Stable Isotopes in High Temperature Geological Processes 0939950200

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REVIEWS

in

MINERALOGY Volume 16

STABLE In

ISOTOPES

HIGH TEMPERATURE GEOLOGICAL PROCESSES

Editors:

John W. Valley, Hugh P. Taylor, Jr., James R. O'Neil Authors: ROBERT N. CLAYTON Department of Geophysical Sciences University of Chicago Chicago, Illinois 60637

HIROSHI OHMOTO Department of Geosciences Pennsylvania State University University Park, Pennsylvania

DAVID R. COLE Geosciences Group, Chemistry Division Oak: Ridge National Laboratory Oak: Ridge, Tennessee 37831

JAMES R. O'NEIL United States Geological Survey 345 Middlefield Road Menlo Park, California 94025

ROBERT E. CRISS United States Geological Survey National Center, Mail Stop 981 Reston, Virginia 22092

SIMON M.F. SHEPPARD C.R.P.G., BP 20, 54501 15 rue Notre Dame de Pauvres Vandoeuvre-les-Nancy Cedex, France

ROBERT T. GREGORY Department of Earth Sciences Monash University Clayton, Victoria 3168 Australia

BRUCE E. T AYLOR Geological Survey of Canada 601 Booth Street Ottawa, Ontario, Canada KIA OE8

T. KURTIS KYSER Department of Geology University of Saskatchewan Saskatoon, Saskatchewan, Canada S7N OWO

HUGHP. TAYLOR,Jr. Division of Geological and Planetary Sciences California Institute of Technology Pasadena, California 91125

KARLIS MUEHLENBACHS Department of Geology University of Alberta Edmonton, Alberta, Canada T6G 2E3

JOHN W. VALLEY Department of Geology and Geophysics University of Wisconsin Madison, Wisconsin 53706

Series Editor: PAUL H. RIBBE Department of Geological Sciences Virginia Polytechnic Institute & State University Blacksburg, Virginia 24061

16802

COPYRIGHT MINERALOGICAL

REVIEWS (Formerly:

1986

SOCIETY

of AMERICA

in MINERALOGY

SHORT COURSE

NOTES)

ISSN 0275-0279 Volume 16: STABLE

ISOTOPES in High Temperature Geologic Processes ISBN 0-939950-20-0 ADDmONAL COPIES of this volume as well as those listed below may be obtained from the MINERALOGICAL SOCIETY of AMERICA, 1625 I Street, N.W., Suite 414, Washington, D.C. 20006 U.S.A. Reviews in Mineralogy Volume 1: Sulfide Mineralogy, 1974; P. H. Ribbe, Ed. 284 pp. Six chapters on the structures of sulfides and sultosalts: the crystal chemistry and chemical bonding of sulfides. synthesis, phase equi~bria,and petrology. ISBN'" 0-939950-01-4. Volume 2: Feldspar Mineralogy, 2nd Edition, 1983; P. H. Ribbe, Ed. 362 pp. Thirteen chapters on feldspar chemistry. structure and nomenclature; Al,Si order/disorder in relation to domain textures, dillraction patterns, lattice parameters and optical properties; determinative methods; subsohdus phase relations. microstructures, kinetics and mechanisms of exsolution, and ditfusion; color and interference colors; chemical properties; oetormation. ISBN'" 0-939950-14-6. Volume 3: Oxide Minerals, 1976; D. Rumble III, Ed. 502 pp. . Eight chapters on experimental studies, crystal chemistry. and structures of oxide minerals; oxkte minerals in metamorphic and igneous terrestrial rocks, lunar rocks, and meteorites. ISBN# 0-939950-03-0.

Volume 9A: Amphiboles and Other Hydrous Pyriboles-Min· eralogy, 198~; D. R. Veblen, Ed. 372 pp. Seven chapters on biopyribole mineralogy and poIysomatism: the crystal chemistry, structures and spectroscopy of amphiboles: subsolidus relations: amphibole and serpentine asbestos-minerakJgy, occurrences, and health hazards. ISBN# 0-939950-10-3. Volume 9B: Amphiboles: Petrology and Experimental Phase Relations, 1982; D. R. Veblen and P. H. Ribbe, Eds. 390 pp. Three chapters on phase relations of metamorphiC amphiboles (occurrences and theory): igneous amphiboles; experimental studies. ISBN# 0-939950-11-1. Volume 10: Characterization of Metamorphism through Minerai Equilibria, 1982: J. M. Ferry, Ed. 397 pp. Nine chapters on an algebraic approach to cornposibon and reaction spaces and their manipulation: the Gibbs' formulation of phase equilibria; geologic thermobarometry: buffering, infiltration, isotope fractionation. compositional zoning and inclustons; characterization of metamorphiC fluids. ISBN# 0-939950-12-X. Volume 11: Carbonates: Mineralogy and ChemiStry, 1983; R. Nine chapters on crystal Chemistry, polymorphism, microstructures and phase re;ations of the rh0mbohedral and orthorhombic carbonates: the kinetics of CaCO, dissoluUon and precipitation; trace elements and isotopes in sedimentary carbonates: the occurrence, solubility and solid solution behavior of Mg-calcites: geologic thermobarometry using metamorphic carbonates. ISBN# 0-939950-15-4.

J. Reeder, Ed. 394 pp. Volume 4: Mineralogy and Geology of Natural Zeolites, 1977; F. A. Mumpton, Ed. 232 pp. Ten chapters on the crystal chemistry and structure of natural zeolites, their occurrence in sedimentary and Iowijrade metamorphic rocks and closed hydrclogk: systems, their commercial properties and utilization ISBN# 0-939950-04-9. Volume 5: Orthosilicates, 2nd Edition, 1982; P. H. Ribbe, Ed. 450 pp. Liebau's "Classification of Silicates' plus 12 chapters on silicate garnets, c»ivines, spinels and humites; zircon and the actinide orthosilicates; titanite (sphene). chk>ritoid, staurolite. the aluminum sibcates. topaz, and scores of miscellaneous orthosilicates. lridexed. ISBN# 0-939950-13-8. Volume 6: Marine Minerals, 1979; R. G. Burns, Ed. 380 pp. Ten chapters on manganese and iron oxides. the suca poIymorphs, zeolites, clay minerals, marine phosphorites, barites and placer minerals: evaporite mineralogy and chemistry.ISBN# 0-939950-06-5. Volume 7: Pyroxenes, 1980; C. T. Prewitt, Ed. 525 pp. Nine chapters on pyroxene crystal chemistry, spectroscopy, phase equilibria. subsolidus phenomena and thermodynamics: composition and mineralogy of terrestrial, lunar, and meteoritic pvroxenes. ISBN # 0-939950-07-3. Volume 8: Kinetics of Geochemical Processes. 1981; A. C. Lasaga and R. J. Kirkpatrick, Eds. 398 pp. Eight chapters on transition state theory and the rate laws of chemical reactions; kinetics of weathering, diagenesis, igneous crystallization and geochemical cycles; diffusion in electrolytes: irreversible thermodynamICS ISBN# 0-939950-08-1.

Volume 12: Fluid Inclusions, 1984; by E. Roedder. 644 pp. Nineteen chapters providing an introduction to studies of all types of fluid inclusions, gas. liqukS or melt, trapped in materials from the earth and space, and their application to the understanding of geological processes. ISBN# 0-939950-16-2. Volume 13: Micas, 1984; S. W. Bailey, Ed. 584 pp. Thirteen chapters on structures, crystal chemistry, spectroscopic and optical properties, occurrences, paragenesis, geochemistry and petrology of micas. ISBN# 0-939950-17-0. Volume 14: Microscopic to Macroscopic: Atomic Environments 10 Mineral Thermodynamics, 1985; S. W. KieNer and A. Navrotsky. Eds. 428 pp. Eleven chapters attempt to answer the question, . What minerals exist under given constraints of pressure, temperature, and composition, and why?" Includes worked examples at the end of some chapters. ISBN# 0-939950-18-9. Volume 15: Mathematical Crystallography, 1985; by M. B. Boisen, Jr. and G. V. Gibbs. Appro •. 450 pp. A matrix and group theoretic treatment 01 the point groups, Bravais lattices, and space groups presented with numerous examples and problem sets, including solutions to common crystallographk: problems involving the geometry and symmetry of crystal structures. ISBN # 0-939950-19-7.

FOREWORD The editors and authors of this volume presented the thirteenth in a series of short courses on behalf of the Mineralogical Society of America in November 1986, just prior to the annual meetings of MSA and the Geological Society of America in San Antonio, Texas. "STABLE ISOTOPES in HIGH TEMPERATURE GEOLOGICAL PROCESSES" was prepared for the course, and it is the seventeenth volume published by MSA in its now well established series, REVIEWS in MINERALOGY [see detailed list and ordering information on the page opposite]. The text of this book was assembled from authorprepared, camera-ready copy -- thus the wide variety of font types. The Mineralogical Association of Canada will sponsor a short course in May 1987 on the use of stable isotopes in the study of low temperature geological processes, and readers interested in the volume that will result from this undertaking (involving several of the authors of this volume) should write to: MAC, Department of Mineralogy and Geology, Royal Ontario Museum, 100 Queen's Park, Toronto, Ontario, Canada M5S 2C6. Paul H. Ribbe Series Editor September 16,1986

DEDICATION This volume on the stable isotope geochemistry of high temperature geologic processes is respectfully dedicated to Samuel Epstein, Professor of Geochemistry at the California Institute of Technology for the past 30 years. Although the topics of this volume encompass only a small range of the applications of stable isotope geochemistry to which Sam has been a major contributor, this sub-field was to a large degree originated by Sam and his first Ph.D. student, Bob Clayton, in the middle 1950's when they made their pioneering studies of oxygen isotope geochemistry and geothermometry of coexisting minerals in igneous and metamorphic rocks and ore deposits. Sam is now near the age of mandatory retirement, but is still extremely active in a wide range of disciplines, as evidenced by his recent (1985/1986) papers on D/H and l3C/12C studies of meteorites, isotopic studies of plants and animals, D/H studies of water in silicate melts and igneous rocks, and his work on a phosphate-chert-H 0 2 paleotemperature scale, to cite just a few. The field of stable isotope geochemistry was established by H. C. Urey, and A.O.C. Nier provided us with the basic mass spectrometer to do the work. But it is Sam Epstein who was mainly responsible for the flowering and maturing of this field into the enormous range of sub-fields and specialties that we know today (ocean paleotemperatures, high-temperature geothermometry, origins of natural waters, paleoclimatology, glacier research, biologic and geobiologic processes including plant and animal physiology, meteorology, ore deposits, oceanography, weathering and soil formation, and studies of the origin of igneous, metamorphic, and sedimentary rocks, meteorites, and tektites, etc.). Of course, starting with Harry Thode, who might be termed the father of sulfur isotope geochemistry, there are other eminent scientists who contributed immensely to the early development of this field, most of whom were also disciples of Urey: Harmon Craig (carbon isotopes), Irving Friedman (hydrogen isotopes), Cesare Emiliani (paleotemperatures), and John McCrea, Charles McKinney, Sol Silverman, Peter Baertschi, among others. The importance of the various men listed above to the field of geochemistry as a whole is demonstrated by the list of prizes they have been awarded: one Nobel Prize, 4 Day Medals, and 6 Goldschmidt Medals (out of the total of 14 awarded so far). In this dedication, we wish to recognize all of these pioneers. The editors and authors of this volume, in particular, owe a sizable debt to Samuel Epstein. The linkage with the past is clearly seen when one traces the scientific lineage of the contributors to this volume. Of the three editors, one is a scientific 'son' of Sam's, iii

one is a 'grandson', and the other is a scientific 'great-grandson'. Of the 12 authors of chapters, 10 are direct descendants (2 'sons', 2 'grandsons', and 6 'great-grandsons'). Several of Sam's scientific 'grandsons' have in fact worked directly with him as postdoctoral fellows, and 6 of the 12 contributors to this volume received their early training in stable isotopes either as Ph.D. students or as post-doctoral fellows at Caltech. The list does not at all do justice to the extended and widely ranging members of Sam's scientific family who permeate the other sub-fields throughout the field of stable isotope geochemistry and who are not among the authors of this book. Sam takes pride in all of the students and post-doctoral fellows who have worked with him over the years, and it is fair to say that he has left his mark on all of them in some way, particularly through his intuitive 'feel' for certain seemingly intractable but very important problems that in fact can be solved with a little clever laboratory work, a refusal to get bogged down in extraneous and unimportant details, and an understanding of the intrinsic accuracy required for a given measurement to be decisive. There is very little work in stable isotope geochemistry that doesn't utilize or make reference to some aspect of Sam's collected scien tific works.

BIOGRAPHICAL

SKETCH of SAMUEL EPSTEIN

Samuel Epstein was born in Kobryn, Poland (now U.S.S.R.) in 1919. His family moved to Winnipeg, Manitoba, Canada in September 1927, thereby escaping the fate of all of his relatives when the holocaust descended on Poland 14 years later. Sam became a Canadian citizen and grew up in Winnipeg, attending the University of Manitoba where he received a B.Sc. and M.Sc. in chemistry and geology in 1941 and 1942. At this point he switched totally to chemistry and began work on the kinetic reactions of the high explosive RDX at McGill University in Montreal, where he received his Ph.D. in September 1944. Sam then joined the Canadian Atomic Energy Project in Montreal, where he worked on rare-gas fission products. Here he met Harry Thode and also his future wife Diane, whom he married in September 1946, while he was a visiting scientist in Thode's group at McMaster University in Hamilton, Ontario. In 1947, Harold Urey was looking for someone to carry out the paleotemperature project he had started at Chicago. In October 1947, at Thode's recommendation, Sam and Diane moved to Chicago where they established residence in an apartment above Harold Urey's garage (formerly the coachman's quarters). Recognizing the golden opportunity he had in this fascinating research problem, Sam went to work with immense drive and dedication. Some of the most difficult mass spectrometric and analytical problems were solved that first year, but because of visa problems, the Epsteins went back to Canada in October 1948. Sam had become so valuable to the project that Urey personally visited the Immigration Bureau and was finally able to resolve the visa difficulty so that Sam could return to the project in the Spring of 1949. By this time McCrea and McKinney had left the project and Urey's interests had largely turned to the origin of the solar system. So, basically with only the help of Toshiko Mayeda, Sam had to solve most of the remaining problems associated with the development of the carbonate paleotemperature scale. During this period he also started several other projects, including the first survey of the oxygen isotope compositions of natural waters. In June 1952, when Harrison Brown moved from Chicago to Caltech, he invited Sam to come along. This transfer from the University of Chicago, which also included Claire Patterson and Charles McKinney, was the beginning of the geochemistry operation at Caltech. Lee Silver, a graduate student at the time, immediately became integrated into the operation, and Bob Clayton came over from the Chemistry Division to become Sam's first graduate student. The University of Chicago exodus to Caltech was concluded when Heinz Lowenstam and Gerry Wasserburg emigrated in 1953 and 1955, respectively. Sam and Diane became citizens of the U.S.A. in 1953, raised two sons, and are now proud grandparents of three. During his career Sam Epstein has initiated several new sub-fields of isotope geochemistry and has written more than 100 research papers. In recent years he has been widely recognized for his monumental scientific achievements by receiving the Goldschmidt Medal (1977), the Day Medal (1978), and being elected to the National Academy of Sciences (1977) and the American Academy of Arts and Sciences (1977). iv

PREFACE The development of modern isotope geochemistry is without doubt attributed to the efforts, begun in the 1930's and 1940's, of Harold Urey (Columbia University and the University of Chicago) and Alfred O.C. Nier (University of Minnesota). Urey provided the ideas, theoretical foundation, the drive, and the enthusiasm, but none of this would have made a major impact on Earth Sciences without the marvelous instrument developed by Nier and later modified and improved upon by Urey, Epstein, McKinney, and McCrea at the University of Chicago. Harold Urey's interest in isotope chemistry goes back to the late 1920's when he and I.I. Rabi returned from Europe and established themselves at Columbia to introduce the then brand-new concepts of quantum mechanics to students in the United States. Urey, of course, rapidly made an impact with his discovery of deuterium in 1932, the 'magical' year in which the neutron and positron were also discovered. Urey followed up his initial important discovery with many other experimental and theoretical contributions to isotope chemistry. During this period, Al Nier developed the most sophisticated mass spectrometer then available anywhere in the world, and made a series of surveys of the isotopic ratios of as many elements as he could. Through these studies, which were carried out mainly to obtain accurate atomic weights of the various elements, Nier and his co-workers clearly demonstrated that there were some fairly large variations in the isotopic ratios of the lighter elements. However, the first inkling of a true application to the Earth Sciences didn't come until 1946 when Urey presented his Royal Society of London lecture on 'The Thermodynamic Properties of Isotopic Substances' (now a classic paper referenced in most of the published papers on stable isotope geochemistry). With the information discovered by Nier and his co-workers that limestones were about 3 percent richer in 180 than ocean water, and with his calculations of the temperature coefficient for the isotope exchange reaction between CaCO and H20, Urey realized that it might be possible to apply these concepts to determining the paleotemperatures of the oceans. Urey was never one to overlook important scientific problems, regardless of the field of scientific inquiry involved. In fact, he always admonished his students to 'work only on truly important problems!' Urey, then a Professor at the University of Chicago, decided to take a hard look into the experimental problems of developing an oxygen isotope paleotemperature scale. Although the necessary accuracy had not yet been attained, the design of the Nier instrument seemed to offer a good possibility, with suitable modifications, of making the kinds of precise measurements necessary for a sufficiently accurate determination of the 180t60 ratios of both CaC03 (limestone) and ocean water. Enormous efforts would be required to do this, because even if all the mass spectrometric problems could be solved, every analytical and experimental procedure would have to be invented from scratch, including the experimental calibration of the temperature coefficient of the equilibrium fractionation factor between calcite and water at low temperatures. To carry out this formidable study, Urey gathered around himself a remarkable group of students, postdoctoral fellows, and technicians, as well as his paleontologist colleague Heinz Lowenstam. With Sam Epstein at the center of the effort and acting as the principal driving force, the rest, as they say, 'is history.' The marvelous nature of the Nier-Urey mass spectrometer is attested to by the fact that the basic design is still being used, and that there are now hundreds of laboratories throughout the world where this kind of work is being done. For example, the original instrument built by Sam Epstein and Chuck McKinney at Caltech in 1953 is still in use and has to date produced more than 90,000 analyses. University, government, and industrial laboratories have found these instruments to be an indispensable tool. Enormous and widely varying application of the original concepts have been made throughout the whole panoply of Earth, Atmospheric, and Planetary Sciences. In the

v

present volume we concentrate on an important sub-field of this effort. That particular sub-field was inaugurated in Urey's laboratories at Chicago by Peter Baertschi and Sol Silverman, who developed the fluorination technique for extracting oxygen from silicate rocks and minerals. This technique was later refined and improved in the late 1950's by Sam Epstein, Hugh Taylor, Bob Clayton, and Toshiko Mayeda, and has become the prime analytical method for studying the oxygen isotope composition of rocks and minerals. The original concepts and potentialities of high-temperature oxygen isotope geochemistry were developed by Samuel Epstein and his first student, Bob Clayton. Also, Bob Clayton, A.E.J. Engel, and Sam Epstein carried out the first application of these techniques to the study of ore deposits. The first useful experimental calibrations of the high-temperature oxygen isotope geothermometers quartz-calcite-magnetite-H~O were carried out initially by Bob Clayton, and later with his first student Jim O'Neil. In the meantime, Sam Epstein and his second student, Hugh Taylor, had begun a systematic study of 180t60 variations in igneous and metamorphic rocks, and were the first to point out the regular order of 180/160 fractionations among coexisting minerals, as well as their potential use as geochemical tracers of petrologic processes. During this period, a parallel development of sulfur isotope geochemistry was being carried out by Harry Thode and his group at McMaster University in Canada. They developed all the mass spectrometric and extraction techniques for this element, and also provided the theoretical and experimental foundation for understanding the equilibrium and kinetic isotope chemistry of sulfur. Starting from these beginnings, most of which took place either at the University of Chicago, Caltech, or McMaster University (but also with important input from Irving Friedman's laboratory at the U.S. Geological Survey, from Athol Rafter's laboratory in New Zealand, and from Columbia, Penn State, and the Vernadsky Institute in Moscow), there followed during the decades of the late 60's, 70's, and early 80's the development and maturing of the sub-field of high-temperature stable isotope geochemistry. This discipline is now recognized as an indispensable adjunct to all studies of igneous and metamorphic rocks and meteorites, particularly in cases where fluid-rock interactions are a major focus of the study. The twin sciences of ore deposits and the study of hydrothermal systems, both largely concerned with such fluid-rock interactions, have been profoundly and completely transformed. Virtually no issue of Economic Geology now appears without 3 or 4 papers dealing with stable isotope variations. No one writes papers on the development of the hydrosphere, hydrothermal alteration, ore deposits, melt-fluid-solid interactions, etc. without taking into account the ideas and concepts of stable isotope geochemistry. Although the present volume represents only a first effort to fill the need for a general survey of this sub-field for students and for workers in other disciplines, and although it is still obviously not completely comprehensive, it should give the interested student an idea of the present 'state-of-the-art' in the field. It should also provide an entry into the pertinent literature, as well as some understanding of the basic concepts and potential applications. Some thought went into the arrangement and choice of chapters for this volume. The first three chapters focus on the theory and experimental data base for equilibrium, disequilibrium, and kinetics of stable isotope exchange reactions among geologically important minerals and fluids. The fourth chapter discusses the primordial oxygen isotope variations in the solar system prior to formation of the Earth, along with a discussion of isotopic anomalies in meteorites. The fifth chapter discusses isotopic variations in the Earth's mantle and the sixth chapter reviews the variations in the isotopic compositions of natural waters on our planet. In Chapters 7, 8, 9 and 10, these isotopic constraints and concepts are applied to various facets of the origin and evolution of igneous rocks, bringing in much material on radiogenic isotopes as well, because these problems require a multi-dimensional attack for their solution. In Chapters 11 and 12, the problems of hydrothermal alteration by meteoric waters and ocean water are considered, together with discussions of the physics and chemistry of hydrothermal systems and the 180/160 history of ocean water. Finally, in Chapters 13 and 14, these concepts are applied to problems of metamorphic petrology and ore deposits, particularly

vi

with respect to the origins of the fluids involved in those processes. It seems clear to us (the editors) that this sub-field of stable isotope geochemistry can only grow and become even more pertinent and dominant in the future. One of the most fruitful areas to pursue is the development of microanalytical techniques so that isotopic analyses can be accurately determined on ever smaller and smaller samples. Such techniques would open up vast new territories for exploitation in every aspect of stable isotope geochemistry. Exciting new methods have recently been developed whereby a few micromoles of CO2 and S02 can be liberated for isotopic analyses from polished sections of carbonates and sulfides by laser impact. There are also new developments in mass spectrometry like RIMS (resonance ionization mass spectrometry), Fourier transform mass spectrometry and the ion microprobe that offer considerable promise for these purposes. Stable isotope analyses of large-sized samples (even those that must be obtained by reactions of silicates with fluorinating reagents) have now become so routine and so rapid that they represent an 'easy' way to gather a lot of data in a hurry. In fact 'mass production' techniques for rapidly processing samples are starting to become prevalent, so much so that one of the biggest worries in the future may be that a flood of data will overwhelm us and outstrip our abilities to carefully define and carry out sampling strategies, as well as to think carefully and in depth about the data. An organized system of handling the D/H, 13C/12C, ION/14N, 180t60, and 34Sj32S data, and/or a computerized data base that could be manipulated and added to would be a useful path to follow in the future, particularly if it were integrated into a larger data base containing radiogenic isotope data, major- and trace-element analyses, electron microprobe data, x-ray crystallographic data, and petrographic data (particularly modal data on mineral abundances in the rocks). The editors wish to thank the authors for meeting most of the deadlines associated with the preparation of this volume and for preparing the final typed versions of their manuscripts. We also thank all the individuals who graciously gave of their time and energy in reviewing and helping to improve the various manuscripts: R. Becker, P. Brown, R. Criss, B. Giletti, C. Johnson, B. Marsh, T. Mayeda, W. McKenzie, J. Morrison, P. Nabelek, E. Ripley, R. Rye, S. Savin, D. Stakes, L. Toran, and H. Wang. A particularly noteworthy contribution to this volume was made by Robert E. Criss whose careful reviews and critical comments substantially improved several chapters. We also thank A. Gunther, M. Hass, L. Marnoch, L. McMonagle, S. Morris, J. Murochick, and M. Wilson for their major editorial and typing efforts. We are greatly indebted to Paul H. Ribbe, who as series editor of Reviews in Mineralogy, was responsible for preparing camera-ready copy, and to Barbara Minich at M.S.A. Headquarters, who provided much needed assistance on various logistical and administrative problems. We are also grateful to M. Strickler and C. Ribbe for their assistance with additional typing, drafting and editorial work, all carried out at the Department of Geological Sciences, Virginia Polytechnic Institute and State University.

James R. O'Neil Menlo Park, California

Hugh P. Taylor, Jr. Pasadena, California

September

vii

1, 1986

John W. Valley Madison, Wisconsin

TABLE of CONTENTS Page II iii v

COPYruGHT; ADDnITONALCOprnS FOREWORD; DEDICATION PREFACE

Chapter 1 James R. O'Neil THEORETICAL and EXPERIMENTAL ASPECTS of ISOTOPIC FRACTIONATION 1 2 2 3 4 5 7 7 8 9 9 11 13 13 16 18 19 20 20 22 23 23 24 25 28 28 28 30 31 33 36 37

IN1RODUCTION KINETIC and EQUILIBRIUM ISOTOPE EFFECTS Kinetic Isotope Effects Equilibrium Isotope Effects The FRACTIONATION FACTOR The PARTITION FUNCTION Translational Partition Function Rotational Partition Function Vibrational Partition Function CALCULATION of EQUILIBRIUM CONSTANTS for ISOTOPE EXCHANGE REACTION Gases Condensed Phases FACTORS INFLUENCING the SIGN and MAGNITUDE of a Temperature Chemical Composition Crystal Structure Pressure LABORATORY DE1ERMINATIONS ofISOTOPIC FRACTIONATION FACTORS Two-direction Approach Sample calculation of 1oJlna Pseudo isotope exchange reactions Problems with the two-directional method

Partial Exchange Technique Three-Isotope Method Stable Isotope Fractionation Curves STABLE ISOTOPE TIIERMOME1RY Scope Tests for Equilibrium Present Status CONCLUSIONS ACKNOWLEDGMENTS REFERENCES

Chapter 2 David R. Cole & Hiroshi Ohmoto KINETICS of ISOTOPIC EXCHANGE at ELEVATED TEMPERATURES and PRESSURES 41 42 42 44 47

IN1RODUCTION BASIC CONCEPTS in ISOTOPE EXCHANGE REACTIONS Homogeneous versus Heterogeneous Reactions Rate Law for Isotope Exchange Reactions Determination of Rj from F and Its Relation to kf' the True Rate Constant viii

49 52 55 57 58 58 60 61 63 63 74 74 76 77 78 81 83 83 84 86 87

Determination ofD, the Diffusion Coefficient The bulk exchange technique Microbeam analytical techniques MECHANISMS and RATES of ISOTOPE EXCHANGE in HOMOGENEOUS SYSTEMS Kinetics of Isotopic Exchange Reactions in Solutions The sulfate-sulfide system The sulfate-water system Kinetics of Isotopic Exchange Reactions Between Gases MECHANISMS and RATES of ISOTOPE EXCHANGE REACTIONS in HETEROGENEOUS SYSTEMS Isotope Exchange Accompanying Surface Reactions Rate model Rates and activation parameters The relationship between rf and water/solid ratio Isotope Exchange Accompanying Diffusion The effect of temperature on rates of diffusion Effects of pressure on the rates of diffusion Anisotropy in diffusion Water in minerals Comparison of the Surface-Reaction and Diffusion Models SUMMARY ACKNOWLEDGMENTS

Chapter 3 ISOTOPIC 91 92 92 92 93 93 93 93 97 98 99 99 101 101 101 101 103 103 103 104 106 107 107 108 110 111 111 111 112 113

Robert T. Gregory & Robert E. Criss EXCHANGE in OPEN and CLOSED SYSTEMS

IN1RODUCTION BASIC PRINCIPLES Isotopic Exchange Reactions Delta Space Conservation of Mass CLOSED SYSTEMS General Statement Representation in Delta Space Temperature Effects Transformation to Other Coordinate Systems ,1-,1 plots 8-,1plots Isotherm plots Summary: Closed Systems OPEN SYSTEMS General Statement Kinetic Effects Elementary rate law "Closed" system exchange model Open system exchange model "Buffered" open system exchange model Interpretation of the Kinetic Models Fluid/rock ratios Exchange trajectories versus isochronous arrays Calculation of effective fluid/rock ratiosfrom disequilibrium arrays Summary: Open Systems APPLICATIONS to NATURAL SYSTEMS General Statement Plagioclase-Pyroxene from Layered Gabbros Primary magmatic compositions ix

113 114 114 114 116 120 120 122 123 124 124 125 126

Temperatures offluid-rock interactions Fluid/rock ratios Fluid isotopic compositions and pathlines Mineral Pairs from Granitic Rocks Precambrian Siliceous Iron Formation: Quartz-Magnetite Mineral Pair Systematics Applied to Upper Mantle Assemblages Eclogite mineral pairs Peridotite mineral pairs Impact of an open system model on the evolution of the upper mantle Summary: Natural Systems CLOSING STATEMENT ACKNOWLEDGMENTS REFERENCES

Chapter 4 Robert N. Clayton HIGH TEMPERATURE ISOTOPE EFFECTS in the EARLY SOLAR SYSTEM 129 129 129 131 131 132 132 134 137 139

IN1RODUCTION PLANETARY PROCESSES Achondrites and the Moon Ordinary Chondrites Carbonaceous Chondrites NEBULAR PROCESSES Evaporation and Condensation Isotopic Anomalies FUN Inclusions REFERENCES

Chapter 5 T. Kurtis Kyser STABLE ISOTOPE VARIATIONS in the MANTLE 141 142 142 144 146 152 152 155 157 158 160 162

IN1RODUCTION OXYGEN ISOTOPE COMPOSnITONS Mafic Lavas Mantle Xenoliths Processes Controlling the 180/160 Ratio of the Mantle Ancient Oxygen Isotope Compositions CARBON NI1ROGEN SULFUR HYDROGEN CONCLUDING REMARKS REFERENCES

Chapter 6 Simon M.F. Sheppard CHARACTERIZATION and ISOTOPIC VARIATIONS in NATURAL WATERS 165 165 166 167 167

IN1RODUCTION Concept of Combined Isotope Approach Defmition of Principal Water Types ISOTOPIC CHARACTERISTICS of NATURAL WATERS Ocean Waters x

167 167 168 168 170 172 173 174 175 177 178 178 179 180 181

Present-day Ancient Meteoric Waters Present-day Ancient Connate and Formation Waters Metamorphic Waters Magmatic Waters Organic Waters Hydrothermal Waters Exotic Waters OtherWaters CONCLUSIONS ACKNOWLEDGMENTS REFERENCES

Chapter 7

Bruce E. Taylor MAGMATIC VOLATILES: ISOTOPIC VARIATION of C, H, and S

185 IN1RODUCTION 185 SOLUBILITY, SPECIATION, and CHEMICAL COMPOSITION 185 Solubility and Speciation 185 Carbon 186 Hydrogen 187 Sulfur 187 Composition of Magmatic Gases 187 C, H, and S and Mafic Glasses 189 C, H, and S in Felsic Glasses 190 ISOTOPIC FRACTIONATION and MIGRATION of VOLATILES 190 Isotopic Fractionation 190 Carbon 190 Hydrogen 190 '!20 and hydrous minerals 191 H20 and hydrous magmas 195 Sulfur 195 Isotopic Variation During Magmatic Processes 196 Contamination-assimilation 196 Contamination-exchange 196 Degassing 197 Volatile Migration in Magmas 198 CARBON ISOTOPES 198 Volcanic Gases 198 Carbon dioxide 201 Methane 201 Carbon Dioxide in Vesicles 201 Carbon Isotopes in Basaltic Glass 204 Carbon in Mafic and Felsic Rocks 204 HYDROGEN ISOTOPES 204 Volcanic Gases 207 ~O in Fluid Inclusions 207 Mafic Magmas 207 Felsic Magmas 207 Hydrogen Isotopes in Basaltic Glasses 211 Hydrogen Isotopes in Felsic Plutons 213 SULFUR ISOTOPES 213 Volcanic Gases xi

214 218 218 219 220

Basalts Andesites CONCLUSIONS ACKNOWLEDGMENTS REFERENCES

Chapter 8

Hugh P.Taylor, Jr. & Simon M.F. Sheppard IGNEOUS ROCKS: I. PROCESSES of ISOTOPIC FRACTIONATION and ISOTOPE SYSTEMATICS

227 229 230 230 231 233 233 234 237 239 241 241 242 244 246 249 249 252 252 252 252 253 253 253 253 254 254 254 254 256 256 259 260 260 260 263 265 266 268 269

IN1RODUCTION GENERAL 180/160 and D/H VARIATIONS in IGNEOUS ROCKS PRIMORDIAL ISOTOPE RATIOS Oxygen Isotopes Hydrogen Isotopes CLOSED-SYSTEM EFFECTS Rayleigh Fractionation versus Equilibrium Crystallization Equilibrium 180/160 Fractionations between Crystals and Melt Evidence from Natural Igneous-Rock Suites Mineral-Melt D/H Fractionations and Magmatic Differentiation Effects OPEN-SYSTEM PROCESSES The Effects of Assimilation Oxygen Isotope Effects Radio&enic Isotope Effects 87Sr_ 0 Effects during Assimilation-Fractional Crystallization Adamello Massif, Northern Italy EXCHANGE EFFECTS at the MARGINS of MAGMA BODrnS SOURCE-ROCK RESERVOIRS AND MELT GENERATION Isotopic Compositions of Possible Source Rocks Oceanic crust Sedimentary rocks Metasedimentary rocks Archean cratons Granulite-facies lower continental crust Upper mantle Preexisting igneous rocks Low- 180 rocks formed by meteoric-hydrothermal alteration Formation waters or marine waters Source Contamination versus Crustal Contamination Sunµ_nary LOW - 180 MAGMAS LOW-and HIGH-DEUTERIUM MAGMAS The VOLCANIC ROCKS of ITALY General Features Alban Hills Volcanic Center M. Vulsini Volcanic Center Mixing Models Involving Tuscan Basement Rocks Summary ACKNOWLEDGMENTS REFERENCES

Chapter 9 Hugh P. Taylor, Jr. IGNEOUS ROCKS: II. ISOTOPIC CASE STUDIES of CIRCUMPACIFIC MAGMATISM 273

IN1RODUCTION xii

273 273 277 278 279 281 284 286 286 288 291 292 294 294 295 296 297 300 300 300 301 303 304 306 306 306 308 312 314 314 315 315 316

CALC-ALKALINE VOLCANIC ROCKS in the ANDEAN CORDILLERA 180/160 Ratios in Late Cenozoic Andean Volcanic Rocks The Central Volcanic Zone (CVZ) in Peru The Northern Volcanic Zone (NVZ) in Colombia and Ecuador Comparison of the NVZ and the Peruvian CVZ Comparison of the Southern CVZ with the SVZ and AVZ Summary The PENINSULAR RANGES BATHOLITH (PRB) of SOUTHERN and BAJA CALIFORNIA General Statement 180/160 Ratios Other Isotopic and Geochemical Gradients Origin of the Isotopic Variations in the PRB San Jacinto-Santa Rosa Mountains Block OTHER CRETACEOUS GRANmC BATHOLITHS in the UNITED STATES Relationship to the Peninsular Ranges Batholith Regional Isotopic Systematics Idaho Batholith Summary OXYGEN and S1RONTIUM ISOTOPE STUDrnS of WESTERN PACIFIC ISLAND ARCS Geologic Setting and Sources of Data Mariana and Volcano Arcs Japan and Izu Arcs SiO versus K 0 80 RHYOLITE MAGMAS in WESTERN NORTH AMERICA ORIG~ of General Statement Catastrophic Isotopic Changes in Magmas During Caldera Collapse, Yellowstone Volcanic Field Origins of the Low- 180 Magmas in the Yellowstone Caldera Complex Low- 180 Rhyolite Magmas Elsewhere in the Western U.S.A. The Low- 180 Magma Problem Emplacement into a rift-zone tectonic setting Chemical composition ACKNOWLEDGMENTS REFERENCES

wi?1

Chapter 10 Simon M.F. Sheppard IGNEOUS ROCKS: llI. ISOTOPIC CASE STUDIES of MAGMATISM in AFRICA, EURASIA and OCEANIC ISLANDS 319 319 319 323 324 326 329 332 335 336 337 340 342 342 344

346

IN1RODUCTION ANOROGENICMAGMATISM Oceanic Islands North Atlantic or Brito-Arctic Igneous Province Primar;, unmodified magmatic isotopic compositions Low- 1 0 magmas Gardar Igneous Province Granitic Rocks of East and South China Alkaline Ring -- Complexes in Africa and Arabia Arabian complexes Ring-complexes of Cameroun and Nigeria Summary OROGENIC MAGMATISM Plutonic Belts of the Himalaya- Transhimalaya Transhimalaya batholith High, north and "Lesser Himalaya" belts xiii

349 349 353 356 358 359 362 365 367 368

Variscan Magmatism 180/160 ratios and type of magmatism Nature of source materials Caledonian Magmatism of Northern Britain Younger basic intrusions 'Older' and 'younger' granites Archaean Granites of Southern Africa Concluding Remarks ACKNOWLEDGMENTS REFERENCES

Chapter

373 374 374 375 379 383 387 387 387 391 393 393 395 397 397 400

402 405 407 408 411 411 413 413 415 417 418 420 421 422

IN1RODUCTION FLUID DYNAMICS in a PERMEABLE MEDIUM Basic Principles Free Convection Permeability and Porosity Theoretical Scaling Law, Cooling Times, and WaterlRock Ratios MODERN METEORIC-HYDROTHERMAL SYSTEMS Geologic Settings of Geothermal Systems Origin and Composition of Geothermal Fluids Physical State of Geothermal Fluids ISOTOPIC EFFECTS in HYDROTHERMALLY-ALTERED ROCKS Stable Isotopic Systematics of Altered Rocks Effects of Alteration on Geochronologic Systems FOSSIL METEORIC-HYDROTHERMAL SYSTEMS General Occurrence and Character Isotopic Relationships in the Skaergaard Intrusion Numerical Modeling of the Skaergaard Intrusion WaterlRock Ratios in the Skaergaard Intrusion Lake City Caldera Idaho Batholith Yankee Fork District Meteoric-Hydrothermal Ore Deposits PE1ROGRAPHlC, CHEMICAL, and PHYSICAL ASPECTS of ROCK ALTERATION Volcanic Country Rocks Granitic Plutons Layered Gabbro Bodies Contrasting Effects in Gabbros and Granites SUMMARY ACKNOWLEDGMENTS REFERENCES

Chapter

425 426 426 428 428 429

11 Robert E. Criss & Hugh P. Taylor, Jr. METEORIC-HYDROTHERMAL SYSTEMS

12

KarIis Muehlenbachs ALTERATION of the OCEANIC CRUST and the 180 HISTORY of SEAWATER

IN1RODUCTION CURRENT SEA FLOOR PROCESSES Low Temperature Processes High Temperature Processes Metavolcanic rocks Dikes xiv

429 431 431 435 436 437 439 443

Gabbros Plagiogranites ON-LAND EXPOSURES of the SEAFLOOR MID-OCEAN RIDGE HOT SPRINGS MODELLING OF MID-OCEAN RIDGE HYDROTIffiRMAL SYSTEMS 180 BUDGET at MID-OCEAN RIDGES 0180 of Ancient Oceans REFERENCES

Chapter 13 STABLE 445 445 446 447 448 450 451 451 452 454 458 461 461 463 464 465 465 465 467 470 471 473 475 475 476 478 480 481 486

ISOTOPE

John W. VaIIe~ GEOCHEMISTRY

of METAMORPHIC

IN1RODUCTION ISOTOPIC THERMOME1RY METAMORPHIC VOLA T1LIZATION Batch Volatilization Rayleigh Volatilization Dehydration Decarbonation Mixed Volatile Reactions Coupled O-C Depletions CONTACT METAMORPHISM Volatilization During Contact Metamorphism Fluid Infiltration During Contact Metamorphism Controls of permeability Calculation of fluid/rock ratios Skarn The Effects of Variable P-T or Disequilibrium Polythermal exchange Graphitization REGIONAL METAMORPHISM Fluid Convection During Regional Metamorphism Isotopic Exchange by Diffusion and Recrystallization The Scale of Oxygen Isotope Exchange During Regional Metamorphism Granulite Facies Metamorphism The role off!uids in granulite genesis 8180 and 8l3c in granulites The Adirondacks as a case study Low- and high_l80 granulites; low_l80 eclogites ACKNOWLEDGMENTS REFERENCES

Chapter 14

Hiroshi Ohmoto

STABLE ISOTOPE GEOCHEMISTRY 491 493 493 494 494 494 495 495 496 498

ROC

of ORE DEPOSITS

IN1RODUCTION APPLICATIONS of STABLE ISOTOPES as GEOTHERMOMETERS Hydrogen Systems Oxygen Systems Carbon Systems Sulfur Systems HYDROGEN and OXYGEN ISOTOPE GEOCHEMIS1RY of HYDROTHERMAL SYSTEMS Methods of Estimating the oD and 0180 of Ore Fluids Hydrogen and Oxygen Isotopic Characteristics of Reference Waters Hydrogen and Oxygen Isotopic Characteristics of Recycled Waters xv

502 502 505 505 506 506 506 507 508 508 509 509 512 513 513 513 518 520 523 528 528 530 532 534 537 537 539 540 542 544 545 551 553 555 556

Isotopic Zoning in Wall Rocks Problems in the Quantification of Water/Rock Ratios Quantification of Hydrological and Geochemical Nature of Ore-forming Systems CONTRASTS BETWEEN CARBON-SULFUR and HYDROGEN-OXYGEN SYSTEMATICS Causes ofIsotopic Variation Isotopic Equilibrium Isotopic Effects during Mineralization Multiple Sources CARBON ISOTOPE GEOCHEMIS1RY ofHYDROTIIERMAL SYSTEMS Isotopic Variation during Geochemical Cycles of Carbon in Near-surface Environments Carbon Isotopic Composition of the Mantle Isotopic Relationships among Aqueous Carbon Species Methods of Determining the Sources of Carbon in Ore Deposits SULFUR ISOTOPE GEOCHEMIS1RY ofHYDROTIIERMAL SYSTEMS Sulfur Isotopic Characteristics of Reference Reservoirs Sulfur Isotopic Characteristics of Recycled Seawater-sulfur Isotopic Relationships Among Aqueous Sulfur Species Sulfur Isotopic Relationships Between Fluid Species and Minerals and Between Co-existing Minerals Methods of Determining the Sources of Sulfur in Ore Deposits SULFUR ISOTOPES in MAGMATIC SYSTEMS Sy,eciation and Solubility of Sulfur in Silicate Melts 0 4S Values of Mantle-derived Igneous Rocks Assimilation of Crustal Sulfur by Mafic Magmas and the Formation of Cu-Ni Sulfide Ores Assimilation of Crustal Sulfur by Felsic Magmas Sulfur Isotopic Characteristics of Magmatic Fluids GENETIC MODELS for ORE DEPOSIT TYPES Porphyry and Skarn Type Deposits Base- and Precious-metal Veins, and Replacement Deposits Massive Sulfide Deposits of Submarine Volcanic Association Shale/Carbonate-hosted Zn-Pb Deposits Mississippi Valley-type Deposits Red-bed Associated Cu Deposits CONCLUDING REMARKS ACKNOWLEDGMENTS REFERENCES

Appendix: TERMINOLOGY and STANDARDS 561 561 561 562 563 564 564 565 565 565 565 567 567 569 569

TERMINOLOGY The 0 Value Isotope Exchange Reactions The Fractionation Factor, a 103lna and the ~ Value The e Value Fractionation Curves Crossovers Reversals STANDARDS Oxygen Hydrogen Carbon Sulfur REFERENCES xvi

James R. O'Neil

Chapter 1

James R. O'Neil

THEORETICAL and EXPERIMENTAL ASPECTS of ISOTOPIC FRACTIONATION INTRODUCTION Light stable isotope geochemistry is concerned with variations in the isotopic ratios of only six elements: H, C, N, 0, Si, and S. Boron is sometimes added to this list, but its isotopic ratios are measured by techniques that are different from those used in conventional stable isotope laboratories. These elements have several characteristics in common: (1) They have low atomic mass. Isotopic variations have been looked for but not found for heavy elements like Cu, Sn, and Fe. (2) The relative mass difference between the rare (heavy) and abundant isotope is large. For example, compare the values of 12.5 and 8.3 percent for the pairs 180_160 and 13C_12C, respectively, with the value of only 1.2 per cent for 87Sr_86Sr. The relative mass difference between D and H is almost 100 percent and hydrogen isotope fractionations are, accordingly, about ten times larger than those of the other elements of interest. (3) They form chemical bonds that have a high degree of covalent character. Attesting to the importance of bond type to isotopic fractionation, the 48Ca/40Ca ratio varies little in terrestrial rocks despite the large relative mass difference (only D-H is larger) between the isotopes (Russell et aI., 1978). (4) The elements exist in more than one oxidation state (C, N, and S), form a wide variety of compounds (notably 0), and are important constituents of naturally occurring solids and fluids. (5) The abundance of the rare isotope is sufficiently high (tenths to a few per cent) - to assure the ability to make precise determinations of the isotopic ratio by mass spectrometry. Depending on the instrument used, the analytical error of deuterium analyses is up to ten times larger than those of the other elements because of the low abundance of deuterium (about 160 ppm) in nature. Natural variations in isotopic ratios of terrestrial materials have been reported for other light elements like Mg and K, but such variations usually turn out to be laboratory artifacts. The case of magnesium is fairly straightforward. Aside from the fact that its bonds are dominantly ionic in character, magnesium is almost always surrounded by the same atomic environment (an octahedron of oxygen) in nature. Thus with little or no possibility of site preference in magnesium compounds, conditions are not favorable for isotopic fractionation of this element in nature. In any event, variations in stable isotope ratios of light elements other than the seven mentioned above are small in terrestrial substances. The reasons for this are not completely understood and are only loosely discussed in terms of characteristics such as those noted above. These characteristics are only observed and are not rigorously tied to theoretical principles. Except

for the case of stable isotope relations in extraterrestrial materials (Chapter deals only with those isotopic variations or effects that arise either from isotope exchange reactions or from mass-dependent fractionations that accompany physical and chemical processes occurring in nature or in the laboratory. While ultimately quantum mechanical in origin, such isotope effects are governed by kinetic theory and the laws of thermodynamics. Natural variations in the stable isotope ratios of the heavy elements of geologic interest like Sr, Nd, and Pb involve nuclear reactions and are governed by other factors including the ratio of radioactive parent and daughter, decay constants, and time.

4), the discipline of stable isotope geochemistry

Essential to the interpretation of natural variations of light stable isotope ratios is knowledge of the magnitude and temperature dependence of isotopic fractionation factors between the common minerals and fluids. These fractionation factors are obtained in three ways:

(1) Semi-empirical calculations using spectroscopic data and the methods of statistical mechanics. (2) Laboratory calibration studies. (3) Measurements of natural samples whose formation conditions are well-known or highly constrained. In this chapter methods (1) and (2) are evaluated and a review is given of our present state of knowledge of the theory of isotopic fractionation and the factors that influence the isotopic properties of minerals. For further information on nuclear properties and isotopes in general, consult the texts by Faure (1977) and Hoefs (1980).

KINETIC

AND EQUILIBRIUM

ISOTOPE

EFFECTS

Kinetic Isotope Effects Kinetic isotope effects are common both in nature and in the laboratory and their magnitudes are comparable to and sometimes significantly larger than those of equilibrium isotope effects. Kinetic isotope effects are normally associated with fast, incomplete, or unidirectional processes like evaporation, diffusion, and dissociation reactions. The examples of diffusion and evaporation are explained by the different translational velocities of isotopic molecules moving through a phase or across a phase boundary. Kinetic theory tells us that the average kinetic energy (K.E.) per molecule is the same for all ideal gases at a given temperature. Consider the isotopic molecules 12C160 and 12C180 that have molecular weights of 28 and 30, respectively. Solving the expression equating the kinetic energies (K.E. = 1/2 Mv2) of both isotopic species, the ratio of velocities of the light to heavy isotopic species is (30/28)1/2, or 1.034. That is, regardless of T, the average velocity of 12C160 molecules is 3.4 percent greater than the average velocity of 12C180 molecules in the same system. This and other such velocity differences lead to isotopic fractionations in a variety of ways. Isotopically light molecules can preferentially diffuse out of a system and leave the reservoir enriched in the heavy isotope. In the case of evaporation, the greater average translational velocities of lighter molecules allows them to break through the liquid surface preferentially, resulting in an isotopic fractionation between vapor and liquid. For example, the 8180 value of water vapor above the ocean (8180 = 0) is typically around -13 permil, whereas at equilibrium the value should only be about -9 permil depending on the temperature of evaporation. The magnitude of the isotopic fractionation reduces to the value of the equilibrium fractionation as the vapor phase approaches saturation or equilibrium vapor pressure. At that point the rates of molecular transfer between liquid and vapor and between vapor and liquid are equal. Condensation, on the other hand, is dominantly an equilibrium process. Molecules containing the heavy isotope are more stable and have higher dissociation energies than those containing the light isotope. Therefore it is easier to break such bonds as 12C_H and 32S_0 than to break bonds like 13C_H and 34S_0. Kinetic isotope effects arising from these differences in dissociation energies can be extremely large in dissociation and bacterial reactions that occur in nature. While it is very important to be aware of kinetic isotope effects, they are relatively rare in high-temperature processes occurring on Earth. On the other hand, transient processes can occur wherby differing rates of isotopic exchange between coexisting minerals themselves or between the minerals and an external fluid can result in assemblages that are grossly out of isotopic equilibrium (see Chapters 2, 3, and 11). Such examples are not explained by kinetic isotope effects but rather by a series of equilibrium isotope exchange reactions that have not gone to completion. Except for some important isotopic variations attributed to evaporation processes during meteorite genesis (Chapter 4), kinetic isotope effects will not be a serious consideration in this course.

2

o

.... CD

o E .....

109.4

105.3

to

o

..... ..10:

>-

e II:

HARMONIC OSCILLATOR

W

Z W ...J

-c

IZ W

I-

o

ZPE

c..

4.1

r INTERATOMIC

DISTANCE

Figure 1. Schematic potentia! energy diagram for the hydrogen molecule with scale at bottom of the curve exaggerated to show relation between n = 0 vibrational energy levels of the three isotopic forms of the molecule. The fundamental vibrational frequencies are: H!, 4405 em>: HD, 3817 cm=: D., 3119 crrr'. With increasing temperature, vibrations of a.1Imolecules become Increasingly anharmonic and the spacings between energy levels (not shown) become smaller and smaller until dissociation occurs. All isotopic forms of hydrogen have the same spectroscopic dissociation energy (109.4 kcal/mole) but chemical dissociation energies and zero point energies (ZPE) that differ by up to 2 kcal/mole. Note that molecules containing the heavy isotope are more stable (have higher dissociation energies) than molecules with the light isotope. Isotopic fractionations between molecules are explained by differences in their ZPE.

Equilibrium

Isotope Effects

Equilibrium isotope effects can be considered in terms of the effect of atomic mass on bond energy. When a light isotope in a molecule is substituted by a heavy isotope, the nuclear charges and electronic distributions remain unchanged. Therefore the potential energy curve (Fig. 1) remains unchanged. In the simplest case, the diatomic molecule in the harmonic oscillator approximation, the vibrational energy levels are given by: E where n h 1I

that

= 0, 1, 2, 3, '" = Planck's constant = = frequency

= (n

+ 1/2)hll

(1)

6.624 x 10-27 erg-sec.

(sec:']

At n = 0, the ground vibrational state, E = 1/2hll. This is the vibrational energy molecules possess even at a temperature of absolute zero and is called the 'zero-

3

point energy' (ZPE). Most molecules of a gas are in the ground vibrational state at room temperature. The ZPE is the distance between the bottom of the the potential energy well and the zeroeth vibrational energy level and is shown for D2 in Figure 1. The frequency v is related to mass by Hooke's Law _1

V=

27rV

Ir

(2)

µ

MAMB for molecule MA+MB AB whose constituent atoms have atomic weights MA and MB. In spectroscopic and thermodynamic calculations, frequency is normally expressed in wave numbers w in units of em". w = vic, where c is the velocity of light .. On isotopic substitution, k is unchanged because it depends only on the shape of the potential energy curve. However, µ changes. If atom A is replaced by its heavier isotope A' , where k

=

force constant

(dyne/em),

=

and µ

> V
(13C/12C)A' (180/160)A> etc. At equilibrium, a is related, to the very good approximation that the isotopes are randomly distributed among all possible sites in the molecule, to the equilibrium constant K for the isotope exchange reaction between the two substances (Bigeleisen, 1955). In general, a = Kiln

(4)

where n is the number of atoms exchanged in the reaction as written. It is a factor analogous to a distribution coefficient and is the most important quantity used in evaluating stable isotope variations observed in nature. Different authors report equilibrium fractionation factors as a, Ina, 1031na, K, InK, ¤, and .6. (see Appendix 1). Each of these symbols will be used in this chapter in order to familiarize the reader with all usages. As we saw above, isotopic fractionations can be described in terms of isotope exchange reactions, an example of which is: 12CO The equilibrium

constant

+ 13CH4 =

K for this reaction K

=

13CO

+ 12CH4

is written

in the usual way:

e COt CH 3

e

2

4)

CO )(13CH4)

2

(5)

Concen trations are used rather than activities or fugacities because ratios of activity coefficients for isotopically substituted molecules are equal to unity. When there is more than one atom of the isotopic element in the chemical formula, as in Si1802 or CD4, all atoms in the substance are the isotope indicated. This is by custom and meaningful only for simplifying calculations. Substances with such chemical formulas do not exist in nature. For isotope exchange reactions, the total energy change is just the difference in .6.ZPE between the two molecular species. As mentioned above, a typical value for the change in energy of an isotope exchange reaction is only about 20 caljmole. Note that like all equilibrium constants, the equilibrium constants for isotope exchange reactions are temperature dependent. This is the basis for their use in thermometry.

THE PARTITION

FUNCTION

The principal thermodynamic functions, including the equilibrium constant, can be expressed in terms of the partition function, a mathematical relation arising from statistical mechanics. Partition functions contain all the energy information about a molecule and they are used to calculate equilibrium constants (fractionation factors) for isotope exchange reactions. Recall that the internal energy of a molecule Ein• can, to a first approximation, be represented as a simple sum of all forms of energy: translation (tr), rotation (rot), vibration (vib), electronic (el) and nuclear spin (sp). Eint

=

Etr

+ Erot + Evib + Eel + Esp

(6)

For our purposes the last two terms are negligible and will be ignored in the treatment that follows. At any instant, the value of Ein• and the distribution of internal energy among the individual terms may vary in different molecules of the same kind. In an equilibrium assemblage at temperature T, the fraction of molecules having energy Ein• can be expressed as

(7)

5

where no = number of molecules with zero-point energy only nE = number of molecules having Einl gi = statistical weight k = Boltzmann's constant = 1.381 x 10-18 erg/oK. It is possible that there may be more than one state corresponding to the energy level If so, the level is said to be 'degenerate' and must be assigned a statistical weight that is equal to the number of superimposed levels. The summation of all terms on right hand side of equation 7 is by definition the partition function Q, also called 'sum-over-states,' and the 'statistical sum':

Q

"

= LJgie

-EJkT

E.. (g;) th~ the

(8)

This function is first met in statistical mechanics as the denominator of the Boltzmann distribution law written in its most general form. The average energy of an assemblage of molecules will be the ordinary internal energy E. If the allowed energies of the whole system are E1, E2, ... Ep the average energy will be

E

E -

~

E. "-

-E.JkT

E g."E·e

Il:

LJ

,

-

"

LJgie

Substituting Q for the denominator in equation derivatives of Q with respect to T, we have E

=

(9)

-E.JkT

9 and recasting

in terms

of partial

kT2 aInQ

(10)

aT

and one connection between the thermodynamic functions and partition functions is seen. Statistical mechanics deals with large numbers of individual particles whereas thermodynamics deals with large-scale systems containing very many particles, the usual measure being the mole, or 6.02 x 1023 molecules. Thus a distinction is made between molecular and molar partition functions. You will often see the thermodynamic functions written in terms of molar partition functions (and R rather than k). For example, E S = T

+ RlnQ

(11)

Equilibrium constants for any reaction can be written in terms of the partition functions of the reactants and products. K is written in the normal way except that Q is used rather than the activity. For the carbon isotope exchange reaction between CO and CH4 discussed above, the equilibrium constant can be written

K

=

Q(13CO)/Q(,2CO) Q( 13CH4)/ Q( 12CH4)

For the general case of an isotope exchange reaction aAl an expression follows:

can be written

K

+ bB2

= aA2

for the equilibrium =

(12)

between substances

A and B,

+ bBl constant,

(QA,)a(QB/

(Q2/QI)1

(QAl(QB/

(Q2/QI)~

(13) or fractionation

factor,

as

(14)

where the subscripts 2 and 1 refer to molecules totally substituted by the heavy and light isotopes of an element, respectively. In order to calculate equilibrium constants for isotope exchange reactions, our ultimate goal will be to calculate partition function ratios for the different substances of interest. To begin with we will write expressions for the partition functions (and partition function ratios) of diatomic molecules that are (1) ideal gases, (2) rigid rotors, and (3) harmonic oscillators. We will then generalize to the poly atomic case, and finally, introduce the complications of treating condensed phases. 6

It follows from equation 6, and to the same approximation, that the total partition function for an ideal gas is equal to the product of partition functions for each form of energy:

(15) Partition functions have been developed for each of these forms of energy and they will be examined in turn. Through the use of very good approximations, we will be able to express Q2/Q1 as a function only of vibrational frequencies and temperature. Translational

Partition

Function

All forms of energy are quantized; that is, they can assume only certain discrete values. Above about 2°K, the quanta of translational energy are so small, and the energy levels are so closely spaced, that the summation in the expression for the translational partition function can be evaluated as an integral Q tr

=

'"

LJgtre

-E,,/kT

=

Je

-E.r/kT

d n

(16)

where dn is the number of energy levels in the energy range dE. mechanics we know that the energy of translational motion of a particle of side a is, for each degree of freedom,

From quantum in a cubical box

(17) and

(18) where, if T

=

constant, A

Substituting freedom

these

values

h2 2 8a mkT

=

for E,,/kT

=

into

constant

equation

16, we have

for each

degree

of

00

Qtr --

J e-n2~dn -- "2V 1 . ff _ (271mkT)'/2 >: h a 0

(19)

For three degrees of freedom, Qtr = (2rrmkT)3/2

h3

V

(20)

where V = a3, the volume of the cube. Furthermore the result is valid for a volume of any shape. We may replace m by the molecular weight M, and when ratios are made to obtain the translational partition function ratio, everything cancels but the molecular weights.

(21) Thus the isotopic fractionation arising from translation is a function only of the ratio of molecular weights raised to the 3/2 power and is independent of temperature. Rotational

Partition

Function

The solution to the Schrod inger equation for a diatomic molecule in the rigidrotator model (consider the molecule as a dumbbell rotating about a center of mass) allows the following energies:

E

= j(j

+ l)h2

j(j

8rr2µr2

+ l)h2 8rr2r

7

(22)

where j = rotational quantum number I = moment of inertia = µr2 µ = reduced mass r = interatomic distance There are two complications that enter into the rotational partition function: the degeneracy of the rotational levels and the symmetry of the molecular eigenfunctions. Diatomic molecules have two axes of rotation around which rotational energy can be distributed. The number of ways of distributing j quanta of energy between the two axes equals 2j + 1, because in every case except j = 0 there are two possible alternatives for each added quantum. The statistical weight of a rotational level j is therefore 2j + 1. The rotational partition function now becomes Qrot

=

+ l)ej(j

E(2j

2

2

+ l)h /81r IkT

(23)

Except for the case of hydrogen isotopes, the spacings between energy levels are less than kT. Again because of these small spacings the sum can be approximated by an integral and evaluated in closed form to give the classical partition function

Qrot

= 81r2JkT h2

(24)

diatomic molecules (14N14N, 160160,etc.) only all odd or all even j 's are allowed, depending on the symmetry properties of the molecular eigenfunctions. If the nuclei are different ('4N1fiN, 160180, etc.) there are no restrictions on the allowed j's. Therefore a symmetry number (1 must be introduced. For diatomic molecules (1 is either 1 (heteronuclear) or 2 (homonuclear). Equation 24 also holds for linear poly atomic molecules, with (1 = 2 if the molecule has a plane of symmetry (like CO2) and (1 = 1 if it does not (like N20). For a nonlinear polyatomic molecule,

In homonuclear

_ Qrot -

81r2(81r3 ABC)'/2(kT)3/2 3

(25)

(1h

In this equation A, B, and C are the three principal moments of inertia of the molecule. The symmetry number (1 is equal to the number of equivalent ways of orienting the molecule in space. For example: H20, (1 = 2; NH3, (1 = 3; CH4, (1 = 12. Except for the case of exchange reactions involving hydrogen isotopes, the classical partition functions are adequate and the rotational partition functions reduce to 12

(11

= -I

(Q2/Ql)rot

(26)

(12 1

for diatomic

molecules and

(27.) for polyatomic Vibrational

molecules.

Partition

Function

In evaluating a partition function for the vibrational degrees of freedom molecule we will take the energy levels of a harmonic oscillator. Repeating equation EVib =

(n

of a 1,

+ 1/2)hv

At low temperatures vibrational contributions are usually small and this approximation is adequate. However, it must be kept in mind that at higher temperatures the anharmonicity of real vibrations can be large. Anharmonicity corrections must sometimes be taken into account when making exact calculations of isotopic partition function ratios (Richet and Bottinga, 1976).

8

The spacing between vibrational energy levels is large compared to kT (the average thermal energy of a molecule) and the summation terms of the vibrational partition function cannot be integrated as was possible for both the translational and rotational cases. However, the series can be evaluated in closed form to give the exact expression e-hv/2kT

=

Qvib

If U

=

= hcw/kT,

hll/kT

Qvib

for diatomic

(28)

L./L'"

molecules,

U2

=

e- / 1 - e-u

(29)

and Qvib

=

II e -Ud2 i

for polyatomic

molecules.

The vibrational

partition

(30)

1 - e ..

function

ratio for poly atomic molecules is then -U~/2 -uu e 1- e (Q2 / QI) = IIu -u /2' -u ie l-e~

(31)

where the i's are frequency indices for the normal modes of vibration. For molecules with n atoms, there are (3n - 6) frequencies for a non-linear molecule and (3n - 5) frequencies for a linear molecule.

CALCULATION OF EQUILIBRIUM CONSTANTS FOR ISOTOPE EXCHANGE REACTIONS

From equation 14, we know that equilibrium constants for isotope exchange reactions are calculated from the partition function ratios of the two substances participating in the reaction. For simplicity here, isotope exchange reactions are always written such that one atom is exchanged. Thus the factor n (number of atoms exchanged) that some authors use in the mass ratio terms will not appear in the equations that follow. Multiplying together the partition function ratios developed above for the three principal forms of energy of a molecule results in the following expressions:

(32) for diatomic

molecules and

_ Q2/Q 1--

0"1 0"2

A 2 B 2 C 2 )1/2( M 2 )3/2 IIe -U~/2 . 1 - e -uu --( AlBlCl MI i e-Uu/2 1 _ e-u~

(33)

for poly atomic molecules. These equations can be simplified further by using the Teller-Redlich theorem which is, for the case of the diatomic molecule, 3/2

m2

(

-

m,

)

11 ( MI 12 M2

-

9

) 3/2

U2 _ --1 Ul

spectroscopic (

)

34

A corresponding equation can be written for the case of polyatomic molecules. By use of this relation we can avoid calculating moments of inertia and are able to calculate the partition function ratios from the vibrational frequencies alone. This results in fairly simple, U-dependent expressions for partition function ratios that are exact to the approximation that the molecules are ideal, rigid rotators, and have harmonic vibrations: 3/2 U -U /Z -U 0"1 m2 Z e 2 l-e' Qz/Q1 = _.--._(35) 0"2 ( m , ) UI e-U,/2 l_e-U2 for diatomic

molecules,

and

Q2/QI

0"1 ( m2 = 0" 2 m1

) 3/23n

- 6

U

i

U Ii e-U 11/2 1 _ e-

e -U2t!2

1 _ e-ull

Zi II -._-._~~ U21

(36)

for poly atomic molecules. These expressions were the starting points for the pioneering calculations of isotopic fractionation between simple gaseous molecules by Urey (1947) and Bigeleisen and Mayer (1947). The Bigeleisen and Mayer treatmen t is very useful in illustrating theoretical points such as the various expectable temperature dependencies of isotopic fractionation factors (see below) but the Urey treatment is easier to use in making calculations and the results are slightly more accurate. The partition function ratios employed in these calculations are called 'reduced' partition function ratios (sometimes designated by the letter f) and are equal to the ratios above multiplied by (mJm2)3/2. Recalling that (mJm2)3/2 is the partition function ratio for an atom (possessing translational motion only), the reduced partition functions are recognized as equilibrium constants for exchange reactions between the compound considered and the separated atoms of the isotopic element. Henceforth in this chapter, Q2/Q1 will refer to reduced partition function ratios. To put defined

equation

36 into

a more

convenient

form

for calculation,

Urey

(1947)

(37) and expanding

in terms of the 8's obtained

InQ2/Q1

=

U2i In-0"1 + EIn-+~ 0"2 i U1i

i

3}

{ coth xJcoth2xi - 1)8 + ... i

(38)

where terms higher than 8i3 can be neglected. This is the equation that Urey used to calculate values of QiQ1 for a large number of gaseous molecules. The fundamental vibrational frequencies of molecules composed of the abundant isotope are readily available in the spectroscopic literature. In rare cases spectroscopic data are available for molecules containing the heavy isotope, but normally the 'frequency shift' due to isotopic substitution must be calculated. The harmonic oscillator approximation can be used to calculate this shift but the approximation is crude and force-field models are used when available. In tabulations of calculated reduced partition function ratios, the ratios are given as either (Q2/Qy/n or as l/n(ln Q2/QJ where n is the number of atoms of the isotopic element in the compound. The number n is introduced merely to simplify use of the tables in calculating equilibrium constants for isotopic exchange reactions written in the customary way such that only one atom is exchanged between the two substances. Richet et al. (1977) made the best possible calculations of Q2/Q1 for a large number of gaseous molecules (many of geologic interest) using the latest available frequencies and taking into account modern theoretical developments including anharmonicity corrections, quantum-mechanical corrections to the rotational partition function, and rotation-vibration interactions. These authors point out that the main source of error in the calculation of isotopic fractionation factors is the uncertainty in the vibrational molecular constants. Errors as small as 1 em:' in the frequency shift of a vibration can 10

result in errors in the value of isotopic analyses. Condensed

Q'

that

are larger

than

the accuracy

limits of modern

Phases

The theory developed for perfect gases could be crudely extended to condensed phases if we could express the partition function of the liquid or crystal in terms of a set of vibrational frequencies that correspond to its various fundamental modes of vibration. Crystalline solids can be treated as giant molecules consisting of N atoms held together by elastic forces. As noted above, a poly atomic gaseous molecule has 3N _ 6 degrees of freedom, but for a system where N is very large, we can use 3N vibrational degrees of freedom and neglect the 6. Both Einstein and Debye developed models of crystalline solids in which they assumed that these 3N vibrations arise from independent harmonic oscillators. Einstein assigned a single frequency to all the oscillators whereas Debye used a spectrum of vibrational frequencies for the crystal. Their models fit experimental data for molar heat capacities very well. In fact, it is from heat capacity data that the Einstein-Debye functions are established for use in calculating Q2/QI' Minerals contain functional groups like C03, OH, or various atomic groupings of AI-O and Si-O, etc., whose 'internal' vibrational frequencies are related to corresponding frequencies in solution or in the gaseous state. The frequencies of these 'optical modes' can usually be measured by conventional (IR, Raman) optical spectroscopy, but can also be calculated from measurements of more complicated spectra and from Einstein functions. In addition to the internal vibrations there are lattice vibrations (librations) that arise from motions of the particular arrangement of atoms as a whole. These lattice, or 'acoustical modes', can be investigated with modern methods like phonon spectra and neutron scattering, but can be calculated from Debye functions as well. It is instructive to look at typical values of partition function ratios and to consider the relative contributions of the optical and acoustical modes to the total partition function ratio of a crystalline solid. The reduced partition function ratios for the optical and acoustical vibrations of Si02 (quartz), CaC03 (calcite), and U02 are given in Table 1 along with the observed or calculated frequencies of the optical vibrations. To obtain permil fractionations between two substances from data presented as they are in this table, you merely subtract the partition function ratio of one substance from that of the other. For example the fractionation between quartz and calcite at 25°C is 103.7 - 98.9 = 4.6 permil. There are (3N - 3) vibrations for the optical modes (some are degenerate), where N is the number of atoms in the unit cell, whereas for the acoustical modes there is a continuous spectrum of vibrations that is distributed over a range from zero up to a maximum frequency called the Debye cut-off frequency. As expected, the acoustical modes constitute a relatively small percentage of the total partition function ratios: 5.94 for quartz, 8.95 for calcite, and only 0.22 percent for U02. Using the simple harmonic oscillator factor of (M2/M1)1/2 to calculate frequency shifts for acoustical vibrations when they are relatively large is clearly unsatisfactory. However, for oxides of heavy atoms (Fe304, U02, Ti02, etc.), the uncertainty in this aspect of the calculation is negligible. Note in Table 1 that the relative vibrational frequencies of the three substances chosen decrease in the order quartz > calcite > > U02. This is the same order of relative lBO-enrichment among these minerals at equilibrium. This 'mass effect' holds in general for suites of related minerals wherein the nearest neighbor interactions with the isotopic element are similar (metal oxides, carbonates, etc.). However, it can be appreciated from the above considerations that replacement of one metal atom by another in such a suite of minerals will affect the vibrational frequencies of the lattice modes. If there is a major structural change in the suite that affects the atomic interactions in a significant way, as is the case for certain sulfide minerals (Hubberton, 1980), the 'mass effect' rule does not hold.

11

Table

1. Fundamental vibrational frequencies and calculated ratios"at 25"C for three different solid substances w(cw·q

Substance

1085 1080 1162 1070 881 1460 712 410 575

SiO.

CaCO,

VO.

•

reduced partition

Optical

ACQustical

Total

97.51

6.16

103.67

90.06

8.85

98.91

71.38

0.16

71:54

function

Expressed in permil as I/n In(QJQ,), where n is the number of oxygen atoms in the unit cell of the crystalline substance and Q. refers to the totally substituted species, such as Sil8Oa, etc. Data from Kawabe (1979), O'Neil et al. (1969), Hattori and Halas (1982) and reterencee therein.

TEMPERA TURE ('K)

go 000

I.

N!Q

0 0

=

0 111

18

16

14

:::;
20 (high frequencies and/or low temperatures), the function G 13

approaches

the value 1/2 and In Q2/QI is proportional

to I/T.

(2) At U < 5 (low frequencies and/or high temperatures), the function G has a slope of U /12 and In Q2/Ql is proportional to U2 and therefore to I/T2. At room temperature hc /k'I' = 5 x 10.3 erg-ern and the highest frequencies for minerals not containing hydroxyl groups are approximately 1000 cm'. Therefore U < 5 for all temperatures above room temperature and temperature dependence (2) is predicted. O-H stretching frequencies are quite large (~3000 em:'] and therefore the temperature dependence of minerals containing this group is expected to be complicated with the I/T2 proportionality coming in only at very high temperatures. At infinite temperature the fractionation factors between all substances become unity (In QA-B =

0). The I/T2 dependence of InK for isotope exchange reactions is at first surprising to those who are used to dealing with the I/T dependence that arises from the relation LlGo = -RTlnK. The answer lies in important differences in the enthalpy terms for chemical and isotopic exchange reactions. H" for chemical reactions, including the analogous partitioning of elements between minerals, is of the order of several kilocalories/mole and changes little with temperature. On the other hand, Hv for isotope exchange reactions is only a few calories/mole and decreases as a function of I/T so that InK decreases as I/T2. It must be emphasized that the theoretical considerations presented here were developed for perfect gases in the harmonic oscillator approximation. Extension of them to condensed phases requires making further and more questionable assumptions. Knowledge of the expectable temperature dependencies of isotopic fractionations among minerals and fluids over the temperature range of geologic interest is critical to the interpretation of laboratory and natural data. Fractionations do not always, or even usually, decrease monotonically to zero (a = 1) with increasing temperature. We know from theory (Urey, 1947) that the sign of the fractionation factor can change ('crossover') with changing temperature. Calculations by Stern et al. (1968) and Spindel et al. (1970), illustrated in Figure 4, elegantly demonstrate that several types of unusual temperature dependencies can arise from the harmonic oscillator contribution (the predominant contribution) to the isotopic fractionation factors between gases. These crossovers, inflections, maxima and minima are common among gases and are seen in fractionations among condensed phases as well. In several laboratory investigations of H, C, and O-isotope exchange equilibria among condensed phases, observations have been made of crossovers (e.g., O'Neil and Taylor, 1967, 1969; Muehlenbachs and Kushiro, 1974; Sakai and Tsutsumi, 1978; Matsuhisa et al., 1979; Graham et aI., 1980; Matthews et al., 1983a) as well as inflections, maxima and minima (e.g., O'Neil and Clayton, 1964; Liu and Epstein, 1984). To date all such observations have involved mineral-fluid or melt-fluid systems. Whether or not such behavior is possible in mineral-mineral systems is as yet unresolved and a matter of considerable debate (see below and Chapter 5). Because of the high vibrational frequencies associated with OH groups, unusual temperature dependence of oxygen isotope fractionations involving hydrous minerals might be expected, but such behavior has not been seen in natural or laboratory data. Kieffer (1982) suggests that crossovers would be unlikely in sets of minerals with comparable compositions like anhydrous silicates because of the regularity in behavior of vibrational modes with degree of polymerization of the Si-O bonds and the monotonic dependence of the partition function on this behavior. Expressions seen in the literature like InK = A + B/T for low temperatures and InK = A/T2 for high temperatures or a more encompassing expression like InK = A + B/T + C/T2 do not allow for unusual temperature dependencies or a return to zero after a crossover (when, for example, A and B are of opposite sign). Such expressions are useful for interpolating data over limited ranges of temperature, but could lead to serious errors if used indiscriminately to extrapolate data. The theory only tells us the temperature behavior of InK in the high- and low-temperature limits, and what these temperature limits are depend on the substances involved.

14

~"'a,l"'o

o.sj,

0.4

'" .s

e

I

I

0.008

I

0.004

'" .:

0

e

-0.4

0

-0.004

t

-0.8

I

A

1.0

1.5

2.0

2.5

3.0

CI.-HON'tj,h'\)Sr

t

-0.008

1.0

3.5

(\/

~

8 1.5

0.010

C>l,"O/ti"OO-

I

" .:

I

I

I

\

0.005

-

0

2.0

2.5 OOHOz'

3.0

3.5

trani-DONO

0.02

'"

0.01

.s

-0.005 0

C -0.010 1.0 0.020

o.o is

'" 0.010

.:

0.005

1.5

-0.005

l\

2.0

1.0

3.5

1.0

1.5

2.0

I

I 0.008

2.5

• ... OF

3.0

3.5

1'1.0;

0.004

'" .: \./

1.5

3.0

I~02/CH~boCH3

I

J

2.5

2.0

2.5

0

-0.004

\ 3.0

E

""I

-0.008

3.5

log T

Figure 4. Examples of different types of temperature equilibria. A: smooth monotonic; B: minimum and minimum and maximum with crossover; E: minimum inflection. After Stern et al. (1968) and Spindel et al.

[

1.0

F 1.5

2.0

2.5

3.0

3.5

log T

dependencies observed for calculated isotopic exchange maximum with no crossover; C: double crossover; D: and maximum with inflection; F: single crossover with (1970).

15

Chemical

Composition

All else being equal, the isotopic properties of a substance depend most importantly on the nature of its chemical bonds. The oxidation state, ionic charge, atomic mass, and electronic configuration of the isotopic elements as well as the elements to which they are bonded are important considerations. In general, bonds to ions with a high ionic potential and low atomic mass are associated with high vibrational frequencies and have a tendency to incorporate the heavy isotope preferentially in order to lower the free energy of the system. For example, consider the difference between the bonding of oxygens to the small, highly-charged Si4+ ion as opposed to the relatively large Fe2+ ion. In natural equilibrium assemblages, quartz is always the most l80-rich mineral and magnetite is always the most l80-deficient mineral and this relation has been confirmed by laboratory experiments (e.g., O'Neil and Clayton, 1964; Clayton et al., 1972; Bertenrath et aI., 1972; and Becker and Clayton, 1976). A word of caution is in order concerning the tendency of substances with higher vibrational frequencies to concentrate the heavy isotope relative to substances with lower vibrational frequencies. The fundamental vibrational frequencies of water (which are between about 1600 and 3900 crn'] are much higher than those of common minerals (whose highest frequencies are around 1000 cm'] and yet most minerals concentrate 180 relative to water at temperatures up to about 400 or 500°C at which point the fractionation can change sign. The fact is that isotopic fractionation depends not only on the absolute frequencies of the substances in question but also on the frequency shifts upon isotopic substitution. Frequency shifts calculated crudely from the square root of the inverse ratio of reduced masses (the harmonic approximation) clearly demonstrate that frequency shifts for the O-H bond (about 1 percent) are very much smaller than those (about 7-8 percent) for bonds between oxygen and elements of higher atomic mass like Si and AI. In the low-temperature region the frequency-shift dependence is dominant (Urey, 1947), and consequently water and hydroxyl groups concentrate the light isotope of oxygen relative to aluminosilicate oxygen until very high temperatures are reached. It is also well to keep in mind that certain vibrational frequencies become dominant at different temperatures and that the sign of the fractionation can change with temperature. Such 'crossovers' are equilibrium phenomena and are distinguished from 'reversals' which refer to non-equilibrium fractionations that are opposite in sign to that of the equilibrium fractionation. Taylor and Epstein (1962) and Garlick and Epstein (1967) drew attention to the regular order of 180 enrichment found in minerals of igneous and metamorphic rocks. After quartz, the alkali feldspars and plagioclase are the next most l80-rich minerals in the rocks in which they coexist. The most important corresponding chemical change in this sequence of framework silicates is the progressive replacement of Si-O bonds by AIo bonds. The isotopic properties of alkali feldspars are not measureably affected by changes in the Na" /K+ ratio either in laboratory systems (O'Neil and Taylor, 1967) or in nature (Schwarcz, 1966). Even substitution of the heavy and large Rb" ion in the feldspar structure produces no noticeable effects at 500°C (O'Neil, unpublished data). These observations imply only a weak electronic interaction between alkali ions and aluminosilicate oxygen in feldspars. The 180 differences between endmembers of the plagioclase series are relatively large (1-2 per mil) even at high temperatures (O'Neil and Taylor, 1967; Matsuhisa et aI., 1979). It is difficult to assess the importance of replacing alkali ions by alkaline earth ions in the series, but based on the previous discussion it is certainly minor in comparison to the concomitant replacement of Si by AI. Taylor and O'Neil (1977) measured a relatively large fractionation of 1.7 permil between grossularite and andradite grown in the laboratory at 600°C, demonstrating the magnitude of the isotopic effect attendant on substituting AI-O bonds for Fe-O bonds. Both Al and Fe are in the same oxidation state (III) in grandite garnets and consequently the effect is caused primarily by the difference in atomic mass between AI and Fe, and the effect this difference has on the vibrational frequencies of the mineral. This mass effect is also apparent in 34S distributions among sulfides, where, for example, ZnS always

16

Table 2. Permill80 M Mg Ca (aragonite) Ca (calcite) Mn Sr Cd Ba

Eb.

AI80(25OC)" 31.2 28.7 28.0

--26.8 26.1 24.5

fractionation

between MCO, and H20

AI80(24OC)"

Radjys (M2+)

Mass (M2+)

7.2 6.8 6.2 6.0 4.7

0.72 1.18 1.00 0.83 1.16 0.95 1.36

H

118

24.3 40.1 40.1 54.9 87.6 112.4 137.4 2QL2.

-----

• Ll.I8O = 100Ina(MCO, - H 0) Data from O'Neil et al. h969) except for hydromagnesite and aragonite (Tarutani et al., 1969).

(O'Neil and Barnes,

1971)

concentrates 34S relative to coexisting PbS (e.g, Sakai, 1957; Gavelin et al., 1960; Stanton and Rafter, 1967). Lawrence and Taylor (1972) found that Fe-rich smectites are about 3 permil depleted in 180 relative to Fe-poor smectites from the same sampling location. In keeping with the mass effect and expected on more rigorous theoretical grounds (Hattori and Halas, 1984), the generally most l80-depleted minerals in nature are found in uraninites (Hoekstra and Katz, 1956). Detailed studies have been made of the relation between chemical composition and the isotopic properties of carbonate minerals. In relation to other classes of minerals, carbonates are l80-rich because oxygen is bonded to the small, highly-charged CH ion. While important, the nature of the divalent cation plays only a secondary role in determining the overall isotopic characteristics of carbonates. Tarutani et al. (1969) investigated the effect of magnesium substitution on oxygen isotope fractionation between CaC03 and H20 at 25°C and found that 180 concentrates in magnesium calcite, relative to pure calcite, by 0.06 permil for each mole-percent MgC03 in calcite. O'Neil et al. (1969) examined the oxygen isotope relations in a series of divalent metal carbonates, the majority of these experiments being done with CaC03, SrC03, and BaC03. As 180 is CaC0 expected, the tendency to concentrate > SrC0 > BaC0 at all 3 3 3 temperatures studied (0° to 500°C). Experiments were also done with CdC03, MnC03, and PbC03 and a comparison of the permil fractionations between these minerals and water at 25° and 2400C is shown in Table 2, together with ionic radii and atomic masses. The isotope effects appear to correlate well with cationic mass, the dependence on cationic size being apparently more complicated. Size appears more important to the internal vibrational contribution of the carbonate ion and mass seems more important to the lattice vibrational contribution. The key experiments in delineating the importance of size and mass are those dealing with the carbonates of Ca and Cd because the two cations have vastly different masses and almost identical ionic radii. When these data were first taken, the same acid fractionation factor was used to correct the raw data for both CaC03 and CdC03, and the equilibrium fractionations between these carbonates and water were the same within experimental error at both 25° and 240°C. That is, CaC03 and CdC03 were originally thought to have identical isotopic properties. As a consequence the differences among the various carbonates could be attributed mainly to differences in their cationic radius, a conclusion of considerable significance to our understanding of the nature of isotopic fractionation in condensed phases. With these data it was possible to develop an equation that related the oxygen isotope fractionation factor between any carbonate and water (or between carbonates) to a function of cationic radius and temperature (O'Neil, 1963). After determinations were later made of acid fractionation factors for the different carbonates (including significantly different factors for CaC03 and CdC03) by Sharma and Clayton (1967), the original interpretation was abandoned. Unpublished experiments by the author and his colleagues now indicate that carbonates that react quickly with acid, including poorly crystallized naturally-occurring materials like certain

17

protodolomites and all laboratory synthesized carbonates, have about the same acid fractionation factor as calcite within a couple of tenths of a permil. Thus, the original in terpretation must be reconsidered. Based on calculations using a lattice dynamical model developed for carbonates, Golyshev et al. (1981) concluded that the isotopic properties of carbonates are determined primarily by the cationic radius and that the mass effect becomes substan tial only for large masses like Ba and Pb. Apropos to this question, note that the PbC03 data depart slightly from the general trend of the other data with mass. Adler and Kerr (1963) point out that PbC03 is anomalous also in its internal vibrational frequencies, which are lower than would be predicted on the basis of the ionic radius of Pb2+. Suzuoki and Epstein (1976) found that the chemical composition of the octahedral site in hydrous minerals is the dominant factor controlling their relative hydrogen isotope compositions. These authors conducted experiments at from 450° to 800°C and found the following relation for micas and amphiboles: ~D(mineral-water)

=

-22.4(10512)

+(2XAI

-

4XMg

-

68XFe)

(42)

where ~D is the permil fractionation of deuterium between the mineral and water, and X is the mole fraction of the cations in six-fold coordination. Details of this relation are in dispute. For example, mineral-water hydrogen isotope fractionations determined in laboratory experiments are vastly different for the minerals epidote, zoisite, and diaspore whose OH groups are bonded to AI (Graham et aI., 1980) and for brucite (Satake and Matsuo, 1984) and serpentine (Sakai and Tsutsumi, 1978) whose OH groups are bonded solely to Mg. Nonetheless there is abundant evidence from analyses of natural samples that the presence of Fe in octahedral sites can significantly affect the hydrogen isotope properties of micas and other hydrous minerals (e.g., Taylor and Epstein, 1966; Kuroda et aI., 1974; Brigham and O'Neil, 1985). All else being equal, it is generally true that the higher the Fe/Mg ratio in a hydrous mineral, the lower is its deuterium content. For example, muscovite always concentrates deuterium relative to biotite or amphibole in natural equilibrium assemblages. When discussing the relation between chemical composition and hydrogen isotope properties of hydrous minerals, one must keep in mind that hydrogen is always bonded to oxygen' in these minerals. Thus although seemingly secondary because of its location, the nature of the element bonded to oxygen in OH groups profoundly affects the vibrational frequencies associated with OH. This is in contrast to the secondary role played by cations (relative to the dominant effect of carbon) in determining the oxygen isotope properties of carbonates discussed above. Hydrogen is extensively hydrogenbonded in some minerals and these effects will be discussed in the section below that deals with structure. Crystal

Structure

The crystal structure of minerals can influence their isotopic properties to an extent that depends on how different the atomic interactions (and their associated vibrational frequencies) are between the various structural forms. Structural effects are minor in importance compared to those arising from the chemical bonding discussed above, but are surprisingly large in some cases. On the basis of limited experiments and calculations, the heavy isotope apparently concentrates in the more closely-packed or well-ordered structures. As mentioned above, OH groups in the minerals brucite and serpentine are coordinated solely to Mg and there is no evidence of hydrogen bonding in these minerals. Nonetheless the hydrogen isotope behavior of these minerals is quite different. Satake and Matsuo (1984) explain this observation in terms of a structural effect arising from distortion of the Mg-octahedron in the serpentine (clinochrysotile). The Mg-OH bond length is shorter in serpentine than in brucite where there is no such distortion. The 180 and D permil fractionations between ice I and liquid water at O°C are 3.0 and 19.5, respectively, and arise chiefly from differences in the degree of hydrogen bonding (order) and lattice vibrational effects (e.g., O'Neil, 1968). The 180 fractionation between D20 and H20 is over 15 permil at 25°C (Staschewski, 1965) implying a more 18

ordered structure for D20, and this is in agreement with many other lines of evidence concerning the structure of liquid D20. Because these are fairly large isotope effects relative to experimental error of isotopic determinations, an isotopic fractionation technique could be used to study bonding characteristics of the various forms of ice. The 180 permil fractionations between aragonite and calcite at 25°C is rather small at 0.5-0.6 (Tarutani et aI., 1969; Golyshev et aI., 1981) The 13C fractionation at this temperature is considerably larger at 1.8 (Rubinson and Clayton, 1969) or 4.0 (Golyshev et al., 1981). It is noteworthy that the carbon atom exhibits the greater isotope effect. Enrichments of the heavy isotopes in the denser aragonite relative to calcite have also been observed in marine and fresh water pelecypods (Keith et al., 1974). In the series of alkaline earth carbonate examined by O'Neil et al. (1969), no consistent differences between the isotopic behavior of hexagonal and orthorhombic carbonates were observed. In the series of sulfides examined by Hubberton (1980), structure apparently plays a significan t role in determining the isotopic properties of sulfide minerals. Several observations indicate that crystal structure or even the presence of structural water is not important to the oxygen isotope properties of silica species. Unpublished experiments by the author indicate that there is no measureable fractionation between cristobalite and quartz at 500°C. Even at very low temperatures no significant structural effect is present. For example, radiolaria and authigenic quartz formed at low temperatures from ocean water have 8180 values in the relatively narrow range of 36-39 permil (Mopper and Garlick, 1971; Savin, 1970; Knauth and Epstein, 1976). Although possibly fortuitous, the oxygen isotope fractionation curve for the diatom-water (Labeyrie, 1974) and quartz-water (Clayton et al., 1972) systems coincide at low temperatures. Also the isotopic relations among the diagenetic silica minerals biogenic opal, disordered and ordered cristobalite and microcrystalline quartz determined by Murata et al, (1977) indicate similar isotopic characteristics for all these forms. Shiro and Sakai (1972) calculated a reduced partition function ratio for f)-quartz at the transition temperature (573°C) that is about 0.8 permil smaller than that of a-quartz, the more dense crystal structure. Kawabe (1978) calculated an even larger value of 1.5 permil for the a-f) effect. However, these differences are not observed in the laboratory studies of the quartz-water fractionation (Clayton et al., 1972; Matsuh isa et al.,1979). One of the largest isotopic effects associated with structure is found in the carbon system. Although only calculated and not yet verified by laboratory experiment, the fractionation between graphite and diamond ranges from a large value of 11.5 permil at O°C to the still measureable value of 0.4 permil at 1000°C (Bottinga, 1969). As with other cases, the heavy isotope concentrates in the more dense phase. The mineral pectolite provides another case of a very large isotope effect that is presumably structurally controlled. This mineral has the uniformly lowest 8D values (-429 to -281) of any terrestrial mineral (Wenner, 1979). The octahedral cation composition of pectolite, Ca2NaH(Si03)3' cannot account for the unusually low 8D values, and the strong hydrogen bonding present within this mineral is probably responsible for the effect. The role of hydrogen bonding in affecting hydrogen isotope properties of minerals is discussed by Suzuoki and Epstein (1976) and Graham et al. (1980). The latter authors suggest that the shorter the O-H--O bridge in the hydrogen bonds of the mineral, the lower will be its deuterium content. Pressure Because the change in molar volumes of solids on isotopic substitution is small, typically hundredths to tenths of a percent, it has generally been assumed that the effect of pressure on isotopic fractionation between minerals is negligible. However, Joy and Libby (1960) suggested that the oxygen isotope fractionation between CaC03 and Hp might be measureably pressure dependent at low temperatures. This system, or any mineral-water system, could be particularly sensitive to pressure effects because isotopic substitution of the centrally symmetric oxygen atom in H20 should not produce a volume change sufficient to offset the volume change of the mineral. From another point

19

of view, pressure effects might be expected for mineral-gas or melt-gas systems because the isotopic properties of the gas might change drastically with big density changes while those of the melts or minerals remain unaffected. The pressure effects calculated by Joy and Libby (1960) were not observed in the experiments of Clayton et al. (1975) who measured the oxygen isotope fractionation between CaC03 and H20 at 500°C from 1 to 20 kbars. Clayton et al. (1975) point out that root-mean-square values of C-O bond lengths (depending on vibrational amplitudes) were used in the calculations of Joy and Libby, and if mean values of the C-O distance are used, the calculated pressure effects are markedly less, in agreement with experiment. Because vibrations are anharmonic, the species containing the lighter isotope has a longer mean bond length (see Fig. 1). For an oxygen isotope exchange reaction between two phases that have comparable changes in molar volumes on isotopic substitution (e.g., two minerals), Clayton (1981) suggests that about 90 percent of the effect on each phase would cancel out. On the basis of reasonable estimates of molar volume changes, he further suggests that pressure effects on oxygen isotope fractionation should be less than about 0.1 permil at 20 kbars or less, that is, negligible for crustal rocks. Considering that the abundance of 180 is only about 0.2 percent in minerals, the possibility of pressure effects becomes even more remote. Pressure effects have been invoked to explain unusual oxygen of some kimberlitic eclogites (Garlick et aI., 1971) and olivine from rocks (Pinus and Dontsova, 1971). From the above discussion it time that' factors other than pressure are probably responsible for isotope compositions.

isotope compositions a suite of ultramafic would appear at this these unusual oxygen

Insufficient knowledge of the pressure that prevailed during geological processes often places constraints on the applicability of the chemical and physical thermometers used by petrologists. In this respect, stable isotope fractionations are particularly useful in geothermometry because of the apparent lack of dependence on pressure.

LABORATORY Two-direction

DETERMINATIONS

OF ISOTOPIC

FRACTIONATION

FACTORS

Approach

This is the method of choice for determining isotopic fractionation factors in the laboratory but is applicable only to true exchange reactions (Appendix 1). It is analogous to 'reversing reactions' in experimental petrology and is the only method by which the attainment of equilibrium can be unambiguously demonstrated. Measured fractionations at the end of an experiment are proved to be equilibrium fractionations by the fact that the same value is arrived at starting on opposite sides of the equilibrium distribution of isotopes. Exchange reactions afford the unique advantage of having the same rate-controlling factors for both approaches to equilibrium inasmuch as the reactant chemicals are identical to the product chemicals (except in isotopic composition). The majority of hydrogen and oxygen isotope experiments have been done with water as the exchange medium using the technique developed by Clayton (1961). This technique consists of sealing-in small amounts (10-20 mg) of powdered mineral with larger amounts of waters (typically 200 mg) of different isotopic compositions in gold or platinum capsules. The capsules are placed in a conventional hydrothermal apparatus and held at temperature and a confining pressure of normally 1-2 kbar for periods of days to months. If piston cylinders are used, the amounts of mineral and water are much smaller (5-10 mg each) and the pressures are typically 15-20 kbar. The two-approach principle is illustrated in Figure 5, using as an example the exchange reaction between quartz and water at 500°C. The initial 8180 value of quartz is + 10.0 and those of waters A, B, and Care -5.0, +5.0, and +15.0, respectively. Initial values of .6.180(q_w), defined as 8180(quartz) - 8180(water), are accordingly +15.0, +5.0, and -5.0, respectively. These values change with time and are shown to approach the

20

Table 3. Data. for Experiments (see text)'.

1-4 dealing with laboratory

calibration

studies

T ("0)

Substa.nce

Weight (mg)

618()lAl'lai

618()su.l

500

calcite water-l

20.3 199.0

14.48 10.42

13.32 (10.48)

2

500

calcite water-2

20.2 195.5

14.48 26.21

28.16 (25.44)

3

600

quartz water-3

15.6 192.4

9.60 -6.43

-2.74 (-5.92)

4

600

quartz

18.2 200.0

9.60 20.62

17.76 (20.24)

Experiment

numbers in parentheses

water-4

calculated by material balance

c w

15 k-

C>

z




7

J:

'"

x w

'",._

Q)

3

-c

-

I

..

-1 I

a: «

:J


feldspar> biotite> magnetite. This is the order found for most granites, but sometimes the feldspar is isotopically heavier than the quartz (as in certain plagiogranites), and in other cases, ,6.l80(q_f) will have high values like 5 or 6 (When values like 1.3 to 1.8 are normal). Such granites have interacted with extraneous fluids at low and high temperatures, respectively, and the various minerals have exchanged to different extents with these fluids effecting an obviously disequilibrium assemblage (Chapters. 2, 3, 11). In a rock containing n minerals, there are n - 1 independent isotope thermometers available if the appropriate fractionation factors are known. Concordancy among these temperatures is an excellent test for isotopic equilibrium in the rock. This test is exactly analogous to the age concordancy test when dating a rock by more than one method. It may be that two or more 'refractory', or 'non-labile', minerals (like pyroxene or magnetite) have retained their original isotopic compositions and a record of the formation temperature of a rock while others (like feldspar) may have lost this record through retrograde isotopic exchange or exchange during a later event. Javoy et al. (1970) presented a graphical procedure called the 'isotherm method' that readily indicates both temperatures of equilibration and the presence of disequilibrium isotopic relations. It is based on one of the equations mentioned above that are commonly used to relate temperature and fractionation factors (between substances x and y) over limited ranges of temperature: 1031nO'x_y= Ax_y(1061'""2)+ Bx_y , where A and B are empirically

determined

constants.

(48)

Rearranging,

1031nO'x_y- Bx_y = Ax_y(1061'""2)

(49)

One mineral, normally the heaviest mineral in the rock (often quartz), is chosen as a reference mineral, R. This mineral is then paired successively with every other mineral M, in the assemblage, and values of 103InO'R_M'AR.M, and BR_M are tabulated. Plotting the function on the left hand side of equation 49 agaInst Ax_ shlould yield a straight line that passes through the origin if the minerals are in isotopi/equilibrium. Disequilibrium is indicated when the points are not co-linear. The temperature is calculated from the slope 1061'""2. Full exploitation of the method requires precise knowledge of the constants A and B, and, unfortunately, these constants are in a state of revision at the present time. An example of the kind of plot obtained when a self-consistent set of constants (Bottinga and Javoy, 1973, 1975) is applied to analyses of granitoid rocks is shown in Figure 10. Even if the temperatures are not correct because the constants may be in error, the method is useful in identifying equilibrium assemblages. Present

Status

The subject of stable isotope thermometry, particularly oxygen isotope thermometry, has been reviewed extensively (e.g., Clayton and Epstein, 1961; Bottinga and Javoy, 1973, 1975; Deines, 1977; Clayton, 1981). Despite disagreements among fractionation factors determined by different techniques and in different laboratories, even imperfectly known fractionation factors can be judiciously employed in certain cases to obtain meaningful geologic information. Isotopic fractionation factors between many important geologic fluids are known very well and agreement between calculated and experimentally-determined values is excellent. Henley et al. (1984) compiled such data and constructed fractionation curves for systems of potential use as geothermometers for hydrothermal systems (Fig. 11). Problems abound in both theoretical and experimental aspects of isotope thermometry, but interest remains high in resolving them because of the great potential of the method. Oxygen isotope fractionations between several common minerals and

31

8rx

en" Ix

"

e .!: 0 0 0

:~

t

810TlT'/

570°C

4 520°C

USCOVITE

K-FELDSPAR

0

QUARTZ

0

2

4

A

6

o-x

Figure 10. Isotherm plot for granodiorite specimen from the Papoose Flat pluton temperatures and presence of non-equilibrium assemblages are determined. Data from constants A and B from Bottinga and Javoy (1973, 1975).

40

illustrating how Brigham (1984);

1000 Ii)

c: 0

..e 0

800

-

-£

30

0

N

r.

"c..:

t1

s o

-

20

N

r. r.. o

o o

0

e E

10

0 0 0

o -4

TEMPERATURE

Figure 11, Pertinent isotopic fractionation After Henley et al. (1985)

°c

curves for use in estimating

32

tempera.tures of geothermal

fluids.

water have been determined in a single laboratory (University of Chicago) using the most advanced techniques available. The data look excellent and are generally internally consistent, but the inferred fractionations between minerals imply formation temperatures for natural assemblages that are often too low at high temperatures and too high at low temperatures compared with other temperature estimates. For example, L\180(quartz-alkali feldspar) is typically about 1.5 permil in granitic rocks. Using the Chicago fractionation curves, this fractionation would indicate a formation temperature of something like 400°C. If the curves are indeed correct, there is the important implication that all such rocks have undergone retrograde isotopic exchange down to this temperature. There are several arguments that would suggest that this is unlikely, although rapid diffusion of some oxygen-containing species in certain minerals like feldspar could possibly account for the effect (Giletti, 1986). Results of recent experiments by the Chicago group using calcium carbonate as the exchange medium are in conflict with their earlier data using water as the exchange medium (Mayeda et al., 1986). Although not yet resolved, the problem may rest solely with the quartz-water fractionation. There is an assumption made in all previous discussions of oxygen isotope thermometry that isotopic fractionations between anhydrous silicates must decrease monotonically to zero with increasing temperature. No provision has been made for crossovers or other features of fractionation curves that have been noted above. This assumption influences dramatically how natural and laboratory data are extrapolated and then interpreted. It is clear that many sets of data, if extrapolated with some normal smooth function, would not go directly to zero on a standard plot such as Ina 2 versus T- . Our knowledge of the isotopic behavior of condensed phases at high temperatures is incomplete, and it is wise to keep an open mind about the possible shapes of fractionation curves for such systems. Over the last several years many measurements have been made of isotopic fractionations between natural materials whose formation conditions are known very well in the hopes of calibrating systems that have not been investigated in the laboratory. This method has merit but is fraught with obvious uncertainties. No attempt will be made to evaluate this method in this chapter.

CONCLUSIONS The power of stable isotope geochemistry in addressing so many geological problems has justified the enormous and difficult task of determining equilibrium isotope fractionation factors between the common geologic minerals and fluids. An attempt has been made to compile, uncritically, most of the H, C, 0, and S isotope fractionation factors that have been either calculated or experimentally determined in the laboratory. The systems and references are given in Tables 4 and 5. Various authors have critically evaluated such determinations and constructed fractionation curves for their systems of interest (e.g., Fig. 11). Inasmuch as the results of some of the oxygen isotope calibration experiments may be in error because of problems associated with the use of water as the exchange medium, we can look forward to the results of future experiments performed in nonaqueous media. At present there is considerable interest among several research groups in conducting rate and equilibrium experiments in a number of important systems (including melt-vapor systems) at very high temperatures. The fractionation curves for some systems, particularly gases, are known very well. In fact fractionations between the common simple gaseous molecules can now be calculated with extreme precision and for the entire range of geologic interest. It is highly desirable to have available reliable methods of calculating fractionation factors in order to avoid the kinds of problems encountered in attempting to determine them in the laboratory. Our understanding of isotopic fractionation among condensed phases is imperfect but we now have fairly good

33

I'able 4. Compilation of calculated and experimentally isotope fractionation factors.

determined

H dro en System

Ox

Reference

;erpentine-H2O

Saka.i a.nd Tsutsumi

,pidote-H2O

Graham

oxygen and hydrogen

(1978)

en

System

Reference

Quartz-H2O

Clayton et al. (1972)

et al. (1980)

Shiro and Sakai (1972)

Jlinozoisite-H2O

do

Bottinga

~oisite-H20

do

Becker and Clayton (1976)

Suzuoki and Epstein (1976) .!useovite-H2O

Matsuhisa

do

Lloyd (1968)

Barite-Hp

Robinson and Kusakabe

Albite-H2O

O'Neil and Ta.ylor (1967)

Chiba et al. (1981)

)hlorite-Hp

Graham

(aolinite-H2O

Liu and Epstein (1980) Lambert

et al. (in press) and Epstein (1980)

Irucite-H2O

Satake and Matsuo (1984)

rronarH2O(I)

Matsuo et al. (1972)

12O(I}HP(v)

Bottinga Anorthite-H2O

Bottinga Matsuhisa Carbonates-H2O

Rennow (1970)

Kakiuchi

and Friedman

and Matsuo (1979)

Pyroxene-H2O

et al. (1979) a.nd Clayton (1966)

O'Neil and Taylor (1967) and Javoy (1973)

Matthews Bottinga

Matsuo et al. (1964)

et al, (1983) and Javoy (1973)

Garnet-H2O

Ta.ylor (1976)

Biotite-H2O

Bertenrath

Taylor and O'Neil (1977)

Weston (1955)

12O(s)-HP(I)

Northrop

Bottinga

(1975)

Merlivat and Nief (1966)

IP(s)-HP(v)

and Javoy (1973)

O'Neil et al. (1969) Muscovite-H2O

Majzoub (1971) Stewart

et al. (1979)

O'Neil and Taylor (1967)

Merlivat et al. (1963) (1968a)

Posey and Smith (1957)

and Friedrichsen

Kuhn and Th urkauf (1958) Merlivat and Nief (1966)

Bottinga Rutile-Hp

O'Neil (1968)

(1975)

and Javoy (1973)

Addy and Garlick (1974)

Arnason (1969)

Matthews

(1972)

120(s)-2.5 M NaCI

Stewart

Matthews

et al, (1979)

IsO+-H2O

Heinzinger and Weston (1964a)

Illite-Hp

James and Baker (1976)

12O(v}CH.

Bottinga

Suess (1949)

Zoisite-H2O Scheelite-H2O

Matthews

12O(v}H2(g)

Bottinga

(1969a)

Powellite-H2O

do

Bottinga

(1969a)

U02-UOs-H2O

Hattori

Horibe and Craig (unpub.)

Magnetite-H2O

Becker (1971)

)H.(g}H2(g) Ip(struc.}HzO(I)

(1964) (1969a)

et al. (1983)

Wesolowski and Ohmoto (1986) and Halas (1982)

Kuroda et al. (1982)

Bertenrath

Galley et al. (1972)

Bottinga

et al. (1972) and Javoy (1973)

Hydromagnesite-

do

Ip(I}H2S(g)

H2O Mg-calcite-H2O

Tarutani

Airabilite-H2O

Stewart (1974)

HzO(s}H2O(I)

O'Neil (1968)

lorax-H2O

Matsuo et al. (1972) H20-2.5 M NaCI

Stewart (1975)

melt

iaylussite-H2O

Taylor and Westrich (1985)

O'Neil and Barnes (1982)

Heinzinger and Weston (1964b)

IzO(v)-rhyolite )H--H2O(I)

(1975)

and Javoy (1973)

Matsuhisa

Ehbalt and Knott (1965) Bottinga

et al. (1979)

Anhydrite-H2O

do

liotite-H2O

and Javoy (1973)

et al, (1969)

Weston (1955)

do

)opper-sulfate-H2O

Heinzinger (1969)

HP(s}HzO(g)

Matsuo and Matsubaya

:rystal hydrates-H2O :ypsum-Hp

Barrer and Denney (1964)

Hp+-HP(I)

(1969) Thornton

Fontes and Gonfiantini

OR-H2O(I)

[2(g}HP(I)

Rolston et al. (1976)

CO2(g)-D2O

Staschewski

12O(s)-D2O(v)

Matsuo et al. (1964)

CO2(g)-H2O

do

(1962)

do Green and Taube (1963)

(1967)

(1964)

O'Neil and Adami (1969)

JHs-HP-CH.-HF'-

Bottinga

HCN-H,tl-HCl-

34

and Craig (1969)

Table 4 (continued). Hvdrozen System

Oxvzen

Reference

System

Reference

Richet et al. (1977)

Blattner

(1973)

Horibe et al. (1973) O'Neil et al. (1975) Bariac et al. (1980) Brenninkmeijer

et al. (1983)

CO2(g)-C02(I)

Groots et al. (1969)

CO2(g)-C02(aq) °2(g)-°2(aq) Mirabilite-H20

Kroopnick

Gypsum-H20

Gonfiantini

Vogel et al. (1970) and Craig (1972)

Stewart (1964) and

Fontes (1963) HgP0.

liberated

CO2-Carbonates

Sharma and Clayton (1965) Rosenbaum and Sheppard

Series of Carbonates

(1986)

Golyshev et al. (1981)

CO2-CO·OCS-SO.NO-N20-S02 N02-02-H.o

Table 5. Compilation of calculated isotope fractionations.

and experimentally

Richet et al. (1977)

determined

Sulfur System

Carbon

Reference

HSO.--S-H2S

Oana and Ishikawa (1966)

FeS2-ZnS-PbS-S FeS2-ZnS-PbS

Kajiwara

S02-S-H"s FeS2-HSO; ZnS-HS-PbS

Grootenboer

System

Reference

Calcite-HCO.-

Emrich et al. (1970)

(1969)

Rubinson

et al. (1969)

Aragonite-HCO.

and Clayton (1969)

do

Grinenko and Thode (1970)

Aragonite-Calcite

Nakai (1970)

Gaylussite-COt

Schiller et al. (1970)

Trona-H20

Matsuo et al. (1972)

Calcite-Grap hite

Bottinga

FeS2-CuFeS2FeS-ZnS-PbS

sulfur and carbon

Kajiwara

and Krouse (1971)

FeS .. PbS-S

Solomons (1971)

S02-S-H2S Zns-HS'-PbS

Thode et al. (1971) Kiyosu (1973)

ZnS-PbS

Czamanske

do Matsuo et al. (1972)

Diamond-Graphite CO2(g)-CO.(I) HCO.--(aq)-C02(g)

(1969a)

do Grootes et al. (1969) Malinin et al. (1967) Mook et al. (1974)

and Rye (1974)

Emrich et al, (1970)

Elcombe and Hulston (1975)

CO.(aq)-C02(g)

Thode et al. (1965)

HSO;-S-H2S

Robinson (1973)

CO2-CH.

Bottinga

PbS-S

Puchelt and Kullerud (1970)

CO2-Diamond

H"s(g)-H2S(aq)

Sharan et al, (1974)

CO2-Calcite

S02(g)-H2S(I)

Sakai (1957)

SO;'"-(aq)-H2S(g) S2--S02(g) HS--S2SO.2--S2

Baertschi

(1957)

Vogel (1959)

Thode et al. (1977)

Northrop

Sakai (1968)

Bottinga

do

and Clayton (1966) (1968b)

Emrich et al. (1970)

do

Graphite-CH.

Bottinga

Miyoshi et al. (1984)

CO2-tholeiite

Bi"s.-so

Bente and Nielson (1982)

Series of Carbonates

Series of Sulfides

Bachinski (1969)

CO2-OCS-HCN-CS2

SO.-S02-0CS-CS2CS-S2-H"s

(1964)

do

CH.-CO-CS Richet et al. (1977)

35

melt

(1969a)

Javoy et al. (1978) Golyshev et al. (1981) Richet (1977)

methods of making empirical calculations of fractionation factors (e.g., Hulston, 1978; Kieffer, 1982). The methods await testing with forthcoming modern spectral data including those taken on synthetic minerals containing a significant amount of the heavy isotopes.

ACKNOWLEDGMENTS The author is indebted to Bob Clayton, Sam Epstein, Hugh Taylor, Yan Bottinga and Richard Becker for many years of illuminating discussions of the subtleties of isotopic fractionation. Helpful comments on earlier versions of this chapter were made by Richard Becker, Bill McKenzie, John Valley, and Tosh Mayeda. Special thanks are given to Anita Grunder, Pat Dobson and John Chesley for their long-suffering instructions on the use of the Stanford Vax system used in preparing this manuscript.

36

38

39

40

Chapter 2

David R. Cole & H. Ohmoto

KINETICS

of ISOTOPIC

TEMPERATURES

EXCHANGE

at ELEVA TED

and PRESSURES

INTRODUCTION Isotopic disequilibrium provides an opportunity to investigate the temporal relationships in geologic systems. However, a knowledge of the rates and mechanisms of stable isotope exchange is needed for the interpretation of isotope disequilibrium processes in nature. Recent advances in analytical techniques (e.g., the ion microprobe), coupled with new experimental rate data, permit the quantification of time-dependent isotopic behavior preserved in the rocks. Unfortunately, our understanding of isotopic exchange kinetics is meager compared to our knowledge of the thermodynamics of isotope exchange reactions (see Chapter 1 by O'Neil). Nevertheless, our knowledge of the kinetics of stable isotope exchange has increased significantly in the last 10 years. Field studies have revealed the presence of mineral assemblages clearly out of isotopic equilibrium (e.g., see Taylor and Forester, 1979; Gregory and Taylor, 1981; Criss and Taylor, 1983) or yielding isotopic geothermometer temperatures inconsistent with phase-equilibrium evidence. Isotopic disequilibrium occurs most commonly in plutonic and regionally metamorphosed rocks wherein retrograde exchange of oxygen (and commonly hydrogen) has taken place. For example, Anderson et al. (1971) calculated substantially lower plagioclase-magnetite oxygen isotope temperatures in mafic intrusions, compared to the solidus temperatures for the composition investigated. They attributed these results to post-crystallization exchange at subsolidus temperatures. Extreme examples of isotope disequilibrium have been observed where convective hydrothermal fluids have interacted with shallow intrusive bodies (e.g., see Taylor and Forester, 1971,1979). Typically, feldspars undergo continuous oxygen isotopic exchange during subsolidus rock-water interaction, whereas quartz and pyroxene typically retain their magmatic isotopic signature (e.g., Criss and Taylor, 1983; Taylor and Forester, 1979). The foregoing observations concerning retrograde oxygen isotopic exchange and disequilibrium are not unique to high temperature systems. Lawrence and Kastner (1975) observed significant oxygen isotope exchange in detrital feldspars deposited with carbonates (Precambrian to Pennsylvanian). They found no evidence of recrystallization, and invoked a "diffusional" mechanism for isotopic exchange. Conversely, Yeh and Savin (1976) observed a relationship between particle size and the extent of oxygen isotopic exchange between detrital clays and seawater, and proposed that the degree of equilibration was a function of the extent of chemical reaction between the clays and seawater (i. e., the degree of recrystallization of the clays). Clayton et al. (1978) concluded that oxygen isotope exchange in silt-size quartz was sufficiently slow over a period of many millions of years of shallow burial or weathering to permit the oxygen isotope ratio of this mineral to be used to trace the origin of eolian and fluvial additions of minerals to continental soils and pelagic sediments. These are but a few examples of studies that demonstrate the ex41

istence of isotopic disequilibrium in the rock record. Collectively, these and other numerous studies not cited indicate the following: (1) isotopic disequilibrium can occur at high as well as at low temperatures; (2) the rates of isotopic exchange range from slow to moderate, such that significant isotopic changes may occur subsequent to initial isotopic equilibration; (3) different minerals exhibit varying susceptibilities to retrograde exchange (e.g., feldspars versus quartz); and (4) the mechanisms of isotope exchange are varied and depend on the geochemical conditions at the time of interaction. This chapter presents an overview of the kinetics of isotope exchange reactions. We emphasize the kinetics of high-temperature/high-pressure behavior, and avoid discussion of kinetic isotope effects (see Chapter 1). Our intent is to describe the experimental and computational methods used to obtain rates of isotope exchange for a variety of possible exchange mechanisms. First, we describe a generalized rate law for isotope exchange reactions and discuss some of the techniques used to estimate rates. We then examine the rates and mechanisms of selected homogeneous reactions, i.e., in the gas phase or solutions. Finally, we detail rates and mechanisms of isotope exchange between solids and either fluids or gases (heterogeneous systems). For examples of the application of isotope rate data to quantifying geologic systems, we refer the reader to the following comprehensive studies: homogeneous systems - Ohmoto and Lasaga (1982, H2S-SO.), Chiba and Sakai (1985, H20-SO.), Giggenbach (1982, CO2 -CH.); heterogeneous systems Bottinga and Javoy (1975), Norton and Taylor (1979), Parmentier (1981), Cathles (1983), Cole et al. (1983), Giletti (1986). In addition to the tutorial aspects, we tabulate rate data for isotope exchange relevant to geologic systems.

BASIC CONCEPTS

IN ISOTOPE EXCHANGE

REACTIONS

Evaluation of rates from isotope exchange experiments depends on several considerations discussed below, including: (1) the similarities and differences between homogeneous and heterogeneous systems, (2) a rate law applicable to many homogeneous or heterogeneous systems, (3) the relationship between the overall rate of isotope exchange and the true rate constant, and (4) the definition and determination of diffusion coefficients in mineral-volatile systems. Homogeneous

versus Heterogeneous

Reactions

Isotope exchange among the various geologic phases - i.e., solids, fluids, and gases - can be conveniently divided into two categories: homogeneous and heterogeneous. Homogeneous reactions may be defined for the purposes of this discussion as reactions in which isotopic exchange occurs between reactants that are uniformly distributed in the same macroscopic phase. Examples are the sulfur isotope exchange between SOa- and H2S in an aqueous solution, oxygen isotopic exchange between water amd dissolved SOa -, and carbon isotope exchange between gaseous CO2 and CH.. In contrast, heterogeneous reactions involve species present in different macroscopic phases, such as the exchange of sulfur in H2S with that in a sulfide mineral, or the exchange of oxygen or hydrogen between water and a mineral. The

rates

of

isotopic

exchange

in homogeneous

42

and

heterogeneous

[hom

Ie.; c-,

~

~ I

Reactants

UJ

Product>

Reaction

Figure 1. Schematic reaction (solid line) (1985) •

co-ordinate

representation of the transition state theory of a homogeneous and a heterogeneous reaction (dashed line). Taken from Gasser

systems are sometimes determined by the rates of the actual chemical steps, i.e., by the rates at which bonds are broken and made. They may also be determined by transport phenomena, such as diffusion and flow, and sometimes by all of these processes. Although the mechanisms may vary significantly, the principles of collision and activation apply as much to heterogeneous reactions as to gas reactions and reactions in aqueous solutions (Richardson, 1974). The rates of homogeneous gas reactions increase temperature according to an equation of the type

exponentially

with

-E /RT

k

=

A e

a

o

(1)

where k is the rate constant. The quantity E is known as the activation energy and A , the pre-exponential facto!, is a term which is only weakly dependent 8n temperature. For molecules of a gas (or in solution) to react isotopically with one another, they must come together, temporarily forming some kind of complex which then breaks up to give reaction products. Although there may be a number of different paths by which two reactants can give products, we may picture the way in which the energy of one path varies along a so-called reaction coordinate leading from reactants to products (see Fig. 1 from Gasser, 1985). This figure compares the energy requirements for a gas-phase bimolecular reaction in the absence of a catalyst (homogeneous) with the energy for the reaction taking place on a catalyst (heterogeneous). The highest point on each curve is the transition state. The true activation energy for the heterogeneous reaction is from the minimum representing the energy of the adsorbed reactants to the surface transition state. Note that there are typically small activation energies for catalyzed reactions (E ) het 43

and for formation of the transition state on the surface. In the case of the heterogeneous reaction, excitation to the surface transition state is assumed to be the rate-determining step (see Lasaga, 1981c, for more details). It follows from this discussion that heterogeneous reactions (e.g., surface reactions) involving isotopic exchange may follow a complex path that can include: (1) transport to the surface, (2) physical adsorption onto the surface, (3) surface reaction (e.g., chemisorption or formation of a new phase) with subsequent isotope exchange, (4) transport into the solid (e.g., a moving reaction front, vacancy diffusion, etc.) with further isotopic exchange, (5) counter-diffusion of the exchanged species out of the solid, and (6) desorption. As complicated as this may appear, reactions in homogeneous systems can be no less complicated, particularly when one considers the myriad of reactions that can occur between various gaseous or aqueous species containing the isotope of interest. Rate Law for Isotope Exchange

Reactions

An isotopic exchange reaction can be defined as a chemical reaction in which the atoms of a given element interchange between two or more chemical forms of the element. McKay (1938) was the first to derive a law for the simple case of one exchangeable atom (radioactive) per molecule. Since then, others have published similar derivations (e.g., Duffield and Calvin, 1946; Harris, 1950; Myers and Prestwood, 1951; Alberty and Miller, 1957; Muzykantov, 1980; and Friedlander et al., 1981). We derive below Northrop and Clayton's (1966) rate law, which is applicable to a variety of systems involving exchange of two stable isotopes (e.g., 180 and 160, and 3·S and 32S) through either homogeneous or heterogeneous reactions. Because there are significant differences in the nature of the isotope exchange between homogeneous and heterogeneous systems (and even within them), it should be kept in mind that the derivation presented below will need to be adjusted to fit the particular application at hand. The isotopic relationships that are pertinent to the interaction between two chemical species (AX and BY) and which are key to the development of a generalized rate equation for a closed system are given in the following schematic bar graph: Species BY (initial)

Species AX (initial)

• X~ X~

). X2

• •

e
collide with a mineral surface forming a surface complex, with Y2 atoms leaving the surface into the solution, then from equation 7 we can have

is the Xl concentration

where ~

in solution,

1

48

(Y2/Y)

is the mole

frac-

tion of Y 2 in the solid, and A is the specific surface area of the solid. The probability of attaching Xl to the surface through collision of a fluid with the surface is proportional to the product of these three terms. The true rate constant, k , incorporates how the collision f occurs and how the activation barrier is overcome (A.C. Lasaga, pers. comm., 1986). Determination

of D, the Diffusion

Coefficient

The rate of isotope exchange under certain geological conditions depends on the type and rate of diffusion of the isotope-bearing species in the system - e.g., H20 or CO2 into a crystal (a heterogeneous process). In practice, diffusion in minerals occurs both by volume diffusion through regions of good crystal structure and by a variety of short-circuit diffusion mechanisms where atoms or molecules move along paths of easy diffusion (see Fig. 3). These easy diffusion paths may involve surface or line defects in the crystal, such as grain boundaries, dislocation lines, or fast diffusion directions on free surfaces (Manning, 1974). Similarly, volume diffusion mechanisms in crystals usually depend on the presence of point defects, such as vacancies or interstitial atoms (see Lasaga, 1981b, for details on the relationships between defects and diffusion). The rate of diffusion is represented by D, the diffusion coefficient, which is defined as the proportionality constant between the flux of material, J, and a gradient, as in Fick's first law

ac ax

J = -D(-)

(16)

'

where C is concentration (e.g., 180), x is distance, and J is the flux of atoms which cross 1 cm2 / sec of a surface oriented perpendicular to the diffusion direction x. The minus sign is present to make J positive, because C decreases with increasing x in the direction of diffusion. Equation 16 can apply only to the special case wherein the concentration gradient is exclusively a function of the direction x. In the general case where gradients exist in three perpendicular directions (i.e., along x, y, and z coordinates), Fick's law assumes the form J

=

(17)

-DVC

Fick's second law may be derived from equation 16 by considering the variation of J with x (e.g., Darken and Gurry, 1953). This analysis leads to the expression (18)

=

=

For steady-state conditions, we have dC/dt OJ thus, dC/dx constant. Solutions to these equations for non-steady-state conditions and various grain geometries (e.g., plate, cylinder, sphere) have been derived by numerous workers, most notably Jost (1960) and Crank (1975). Most of these solutions assume that D is independent of the concentration (i.e., eqn. 18). Fick's second law (18) can be solved for C as a function of x and t provided that the distribution of diffusing species is known at some

49

I I I I

j

SURFACE

Figure 3. Schematic diagram illustrating possible paths of volume diffusion, grain boundary diffusion, and surface diffusion (from Manning, 1974). The multitude of paths allows volume diffusion to be dominant at high temperatures despite the higher mobility expected along the individual short-circuit (surface and grain boundary) paths.

c+

Figure 4. cylinder.

Concentration profiles of various time for diffusion C refers to concentration, and X, the depth.

from a thin film into a

initial instant of time (t = 0). The solutions can be used to calculate D from experimental data on the concentration profile after diffusion is allowed to occur. To illustrate, consider a hypothetical experiment where a semi-infinite cylindrical silicate mineral (180 absent) is positioned so that one end is in contact with a very thin fluid film (180 enriched). Let the cylinder sit for some time t , holding at the temperature for which we desire to measure the diffusion coefficient. Finally, the specimen is cut into thin serial sections normal to the axis of the 50

cylinder, and each slice is analyzed for 180, providing a concentration profile along the cylinder axis. Fick's second law can be solved for this situation (see Crank, 1975) with the result (19) where M is the total amount of 180 originally in the thin film, A is the cross-sectional area of the cylinder, and x is the distance along the cylinder axis measured from the end. D can be determined from the experimental data by choosing a value for D such that equation 19 matches the experimental data. However, an easier way is to take natural logarithms of both sides of equation 19

M

2

- ~ + ~n I ~nC - 4Dt A(nDt)

(20)

A plot of ~nC against -x2/4t then gives a straight line with a slope of l/D. Figure 4 shows a plot of C against x according to equation 19 for various times t. At t = 0, all of the 180 is concentrated in the film at x = O. For t > 0, 180 spreads into the cylinder until, at very long time (t = ~), 180 ~ O. In the case of isotopic exchange, we generally measure the selfdiffusion coefficient which is defined as the rate of transport of a given species through a host with a bulk composition that is composed, in large part, of that species (e.g., 0 in silicates, C in carbonates). Requirements for a successful diffusion experiment include: (1)

the measurement of concentration as a function of position and time, at various temperatures and pressures,

(2) the absence of any chemical reaction between solid and volatile

- i.e., P-T-X maintained,

conditions are such that mineral stability is

(3) the solid phase is isotopically homogeneous and defect-free -

i.e., has been annealed prior to experimentation, (4) for cases where the ratio of the volume of the volatile to volume of solid is small, the amounts of each phase, as well as grain size and geometry, should be known (see Crank, 1975). The temperature dependence of diffusion coefficients described by the Arrhenius relation (same form as eqn. 1), (-E

D

=

A e o

a

can

be

/RT) (21)

A plot of log D versus T-1 gives a straight line over a significant range of temperature. On this plot, the pre-exponential factor A (sometimes called the "frequency factor") is derived from the intercept~ and the activation energy, Ea' is derived from the slope of the line.

51

Both of these parameters are independent of temperature, but depend on the identity of the diffusing species and the composition of the matrix crystal. The concepts of activation energy and frequency factor are based on theoretical and experimental evidence for diffusion in crystalline materials. A is related to the jump frequency, jump distance, defect structure, an~ geometry of the crystal lattice (Manning, 1968). E is related to the energy of formation of imperfections and to the eRergy of motion required to cause an atom to jump from one site to another. We should point out that there may be distinct changes in the slope of the Arrhenius line, and hence E , as different diffusion mechanisms become operative. At the highest t~mperatures, the defect concentration (i.e., the number of vacancies and interstitial ions, etc.) controlling the rate of volume diffusion will be dominated by thermally generated defects (Shewmon, 1963). Under these conditions, an intrinsic diffusion regime develops and E has its maximum value. At lower temperatures, the proportional contr1bution to the defect concentration from impurity ions and other defects (e.g., dislocations and grain boundaries) increase, until they eventually exceed the intrinsically generated defects. When this state is achieved, the extrinsic diffusion regime has been reached, and the change is marked by a kink in the Arrhenius plot, and a lowering of E (see Lasaga, 1981b). a The bulk exchange technique. The maj ority of diffusion coefficients described in the literature have been determined by measuring the total amount of isotopic exchange between the mineral (e.g., silicate, carbonate, oxide) and a volatile phase (e.g., H20, CO2, O2), Typically, crys t.aLl.Lne material is ground to a fine powder, sieved to a limited range of grain size, and then reacted with a volatile phase. The isotopic composition of the volatile phase need only differ from that of the solid by a few permil. The isotopic ratio of the solid and/or the volatile is then analyzed by conventional mass spectrometry. For better results, the fraction of isotope exchange (eqn. 11) should attain a value of at least several percent (usually ~10) in order to demonstrate that more than merely superficial exchange has occurred. Many diffusion coefficient calculations based on bulk exchange experiments have assumed that diffusion occurred from a well-stirred reservoir (usually of limited volume) into a solid of well-known geometry. For this situation, it is usually necessary to select a suitable geometrical model for the solid - e.g., sphere, cylinder, or plate - and specify its effective diffusion radius. Inspection of equations presented by Crank (1975) indicates the following: (1) Many of the equations of grain geometry.

take on a very similar

form, regardless

(2) Similarities notwithstanding, there are significant differences between expressions for different grain shapes, and between expressions for a particular grain geometry. This observation indicates the need for caution in selecting the appropriate expression based on geometry. In addition, the run conditions must also be considered - i.e., long time versus short t ime ; small, moderate, or large volume ratio of volatile to solid. (3) The ratio of the volume of the volatile

52

to

the

volume of the

b 0.10

v 0.05

/f,sec

OL- __ ~ __ J_ __ -L__-L__~ o 100 200 300 400 500

Figure 5. Results of "0 (Sa) and 13C (5b) exchange between annealed and CO2, from Anderson (1969). See equation 22 for a definition of v.

calcite

(44-62µ)

solid ([3) must be taken into consideration and corrected equilibrium isotope partitioning (K') for cases where volume of the volatile is small (Cole et al., 1983).

for the

Although analytical expressions can be solved to give D, graphical techniques are available which give reasonable estimates. One example where graphical analysis has proved successful is in the evaluation of diffusion into a solid from a gas (or fluid) reservoir of changing isotope composition. Anderson (1969) used an approach described by Carman and Haul (1954) and Haul and Stein (1955) to measure diffusion coefficients of carbon and oxygen in calcite reacted with isotopically labeled CO2, The required boundary condition is that the flux of tracer entering the solid at the surface must equal the flux of tracer leaving the gas. Although this technique is sensitive only if the penetration of the diffusion species can be measured at greater depths, Anderson (1969) observed that the overall extent of exchange did not exceed 12% in any run (T = 650-850°C, duration = 20-71 hours). Because of this limited penetration, he assumed that_the solid grains were equivalen! to slabs of uniform thickness, L(= l/pA), where p is the density and A is the specific surface area. Anderson (1969) used the following expression to evaluate D 0C0 (t) e

v2

- °Cc(i)

2

(22)

erfc(v)

0C0 (i)

- °CC(i) ,

2

where v = (Dt)!/L[3, [3= ratio of moles of oxygen or carbon in the gas to moles in the solid 0Cc(i) = initial isotope composition of oxygen or carbon

in

calcite at start, 0C0 (i) = initial

isotope

composition

of

2

oxygen

or

carbon in CO2,

0C0 (t)

= isotope

composition

of

oxygen or

2

carbon in CO2 at time t. Alternatively, rather than measure the isotopic compositions of the gas phase, one could measure the isotope .'i1

'·0 0·9

0·, 0·7

a 0·5 0·6 (Dt/I'I'

0·7

0·8

0·9

1-0

b 0·0

1"="1

0-'

0·2

0·)

0-4

0·5 ()'6 (DI/a1)'

O'M

0-7

0·9

1·0

Figure 6. Degrte of equilibration (Mt/M~ or F~ versus (Dt/t') for a plate (a), or (Dt/a') for a cylinder (b) and sphere (c). Numbers on curves

0·,

c

O'OO,L.OO--'O::'.:-, -"'0':.1--'0:':.J:--0::'

show

the

percentage

of total

ally taken up by the solid Taken from Crank (1975).

solute

[11(1

fin-

+ 11)]100.

.•:--;;0';·,--'0;':'6:--:o'O.'c7-';;'0.g (DII(lI)!

values of the solid phase. for carbon diffusion and nCc are

The

corresponding

and 2nC02/3ncc for

values of ~ are nC02/nCC

oxygen

diffusion, where nC02 the number of moles of CO2 and calcite, respectively.

According to equation 22, a plot of v versus t! should yield a straight line through the origin. If so, the slope of this line can be used to calculate the diffusion coefficient. The results from Anderson's (1969) stable isotope exchange experiments are shown in Figures 5a and 5b. These data give good straight lines; however, in most cases the lines do not pass through the origin. Specifically, he obtained both positive and negative intercepts. Despite anomalies such as these, equation 22 has been applied effectively in determining diffusion coefficients for a variety of solid-volatile systems reacted for short durations (e.g., see discussion by Frischat, 1975). Still another approach utilizes graphs provided by Crank (1975). From a knowledge of: (1) the fraction of exchange (F), (2) the sphere or cylinder radius (a), or plate thickness U), (3) time (t), and (4) the corrected volume ratio (~), we can use Crank's Figures 4.6, 5.7 and 6.4 to calculate D for a plate, a cylinder, and a sphere, respectively. These figures are reproduced here (Figs. 6a-c), and show F plotted 54

against(Dt/a2)~ for a sphere and cylinder, and (Dt/~2)! for a plate. Note that these figures are useful only for systems where a solid is interacted with a well-mixed solution of limited volume for long times. Microbeam analytical techniques. Two powerful analytical methods (1) nuclear reaction analysis (NR) or charged particle activation, and (2) secondary ion beam mass spectrometry (SIMS) - have been developed which enable the determination of 180 concentration gradients in solids over a depth range of 25 nm to 10 µro. This depth interval is app'ropri.at;e _for measurement of diffusion coefficients in the range of 10 11 to 10 20 cm2/sec from concentration gradients produced in materials by exchange anneals of 10 hours to one month duration, respectively (Freer and Dennis, 1982). Direct determination of the 180 concentration profile offers distinct advantages over the bulk exchange technique and facilitates (within one experiment) the interpretation of: (a) surface exchange kineticsj (b) solution-reprecipitation phenomenaj (c) dislocation- and damage-enhanced diffusionj (d) diffusional anisotropYj and (e) non-Fickian behavior. In both techniques (NR and SIMS), single-crystal fragments (commonly oriented) of the mineral of interest are reacted with a fluid or gas phase (02 or CO2) having a highly enriched 180 concentration (e.g., 10 to 40% 180). Partial approach to isotopic equilibrium is achieved under controlled laboratory conditions, and the degree of isotopic equilibration (F) is generally less than 1%, as compared with minimum acceptable values of approximately 10% for. the bulk exchange methods. After the exchange, both NR and SIMS provide an 180 concentration profile with depth beneath the crystal surface. (a) Nuclear reaction analysis. The non-destructive microanalysis of trace constituents in solids by direct observation of nuclear reactions and/or backscattered particles using low-energy «2 MeV) accelerators allows the direct analysis of the atomic species in the first few microns beneath the surface (Jaoul et al., 1983). The nuclear reaction must be specific to a particular isotope (e.g., 180) such that a unique relationship exists between the concentration profile and the energy spectrum observed. The most important reaction for the study of 180 depth profiles is 180(p,a)l5N, which occurs with a significant cross-section (i.e., the number of particles, in this case protons, which undergo nuclear reaction as the beam passes into a solid) at proton energies on the order of 700-800 keV. This reaction, along with others such as 180(p,n) 18F, has been used in a variety of modes for the determination of oxygen diffusion coefficients in quartz (e.g., Choudhury et a L, , 1965j Schachtner and Sockel, 1977), forsterite (e.g., Jaoul et al., 1980j Jaoul et aI, 1983j Reddy et al., 1980) and corundum (Reddy and Cooper, 1976). (b) Secondary ion mass spectrometry. Oxygen (also carbon, sulfur) isotopic composition as a function of depth below a solid surface can be measured using an ion microprobe. Atoms from a small area of the target surf ace are ~puttered off by a primary ion beam composed usually of 0 or Ar. A fraction of the sputtered atoms is ionized, and this may be collected to form a secondary ion beam which is analyzed on a mass spectrometer. This destructive analytical technique is capable of providing isotopic and compositional information with depth beneath the oriented sample surface.

55

a.

DEPTH

PROFILE OF 180 IN QUARTZ

40

ecc-e,

'.

I kII. 7.0'"

-,

.

..

'

"

'0

.-, "

00

'0

~O..· "'';0''

20

30-·····~~~····~~..·~.. SCAN

o

NUMBER

o.s

1.0

1.5

DEPTH (microns)

b.

INVERSE ERF PLOT FOR LONG PROF'LE

::: 2

'"

20

o.s

o

30

40

SCAN

NUMBER

50

6Q

1.0 OEPTH

(microns)

Figure 7. (a) Oxygen-18 concentration (C ) versus depth into a quartz crystal (Giletti and Yund, 1984). Points are total sign~l for masses 16 and 18 with the background subtracted. The triangles represent measurements made while sputtering through gold coating

on sample.

(b).

Data

concentration ratio of equation is shown as solid line.

from

Figure

7a calculated

23 and plotted

versus

as

inverse

depth.

error

function

Least-squares

fit

of

the

to data

For a discussion of the requirements necessary to obtain valid isotope ratio profiles, see Giletti et al. (1978). Figure 7a illustrates ion-microprobe data for quartz-water 180/160 exchange at 800°C and 1 kbar (Giletti and Yund, 1984). From these data, self-diffusion of the oxygen isotopes can be modeled by assuming diffusion into a semi-infinite medium (crystal), the surface of which is maintained at a constant isotopic composition different from that initially in the crystal. Crank (1975, p. 32) gives the following equation for one-dimensional diffusion in a semi-infinite medium with constant surface concentration: erf (_x_)

(23)

2./Dt where C , C , and Cl are, respectively, the 180 concentrations at a depth xxfrog the surface, at an infinite depth in the crystal (the natural 180 concentration), and at the crystal surfacej t is the run durationj and D is the diffusion coefficient. Experiments are designed so that only a small fraction of the 180 in the fluid (or

gas) actually enters the solid. The oxygen isotopic composition of the fluid does not change significantly during the experiment, which makes C1 constant. Equation 23 yields a curve similar to that given by the data in Figure 7a. By taking the inverse error function of the concentration ratio from equation 23, a straight line can be fit to the data by least-squares analysis, as shown in Figure 7b. The slope of this line is proportional to (4Dt)-!. See Freer and Dennis (1982) for a summary of the advantages and disadvantages of the SIMS technique, as well as for the NR and bulk exchange methods.

MECHANISMS

AND RATES OF ISOTOPE EXCHANGE

IN HOMOGENEOUS

SYSTEMS

Interpretations of the thermal histories of geologic systems through the use of isotope geothermometer pairs depend critically on the assumption that isotope equilibrium is attained between the major species. Slow exchange rates may therefore have a profound effect on the applicability of a particular isotope geothermometer to natural systems. Isotopic equilibration in solutions or gases can be very slow, with half-times of reaction on the order of years to hundreds of years. For example, early work by Lloyd (1968) on oxygen isotopic exchange between SOa - and H20 under hydrothermal conditions and a more recent high temperature study on carbon isotopic exchange between CO2 and CH4 by Sackett and Chung (1975) indicate very sluggish reaction rates. In fact, Sackett and Chung (1975) observed no carbon isotope exchange between CO2 and CH. for times as long as 136 hours at 500°C. Northrop and Clayton's (1966) rate expression for isotopic exchange demonstrates the dependence of the overall rate on the concentrations or amounts of the equd Ldbrat.Lng species (see eqn. 12). The rate law is established by monitoring the time dependence of the isotopic compositions of the species that take part in the reaction, and by determining how this dependence is affected by altering the constraints on the reacting system. In the case of isotope exchange between two gaseous species (e.g., CO2 and CH.), the isotopic composition of one or both species should be measured as a function of time at various temperatures, pressures, and initial concentrations. Similarly, isotope exchange between aqueous species in solution (e.g., SOa- - H2S) should be monitored as a function of not only time and the aforementioned variables, but also ionic strength and pH. The pH dependency is related to the formation of aqueous species which may participate, as intermediaries, in the isotope exchange process. Changes in speciation will result from variations in pH, temperature, pressure, and solution composition (e.g., see Weston and Schwartz, 1972; Lasaga, 1981c). The intent of this section is to illustrate how changes in the magnitudes of the variables described above (1) influence the rate of isotope exchange and (2) can lead to an interpretation of the mechanism(s) of exchange. It should be noted that the identities of trace species that act as intermediaries in the reaction sequence may be elusive, and therefore it may be necessary to infer their presence from indirect evidence. Three examples are described below: the sulfur isotope exchange kinetics between aqueous sulfate and sulfide (Ohmoto and Lasaga, 1982), the oxygen isotope exchange kinetics between sulfate and water (Chiba and Sakai, 1985), and carbon isotope exchange kinetics

57

between CO2 and CH4 (Harting and Maass, 1980). Kinetics of Isotopic Exchange Reactions

in Solutions

The sulfate-sulfide system. Ohmoto and Lasaga (1982) proposed the following general rate law for sulfur isotopic exchange between aqueous sulfate and sulfide:

(24)

where k is the rate constant, t is time (sec), [l:SOa-] and [S2-] are molal concentrations of all oxidized and reduced sulfur species in solution, respectively, and aO, a and ae are, respectively, the fractionation factors at t = 0 (initial condition), at the end of the experiment, and at equilibrium. They expressed the reaction rate as a second-order law, where R is the overall rate (25) Ohmoto and Lasaga (1982) used equation 24 to compute rate constants from available experimental data on the partial exchange of sulfur isotopes between aqueous sulfates and sulfides. These experiments covered a wide variety of starting materials (e.g., So, Na2S0. + NaHSO + H2S + NaHS, Na2S203' Na2S + Na2S04 + H2SO., etc.) and compositions, temperatures (100-405°C), run durations (~10 to 9000 hrs.), and pH's (2 to 9 at temperature). The results of the calculations are presented on an Arrhenius diagram in Figure 8 where log k is pl~tted against l/T with k in units of kg/mol/hr (molal concentration 1 time 1). The rate constants are strongly dependent on temperature and pH. For Na-bearing hydrothermal solutions, Ohmoto and Lasaga (1982) found that the rate constants: (1) decrease by 1 order of magnitude with an increase in pH by 1 unit at pH's less than approximately 3, (2) remain constant in the pH range of about 4 to 7, and (3) decrease at pH values greater than 7 (Fig. 9). The activation energy for the reaction also depends on pH; 18.4 ± 1 kcal/mole at pH = 2, 29.6 ± 1 kcal/mole at pH = 4 to 7, and between 40 and 47 kcal/mole at pH near 9. In order to explain the observed pH dependence of the rate constant and of the activation energy, Ohmoto and Lasaga (1982) proposed a model involving thiosulfate (e.g., H2S203, H2S0~, S20~-, NaS20~) molecules as reaction intermediates. In this model, the intramolecular exchange of sulfur atoms in thiosulfate (i. e., H2 ,',S- S03 -7 H2S - "'S03' where indicates 3·S) is the rate-determining step. Recent results presented by Uyama et al. (1985) from sulfur isotope exchange experiments in the aqueous system thiosulfate-sulfide-sulfate support the view that thiosulfate is an intermediate in the isotope exchange between sulfate and sulfide. However, their study did not confirm that the intramolecular exchange is the rate-determining step.

*

The time required to attain sulfur isotopic equilibrium between aqueous sulfates and sulfides will increase with: (1) a decrease in total sulfur concentration and temperature, and (2) an increase in pH (see Ohmoto, Chapter 14). For example, a hydrothermal solution at 250°C, with l:S ~ 0.01 moles/kg and a pH between 4 and 7, reaches equi58

(1/T) 1.5

103

X

2.0

2.5

2rr--,---,,---.--~-.------~--------~ A-B

.... I

',

....

',.10

~(84l

"""

,

-6

" 400

.........

100

300

Figure 8. Arrhenius plot of log k versus 1fT for sulfur isotope exchange between aqueous sulfates and sulfides (from Ohmoto and Lasaga, 1982), k in units of kg/mole/hr, Numbers in parentheses are the calculated in-situ pH values. For the meaning of the symbols and letters, refer to Ohmoto and Lasaga (1982). Arrows indicate mininrum or maximum k values. Scale on right gives the time in years to achieve F = 0,9 if ES = 10-' m; *pH computed at 350·C.

6 5

~ 4 :J

~0 N

3

01

2

.....

~

o~~--~--~~~~--~~~~--~ 1

2

4

5 6 pH in situ

7

8

9

10

Figure 9. Relationship between pH and half-life (in hours) of oxygen isotope exchange between dissolved sulfate and water for ENa - 0.1 and ES = 0.01 m, (Solid lines, from Chiba and Sakai, 1985). Dotted line is the relationship between pH and the half-life of sulfur isotope exchange in aqueous sulfate-sulfide systems for ENa • 0,1 and ES - 0,01 m (Ohmoto and Lasaga, 1982),

S9

librium in about 4 years. A decrease in pH to 2 results in an equilibration time of only 3 days, whereas the time increases to 105 years for a pH = 9. A drop in temperature to 150°C results in equilibration times of about 0.5 yrs, 4000 yrs and 109 yrs for pH's of 2, 4-7 and 9, respectively. Also, an order of magnitude decrease in ~S produces an order of magnitude increase in the equilibration time. The sulfate-water system. The rate of oxygen isotope exchange between dissolved sulfate and water has been measured recently by Chiba and Sakai (1985) at 100, 200 and 300°C. Their rate equation for the exchange of oxygen isotopes between sulfate and water is given in the general form as -~n(l - F)4XY (4X + Y)t

(26)

where X and Yare the concentrations of ~SOa and ~H20, respectively, t is time (sec), F is the fraction of oxygen isotope exchange (see eqns. 10 and 11), the constant 4 accounts for the number of oxygen atoms in sulfate, and R is the overall reverse (r) rate of oxygen isotope ex-

r4

change for the reaction

(27)

Equation 27 is one of four reactions Chiba and Sakai (1985) propose assuming second-order reaction proceeding through a collision between two species. The other reactions are based on different substitutions of 180 and 160 in sulfate (e.g., S 1801603' S 18021602' etc.). Because they sampled each experiment through time, they were able to effectively use a plot of ~n(l - F) versus run time to obtain rates from the slopes of straight lines, -R (4X + Y)/(4XY), originating at ~n(l - F) = 0 and t = O. r4 The isotope exchange rates observed by Chiba and Sakai (1985) are strongly dependent on temperature and pH (see their Fig. 2). By combining the temperature and pH dependence of the reaction rate, they found the exchange reaction to be first-order with respect to sulfate. To determine this, Chiba and Sakai (1985) calculated the concentrations of the major forms of sulfate (i.e., H2S0~, HSO:, SOa- and NaSO:) in solution that could participate in collisions with water as a function of temperature and proton concentration. This approach required the use of mass action, mass balance, and proton balance equations. From the pH dependence, they deduced that the isotope exchange reaction between dissolved sulfate and water proceeds through collision between H2S0~ and H20 at low pH's (i.e., pH = 2.3 to 2.7 at 100°C; pH = 4.0 to 5.5 at 200°C), and between HSO: and H20 at intermediate pH's (i.e., pH = 6.1 to 7.3 at 300°C). The temperature dependence low pH mechanism is given by log k

of the isotopic

12.2 - 4580/T

,;;n

.

exchange

rate

for the

(28)

The activation energy of the exchange between H2S0~ and H20 was calculated to be 20.9 kcal/mole (Chiba and Sakai, 1985). This value falls in the range of E given by Hoering and Kennedy (1957) for exchange between sulfuric acid ~nd water, namely 20.4 to 31.3 kcal/mole from 10 to 100°C. Additionally, Chiba and Sakai's (1985) value is reasonably close to the range of activation energies Ohmoto and Lasaga (1982) give for sulfur isotope exchange between aqueous sulfates and sulf ides j viz., 18.4 to 29.6 kcal/mole for the pH range of 2-7. Based on the values obtained for the half-life of oxygen isotope exchange reaction between dissolved sulfate and water (Fig. 9), Chiba and Sakai (1985) conclude that oxygen isotope geothermometry utilizing the sulfate-water pair is applicable for estimating temperatures of geothermal reservoirs. The rates of oxygen and sulfur isotope exchange in the system S-O-H-Na are compared in Figure 9. In general, the half-lives of oxygen isotope exchange are much shorter than the half-lives of sulfur isotope exchange calculated from rates given by Ohmoto and Lasaga (1982) in the experimental temperature and pH range investigated by Chiba and Sakai (1985). The rate of sulfur isotope exchange is slower than the rate of oxygen isotope exchange, because the sulfur atom in a sulfate ion is shielded by four oxygen atoms which act as a barrier against the sulfur exchange. Also, in the mechanism of sulfur isotope exchange proposed by Ohmoto and Lasaga (1982), one of the s-o bonds in a sulfate ion must be broken to form an intermediate species, thiosulfate ion, and a water molecule. This implies that the sulfur isotope exchange should be accompanied by oxygen isotope exchange. Kinetics of Isotopic Exchange Reactions

Between Gases

By analogy with homogeneous isotope exchange reactions in solution detailed above, we can presume that isotopic exchange between gaseous species occurs through either: (a) simple molecular collisions, (b) chemical reaction with the formation of intermediates (analogous to the case of thiosulfate and sulfur isotope exchange), or (c) some combination of (a) and/or (b) plus an added element of complexity - e.g., catalysis by the container wall (or in a geologic setting, catalysis along the surfaces of mineral grains surrounding pores or lining fractures). The potential importance of catalysis is exemplified by results obtained by Brandner and Urey (1945) who found the rate of exchange of the 13C isotope between CO and CO2 at elevated temperatures (~860-920°C) to be catalyzed on the surface of quartz, gold, and silver. In addition, the isotopic reaction rate is accelerated by the presence of H2 or H20(v). They concluded that H2 and H20 were partially adsorbed on the reaction vessel wall, creating sites for further reaction to take place. Typically, isotope exchange reactions among gases are geologically very rapid. Carbon isotope equilibrium between CO and CO2 is attained within minutes at high temperatures, as described above. Sulfur isotope equilibrium between S02 and H2S is apparently reached within about one day at temperatures between 527 and 1027°C (Thode et al., 1971). Isotopic equilibrium (oxygen and hydrogen) is nearly instantaneous during the separation of H20( v) from H20( 1) at elevated temperatures (e.g., Bottinga, 1968). Isotope exchange reactions between CH. and various hydrogen species, e.g., T2, H2, D2, etc. are extremely fast at 2SoC (e.g., see Kandel, 1964).

61

The carbon isotope exchange reaction between CH4 and CO2, however, is very sluggish, even at elevated temperatures (e.g., see Sackett and Chung, 1975). Not only does the slow isotopic exchange rate diminish its usefulness as a geothermometer, but if the mechanism of isotope exchange is linked to the oxidation-reduction reaction (29) then we might conclude that chemical equilibration is also slow. Thus, this reaction may be less important in controlling redox equilibria in hydrothermal fluids than previously assumed (see Chapter 14). Sackett and Chung (1975) observed no carbon isotope exchange between CO2 and CH. reacted at SOO°C for up to 10.5 days in the presence of potentially catalytically active Ca-montmorillonite. These results were interpreted as experimental confirmation of the lack of carbon isotope exchange between CH. and CO2 at high temperatures. Harting and Maass (1980), however, observed limited carbon isotopic exchange between CO2 and CH4 by allowing 667. 13CH. to react with CO2 of natural isotopic composition for 16 hours at temperatures ranging from 500 to 680°C. They reported second-order rate constants derived from the following relationships: (30) (31) where

X

represents

the atom fraction

of the exchanged

isotope, W13CC02 13CH4J is the measured change in the isotopic composition of CO2, [ and [12C02J are the atom fractions of these species in the gas mixture used in the experiment, and t is the reaction time in years. Their results yield k2 values of approximately 10-4 to 10-1 atomi.-l year-1 for the temperature interval of 500 to 600°C. They obtained an activation energy of about 47 kcal/mole. Harting and Maas (1980) estimated that carbon isotope equilibrium between CO2 and CH. would only be achieved at 400°C after about 8 x 10' years. Their results, coupled with those of Sackett and Chung (1975), suggest that under normal geothermal conditions with temperatures of approximately 200°C, isotopic exchange does not reach equilibrium. In other words, for natural gas deposits which do not experience higher interim temperatures, the carbon isotopic ratio reflects that of the source. Giggenbach (1982) reinterpreted Harting and Maass' data in terms of the known carbon isotopic ratios found in different natural gas and geothermal wells throughout the world. He points out that in view of the slow rate of chemical and isotopic equilibration, isotopic ratios only serve as an accurate geothermometer for very deep wells and that the results may otherwise be biased by secondary reactions or by a net flux of CH. or CO2 with incongruent compositions. Ohmoto (Chapter 14) notes that the results from the experiments on CO2 -CH. described above may not be applicable to natural hydrothermal systems because the isotope exchange was conducted under essentially anhydrous conditions (H20-free). He contends that carbon isotop~ exchange between CO2 and CH4 may depend on the activities of H20 and H 62

as well as CO2 and CH., with the reaction proceeding through some intermediate species such as acetic acid (CH3COOH). Clearly, further experimentation is needed to test these ideas.

MECHANISMS AND RATES OF ISOTOPE EXCHANGE REACTIONS IN HETEROGENEOUS SYSTEMS The previous section dealt with isotope exchange reactions occurring between reactants uniformly distributed in a single phase. However, isotopic exchange may also occur between reactants in different phases. Isotope exchange during mineral-fluid interaction can occur by means of: (1) solution-precipitation, (2) chemical reaction involving the formation of a new phase, or (3) diffusion (Giletti, 1985). The first two of these categories can be termed surface reactions (Cole et al., 1983). The diffusion mechanism involves isotope exchange by volume diffusional transport to and across the faces of a crystal which remains a single solid reservoir with constant dimensions and shape (Giletti, 1985). In the case of a gas phase (e.g., CO2, O2, etc.) reacting with a solid, diffusion is the dominant mechanism of isotope exchange (e.g., see Anderson, 1969). Giletti (1985) provides additional qualitative details. Our intent in this section is to discuss some of the experimental results obtained from heterogeneous rate studies and to demonstrate that, regardless of the reaction mechanism, rates of isotope exchange can be described in terms of a single set of parameters. These parameters include temperature, which fixes the rate constant (e.g., D for diffusion), pressure, the grain size and grain shape (e.g., sphere, plate, etc.), and the solution-to-solid mass ratio. Additionally, we intend to show how changes in these parameters affect the rates of isotope exchange between a mineral and a volatile phase. We will also compare the overall rates of isotopic equilibration for the two major mechanisms: diffusion and surface reaction. Isotope Exchange Accompanying Surface Reactions Isotopic exchange in mineral-fluid systems that are far from chemical equilibrium may be controlled largely by surface reactions (e.g., O'Neil and Taylor, 1967; also see Cole et aL, , 1983; Giletti, 1985). Experimental reactions between high-temperature chloride solutions and feldspars studied by O'Neil and Taylor (1967) and Merigoux (1968) indicate that Na-K cation exchange is always accompanied by oxygen isotopic exchange. O'Neil and Taylor (1967) proposed a mechanism of fine-scale recrystallization involving a reaction front moving through the crystal with local dissolution and redeposition in a fluid film at the interface between the exchanged and unexchanged feldspar. Chloride ion was detected along microcracks in the reactant, indicating that armoring of the original grain by pseudomorphic product layers did not severely restrict communication between the aqueous fluid and the unexchanged feldspar. Solution-precipitation has been observed for isotope exchange experiments that involved the reaction of other phases with aqueous solutions, such as carbonates, micas, and sulfates (Table 1). The presence of aqueous chlorides (e.g., NaCI, KCI, etc.) sets these experiments apart from most diffusion experiments, where pure water is typically used. The occurrence of secondary product phases based on mineralogic and X-ray diffraction data obtained from these

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