isotopic compositions of unevaporated waters (Passey and Ji 2019) could be improved with more sophisticated methods such as Bayesian analysis (e.g., Bowen et al. 2018). Leaves come in a range of physiologies (i.e., blades of grass, conifer needles, typical hardwood leaves) for which detailed d18O–δD models have been developed (Cernusak et al. 2016). It will be important to expand these models and observations to triple oxygen isotopes, both in terms of understanding biogeochemical fluxes of O2 and CO2 (which are influenced by leaf water), and understanding the compositions of water available to herbivores. Very little of the taxonomic diversity of land vertebrates has been explored (e.g., reptiles, birds), and the work on mammals summarized above is only a starting point. If we are to use triple oxygen isotopes of vertebrate biominerals to reconstruct paleoecology, paleoclimate, and paleo-atmospheric composition, then we will need exhaustive study of modern organisms in relation to their environments and physiologies, and the further development and refinement of body water models.

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Finally, improvement in inter-laboratory reproducibility is urgent and imperative. Yeung et al. (2018) show that pressure-baseline corrections or continual referencing to well-defined, isotopically-disparate materials (i.e., VSMOW2 and SLAP2) is necessary for accuracy at the 10 per meg level. In terms of standardization protocols, the field is still in the ‘wild west’ stage compared to more mature fields with similar analytical challenges. Taking carbonate clumped isotopes as an example, a key paper (Dennis et al. 2011) was published 5 years after the first clumped isotope papers were published, outlining a rigorous protocol for standardization. This protocol involved routine analysis of reference materials spanning a wide range in both bulk isotopic composition (d13C and d18O), and in magnitude of the ∆47 clumping signal. This protocol was almost universally-adopted, and as a result there is remarkable interlaboratory agreement in the field (e.g., Petersen et al. 2019). The analogous approach for ∆′17Ο in carbonates would be to employ a suite of at least three, and preferably four carbonate materials, two of which span a wide range in d18O and have fairly high ∆′17O, and one (or two) of which span a similar range in d18O and have fairly low ∆′17O. Routine analysis of such materials would allow for monitoring of, correction for, issues of scale compression (in the ∆′17Ο space), as well as accuracy.

ACKNOWLEDGEMENTS First and foremost, we express gratitude to the talented group of students and postdocs with whom we’ve journeyed into the world of triple oxygen isotopes, including our ‘founding’ crew at Johns Hopkins University (Shuning Li, Huanting Hu, Haoyuan Ji Sophie Lehmann, Nicole DeLuca, and Jessica Moerman), and those who have carried the torch at Michigan (Ian Winkelstern, Emily Beverly, Drake Yarian, Phoebe Aron, Elise Pelletier, Sarah Katz, Natalie Packard, Joonas Wasiljeff, Tyler Huth, Nick Ellis, and Julia Kelson). We thank Andreas Pack and Ilya Bindeman for giving us the opportunity to write this chapter, and Jordan Wostbrock and an anonymous reviewer for insightful reviews.

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Small Triple Oxygen Isotope Variations in Sulfate: Mechanisms and Applications Xiaobin Cao International Center for Isotope Effects Research School of Earth Sciences and Engineering Nanjing University Nanjing 210023 PR China [email protected]

Huiming Bao International Center for Isotope Effects Research School of Earth Sciences and Engineering Nanjing University Nanjing 210023 PR China and Department of Geology & Geophysics Louisiana State University, Baton Rouge, LA 70803 USA [email protected]

INTRODUCTION Sulfate is the most abundant electron acceptor in the ocean today. A large fraction of the buried organic matter in marine sediments is re-mineralized through microbial sulfate reduction (MSR) during which the sulfate is reduced to H2S (Jørgensen 1982; Kasten and Jørgensen 2000). The H2S can be re-oxidized to sulfate or buried as pyrite in sediments (Jørgensen 1977). The burial of pyrite ultimately contributes to the rising of atmosphere O2 concentration (Berner and Canfield 1989). Sulfate, meanwhile, can be buried as gypsum and anhydrite in evaporites (Claypool et al. 1980; Crockford et al. 2019; Spencer 2000) or as barite in sedimentary rocks (Hanor 2000; Bao et al. 2008; Peng et al. 2011; Griffith and Paytan 2012; Crockford et al. 2016). Sedimentary rocks can be uplifted and weathered with or without being subducted, melted, or metamorphosed. Thus, the initially buried sulfur minerals are transformed and eventually turned to sulfate under oxidizing atmosphere through pyrite oxidation and evaporite dissolution (Bottrell and Newton 2006). Any sulfur-bearing minerals in igneous and metamorphic rocks will also eventually be released as sulfate upon oxidative weathering and carried to the oceans. The oxygen isotope composition of sulfate reveals the chemical pathways sulfate has experienced during its formation and consumption in sulfur cycling (Fig. 1). Secondary atmospheric sulfate can carry atmospheric O3 and/or O2 signature (Savarino et al. 2000; Harris et al. 2013; Bao 2015). At the surface, sulfate formed through sulfide mineral oxidation carries atmosphere O2 and ambient water oxygen isotope signatures (Bao 2015). During MSR, 1529-6466/21/0086-0014$05.00 (print) 1943-2666/21/0086-0014$05.00 (online)

http://dx.doi.org/10.2138/rmg.2021.86.14

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Figure 1. A global sulfur cycle in light of sulfate oxygen sources and sinks. Grey texts are sulfur reservoirs, bold black texts list the potential sources of oxygen for product sulfate during sulfur oxidation, MSR refers to microbial sulfate reduction, and arrows mark processes.

sulfate can exchange its oxygen isotope composition with ambient water via intermediates toward thermodynamic equilibrium (Wortmann et al. 2007; Zeebe 2010), erasing some or all the O2 and water oxygen isotope signatures the sulfate may have acquired initially (Mizutani and Rafter 1973; Fritz et al. 1989; Brunner et al. 2005). Evaporite sulfate represents well the contemporary seawater sulfate of geological times (Claypool et al. 1980; Crockford et al. 2019). Sulfate’s oxygen isotope composition has received less attention than sulfate’s sulfur isotope composition, due largely to oxygen’s multiple sources and variable non-equilibrium isotope signatures. The normalized 18O/16O ratio or the δ18O value is traditionally measured (Lloyd 1967, 1968). In the last 20 years, data on triple oxygen isotope composition (i.e., Δ′17O ≡ δ′17O − 0.5305  ×  δ′18O) of sulfate has been accumulating. Distinctly large positive and negative 17O anomalies have been found in the atmosphere and/or geological sulfate deposits (see review papers Thiemens 2006; Bao 2015; Crockford et al. 2019). These discoveries have provided exciting new insights into past atmospheric processes associated with volcanism (Bao et al. 2010), desert salt deposits (Bao et al. 2000a,b), snowball Earth (Bao et al. 2008, 2009), and gross primary productivity (Crockford et al. 2018; Hodgskiss et al. 2019). Over the years, researchers have discovered that there are analytically resolvable differences in the Δ′17O of sulfate produced by entirely mass-dependent reactions that do not involve O3, an oxidant bearing a large 17O anomaly (Bao et al. 2008; Sun et al. 2015; Killingsworth et al. 2018; Waldeck et al. 2019; Hemingway et al. 2020). We call these differences small triple oxygen isotope variations or small 17O deviations (Bao 2019). Apparently intriguing patterns have been reported and geological and environmental significances inferred. However, interpreting small sulfate Δ′17O data is not a trivial matter. In this chapter, we will explore the origins of small 17O deviations or small Δ′17O values in sulfate. Large positive or negative sulfate 17O anomalies will, therefore, not be covered here, and the readers can refer to recent reviews (Thiemens 2006; Bao 2015; Crockford et al. 2019) for details. Small sulfate Δ′17O values are sensitive not only to source of oxygen but also to reaction mechanisms because equilibrium and kinetic processes generate different small non-zero Δ′17O values (Young et al. 2002; Angert et al. 2004; Barkan and Luz 2007; Pack and Herwartz 2014; Bao et al. 2015). Sulfate reduction drives the remaining sulfate oxygen toward isotope equilibrium with ambient water, resulting also in a change of the small sulfate Δ′17O value. Since the change during sulfate reduction process is largely controlled by ambient water isotope composition, this review will focus more on reaction mechanism and associated oxygen isotope effects on sulfate formed via pyrite oxidation. We adopt the approach of isotopologue-specific kinetic analysis (Cao and Bao 2017; Cao et al. 2019),

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which helps to identify and subsequently estimate the most important parameters in determining sulfate’s small Δ′17O values. Isotopologue specific kinetic details during sulfate redox reactions are sketchy at this time and we will approach the problem using endmember scenarios. The intrinsic triple isotope parameters determined will then be used to construct Δ′17O − δ18O space for sulfates derived from different endmember scenarios. Such Δ′17O − δ18O space should be applicable not only to small Δ′17O but also to the δ18O or large Δ′17O values, and therefore can be tested and further revised. Specific examples on riverine and lake sulfate data will be analyzed to show potential applications. Analytical methods and issues in measuring small sulfate Δ′17O and future research opportunities are outlined in the end.

TRIPLE OXYGEN ISOTOPE SYSTEM Oxygen has three stable isotopes, i.e., 16O, 17O, and 18O. The δ notation is introduced to describe their small relative abundance variation in nature, and it is defined as (McKinney et al. 1950)

 17,18 R  (1)  17,18 O   17,18 sample  1   1000 ‰ R ref   where 17,18R is the mole ratio of 17,18O/16O; Rsample and Rref refer to R value for samples of interest and reference, respectively. Standard Mean Ocean Water (SMOW) (Craig 1961) (later Vienna-SMOW) is the reference material in most oxygen isotope studies. The notion of δ′ is often used in triple oxygen isotope community for its many advantages (Miller 2002; Young et al. 2002). Here (Hulston and Thode 1965)  17,18 R   17,18 O  ln  17,18 sample   1000 ‰ R ref  

(2)

When oxygen isotopes fractionate in a defined process, the corresponding fractionation factor is defined as (McCrea 1950) 17,18

 AB 

17,18 17,18

RA RB

(3)

where A and B are reactant and product or the transition state of a reaction path and the reactant, respectively. When A and B reach isotope equilibrium, α is the equilibrium isotope effect (EIE). When A and B is the transition state and the reactant, respectively, α is the kinetic isotope effect (KIE) (Bigeleisen and Wolfsberg 1958; Bao et al. 2015). EIE and KIE are two fundamental parameters of isotope fractionation. When we venture into the high-dimensional triple oxygen isotope relationship between 17αAB and 18αAB, the community has invented a designated Greek symbol. This is the θ value or the triple isotope exponent, defined as (Mook 2000; Angert et al. 2003; Barkan and Luz 2005, 2007; Cao and Liu 2011) 

ln 17  AB ln 18  AB

(4)

For mass-dependent processes that have fractionation larger than a few per mil, the θ normally varies between 0.5 and 0.5305 (Bao et al. 2015; Dauphas and Schauble 2016; Hayles et al. 2017). Often, a defined process cannot be an elementary process. In that case, the θ is apparent or diagnostic for that defined process or processes. The θ value only exists when a process is specified, but any oxygen-bearing compound can have its δ17O and δ18O values, and thus, its small 17O deviation, i.e., the Δ′17O value. The Δ′17O is calculated once a reference slope C is given (Angert et al. 2003; Pack and Herwartz 2014),

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(5)

 17 O   17 O  C   18 O

We recommend a C value of 0.5305 mainly because this value is the triple oxygen isotope exponent at high-temperature limit for all equilibrium processes (Cao and Liu 2011; Pack and Herwartz 2014). Detailed arguments can be found in Bao et al. (2016).

SULFOXYANIONS–WATER OXYGEN ISOTOPE EXCHANGE Sulfur has multiple sulfoxyanion species. Among them, sulfate (SO42−) is the final stable form during the oxidation of sulfur-bearing compounds while sulfite (SO32−) is arguably the most important intermediate with thiosulfate (S2O32−) being somewhat important during pyrite oxidation. The kinetic and equilibrium oxygen isotope exchange between the three sulfoxyanions and water are crucial to interpreting oxygen isotope compositions in sulfate. They will be briefly reviewed here.

Sulfate–water system Sulfate is a non-labile oxyanion. Experimental results indicate its oxygen isotope composition remains unchanged for 109 years at most Earth surface conditions (Zak et al. 1980; Chiba and Sakai 1985; Rennie and Turchyn 2014). The preservation of large positive and negative non-mass-dependent 17O anomalies from ~30 Ma (Bao et al. 2010), 635 Ma (Bao et al. 2008, 2009), and from the mid- and early Proterozoic samples (Crockford et al. 2018; Hodgskiss et al. 2019) attests to sulfate oxygen’s endurance. When microbial sulfate reduction occurs, however, the sulfate in solution can exchange oxygen isotopes with water via intermediate sulfite due to reversibility of enzymatic reactions (see section Microbial Sulfate Reduction). Sulfate δ18O has been observed to be 14.8‰ to 28‰ higher than that of ambient water during MSR (Zeebe 2010; Brunner et al. 2012; Antler et al. 2017; Bertran et al. 2020). The variation may reflect different degrees of reversibility. At 0  °C to 150 °C, the equilibrium oxygen isotope fractionation between sulfate and water is predicted computationally to follow (Zeebe 2010) EQ 1000  ln 18 SO  2.68  106  T 2  7.45 2 4 H2 O

where T is the temperature in Kelvin. At 25 °C, 1000 ln  

EQ SO24  H 2 O

(6)

is at ~ 23‰.

Currently, there is no experimental or theoretical calibration of the equilibrium triple EQ . In this volume, equilibrium oxygen isotope exponent for sulfate–water system, i.e. SO 2 4 H2 O EQ θ values for a series of sulfate minerals and water, i.e. SM ,  H 2 O were estimated theoretically EQ is to range from 0.5242 to 0.5246 (Schauble and Young 2021, this volume). Because CO 2 3 H2 O EQ EQ determined to be slightly smaller than calcite H2 O (Guo and Zhou 2019), SO24 H2O is expected to EQ be smaller than SM  H 2 O , and assumed to be 0.524 here. This value will be applied to construct endmember sulfates in Δ′17O–δ18O space.

Sulfite–water system Here we use sulfite to represent all the dissolved S(IV) species, including dissolved sulfur dioxide (SO2(aq)), bisulfite (SHO3−), sulfite (SO32−), and pyrosulfite (S2O52−) (Horner and Connick 2003). Bisulfite has two isomers, HSO3− where the hydrogen is bonding to sulfur and SO3H− where the hydrogen is bonding to oxygen. Oxygen isotope exchange between sulfite and water occurs via three proposed chemical reactions (Betts and Voss 1970; Horner and Connick 2003). k7 a

  SO3H   H     SO2  H 2 O k 7 a

SO H  

3

*

k7 b * * 2    SHO3     SO2    H 2 O   SO3 k 7 b

(7a) (7b)

Small 17O Variations in Sulfate: Mechanisms and Applications

SO H  

3

*

k7 c * * 2    SHO3    S2  O2  O3   H 2O  k

467 (7c)

7 c

where ‘*’ denotes oxygen from the SO3H− species prior to exchange. When bisulfite is the dominant species, the exchange rate is determined by (Horner and Connick 2003)





1 (8) k7 a H    k7 bc SHO3   3 where at 25  °C k7a and k7bc (k7bc = k7b + k7c) are 1.4 × 108 M−1s−1 and 8.0 × 103 M−1s−1, respectively (Horner and Connick 2003). When sulfite is the dominant species, the exchange rate is (Horner and Connick 2003) rex 

2

 rex

SO32     H   Q4 1  k7 a  k7 bc   3 Q2  Q2 1  Q4  

(9)

where SO32    H   SO3H   Q2   Q  4 SHO3   HSO3  , The values of Q2 and Q4 are 10−6.34 and 4.9, respectively (Horner and Connick 2003). Considering internal consistency, we adopt the value 4.9 instead of the newly determined result 2.7 (Eldridge et al. 2018) for Q4 because k7a and k7bc were initially determined using Q4 of 4.9. Using the values of k7a, k7bc, Q2, and Q4 given above and 0.75 for the activity coefficient of hydrogen ion [H + ] at pH 8.9 and [SO32−] at 0.3 M, we estimated the half-life of sulfite– water oxygen exchange to be 75 s, which is consistent with the experimentally obtained 78 s at the given chemical condition (Betts and Voss 1970). At pH 9.8, the exchange half-life is estimated to be 79 min, being consistent with the 82 min determined by Betts and Voss (1970) but is inconsistent with the 24.3 min determined by Wankel et al. (2014). The cause for the discrepancy is unclear but may have to do with the pH buffer glycine used by Wankel et al. (2014) because glycine, a potentially general acid catalyst (Horner and Connick 2003), could have catalyzed the exchange reactions. At pH of 7, the half-life is estimated to be less than 1s for dilute solutions (e.g. 0.1 mM). In addition, exchange rate is dependent on [SO32−], as shown in Equations (8) and (9). These analyses demonstrate that oxygen isotope exchange between sulfite and water is rapid, especially at low pH conditions.

Although the equilibrium isotope fractionation between individual sulfite species and water varies only with temperature, the fractionation between total dissolved S(IV) and water, EQ i.e. 18 SO , is pH dependent because sulfite species partition is pH dependent (Müller et 2 3 H2 O EQ al. 2013b). The value of 1000 ln 18 SO at 23 °C was determined to be 11.5‰ and 7.9‰ 2 3 H2 O at pH 7.2 and 8, respectively (Brunner et al. 2006). The pH and temperature dependence of EQ was also observed subsequently and determined to be (Wankel et al. 2014), 1000 ln 18 SO 2 3 H2 O  13.61  0.299  pH  0.081  t  EQ 1000  ln 18 SO  1000  ln   1 2 3 H2 O 1000  

(10)

where t is temperature in Celsius in the range of 2 °C to 95 °C and pH in the range of 4.5 EQ to 9.8. According to Equation (10), the 1000 ln 18SO at 23 °C should be 9.5‰ and 2 3 H2 O 9.3‰ at pH 7.2 and 8, respectively. This is different from an experimentally determined EQ value of 15.2‰ at 22 °C, a value displaying no pH dependence in the range 1000 ln 18 SO 2 3 H2 O of 6.3 to 9.7 (Müller et al. 2013b). The difference between the three experimental studies is

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EQ as large as 7.3‰. As of now, the value of 1000 ln 18 SO lies between 7.9‰ and 15.2‰ at 2 3 H2 O 22 °C and further calibration effort is warranted. This issue will be revisited later. EQ , has Triple oxygen isotope exponent for equilibrium sulfite–water exchange, i.e., SO 2 3 H2 O not been calibrated. However, due to the overall S–O bonding similarity between SO42− and EQ EQ EQ  ≈ SO and thus the value 0.524 is adopted for SO to SO32−, we assume that SO 2 2 2 3 H2 O 4 H2 O 3 H2 O construct endmember sulfates in Δ′17O–δ18O space.

Thiosulfate–water system Although thiosulfate (SSO32−) has a chemical structure similar to that of sulfate, experimental results show that thiosulfate readily exchange oxygen isotopes with water (Pryor and Tonellat 1967; Betts and Libich 1971). At pH > 5, oxygen exchange between thiosulfate and water proceeds mainly through thiosulfate–sulfite–water exchange pathway in which sulfite acts as a catalyst (Betts and Libich 1971). Two chemical reactions are responsible for the oxygen exchange (Betts and Libich 1971) 2 * 2 11 a   SO32   S * SO32     SSO3  SO3 k

(11a)

* 2 11 b   SO32   H 2 * O    S O3  H 2 O k

(11b)

k

11 a

k

11 b

where ‘*’ denotes the sulfur and oxygen prior to the change in thiosulfate and water, respectively. Reaction (11b) refers to an overall oxygen exchange reaction represented by chemical reactions (7a–7c). When pH is in the range of 5 to 10, the oxygen exchange rate between thiosulfate and sulfite is far slower than the one between sulfite and water, hence the overall exchange rate between thiosulfate and water can be approximated by the slower step, i.e., the exchange rate between thiosulfate and sulfite (Betts and Libich 1971) rex  3k11a SSO32   SO32  

(12)

and at 25 °C k11a = 2.07 × 10−4 M−1s−1. When pH goes up to the range of 10 to 11, the two rates are comparable, therefore, the overall oxygen exchange rate is determined by both thiosulfate–sulfite and sulfite–water exchange rates. At even higher pH, e.g., above 11, the rate of thiosulfate–sulfite exchange is faster than that of sulfite–water exchange, thus, the overall exchange rate can be estimated by Equation (9). In acidic condition (pH