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Chemical Geology 372 (2014) 119–143

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Chemical Geology

j ourna l homepage: www.e lsev ie r .com/ locate /chemgeo

Frontiers of stable isotope geoscience

John M. Eiler a,⁎, Brigit Bergquist b, Ian Bourg c, Pierre Cartigny d, James Farquhar e, Alex Gagnon f,Weifu Guo g, Itay Halevy h, Amy Hofmann i, Toti E. Larson j, Naomi Levin k, Edwin A. Schauble l, Daniel Stolper a

a Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, United Statesb Department of Earth Sciences, University of Toronto, Toronto, Ontario MSS 3B1, Canadac Earth Sciences Division, Lawrence Berkeley National Lab, Berkeley, CA 94720, United Statesd Laboratoire de Géochimie des Isotopes Stables Institut de Physique du Globe de Paris, PRES Sorbonne Paris Cité, Univ Paris-Diderot, 1 rue Jussieu, 75005 Paris, Francee Department of Geology, University of Maryland College Park, College Park, MD 20742, United Statesf School of Oceanography, University of Washington, Seattle, WA 98195, United Statesg Woods Hole Oceanographic Institution, Woods Hole, MA 02543, United Statesh Weizmann Institute of Science, Rehovot 76100, Israeli Department of Chemistry, Franklin & Marshall College, Lancaster, PA 17604, United Statesj Jackson School of Geosciences, University of Texas at Austin, Austin, TX 78712, United Statesk Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218, United Statesl Department of Earth and Space Sciences, UCLA, Los Angeles, CA 90095, United States

⁎ Corresponding author.E-mail address: [email protected] (J.M. Eiler).

http://dx.doi.org/10.1016/j.chemgeo.2014.02.0060009-2541/© 2014 Published by Elsevier B.V.

a b s t r a c t
a r t i c l e i n f o
Article history:Received 21 June 2013Received in revised form 31 January 2014Accepted 7 February 2014Available online 28 February 2014

Editor: David R. Hilton

Keywords:Stable isotope geochemistryMass independentClumped isotopePosition-specific isotope effects

Isotope geochemistry is in the midst of a remarkable period of innovation and discovery; the last decade (or so)has seen the emergence of ‘nontraditional’ stable isotopes of metals (i.e., variations in isotopic compositions ofMg, Fe, Cu, etc.), a great expansion of mass-independent isotope geochemistry, the invention of clumped isotopegeochemistry, and new capabilities for measurements of position-specific isotope effects in organic compounds.These advances stem from the emergence of multi-collector plasma mass spectrometry, innovations in gassource mass spectrometry, infrared absorption spectroscopy, and nuclear magnetic resonance techniques.These new observations demand new connections between isotope geochemistry and the chemical physicsthat underlie isotopic variations, including experimental study and modeling of vibrational isotope effects,photochemical isotope effects, and various nuclear volumeandmagnetic effects. Importantly, such collaborationsalso have something to offer chemists and physicists because the novel observations of emerging branches ofstable isotope geochemistry hold the potential to reveal new insights into the nature of chemical bonds andreactions. This review looks broadly across the frontiers of new methods and discoveries of stable isotopegeochemistry and the fundamental chemical–physics problems they pose, focusing in particular on the mostpressing problems in: kinetic isotope effects in complex systems; mass independent isotope geochemistry(both the strong effects in photochemical reactions and the subtle variations of more conventional reactions);clumped isotope geochemistry; and the position-specific isotopic anatomies of organic molecules.

© 2014 Published by Elsevier B.V.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1201.1. Recent analytical innovations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1211.2. Discoveries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1211.3. Puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1211.4. The dialog with chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

2. On beyond equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1222.1. Some founding principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1222.2. Evaporation and condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1232.3. Molecular diffusion in gases and liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1232.4. Metal ligand-exchange reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1242.5. Questions and needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

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120 J.M. Eiler et al. / Chemical Geology 372 (2014) 119–143

3. Why can't authogenic minerals just behave? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1243.1. Diffusion alone? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1243.2. Desolvation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1243.3. Questions and needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

4. The outer limits of ‘mass dependent’ isotopic fractionation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1254.1. Unusual mass laws associated with equilibrium processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1264.2. Mass laws of non-equilibrium processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1274.3. Questions and needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5. O-isotope mass laws as a tool for study of the water cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1275.1. Δ17O in the Hydrosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1285.2. Δ17O in CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1295.3. Questions and needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6. Illuminating mass independent sulfur isotope fractionations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.1. Generation of Archean–Proterozoic S-MIF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.2. Carriers of Archean–Proterozoic S-MIF from atmosphere to surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.3. Preservation of S-MIF in the geological record . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316.4. Questions and needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

7. Mass independent fractionations of heavy metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317.1. Nuclear volume effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317.2. Magnetic isotope effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1327.3. Questions and needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

8. Clumped isotope geochemistry of carbonate species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1338.1. Speleothems and degassing of DIC solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1348.2. Corals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1348.3. Questions and needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

9. Position-specific and clumped isotope effects in organics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1359.1. Natural abundance NMR (‘SNIF-NMR’) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1359.2. High-resolution gas source mass spectrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1369.3. Absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1379.4. Questions and needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

10. Future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13810.1. A diversifying landscape of analytical technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13810.2. Exploration of novel isotopic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13810.3. Limits of conventional theories of fractionation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13810.4. First-principle computational tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

1. Introduction

The nuclear, physical and biological chemistry of isotopes hasprofoundly influenced the geosciences; these fields underpin the cali-bration of geological time scales (e.g., Patterson et al., 1955; Bowringand Schmidz, 2003), reconstructions of past climates (e.g., Epsteinet al., 1951; Zachos et al., 2001), ‘tracer’ studies in the hydrosphereand atmosphere (e.g., Dansgaard, 1964; Jouzel et al., 1997), and numer-ous other geological and geochemical tools. This discipline is in themidst of a sustained burst of innovation and discovery as dramatic asany period since its foundation in the 1940's and 50's. New analyticaltechniques for isotope geochemistry have increased the scope of thediscipline, adding to both the list of elements that can be analyzed andthe properties of isotope distribution that can be interrogated, includingmass laws of fractionations, position-specific isotope effects and isoto-pic ordering or ‘clumping’. These methodological innovations have ledto a variety of discoveries that are playing central roles in the study ofearth history and processes. But, many of these discoveries involvephenomena beyond our basic understanding of the chemistry of isotopes.

Recent decades have also seen noteworthy advances in ab initio andmolecular dynamic models of the structures and energetics of chemicalcompounds (e.g., Becke, 1993). These advances have enabled the first-principles modeling of molecular structures and isotope effects onmolecular properties and dynamics for complex materials with unprec-edented levels of accuracy (Car and Parrinello, 1985; Panagiotopoulos,1987; Laio and Parrinello, 2002), including solute–solvent interactionsand phase interfaces, (e.g., Kolmodin et al., 2002; Sharif et al., 2006) —the sorts of materials most relevant to many earth science problems

(Varma and Rempe, 2006; Bourg and Sposito, 2011; Stack et al., 2012).These methods are capable of illuminating the chemical physics ofisotope fractionations (Dreisner et al., 2000; Hill et al., 2010; Rustadet al., 2010) and have been widely applied to classic problems in tradi-tional stable isotope geochemistry (e.g., the carbon isotope fractionationassociated with photosynthetic carbon fixation; Tcherkez et al., 2006).But this work has not yet been brought to bear on most of the new ob-servations coming from novel branches of stable isotope geochemistry.

Thus, isotope geochemistry and the chemical physics of isotopes areboth in an unusual period of their development — each has separatelymade substantial progress on their own, but would benefit by turningtheir attention on common sets of new goals. Some of the greatestpast discoveries and advances in understanding of the isotopegeosciences have come from such collaborations — for example, theinvention of quantitative paleoclimate reconstructions was based onisotope effects on vibrational energies of chemical bonds (Urey, 1947);the discoveries of metabolic and other biological isotopic fractionations(e.g., Dole and Jenks, 1944) led to new insights into biochemical kineticsand new biogeochemical tools (e.g., Farquhar et al., 1989); discoveriesof mass-anomalous isotope effects in nature (i.e., departures fromcanonical mass laws followed by common fractionation mechanisms;Clayton et al., 1973; Mauersberger, 1987), led to fundamental researchin isotope effects in photochemistry and other gas phase reactionsdominated by electronic transitions (e.g., Thiemens and Heidenreich,1983; Mauersberger et al., 1999; Thiemens et al., 2012) and fundamen-tal chemical–kinetic theory (e.g., Gao and Marcus, 2001), which in turnhas led to further discoveries regarding the history of the Earth's atmo-sphere (Farquhar et al., 2000a). From a geoscientist's point of view, the

121J.M. Eiler et al. / Chemical Geology 372 (2014) 119–143

purpose of this dialog between geochemistry and chemistry is to devel-op a deep understanding of isotopic tools for deciphering naturalenvironments. From the physicist's or chemist's point of view, suchresearch permits a wide-ranging exploration of natural laboratories insearch of new isotope effects that can be used to refine our understandingof chemical structures and reaction mechanisms.

The purpose of this paper is to review the last decade (or so) ofdevelopments in isotope geochemistry, principally in an effort totempt the present generation of chemists and geoscientists into produc-tive and insightful collaborations. The remainder of this introductionbriefly reviews some of the most relevant recent developments inisotope chemistry and geochemistry; the remainder of this paper isthen organized around a series of case studies that we feel best exemplifyfuture opportunities. This paper is an outgrowth of a 2011 workshop onthese subjects, organized by the Department of Energy and attended by25 geochemists, chemists and geologists, including the authors andothers listed in the Acknowledgments.

1.1. Recent analytical innovations

Twenty years ago, a young stable isotope geochemist needed to beaware of only one sort of analytical instrument — the Nier-type gassource isotope ratio mass spectrometer — and the field rarely consid-ered subjects beyond the bulk isotopic compositions of the light, volatileelements (H, C, N, O, S). The emergence of multi-collector plasma massspectrometers has extended this field to metals that could not beanalyzed routinely and precisely by traditional gas source and thermalionization instruments (e.g., Cu, Fe, Zn, Ni; e.g., Halliday et al., 1995).Improvements in ion microprobes have enabled in situ, micron-scalemeasurements of solids with precision approaching that achieved bychemical extraction and gas source mass spectrometry (Kita et al.,2009). Improved analytical methods and approaches to standardizationhave resulted in measurements of elements with more than two stableisotopes (i.e., O and S isotopes; e.g., Luz et al., 1999)with unprecedentedprecision, revealing subtle variations in mass laws governing stableisotope fractionations. Most recently, a high-resolution gas sourcemulti-collector mass spectrometer has been created (Eiler et al., 2012)that is capable of analyzing isotopologues of molecules and theirfragments with resolution of isobaric interferences (e.g., 13CH4

from 12CH3D), extending the field of clumped isotope geochemistry —

i.e., analysis of multiply substituted isotopologues (Eiler, 2007) fromsimple compounds like CO2 and O2 to a wide range of isotopic systemsand compounds, including volatile and semi-volatile organics. All ofthese technical developments figure prominently in the subjectsdiscussed in this paper. Outside the realm of sector mass spectrometry,absorption spectroscopy has emerged as a precise and highly efficientand field-portable method for isotope ratio measurements of simplemolecular gases (see recent review by Griffis (2013)). And, nuclearmagnetic resonance spectroscopy has demonstrated the capacity tomake precise measurements of C and H isotope ratio at natural abun-dances for individual structural sites in complex organic molecules;this effect was demonstrated over 30 years ago (Martin and Martin,1981), but only recently expanded to a wide range of applied problems(e.g., the n-alkanes; Gilbert et al., 2013). These more specialized butpotentially powerful emerging technologies also figure prominently insome sections of this review.

1.2. Discoveries

This recent surge in analytical capabilities has led to observationaldiscoveries that have transformed our approaches to and understandingof some of the major problems in Earth science: The stable isotopegeochemistry of metals has emerged as a large, multi-faceted disciplinethat is perhaps the fastest growing tool in environmental geochemistry,paleoclimate research and cosmochemistry (Johnson et al., 2004). Themass-independent isotope geochemistry of S has revolutionized the

study of the rise of atmospheric oxygen early in Earth history(Farquhar et al., 2000a). More subtle variations in mass laws for S andO isotope fractionations provide a new basis for studying modern bio-geochemical and atmospheric cycles of these elements (e.g., Farquharet al., 2007). Similarly, the 17O/16O–18O/16O systematics of waterhave provided hydrology with a powerful new tool (e.g., Landaiset al., 2008). Measurements of multiply substituted (13C and 18O)isotopologues of CO2 and carbonate have led to a new approach topaleothermometry that is changing the way we study ancient earthclimate, altimetry, and related problems (e.g., Finnegan et al., 2011).Isotope ratio measurement by absorption spectroscopy has enabledfield-deployable devices that are revolutionizing environmental stableisotope geochemistry (e.g., Griffis et al., 2004). Site-Specific NaturalIsotope Fractionation-Nuclear Magnetic Resonance (SNIF-NMR) is a rela-tively specialized technique at present, but has demonstrated applica-tions to the forensics of agricultural compounds and explosives(Remaud et al., 1997), and could grow to form the basis of a wide rangeof new sub-disciplines in environmental geochemistry, geobiology, andmeteoritics and cosmochemistry. High-resolution gas source mass spec-trometry recently produced the first precise ‘clumped isotope’ thermom-eter for an organic molecule (methane; Stolper et al., 2014, submitted forpublication), and ongoing work suggests that this tool will significantlyimpact our understanding of petroleum deposits and the biogeochemis-try of methane (Stolper et al., submitted for publication), and maysoon be extended to a variety of more complex organic compounds(Eiler et al., 2013b).

1.3. Puzzles

Many of these new measurements and applications are concernedwith properties of isotopic substances that are relatively unfamiliar andlittle understood. The stable isotope geochemistry of metals can beinterpreted generally through conventionalmodels of equilibriumandki-netic fractionations, but detailed understanding currently lags far behindthat accumulated through decades of research in ‘traditional’ branches oflight-element stable isotope geochemistry. Furthermore,manymetal sys-tems seem to experience kinetically controlled fractionations that are atthe murky outer edges of our understanding of conventional isotope ef-fects. The interpretation of ‘mass independent’ isotope fractionations(or, more generally, the isotope systematics of elements like O, S or Hgthat have 2 ormore stable isotope ratios) has encountered two problems:The largest mass independent isotopic anomalies examined by this fieldarise from photochemical, magnetic and/or nuclear volume effects thathave been studied in detail for only a few chemical compounds and reac-tions (e.g., ozone and SO2 photochemistry). There is much about suchfractionations that we do not understand (although there is a recentprogress with experimental and theoretical study of these and other spe-cies, such as CO; Chackraborty et al., 2012). And, second, mass dependentfractionations of elements having multiple isotope ratios can exhibitsubtle but measurable variations in mass law (i.e., mass dependentslope in a plot of one isotope ratio vs. another). These variations arisefromunderstood principles of chemical physics and are potentially usefulin that they could give rise to new geochemical tools. But, there is verylittle substantive information showing how these mass laws vary in geo-chemically interesting systems. Similarly, the intramolecular fraction-ations that are the subject of clumped-isotope and SNIF-NMRmeasurements can be understood as consequences of the same fraction-ation mechanisms commonly used to interpret conventional (bulk)stable isotope data, but have been investigated in detail for only a handfulof examples (e.g., ordering, or ‘clumping’, of 13C with 18O in CO2 andcarbonates; Eiler, 2011).

1.4. The dialog with chemistry

The geochemical tools we think of as core to traditional stableisotope geochemistry — e.g., carbonate-water thermometry, the vapor


pressure isotope effect for water, or the photosynthetic fractionation ofcarbon isotopes— arose froma dialog between the, at that time, cutting-edge discoveries in physical chemistry (quantummechanics), technicaladvances in analytical chemistry (e.g., the Niermass spectrometer), andexperimental and field-based discoveries in geochemistry andbiochemistry. Similarly, a deep, physically based understanding of theemerging stable isotope disciplines must involve first-principle modelsrooted in the experimental and computational tools of physical andbiological chemistry. These tools have evolved in a variety of waysthat should facilitate this kind of interdisciplinary dialog. Software thatallows ab initio and molecular dynamics simulations of isotopic frac-tionations has become widely available and relatively easy to learnand use, and computers capable of making such calculations, even forrelatively large and complex chemical structures, are increasingly avail-able to earth science research groups. And, there is a growing apprecia-tion that widely known methods for evaluating isotope effects onmolecular vibrational energies must be replaced withmore sophisticat-ed and accurate approaches when examining the subtle, second-orderisotope effects involved in some of the emerging disciplines of stableisotope geochemistry (e.g., Webb and Miller, 2014).

This paper aims to illuminate both the need and opportunity formultidisciplinary studies that combine innovations in analysis, experi-ment and fundamental chemical theory to push forward the emergingdisciplines of stable isotope geochemistry. Most of the followingsections present case studies where analytical advances, discoveriesand physical–chemistry theory come together in focused problemsin stable isotope geochemistry. But we start first with a subject thatunderlies many of the others — a persistent problem that confrontsnearly every tool in every branch of stable isotope geochemistry.

2. On beyond equilibrium

Many of the problems on the frontiers of stable isotope geochemis-try involve the struggle to understand isotopic fractionations inconsis-tent with models of the equilibrium thermodynamics of isotopeexchange reactions first described by Urey in the 1930's and fleshedout by a community of founding figures in the chemical physics ofisotopes in the 1940's and 50's. Some of the best known of these cases

Diffusion

A. Evaporation/Condensation

‘proto-sit

Bucryst

ExchangeCondensation Evaporation

‘correlation’

Fig. 1. Illustration of the chemical and physical processes at play in phase transformations an

involve peculiar photochemical or nuclear effects; we address these intheir own sections below. But there also exists a family of non-equilibrium, or ‘kinetic’, isotope effects that can occur in nearly everygeochemical transformation: evaporation and condensation (Richter,2004; Luz et al., 2009), diffusive transport (Bourg and Sposito, 2008;Beekman et al., 2011), mineral growth and dissolution (Kiczka et al.,2010; Nielsen et al., 2012), redox reactions (Anbar and Rouxel, 2007;Zink et al., 2010), and metabolic reactions (Ripperger et al., 2007;Cobert et al., 2011). Fig. 1 illustrates some of the fundamental processesin such systems that are the focus of this section, several of which aresignificant for subsequent sections.

Kinetic isotope effects often limit our ability to interpret the stableisotope compositions of natural materials; for example, kinetic controlsare implicated in some ‘vital effects’ that complicate paleoclimaterecords, and are major complication in the isotope geochemistry ofnatural waters and water vapors. However, if the kinetic fractionationfactors associated with these non-equilibrium processes can be deter-mined experimentally and/or theoretically (cf., Bourg and Sposito,2008; Maggi and Riley, 2009; Zink et al., 2010; Nielsen et al., 2012),then these effects can provide powerful applied tools, such as novel bio-markers or measures of previously poorly known paleoenvironmentalvariables (e.g., humidity).

2.1. Some founding principles

A useful first step in the discussion of chemical kinetics is to define anomenclature for discussing the case of a one-step transformation ofelement A from state Ainitial to state Afinal, with forward and backwardreaction rates Rf and Rb (such that the overall rate Ro = Rf–Rb):

Ainitial

R f⇌Rb

Afinal ð1Þ

For a trace isotope i, the overall transformation rate iRo can beexpressed as a function of the isotopic compositions of the initial andfinal states (expressed here as mole fractions iXinitial and iXfinal, whichare both assumed to be much less than 1 to simplify the algebra) and

Desolvation

Forwardreaction

Back reaction

Exchange

B. Precipitation from aqueous solutions

Diffusion

es’

lkal

d other chemical reactions, any or all of which may contribute to isotopic fractionations.


the kinetic isotope fractionations ('KIF') associated with the forwardand backward transformations (αf, αb):

iRo¼iR f–iRb¼iXinitialα fR f–

iXfinalαbRb ð2Þ

The KIF factors αf and αb are related to the equilibrium isotopic frac-tionation through αeq= αf/αb; i.e., the equilibrium state corresponds toan exact balance between the forward and back reactions. If we assumesteady-state conditions (diXfinal/dt = 0 = iRo–

iXfinalRo) and define theoverall fractionation of trace isotope i as αo = iRo/(iXinitialRo), we obtainthe following equation for the overall isotope fractionation associatedwith Eq. (1) (DePaolo, 2011):

αo ¼ α f

1þ Rb

Ro þ Rb

α f

αeq−1

! ð3Þ

Inspection of Eq. (3) shows that the overall isotope fractionation fac-tor associated with one-step, steady-state geochemical transformationsdepends significantly on kinetic isotope effects unless Ro bb Rb. Thesame significant role of kinetic isotope effects is predicted (with amore complex form of Eq. (3)) if we relax the condition that iXinitial

and iXfinal are both much less than 1.Kinetic isotope fractionation almost always arises fromNewtoniandy-

namics, i.e., the motions of atoms and molecules (Vineyard, 1957). A no-table exception is chemical reactions involving light elements such as H,N, O, or C where quantum mechanical effects (quantum tunneling,zero-point energies) may contribute significantly to the kinetic isotopeeffect (Bigeleisen, 1949; Eyring and Cagle, 1952; Bigeleisen andWolfsberg, 1958; Scheppele, 1972; Klinman, 2010; Gómez-Gallego andSierra, 2011); even in this case, the Newtonian contribution to the KIF ispresent (Bigeleisen, 1949; Eyring and Cagle, 1952; Bigeleisen andWolfsberg, 1958; Matthews et al., 2001) and often dominates the KIF ofelements as light as C (Nowlan et al., 2003; Kelly et al., 2009).

Themanner inwhich KIF arises from atomic ormolecularmotions isbest understood for three types of elementary transformations: evapo-ration and condensation, diffusion in gases and liquids, and metalligand-exchange reactions.

2.2. Evaporation and condensation

In conditions where diffusive boundary layers are believed to benegligible, such as evaporation of silicate melts (Richter et al., 2007) orliquid mercury (Estrade et al., 2009), mass fluxes across liquid–gasinterfaces are determined by the rates of evaporation and condensation.These rates follow relations derived from the kinetic theory of gases(Knudsen, 1911; Langmuir, 1913; Hirth and Pound, 1960; Richteret al., 2007):

iR f ¼niσ c;iPi;satffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2πmiRT

p andiRb ¼ niσ c;iPiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2πmiRT

p ð4Þ

where Rf and Rb are evaporation and condensation fluxes per surfacearea, ni is the number of atoms of i in the gas species molecule contain-ing i, σc,i is the condensation coefficient (the probability that an incidentmolecule will condense into the liquid phase), Pi,sat is the saturationvapor pressure of isotope i, and Pi is the actual vapor pressure of isotopei. For two isotopes i and j, ni being independent of isotopic mass and αeq

being equal to Pi,satXj,liquid/Pj,satXi,liquid, we have:

α f ¼σ c;i

σ c; j

ffiffiffiffiffiffimj

mi

sαeq ð5Þ

Ifαeq and σc,i/σc,j are close to 1, Eq. (5) simplifies toαf = (mj/mi)0.5, arelationship that is consistent with studies of Fe evaporation from

molten FeO (Wang et al., 1994) and K evaporation from a melt ofchondrule-like composition (Yu et al., 2003). Fractionations closer to 1have been observed for the evaporation of pure Hg [αf(202/198Hg) =0.9933 ± 0.0011 at 22 °C, whereas (mj/mi)0.5 = 0.9900 (Estrade et al.,2009)] and for the evaporation of Mg from molten mixtures of SiO2,Al2O3, MgO and CaCO3 [αf(25/24 Mg) = 0.98704 ± 0.00025 on averageat 1600 to 1900 °C, decreasing with temperature, whereas (mj/mi)0.5 =0.97980 (Richter et al., 2007)]. These results suggest that, in certaincases, the condensation coefficient σc,i may increase with isotopic mass(Richter, 2004; Richter et al., 2007). Molecular dynamic (MD) simula-tions, which are widely used for obtaining molecular-scale insightinto the condensation coefficient σc,i (Tsuruta and Nagayama, 2004;Kolb et al., 2010; Cheng et al., 2011), may provide a means to probethe isotopic mass-dependence of σc,i.

2.3. Molecular diffusion in gases and liquids

Molecular diffusion in gases and liquids can cause significant KIF, forexample, in the gas-phase diffusive boundary layer during water evap-oration (Luz et al., 2009; Kim and Lee, 2011), in the aqueous-phasediffusive boundary layer during air–water exchange of volatile gases(Bourg and Sposito, 2008), in pore water of low-permeability sedimen-tary formations (Lavastre et al., 2005; Bourg et al., 2008; Beekman et al.,2011), and in crystals formed during magmatic differentiation (Tenget al., 2011). For a solute of mass mi diffusing in a solvent of mass m0,in the idealized case where solute and solvent interact only throughinstantaneous, uncorrelated binary collisions, the kinetic theory ofgases predicts that the diffusion coefficient Di has an inverse square rootdependence on the reduced solute–solvent mass μi0 = mim0/(mi + m0)(Chapman and Cowling, 1960; Hansen and McDonald, 1986; Aliet al., 2002). Under these circumstances, the KIF of isotopes i and j(αf = Di/Dj) should equal:

α f ¼ffiffiffiffiffiffiffiμ j0

μ i0

s¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffimj mi þm0ð Þmi mj þm0

� �vuut ð6Þ

Attempts to confirm Eq. (6) using gas-phase measurements arearduous because of the difficulty of ensuring pure diffusive transport.Experimental measurements of D/H and 18O/16O isotope fraction-ation during water vapor diffusion are inconsistent with Eq. (6)[αf(D/H)/αf(18/16O) = 0.84–0.88 for diffusion in air at 20 °C (Merlivat,1978; Luz et al., 2009), whereas Eq. (6) predicts a value of 0.52 fordiffusion in air]. Whether this discrepancy arises from experimentaldifficulties (Kim and Lee, 2011) or from a failure of the kinetic theory ofgases to explain H2O diffusion in air is currently unknown.

Data are more widely available on the isotopic mass dependenceof solute diffusion coefficients in liquids, particularly in water (Mills,1973; O'Leary, 1984; Jähne et al., 1987; Richter et al., 2006; Bourg andSposito, 2007, 2008; Eggenkamp and Coleman, 2009; Bourg et al.,2010; Aupiais, 2011) and in silicate melts (Richter et al., 2003, 2008,2009; Watkins et al., 2009, 2011). These data generally indicate smallerαf-values than Eq. (6). Experiments and MD simulations yield identicalαf-values, confirming that this KIF is a classical mechanical effect (Bourgand Sposito, 2007; Bourg et al., 2010).Where data are available formorethan two isotopes of the same solute, they are consistent with aninverse-power-law dependence of D on isotopic mass (Bourg andSposito, 2007, 2008; Bourg et al., 2010):

Di∝m−βi ð7Þ

with β-values that range from 0 to 0.22 (Bourg et al., 2010; Watkinset al., 2011). Mode coupling theory calculations suggest that the failureof kinetic theory in gases in these instances is caused by solute–solventinteractions having long-time correlations rather than occurringthrough instantaneous uncorrelated collision (i.e., the colliding


molecules interact chemically rather than simply through hard-spherecollisions; Bhattacharyya and Bagchi, 2000; Ali et al., 2002). Thisview is supported by the fact that the β-values of solutes are inverselycorrelated with: 1) the residence times of water molecules in theirfirst solvation shell (Bourg et al., 2010); and 2) with the ratio of solventto solute diffusion coefficients (Watkins et al., 2011), two propertiesthat express the long-time coupling of solute and solvent motions.

2.4. Metal ligand-exchange reactions

A recurring theme in studies of the biogeochemistry of metals inaquatic environments is the importance of ligand-exchange reactions —particularly, binding to organic ligands (Zhu et al., 2002; Corry andChung, 2006; Gussone et al., 2006; Lacan et al., 2006) or to mineralsurfaces (Stumm and Morgan, 1996; Sposito, 2004; Ohlin et al., 2009;Black et al., 2010; Stack et al., 2012) — as the rate-controlling steps inmetal cycling. The important kinetic role of these reactions suggeststhat they may contribute significantly to metal kinetic isotope effects innatural settings.

At first glance, the very wide range of rates and molecular-scaledetails of metal ligand-exchange reactions (Richens, 2005) wouldappear to preclude any generalization on the KIFs associated withthese reactions. A path towards a general model of these KIFs issuggested, however, by the observation that the forward rate constantskbinding of metal-ligand exchange reactions often scale with the water-exchange rate constant kwex of the metal of interest, a relationshipexpressed by the well-known Eigen–Wilkins–Werner relation (Eigen,1963; Stumm and Morgan, 1996; Sposito, 2004; Richens, 2005; Ohlinet al., 2009):

kbinding∝kwex ð8Þ

Eq. (8) suggests that knowledge of themass dependence of kwexmay besufficient to predict the KIF associated with the forward rate of manyligand-exchange reactions, particularly in the case of the more labilemetal ions for which kbinding is relatively insensitive to the nature ofthe incoming ligand (Richens, 2005).

2.5. Questions and needs

The preceding reviewmakes it evident that there already exists a de-tailed theoretical and experimental ‘infrastructure’ from understandingisotopic fractionations controlled by physical and chemical kinetics inrelatively simple systems. Nevertheless, the most obvious need of thefundamental study of kinetic isotope effects is simply more data onmore systems and processes of geological relevance. We've achieved auseful critical mass of experimental constraints and connections tonatural materials for only a few model materials that are important inthe environment and geological record— evaporation and condensationof water; growth of carbonate from aqueous solution. Much must bedone before these concepts can be molded into predictive, quantitativemodels of the isotopic compositions for diverse geologically importantauthigenic solids (silica, clays, sulfates, etc.) and products of biologicallycontrolled or mediated mineral growth.

3. Why can't authogenic minerals just behave?

Our first case study builds immediately on the general principles ofkinetic isotope effects laid out in Section 2, by considering the kineticisotope effects that underlie the common failure of minerals to growin equilibrium with the geological fluids in their environments. Studiesof metal isotopic fractionations during mineral growth from aqueoussolutions (e.g., Johnson et al., 2004; Baskaran, 2011) generally findlarge spreads in isotopic fractionations that cannot be accounted forby theoretically predicted equilibrium fractionation factors (Yamajiet al., 2001; Griffith et al., 2008; Hill and Schauble, 2008; Jahn and

Wunder, 2009; Hill et al., 2010; Rustad et al., 2010; Kowalski and Jahn,2011; Schauble, 2011). These findings constitute a first-order barrierto the application of the emerging field of metal stable isotopes topaleoclimate, paleooceanography and other geochemical problems.

As a general rule, kinetic isotopic fractionations during precipitationof solids from liquids or gases enrich the solid in light isotopes(e.g., Böttcher et al., 2011; Nielsen et al., 2011; Wunder et al., 2011) —generally opposite the direction of equilibrium fractionations in thesesystems (Bigeleisen andMayer, 1947; Bigeleisen, 1965). This presumablyreflects the generally faster rate of transport of light isotopic speciesthrough a liquid or vapor to a growing solid, or faster ‘motion’ throughthe reaction coordinate during irreversible precipitation (Bigeleisen,1949). An open question is whether we can understand these effects inenoughmechanistic detail to develop a general description of the isotopiccompositions of natural materials.

3.1. Diffusion alone?

A recent series of studies combiningmolecular dynamic (MD) simu-lations and laboratory experiments has shown that isotopes of Li+, K+,Ca2+, Cl−, and the noble gases are fractionated via diffusion in liquidwater (Richter et al., 2006; Bourg and Sposito, 2007; Bourg andSposito, 2008; Bourg et al., 2010). For example, in the absence of otherkinetic processes, diffusion of dissolved Ca2+ species through water toa growing solid (e.g., calcite) can enrich the precipitating solid (relativeto the fluid) by ca. 0.4‰ in 40Ca relative to 44Ca at 348 K (Bourg et al.,2010). Laboratory precipitation experiments and natural samples ofcalcite and aragonite indicate a range in δ44/40Ca from ca. +0.5 to−4.0‰ (DePaolo, 2004 and references therein; Nielsen et al., 2011and references therein), where the equilibrium Ca isotope fractionationbetween Ca2+(aq) and calcite is predicted to be of order 0.0 ± 0.1‰(Fantle and DePaolo, 2007). These experiments clearly imply a kineticcontrol of the fractionation, but diffusion of dissolved Ca2+ to thegrowing mineral surface is clearly too small (and expected to be tooconstant) to explain such widely varying experimental results.

3.2. Desolvation

Experiments and molecular-dynamic (MD) simulations indicatethat the kinetics of crystal growth from aqueous solutions can be con-trolled or influenced by the chemical kinetics of desolvation of ionsand/or attachment to a growing crystal surface (deBoer, 1977; Mucciand Morse, 1983; Casey, 1991; Casey and Westrich, 1992; Dove andCzank, 1995; Kerisit and Parker, 2004; Piana and Gale, 2006; Kowaczet al., 2007). It is conceivable that these processes are responsible forthe common observation of large, apparently kinetically controlledfractionations of metal stable isotopes during crystal growth (Gussoneet al., 2003). Recent MD simulations by Hofmann et al. (2012) showthat the desolvation rates (i.e., water exchange rates; kwex) of isotopesof Li+, K+, Rb+, Ca2+, Sr2+, and Ba2+ all follow an inverse power-lawdependence on cation mass (kwex ∝ m-γ). This mass dependencepredicts enrichment of the light isotope in precipitating solids relativeto the surrounding fluid by amounts broadly in the range of experimen-tal results, suggesting cation desolvation is a plausible mechanismfor causing non-equilibrium metal isotope fractionation in aqueoussystems.


While these recentMDmodels provide suggestive evidence regardingthe role of desolvation in kinetic isotope effects during mineral growth(perhaps modified by the more subtle effects of diffusion), there aresignificant limitations in the models themselves: they consider systemsthat are likely too small and time scales too brief to capture all of therelevant chemical physics, largely because of limits to computationalpower (e.g., Geissler et al., 1999; Stack et al., 2012).


The next significant advance in this areamay come fromMD simula-tions, which allow for quantum calculations of atomic velocities andbonding energetics at the time scale of reactions and can providemore realistic (and comprehensive) thermodynamic and kinetic data,or rare-event modeling methods like metadynamics (e.g., Stack et al.,2012) and transition-path sampling (e.g., Kerisit and Rosso, 2009),which enable an evaluation of reaction mechanisms and calculation ofrate constants via the sampling of the relevant energy landscape(s) forprocesses that occur on long timescales otherwise inaccessible by directMD. At present, however, even these approaches will likely still belimited to small molecular systems. As suggested by Rustad (2001),constructing near-molecular-scale (i.e., on the order of 100 s to 1000 sof nanometers) systems accessible by both simulation and experimen-tal observations is the necessary next step forward. One possiblesolution could come from studies of the reactivity and exchange ratesof metal and oxygen sites in small (i.e., fewer than 50 atoms) inorganicmolecules that are symmetrically analogous to phases of geochemicalinterest (e.g., Rustad and Casey, 2012). Such systems can be probedvia a combination of straightforward analytical methods (e.g., spectros-copies) and calculations based on ab initio or molecular dynamicstheory (e.g., Casey et al., 2009).

Finally, in addition to diffusion — and desolvatation — limitedinduced kinetic isotope fractionation, non-equilibrium isotope fraction-ation is also observed in cases where it seems inevitable that crystal–chemical controls dominate; for example, chemical and isotopic sectorzoning in minerals, where crystallographically non-equivalent regionsgrow from the same solutions at broadly similar rates but havemarkedlydifferent compositions (Boyd et al., 1988; Dickson, 1991). This processmay reflect local equilibrium of the chemical or isotopic species betweenthe fluid and a ‘proto-site’ at the surface of the growing crystal — astructural site that differs in coordination, size, or shape from thefinal site in the crystal interior (Watson, 2004). If crystals growrapidly enough, then the proto-sites may transform into their finalbulk-solid configurations more quickly than the time needed for iso-topic re-equilibration of those sites with the adjacent fluid (Watson,2004). While the basic outline of the proto-site hypothesis has beenapplied to several problems and seems like a leading contender toexplain some non-equilibrium phenomena (e.g., sector zonation),much will have to be learned about the structures and chemicalkinetics of growing crystal surfaces and the crystal–liquid boundarylayer before we can understand the isotopic fractionations that occurat this interface.

4. The outer limits of ‘mass dependent’ isotopic fractionation

Several fields of meteoritics, cosmochemistry, atmospheric chemis-try and Precambrian geology are concerned with comparisons of thefractionation behaviors of two or more isotope ratios of the sameelement; for example, comparison of 34S/32S with 33S/32S, or 18O/16O

Fig. 2. Schematic illustration of the nomenclature and composition space of mass-independent i(such as 33S and 34S or 17O and 18O). Ri values are ratios of these isotopes to a reference isotope (eare generally assumed to follow power-law relationships, such that R1 vs. R2 will follow a curvelogarithm of the ratio (or equivalent function of the δ value; panel B). Δi values are defined by

with 17O/16O. In these cases, measured isotopic compositions are gener-ally comparedwith a reference frame of expectedmass dependent frac-tionation behavior; i.e., where the magnitudes of fractionations for twoisotope ratios are a simple function of their relative differences in mass.For example, mass dependent S isotope fractionations are generally as-sumed to follow the power law dependence, α33 = α34

λ33,34 where αi isthe fractionation of the iS/32S ratio and λ33,34 is a constant that dependsupon themass difference between the 34S and 32S-bearing compound ofinterest (~2 amu) vs. that between 33S and 32S-bearing compounds(~1 amu). Note λi,j may be referred to as the mass law exponent ormass exponent. See Fig. 2.

Equilibrium isotope fractionation in the high temperature limit is as-sociated with (in the case of sulfur): λ33,34 = (1/32/1/33)/( 1/32/1/34)~0.515 (see below; note all masses are reported in atomic mass units).This is often taken to be a suitable reference frame for defining massdependent sulfur isotope fractionations (Hulston and Thode, 1965;Farquhar and Wing, 2003; Otake et al., 2008). Other mass dependentfractionations include chemical kinetic isotope effects, diffusion andgravitational fractionations; these generally have broadly similar(though often subtly lower) mass exponents.

There are several cases where natural materials violate these massdependent fractionation behaviors, e.g., anomalously high or low 33S/32Sratios at a given 34S/32S ratio in sulfides and sulfates from Archeansedimentary rocks (Farquhar et al., 2000a), anomalously low 17O/16Oratios at a given 18O/16O ratio in components of primitive meteorites(Clayton, 1993), and anomalously high 17O/16O ratios at a given 18O/16Oratio in ozone from the earth's stratosphere (Heidenreich andThiemens, 1983). These exceptions to referencemassdependent fraction-ation laws are generally described as ‘mass independent fractionations’and are generally measured as a departure from the trend of a massdependent line in a triple isotope reference line; e.g., a plot of 34S/32S vs.33S/32S (Fig. 2). These departures have been illustrated through Δi

values, such as: Δ33S = δ'33S - 0.515 × δ'34S, where δ'xS = 1000 ×ln(δxS/1000 + 1), δxS = ((xS/32S)sample/(xS/32S)standard -1) × 1000,and the constant, 0.515, is the mass law exponent (λ34, 33). Thisdefinition is closely similar to Farquhar and Wing's, 2003 definition,Δ33S = δ33S–(δ34S/1000 + 1)0.515 – 1) × 1000.

The discoveries of large mass-independent isotope anomalies,particularly the sulfur isotope anomalies in minerals in Archean rocksare explored in a later section, below. These effects are mostlyinterpreted to result from atmospheric reactions in which large massindependent effects are associated with photo-dissociation and otherphotochemical reactions and, in the case of ozone, reflect the effect ofmolecular symmetry on rates of dissociation of unstable species.However, interest in these effects have also inspired a broader studyof the mass laws that describe nominally mass-dependent processes(i.e., chemical equilibria, chemical kinetics, diffusion). Some of thiswork specifically asks whether such fractionations might be directly re-sponsible for the multiple-per-mil sulfur isotope anomalies in Archean

sotope geochemistry. Superscripts ‘1’ and ‘2’ denote two rare isotopes of the same element.g., 32S or 16O). δi values follow conventional nomenclature.Mass dependent fractionationsdefined bymass exponent, λ1,2 (panel A). This curve can be linearized by taking the naturalthe deviation from this mass dependent trend (generally reported in units of per mil).

33i-j

1.000

0.515

34i-j

Temperature

α

α

αxi-j

λ33,34

Fig. 4. Schematic illustration of the extreme mass exponents that can arise when conven-tional mass-dependent fractionations undergo crossovers (changes in α from valuesgreater than 1 to less than 1). Because the crossover temperature may differ for the tworelevant fractionation factors (e.g., α33 vs. α34), the mass exponent can deviate stronglyfrom its canonical value for a narrow temperature interval (a few degrees). More subtlenon-canonical λ values may occur over tens of degrees.


materials; some is a more general exploration of mass laws of isotopicfractionation — a subject for which much of our understanding isbased on idealized models and about which more has been assumedthan understood.

4.1. Unusual mass laws associated with equilibrium processes

A premise of the study of mass independent isotope geochemistry isthat equilibrium and conventional (non-photochemical) chemical kineticfractionations exhibit only subtle variations in λ, similar to cannonicalvalues (e.g., for sulfur isotopes, λ33,34 = (1/32–1/33)/(1/32–1/34) ~ 0.515and λ36,34 = (1/32–1/36)/(1/32–1/34) ~ 1.889). For equilibrium fraction-ations, thesemass exponents are functions of the partition function ratiosfor individual molecules, which vary with temperature, bond stiffnessand reducedmass, over a range of ~0.5%, relative (Fig. 3; with exceptionsdiscussed below).

It is recognized that anomalous mass laws (i.e., mass laws thatdiffer significantly from the canonical values) can occur in conventional(i.e., non-photochemical) chemistry as a result of nuclear volume effects(discussed below). However, Schauble (2007) estimates that sucheffects should be negligible for sulfur isotopes. Slight deviation fromcanonical mass laws can arise in reaction networks through the effectsof mass-conservation on systems undergoing distillation or otherdynamic reactions. These effects are typically expected in reactionnetworks that combine mixing, open-system fractionation and sets ofmultiple stepwise and/or branched reactions (Matsuhisa et al., 1978;McEwing et al., 1983; Farquhar et al., 2007). These effects are usuallywell accounted for and involve no novel chemical physics, so we donot discuss them further.

Significant deviations from canonical mass laws can also occurwhenequilibrium (i.e., thermodynamically controlled) fractionations display‘crossovers’ — changes in the sign of values of ln(αi) (Fig. 4). Thetemperatures at which crossovers occur differ subtly among differentisotope ratios (i.e., the crossover temperature for α33 generally willnot exactly equal that for α34). The gaps between crossover tempera-tures are typically expected to be just a few °C (though few such casesare actually demonstrated by experiment or observations of naturalsystems). Within this temperature range, the mass law exponent (λi,j)can take on any value and can vary wildly with small changes intemperature (Skaron and Wolfsberg, 1980; Oi et al., 1985; Kotakaet al., 1992; Deines, 2003). Perhaps more importantly, the mass lawcan differ more subtly, but still significantly, over a broader range of

20 40

0.514

0.515

0.516

SO4-2 –H2S

SO3-–H2SSO2–H2S

CS2 – H2S

60 80

1000xln(α34i,j)

λ33,34

Fig. 3. Calculated variations in the mass exponent (λ33,34) for sulfur isotope exchangeequilibria among various simple compounds (Farquhar et al., 2003). Note the size ofeach fractionation factor (α34

i-j = R34i/R34

j) increases with decreasing temperature, solow temperatures are to the right and high temperatures to the left of this diagram.While all such equilibria are predicted to conform loosely to the canonicalmass dependentrelationship of λ33,34 = 0.515, variations of up to ~0.5% occur, depending upon tempera-ture and the reduced masses of the species in question. Little of this variation has beendocumented through experimental observation, and there is relatively little understand-ing of how these variations will extend to more complex systems (large molecules;phase changes; sorbed compounds).

temperatures near these crossovers. And, more subtly still, the samechemical–physics phenomena that lead to crossovers (and relatedpeculiarities in temperature dependence of isotopic fractionations)lead to variations in mass law. Such variations are best known inmolecules that have little geological relevance (e.g., between SPCl andH2S, and between SOBr or SOCl and SO2). Nevertheless, there are veryfew direct observations of mass laws for sulfur isotope fractionationsaccompanying well understood and thermodynamically controlledreactions, and theoretical explorations of such systems are generallyrestricted to the small, vibrationally simple molecules (see Otake et al.,2008).

Lasaga et al. (2008) suggested that small differences in the vibrationalenergy between the bound states of sulfate during adsorption ontoorganic matter could result in a threshold behavior, whereby one ormore S isotopes are stably bound to a surface while the others are not,causing isotopic fractionations that appear mass independent (or atleast violate common expectations regarding mass dependent fraction-ations). Subsequent re-evaluation of this problem suggested that thethreshold effect in question arose from a truncation error in the approx-imations of Lasaga et al.'s theoretical treatment, and that amore accuratedescription of such systems yields only strictly canonical mass-dependent isotope effects (Balan et al., 2009). However, this conclusionapplies only to simple harmonic oscillators, not to vibrationally complexmaterials having a variety of modes of vibration and rotation that maycombine or compete with each other to produce a net fractionation.

Eiler et al. (2013a) recently observed a non-canonical massexponent, λ33,34 = 0.551 accompanying the vapor pressure isotopeeffect for SF6 ice and sorbate. This is significantly greater than the canon-ical value of 0.515 or any calculated equilibrium mass law (Fig. 3), andappears to have occurred in systems that reached a reversible, time-invariant equilibrium (i.e., this appears to be a thermodynamicallycontrolled fractionation). This effect might be the result of competitionbetween isotope effects on intra and intermolecular vibrations thatdiffer markedly in reduced mass. Analogous effects are previously


recognized for the mass law governing D/H and T/H fractionationsamong phases of methane (Kotaka et al., 1992), and it seems possiblethat this could be more widespread than is generally recognized. Initialattempts to test this hypothesis with first-principle models failed, likelydue to poor description of the phonon spectrum of SF6 ice; this is anattractive target for further, more refined models.

4.2. Mass laws of non-equilibrium processes

The kinetic theory of gases predicts that diffusive or gravitationalfractionations are associated with mass laws that differ subtly but mea-surably from those describing isotope exchange equilibria (Bigeleisenand Wolfsberg, 1958; Young et al., 2002). For example the mass lawdescribing the oxygen isotope fractionation accompanying Knudsendiffusion of CO2 isλ17,18= ln(44/45)/ln(44/46) ~ 0.507,which is signif-icantly lower than the range of values for thermodynamic equilibriainvolving oxygen isotopes (roughly described in the high temperaturelimit by the approximation, λ17,18 = (1/16–1/17)/(1/16–1/18) ~ 0.529).

Anomalous mass laws could also arise during networks of irrevers-ible reactions (including those that contain an equilibrium step), evenif no one step in that network has an anomalousmass law. One exampleis a two-step reaction in which a kinetically controlled step cleaves abond in a transition state molecule that is maintaining an isotopeexchange equilibrium with another substrate. Examples of suchcomplex systems can be found in experiments showing inverse kineticisotope effects (i.e., where products are enriched in heavy isotopescompared to reactants; e.g. Casciotti, 2009). As illustrated in Fig. 5,anomalous mass laws can be produced if the kinetic and equilibriumfractionations are opposite in direction but similar in magnitude. It ispossible that these behaviors of complex reaction networks accountfor previous experimental observations of mass anomalous behaviorin sulfur isotope fractionations. For example, thermochemical sulfatereduction in the presence of water and amino acids at temperaturesbetween 170 and 200 °C generated Δ33S values as high as ~2‰(Watanabe et al., 2009). Similar experiments have yielded Δ33S ashigh as ~13‰ (Oduro et al., 2011). Oduro et al. ascribed these anoma-lous Δ33S fractionations to magnetic isotope effects (Buchachenko,2001 and references therein) based on the relatively subtle accompany-ing Δ36S anomalies (they suggested that nonzero Δ36S in the experi-ments of Watanabe et al. (2009) were the result of mixing).

1000xln(δ18O/1000+1)Reactant

Equilibrium step ( 17,18= 0.529)

Diffusive step ( 17,18= 0.513)

Product

1000

xln(

δ17O

/100

0+1)

Fig. 5. Schematic illustration of the exotic mass laws that can arise in complex reactionnetworks, where two or more steps differ subtly in mass exponent (e.g., the canonicalequilibrium O isotope mass exponent of 0.529 vs. the Knudsen diffusive mass exponentfor oxygen isotope fractionation on water diffusion, 0.513). If these steps differ in sign offractionation (i.e., α18 is greater than 1 for one step and less than 1 for the other), awide range of net λ17,18 values are possible. In the illustrated case, where the equilibriumand diffusive fractionations are similar in magnitude and opposite in sign, λ17,18

approaches infinity (a vertical line).

Additional experimental observations of anomalous mass lawsduring non-photochemical reactions include a report by Miller (2002)of thermal decomposition of carbonates and evidence presented byone of us (Cartigny) at the Basic Energy Science workshop, describingmass laws varying from λ33,34 of ~0.505 to ~0.621 during the partialfluorination of sulfides. These effects may be due to heterogeneoussolid/gas reactions on surfaces, though the exact mechanism remainsunknown. Finally, mass-anomalous effects have been observed duringmass transport of vapor through a temperature gradient (Sun and Bao,2011).

It is possible that effects like those discussed above contribute tonon-zero Δ33S and/or Δ36S values of geological samples, though gener-ally the effects observed experimentally to-date are too subtle toexplain mass-independent fractionations in Archean sedimentaryrocks, or are not consistent with the observed trends of co-varyingΔ33S, Δ36S and δ34S in natural samples (see below). These experimentsdemonstrate, however, that processes yielding anomalous isotopicfractionations likely remain to be discovered.


The principal limitation to our current understanding of the masslaws of processes we conventionally think of as ‘mass dependent’(chemical equilibria; chemical kinetic isotope effects; diffusion) issimple: we have experimentally observed only a small fraction ofthose relevant to geologically important processes. This field has largelydepended on empirical observations of ‘average’ mass laws implied bycompositional variations of natural materials having only the loosestrelationships to one another (e.g., terrestrial rocks; meteoric waters),and theoretical predictions regarding simple, idealized systems. It is es-sential that this subject engages inmorebasic experimental exploration.Suchworkmay simply confirmprejudices and reinforce interpretations.Or it might be eye opening. It is noteworthy that most of the recentefforts in this direction (Miller, 2002; Watanabe et al., 2009; Sun andBao, 2011; Eiler et al., 2013a; P. Schiano's unpublished experimentsdescribed above) have produce results that vary from unexpected tounbelievable. A key element needed in any future experiments iscontrolled isolation of well-known mechanisms, as opposed to thecomplex, largely uncontrolled reactions examined by most of theseinitial studies, and interpretation of experimental results using detailedmodels of the relevant chemical physics.

5. O-isotope mass laws as a tool for study of the water cycle

The abundance of 17O in naturalmaterials is generally described as adeparture from a reference line in a plot of 18O/16O vs. 17O/16O(or equivalent functions), most often defined as: Δ17O = δ'17O–λ ×δ'18O, where δ'xO = 1000 × ln(δxO/1000 + 1), δxO = ((xO/16O)sample/(xO/16O)standard -1) × 1000, and λ is a constant that describes theobserved or assumed mass law of nominally mass dependent fraction-ations (commonly 0.52 or 0.529; e.g., Miller, 2002; Fig. 6). Large positivevalues of Δ17O in atmospheric compounds (Fig. 6a) have been attribut-ed to mass independent isotopic fractionations that can arise in thechemistry of ozone and are then passed to other species (CO2, N2O,sulfate, etc.) through O-exchange reactions (Thiemens et al., 1995,2012). And, the sum of these enrichments is balanced by a small butmeasurable negative Δ17O value in atmospheric O2 (Luz et al., 1999).Indirect evidence for similar mass independent atmospheric effects isfound in ancient mineral deposits on Earth and Mars (Farquhar et al.,1998; Bao et al., 2000, 2009), and subtle variations in the Δ17O ofatmospheric O2 trapped in ice cores have been used as a measure ofsecular variation in biological productivity and respiration (Blunieret al., 2002, 2012).

However, in addition to these large mass independent atmosphericfractionations, it is recognized that small variations in Δ17O in watersand minerals can arise from mass-dependent isotopic fractionations,

Fig. 6. Schematics of triple oxygen isotope variation on two scales: A) major Earth reservoirs, including the terrestrial fractionation line (TFL) defined by the roughly uniform mass-dependent variations of rocks and waters (δ17O= 0.52*δ18O) and the 16-O depleted components of the atmosphere, largely controlled by O associated with ozone chemistry (redraftedfrom Thiemens, 2006); And, B) schematic illustration of the factors that control subtle variations in Δ17O of terrestrial waters, primarily equilibrium precipitation (slope of 0.529) anddiffusion of vapor during evaporation into air (slope of 0.518). Atmospheric moisture formed at low relative humidity (RH) has a high Δ17O value influenced by the strong diffusivefractionation involved in evaporation of its sources, whereas high RH moisture is dominated by equilibrium evaporation and has a smaller Δ17O value. Panel B is based on schematicsin Luz and Barkan (2010); a linearized δ'-notation has been used (see Fig. 2).

Fig. 7. A plot of Δ17O vs. d-excess for rainfall from Niger sampled in a 15 week period inBanizoumbou (distinguished into three divisions of relative humidity –‘RH’– of the airduring collection), and during three different periods of a single squal in Niamey(replotted from Landais et al., 2010). RH was mostly N65% in the first 75 min of thesqual and b65% after. The two gray lines show the expected relationship between d-excessand Δ17O predicted by simple re-evaporation models, assuming a constant isotopic com-position of water vapor. The dashed line is the estimated d-excess vs.Δ17O relationship in a2D squall-line model where Δ17O = 0.75*d-excess +24.5. (See Landais et al. (2010) fordetails of these models.) Note the data are poorly described by any of the models andgenerally exhibit poor correlation of Δ17O with d-excess, contrary to current understandingof the physical meaning of these variables.


due to subtle variations in their mass laws (Matsuhisa et al., 1978; Luzet al., 1999; Young et al., 2002; Hendricks et al., 2005). These effectsare generally overlooked in the analysis of terrestrial materials, eitherbecause they are presumed not to exist or because they are below thelevel of detection at which most oxygen isotopic measurements aremade.

The past 8 years have seen several analytical developments thatdramatically improved the precision of measurements of Δ17O inwater and, most recently, CO2 (Barkan and Luz, 2005, 2012; Packet al., 2013 and references therein); these technical advances havecatalyzed new sub-disciplines of stable isotope geochemistry of Earth'shydrosphere and paleoclimatology.

5.1. Δ17O in the Hydrosphere

High-precision measurements of Δ17O in water have enabled a vari-ety of recent studies of the hydrologic cycle, climate dynamics andpaleoclimate research (Landais et al., 2008; Landais et al., 2010; Luzand Barkan, 2010; Risi et al., 2010; Uemura et al., 2010; Risi et al.,2012; Winkler et al., 2012). The triple oxygen isotopic composition ofmeteoric waters defines an average trend on a plot of δ'17O vs. δ'18Owith a slope of 0.528 (Luz and Barkan, 2010). Note that this slope differsfrom the mean terrestrial value of 0.52 or 0.524 assumed in many pre-vious studies (e.g., Rumble et al., 2007) — one of several instances inwhich the community of scientists working on 17O abundances in natu-ral materials have made different assumptions about the referenceframe of expected mass dependent fractionations. This empirical slopediffers very subtly from that for equilibrium fractionation between liq-uid and vapor water (ln17αeq/ln18αeq= 0.529; Risi et al., 2010). In con-trast, gas-phase diffusion ofwater is defined by a slope (or, equivalently,a mass law exponent, λ) of 0.518 (Barkan and Luz, 2007; Fig. 6b). Themass law that describes the fractionation between water vapor and itsliquid source can vary between these extremes, as a function of the rel-ative humidity at the site of evaporation; i.e., high humidity evaporationwill lie closer to the canonical 0.528 slope line and low humidityevaporation will have a lower slope, producing vapors that lie abovethe reference line in Fig. 6b (and, if evaporation is extensive, residualliquids beneath the line with a slope of 0.528). Therefore, Δ17O valuesof precipitation can be used to evaluate the humidity of the site wherethe vapor source of that precipitation first entered the atmosphere(Luz and Barkan, 2010; Risi et al., 2010). In addition to sourcewater con-ditions, the conditions of ice condensation, re-evaporation, convectiveintensity and mixing of waters can affect Δ17O in precipitation, vaporand surfacewater (Landais et al., 2010; Risi et al., 2010; Risi et al., 2012).

The combination of these factors can make it complicated to teaseapart the source of Δ17O variation in meteoric waters, but this task be-comes tractablewhenΔ17O is used in concert with othermeasurementssuch as d-excess (where d-excess = δD–8 × δ18O; Landais et al., 2008;Risi et al., 2012). In conditions where evaporation is the main processdriving oxygen and hydrogen isotope fractionation in precipitation,Δ17O and d-excess covary linearly because they are both determinedby relative humidity and the isotopic composition of the surroundingvapor (Landais et al., 2010). The relationship betweenΔ17O and d-excesshas been used in paleoclimate studies of ice cores, using Δ17O as ameans to measure and correct for the role of humidity on d-excess,such that the corrected d-excess value can beused as a proxy for temper-ature (another of its controlling variables; Landais et al., 2008). This


approach may be compromised by the finding that Δ17O and d-excessare often poorly correlated, and Δ17O and relative humidity are poorlycorrelated in tropical storm systems (Fig. 7). These findings suggestthat there are other processes (e.g., moisture source, continentalrecycling, and convective activity) in addition to relative humidity thatinfluence Δ17O variation in rainfall.

5.2. Δ17O in CO2

In the 1990's Thiemens and colleagues discovered a large, positiveΔ17O value in stratospheric CO2 (Fig. 6a), which is recognized as a con-sequence of mass independent fractionations in ozone chemistrycoupled with exchange of O among ozone, CO2 and other atmosphericconstituents (Thiemens et al., 1991, 1995). Continued experimentalstudy of relevant reactions, in molecular beam lines and using othermethods, has led to a significant understanding of the chemical physicsresponsible for these effects (see review of Thiemens et al., 2012).

Because tropospheric CO2 is a mixture of stratospheric CO2 having ahigh Δ17O value and terrestrial sources (respiration, ocean outgassing)with near-zero Δ17O values, the Δ17O value of tropospheric CO2 hasbeen proposed as a measure of the relative sizes of terrestrial vs. strato-spheric fluxes to the tropospheric CO2 pool. The catch is that strato-spheric sources are a small part of the tropospheric CO2 budget, so thisapplication is possible only if the Δ17O value of CO2 can be measuredprecisely (Boering et al., 2004; Hoag et al., 2005).

Recent advances in the precision of triple-oxygen-isotope measure-ments of CO2 have opened up new possibilities for using Δ17O in atmo-spheric CO2 to monitor the global carbon budget. In particular, initialevidence suggests that such measurements can distinguish betweenwood combustion, gas combustion and respiration, so that there is po-tential for it to be used as a tracer for anthropogenic CO2 emissions, par-ticularly in urban environments. These emerging methods also provideopportunities to precisely measure Δ17O values in carbonate minerals,i.e., by converting them to CO2 for isotopic measurements. This abilitywill open up new ways to examine water cycles in the geologic recordand as a paleo-CO2 barometer (e.g., Gehler et al., 2012; Pack et al.,2013). The coupling of Δ17O and Δ47 measurements in carbonates (i.e.,carbonate clumped isotope analyses; see below) will be particularlypowerful because the temperature constraints on αwater-mineral pro-vided byΔ47will make it possible to construct δ18O values of the forma-tion water such that Δ17O values of carbonates can be used to estimatethe Δ17O of that water, free of assumptions about the magnitude of thecarbonate-water fractionation, and thereby get at hydrological condi-tions (degree of evaporation, precipitation/climate regime, moisturesources) at the time of mineral formation.


The principal challenge of studies of Δ17O values of meteoric watersand the authogenic minerals that grow from those waters is that theΔ17O variation in rainfall reflects not only the humidity of its moisturesources but also continental recycling, convective activity and other fac-tors. Most studies of Δ17O in terrestrial waters to-date have focused ondocumenting natural variability and understanding the fundamentalprocesses involved in triple oxygen isotope fractionation (Landaiset al., 2006; Barkan and Luz, 2007; Luz and Barkan, 2010). The existingdatabase includes a sparse but broad global survey of meteoric waters(Luz and Barkan, 2010), tropical rainfall (Landais et al., 2010), andplant and soil waters (Landais et al., 2006). These studies have beeninterpreted in light of models simulating Rayleigh distillation of airmasses, either as idealized 1-dimensional columns or using generalcirculation models (Landais et al., 2008; Risi et al., 2010, 2012). And,there have been some exploratory efforts to reconstruct paleoclimatefrom ice cores (e.g., Landais et al., 2008;Winkler et al., 2012). However,the complexity of themeteoric water cycle and the diversity of environ-mental and geological problems that it touches mean that there is a

great need to expand these studies. Particularly pressing needs includedocumenting variations in low- and mid-latitude settings and whereevaporation is not the main driver of oxygen isotope fractionation.This work should include coupled Δ17O and d-excess studies of precipi-tation and associated ground waters, on both the scale of individualstorms and across large regions to understand the full dynamics of therelationship between these parameters. Studies of surface and groundwaters, in particular, will be the key towards developing Δ17O as atool for studying paleoclimate and paleohydrology.

6. Illuminating mass independent sulfur isotope fractionations

The search for mass independent sulfur fractionations (‘S-MIF’)started in the 1960's with the work of Hulston and Thode (1965).Mass-independent signatures, ascribed to solar nebula photochemicalprocesses or cosmic ray spallation, were first documented in Allendeby Rees and Thode (1977) and later in iron and achondrite meteorites(e.g., Gao and Thiemens, 1991; Thiemens et al., 1994) and in organicsulfonic acids from the Murchison carbonaceous chondrite (Cooperet al., 1997). Subsequently, anomalous sulfur isotope ratios werefound inmeteorites fromMars (i.e., the SNC's), and itwas demonstratedexperimentally that ultraviolet photolysis of SO2 (but not of H2S)yielded S-MIF compositions; on this basis S-MIF isotopic anomalies inthe SNC meteorites were ascribed to Martian atmospheric chemistry(Farquhar et al., 2000b, 2001).

This field expanded greatly in scope and significance with thediscovery that pyrite (FeS2) and barite (BaSO4) in sedimentary rocksof Archean and early Paleoproterozoic age, but not in younger rocks,commonly exhibit large (several per mil) mass-independent sulfur iso-tope fractionations (Farquhar et al., 2000a; Fig. 8). Since this discovery,the geological record has beenmore extensively and finely sampled andthe range of observed Archean S-MIF fractionations has reachedapproximately Δ33 = −4 to +14‰ (Farquhar et al., 2000a; Johnston,2011; Guy et al., 2012; Philippot et al., 2012). On the basis of SO2 photol-ysis experiments (Farquhar et al., 2000b, 2001) and atmosphericchemistry models (Pavlov and Kasting, 2002), these isotope anomalieswere ascribed to sulfur photochemistry in an atmosphere with lessthan ~10−5 times the modern atmospheric O2 partial pressure. S-MIFanomalies in modern atmospheric aerosols and in volcanic dust-richhorizons in Antarctic ice cores (Romero and Thiemens, 2003; Baroniet al., 2007, 2008) demonstrate that the chemistry required for S-MIFgeneration occurs in parts of the modern O2-rich atmosphere, thoughthe signal is only preserved in atmospheric aerosol. I.e., the key role ofO2 is not to completely suppress generation of S-MIF anomalies, butrather to prevent them from being preserved in the geological recordby promoting conversion of atmospheric S compounds to sulfate thateventually mixes into the large marine reservoir.

While it is widely accepted that the large S-MIF anomalies ofPrecambrian sedimentary rocks reflect the reduced character of theArchean atmosphere, there are still major hurdles to our understandingof their physical and chemical meaning, the processes that transmittedthis signature from its presumed atmospheric source into the rockrecord, and the quantitative constraints that might be derived fromthe details of the S-MIF record— itsmagnitude and spatial and temporalvariations. We focus here on these questions and refer the reader torecent reviews for a more complete survey of S-MIF (Farquhar andWing, 2003; Johnston, 2011).

6.1. Generation of Archean–Proterozoic S-MIF

Distinctly nonzeroΔ33S values in Archean–Proterozoic rocks (Fig. 8)are generally correlated with non-zero Δ36S; this appears to rule outmagnetic isotope effects, which should influence only 33S (the only Sisotope with a nuclear magnetic moment) as the source of S-MIF(e.g., Ohmoto et al., 2006; Oduro et al., 2011). Additional constraintson the source of S-MIF are suggested by trends in δ34S-Δ33S-Δ36S

Fig. 8. Summary of sulfur isotope compositions of sulfates and sulfides from sedimentary rocks, grouped by age. Note that all mid-Proterozoic to recent samples conform closely to acanonical mass dependent trend whereas Archean and earliest Proterozoic samples exhibit multiple-per mil deviations from that trend (i.e., positive or negative Δ33S values). Data arecompiled from: Farquhar et al., 2000b; Johnston, 2011; Guy et al., 2012; Philippot et al., 2012.


space defined by Archean sedimentary rocks. These materials formarrays in Δ33S-δ34S space with slopes typically between 0.5 and 1(or, slopes between 1 and 2 in Fig. 8; Ono et al., 2003; Kaufman et al.,2007), arguing against processes with modestly anomalous mass laws(which generally have near-zero slopes in this space, or near 0.5slopes in Fig. 8). Typical Archean slopes of −0.9 in Δ36S-Δ33S space(e.g., Kaufman et al., 2007) differ distinctly from values between−7 and −9 that are characteristic of mass-dependent processes(Ono et al., 2006; Johnston et al., 2007). These inconsistencies havebeen taken to reinforce the leading hypothesis that SO2 photolysisis the cause of S-MIF in Archean rocks.

Despite the general consensus that the Archean S-MIF record wasgenerated by UV–photochemistry in a SO2-bearing, anoxic atmosphere,several essential details are unclear. Laboratory experiments examiningSO2 photolysis yield products (H2SO4, S8 aerosols, organo-sulfur com-pounds) and residual SO2 with δ34S-Δ33S-Δ36S fingerprints that dependon the wavelength of light driving the reactions, the bath gas composi-tion and pressure, and the optical thickness of the photolysis column(Farquhar et al., 2001; Masterson et al., 2011; Whitehill and Ono;,2012; Ono et al., 2013a, 2013b). While some broadband photolysis ex-periments successfully match observations of S-MIF in present-daystratospheric sulfate aerosols (Ono et al., 2013a, 2013b), none havebeen able to reproduce the Archean array. Moreover, there is no mech-anistic understanding of the variability in δ34S-Δ33S-Δ36S relationshipsfor these experimental products.

Difficulties in matching Archean S-MIF through direct experimentshave motivated fundamental studies of the absorption spectrum ofSO2, in hopes of finding a part of the spectrum having fractionationsthat can explain the rock record. Subtle differences among the absorp-tion cross sections of the isotopologues of SO2 have been modeled(Lyons, 2007, 2009) and measured (Danielache et al., 2008), and canlead to mass-independent effects during SO2 photolysis. If an atmo-spheric SO2 column is optically thick, photolytic fractionations may bedominated by “self-shielding” — i.e., absorption of light capable ofphotolyzing 32SO2 at high altitude, leading to preferential photolysis ofthe rare isotopologues (33SO2, 34SO2, 36SO2) deeper in the atmosphere(Lyons, 2007, 2009). There appear to be disagreements between calcu-lated S-MIF generated by self-shielding and Archean δ34S-Δ33S-Δ36Srelationships, suggesting that this mechanism either isn't responsiblefor the Archean S-MIF record, or exhibits isotopic systematics we don'tyet understand. A confident evaluation of the self-shielding hypothesis

will depend on accurate and detailed measurements of the absorptionspectra of all SO2 isotopologues.

In an optically thin atmospheric SO2 column (i.e., one in which self-shielding does not occur) S-MIF fractionations arise because, at anygiven wavelength, the absorption cross sections differ between theSO2 isotopologues but not following a simple (or at least easily predicted)dependence onmass. Measured cross sections for isotopologues of sulfurdioxide have improved considerably over the past 5 years, and differ-ences among these cross sections appear to account for a significantamount of the observed S-MIF fractionation in experiments and perhapsin nature (Danielache et al., 2008; Ueno et al., 2009; Halevy et al., 2010).However, S-MIF from preliminary calculations with newly-measured,high-resolution absorption cross sections differs from these previousstudies, suggesting that the spectral resolution of existing cross sectionsis too low to resolve all of the relevant differences among theisotopologues (Lyons et al., 2010).

Mass-independent effects may also arise because isotopologuesdiffer in their oscillator strengths and in their probabilities that photo-excited molecules relax to the ground state and avoid dissociation.The latter effect has been suggested to explain mass-independenteffects in the photo-polymerization of CS2 (Zmolek et al., 1999). Acombination of such effects,which lead to adiabatic crossings and differ-ences in dissociation dynamics, has been suggested to explain mass-independent effects in the photodissociation of CO2 (Bhattacharyaet al., 2000) and CO (Chackraborty et al., 2012). The dependence ofexperimentally produced S-MIF on the pressure of an inert bath gasand on the water vapor content (Farquhar et al., 2001; Mastersonet al., 2011) hints at similar effects during SO2 photodissociation, thoughquantitative model predictions cannot yet be made because of theabsence of a sufficiently accurate potential energy surface for thedissociation of photo-excited SO2.

6.2. Carriers of Archean–Proterozoic S-MIF from atmosphere to surface

The identities of themolecules that carried the Archean S-MIF isoto-pic anomaly to the surface and the sign and magnitude of S-MIF in thedifferent carriers are unclear. Photolysis experiments done to-datewere invariably performedwith SO2 density orders ofmagnitude higherthan realistic atmospheric abundances. Oligomerization of elementalsulfur to ultimately yield S8 aerosols is favored under more realisticconditions, leading to the prevailing view that S-MIF was delivered to

r

E

Fig. 9. Schematic illustration of the electrostatic potential energy of an electron as a func-tion of distance, r, from a nucleus it orbits. The blue curvesmark the potential surface if thenucleus is dimensionless (i.e., a point, which thus has infinite charge density); in this case,E goes asymptotically to -∞ as r goes to 0. However, real nucleii have finite volume, suchthat the potential energywell for an electron that is co-locatedwith the nucleus is finite—relatively shallow for a large, low-charge-density nucleus (green curve) and deeper for asmall, high-charge-density nucleus (red curve). Thus, nuclear volume influences electro-static potential energy and, potentially, energies of chemical reactions. This effect isgreatest for S orbital electrons, which have wave functions that overlap with the nucleus.After Bigeleisen, 1996a, 1996b.


Earth's surface in H2SO4 and S8 aerosols as well as in the residual SO2

(e.g., Farquhar et al., 2000a, 2001; Pavlov and Kasting, 2002; Onoet al., 2003; Zahnle et al., 2006).

Experiments with more realistic SO2 abundances (as low as 2 ppm),and in the presence of realistic abundances of small, gaseous hydro-carbons (CH4, C2H2 and C2H4) have yielded methanesulfonic acid(CH3SO3H), dimethylsulfone [(CH3)2SO2] and similar molecules(DeWitt et al., 2010; Oduro et al., 2012). Sulfur isotope ratios inthese organo-sulfur products are mass-independent (Oduro et al.,2012), leading to suggestions that organo-sulfur compounds generatedby reaction of photo-excited SO2 with atmospheric hydrocarbonscarried S-MIF to Earth's surface (Halevy, 2013).

6.3. Preservation of S-MIF in the geological record

The process (or processes) responsible for S-MIF generation hasbeen translated and modified by the biogeochemical sulfur cyclebefore being written in the observable geologic record. On the onehand, this presents a problem to the interpretation of the geologicalrecord as a simple constraint on past atmospheric chemistry.On the other hand, if the patterns of S-MIF in the geologic record(i.e., spatial and temporal variations in amplitudes of signals) wereobserved in sufficient detail and decoded through models of appro-priate complexity, it might be possible to constrain not only theorigin of S-MIF but also the species and processes that carried thatsignature into minerals. A complete and successful model of theobservable S-MIF record may valuably constrain the characteristicsof Earth's early surface environment.

Models of increasing sophistication account for biogeochemistry andtransport in the oceanic sulfur cycle (Halevy et al., 2010; Halevy, 2013),and for communication of the marine sulfur pool with the reservoir ofsulfur minerals on land (Reinhard et al., 2013). One important conclu-sion derived from these models is that future observations shouldfocus on non-marine and shallow marine environments, where theS-MIF preserved should most closely resemble the original signaldelivered by the atmospheric carriers (Halevy, 2013). And, a recentmodel of the Archean sulfur cycle links increases in the magnitudeof S-MIF as well as its asymmetry (i.e., difference between sulfideand sulfate anomalies) to increasing subaerial volcanism (Halevyet al., 2010). Some parts of the Archean S-MIF record may be toopoorly sampled to reach confident conclusions of this kind (particu-larly where the marine sulfate record is relatively sparse). Neverthe-less, recent discovery of Archean volcanic sediments with thehighest S-MIF magnitude and asymmetry observed to date has rein-forced the importance of subaerial volcanism to the Archean sulfurcycle (Philippot et al., 2012). Whatever their challenges, models ofthis kind have the potential to convert geological records of S-MIFinto specific statements about the sulfur cycle, and to identify impor-tant targets for future observations and experiments.


Major theoretical and experimental efforts will be required tounderstand the isotopic effects of the various mechanisms suggestedto generate S-MIF. A potential energy surface for excited SO2 must becalculated to facilitate modeling of kinetic isotope effects during SO2

photodissociation. High-resolution absorption spectra of all four 3xSO2

isotopologues must be measured to allow calculations of differencesin photo-excitation probabilities. An inherent challenge with suchmeasurements is that SO2 photo-dissociates at the spectral intervals ofinterest, making it difficult to achieve high spectral resolution andsignal-to-noise ratios while maintaining a stable column optical thick-ness of SO2. Experimental photolysis at low integrated column opacitiesand sub-ppm concentrations of SO2 are required to determine S-MIFgenerated under realistic atmospheric conditions. To study the chemicalmechanisms of SO2 photolysis, the products must be identified and

separated more carefully than in past experiments, and their multiple-isotope compositions measured. Improvements in the analysis ofsmall samples (e.g., Paris et al., 2013) will facilitate this.

A broader challenge is to understand the specific chemical pathwaysby which S-MIF signals are deposited on the Archean surface andrecorded in rocks; much work will be required to develop a detailedand realistic picture of these processes. It will be particularly importantto investigate the anoxic gas-phase and aqueous chemistry of organo-sulfur compounds — something that is presently very poorlyconstrained.

7. Mass independent fractionations of heavy metals

Interest in mass independent fractionation of the isotopes of heavyelements began with laboratory experiments on uranium isotope frac-tionation in oxidation/reduction equilibria [U(VI) vs. U(IV) and U(IV)vs. U(III)] (e.g., Fujii et al., 1989). In these experiments, heavy uraniumisotopes were concentrated in chemically reduced species. Equilibriummass dependent fractionation usually favors heavy isotopes in oxidizedspecies (e.g., Bigeleisen andMayer, 1947), because those species' vibra-tional zero point energies are more sensitive to isotope substitution.Furthermore, the magnitude of observed fractionation was not propor-tional to differences in isotopic mass — 234U/238U changed only 14%more than 235U/238U despite a 33% greater mass difference (Fujii et al.,1989; Nomura et al., 1996). And, more generally, commonmass depen-dent chemical isotope effects generally scale inversely with isotopicmass and should be negligibly small for U.

7.1. Nuclear volume effects

Jacob Bigeleisen (1996a) and Nomura et al. (1996) showed thatthese fractionations correlated with spectroscopic observations ofnuclear field shifts in uranium — changes in the energies of electronictransitions caused by variation in the volume (and to some extent theshape) occupied by the positive charge in the atomic nuclei. Specifically,they found qualitative correspondence betweenmeasured nuclear fieldshift energies in atomic vapor (~1 cm−1= 12 J/mol) and the amount ofenergy needed to drive the observed fractionations. Nuclear spin effectswere found to be much smaller.


In spectroscopy, the nuclear field shift effect (schematically illustratedin Fig. 9) occurs because electron densities (especially for s-orbitals) inatoms overlapwith the nucleus. For the simple case of a spherical nuclearcharge distribution, when an electron is inside the nucleus, the nuclearcharge exterior to its location does not exert any net electrostatic attrac-tion. Such electrons are not bound as strongly to a finite-volume nucleusas they would be to a point-charge nucleus. When comparing isotopes ofthe same element, nucleii that take upmore spacewill containmore elec-tron density, and the electronswill be boundmoreweakly. Smaller nucleiof that element hold onto electrons more tightly. Geochemical isotopefractionation will occur when species with different electronic structuresexchange isotopes with different nuclear charge distributions. As a rule,species with more s-electrons preferentially incorporate small (usuallyneutron-poor) isotopes, while s-orbital-depleted species prefer largerisotopes. P-, d- and f-electrons screen s-electrons, reducing their electrondensity inside nuclei, so they tend to have the opposite effect on isotopefractionation. The nuclear field shift effect is particularly interesting forgeochemistry because atomic spectroscopy shows that nuclearfield shiftsincrease rapidly towards the bottom of the periodic table, suggesting thatthis mechanism could lead to significant isotope effects in the heaviestelements (Bigeleisen, 1996a; Knyazev and Myasoedov, 2001; Schauble,2007; Abe et al., 2008a,b). In contrast, mass dependent fractionationsdue to conventional chemical and physical processes decrease as atomicor molecular mass increases (Bigeleisen and Mayer, 1947). Furtherwork (Bigeleisen, 1996b) showed that nuclear field shift fractionationswould exhibit distinctive temperature sensitivity, scaling as T−1, becausemost species remain in their ground electronic states even at elevatedgeological temperatures. Therefore, measurable isotopic fractionationsarising fromnuclear field shiftsmay occur even at relatively high temper-atures. More generally, these effects seem likely to lead to useful tools inthe study of the geochemistry of elements with high atomic number.

Nuclear volume isotope effects have been identified in mercury,thallium and uranium (Schauble, 2007; Stirling et al., 2007; Abe et al.,2008a,b; Weyer et al., 2008; Estrade et al., 2009; Wiederhold et al.,2010; Zheng and Hintelmann, 2010; Ghosh et al., 2013). And results oflaboratory studies of isotopic fractionations of medium-weight metallicelements (e.g., Fujii et al., 2009) raise the possibility that these effectsmight be widely distributed across the periodic table. Nevertheless,mass independent isotopic fractionations do not appear to be commonfor medium-mass elements (e.g., transition metals or Ca) in naturalmaterials, with the exception of meteoric inclusions known to havenucleosynthetic and other exotic fractionation signatures (calcium–

aluminum inclusions of the Fractionated andUnknownNucleosynthesis[FUN] type; Wasserburg et al., 1977; Fujii et al., 2006), and so if nuclearvolume effects exist for these elements they are likely second orderphenomena leading to very small fractionations.

7.2. Magnetic isotope effects

Mercury exhibits pronounced mass independent isotopic variationsin nature, especially for the odd-mass isotopes. The largest of these var-iations — particularly from snow, fish and other biological samples(Bergquist and Blum, 2009; Sherman et al., 2010) — are believed to re-flect a kinetic chemical isotope effect that arises frommagnetic couplingin spin-forbidden reactions (i.e., as has been suggested for some Δ33Sanomalies during sulfate reduction, above; Watanabe et al., 2009;Oduro et al., 2011; see also Buchachenko, 2001 and Bergquist andBlum, 2007). Such ‘magnetic isotope effects’ are a kinetic isotope phe-nomenon that occurs in spin selective reactions containing radical pairintermediates (Buchachenko, 2001). Odd Hg isotopes have non-zero nu-clear spin andmagneticmoments that can interact with the electron spinof unpaired electron radicals. Currently, the only large magnetic isotopeinduced fractionations experimentally produced for Hg are during aque-ous photochemical reactions (Bergquist and Blum, 2007; Zheng andHintelmann, 2009). During photo-dissociation, excited radical pairs canbe produced in triplet (T) or singlet states (S). Triplet states are spin

forbidden from recombining to form the starting product and must un-dergo T → S intersystem crossing in order to recombine. Because of theinteraction of the magnetic moment of the odd nuclei with the unpairedelectron, odd isotopes undergo intersystem crossingmuch faster than theeven isotopes resulting in the enrichment or depletion of oddHg isotopesin the reaction products depending onwhether the radical pair started ina triplet or singlet state (Buchachenko et al., 2007). In order for intersys-tem crossing to compete with dissociation into free radicals, it is neces-sary for the radical pair to be in a solvent cage to extend the lifetime ofthe radical pair. For aqueous photochemical reduction, the water acts asa solvent cage.

Despite this relatively detailed understanding ofMIF in Hg, there arereasons to think that it is not the whole story. First, nuclear volumeeffectsmay also significantly impact the odd isotopes of Hg, and the bal-ance of nuclear volume andmagnetic isotope effects is not clear in everyinstance. And, recent studies of atmospheric samples also show that theeven isotopes of Hg also display small non-mass dependent fraction-ation (Gratz et al., 2010; Chen et al., 2012; Demers et al., 2013; Rolisonet al., 2013). Because the nuclear volume and magnetic isotope effectshould only result in non-mass dependent isotope fractionations forthe odd isotopes in Hg, the mechanism for the even isotope massindependent fractionation is unknown, but may be related to gasphase reactions andmechanisms similar to those for oxygen and sulfur.

Much current research is aimed at distinguishing magnetic frommass-dependent and nuclear-field shift fractionations as the cause(s)of the odd-isotope mass-independent fractionation of Hg. Because Hghas seven isotopes, two of which are odd, it has been suggested thatthe ratio of the mass independent fractionations (Δ199Hg/Δ201Hg)might be unique to the different mechanisms. Theoretically, the ratioofΔ199Hg/Δ201Hg for the nuclear volume effect is predictable frommea-sured nuclear charge radii and should be the same for different transfor-mations. Theoretical predictions of this ratio range from 1.6 to 2.7depending on the nuclear charge radii estimates used (Schauble,2007; Ghosh et al., 2008; Estrade et al., 2009; Wiederhold et al., 2010and references therein). However, earlier experiments were not ableto confirm what estimate was most accurate because nuclear volumeassociated mass independent fractionations are very small and theerror in the ratio was too high. More recently, Zheng and Hintelmann,2010, reported a ratio of 1.61 ± 0.06 (2SE) for a dark kinetic reactionand suggested that it was the result of the nuclear volume effect.However, both the nuclear volume effect and magnetic isotope effectcan occur during kinetic reactions and it was unclearwhether the signa-ture could have been produced by the magnetic isotope effect in thedark. In order to avoid the magnetic isotope effect, Ghosh et al., 2013,performed Hg liquid–vapor equilibrium experiments (similar toEstrade et al., 2009) and confirmed a ratio for the nuclear volume effectof 1.59± 0.06 (2SE). Thus the theoretical prediction for the ratio of ~1.6byWiederhold et al., 2010, using nuclear charge radii compiled in Frickeand Heilig (2004), appears to be the most accurate estimate.

The ratio of Δ199Hg/Δ201Hg for the nuclear volume effect of ~1.6does appear to be significantly different from the ratios observed forthe magnetic isotope effect, which range from ~1 to 1.4 for experimen-tal photochemical transformations involving different Hg species andligands (Bergquist and Blum, 2007; Zheng and Hintelmann, 2009;Chandan et al., submitted for publication). Because the theory behindthe magnetic isotope effect is relatively qualitative, it is difficult toexplain the ratios observed in different photochemical reactions, noreven why they differ from one another. However, the magnetic isotopeeffect is sensitive to numerous factors including hyperfine coupling,lifetime of the radical pair, coupling strength of the radical pair, spin–orbital coupling, diffusion factors, and the nature of the solvent cage(space) in which the reaction occurs (Buchachenko, 2001). Therefore,changing the ligand that the Hg is associated with may affect many ofthe factors that affect the magnetic isotope effect and change the rela-tive rates at which 199Hg and 201Hg undergo T → S state intersystemconversion. Despite a range of ratios observed in experiments, natural


samples are much more consistent. Biological samples that are domi-nated by monomethylmercury have ratios close to 1.3, which is consis-tent with monomethylmercury photo-degradation (Bergquist andBlum, 2009; Sonke, 2011). Whereas, samples dominated by inorganicHg2+ have ratios close to 1.0, which is consistent with the photochem-ical reduction of Hg2+ in the presence of dissolved organic matter(Bergquist and Blum, 2009; Sonke, 2011).


First, experimental and theoretical studies of mass-independentfractionations of heavy elements have focused on gas-phase and aque-ous species, in part because condensed phases are not readily modeledusing current relativistic electronic structure software codes. Sub-stances with metallic bonding, in particular, may be difficult to modelsuccessfully using molecular methods. Second, nuclear shape effectsstemming from non-spherical nuclear charge distributions in oddisotopes have mostly been neglected. One study (Knyazev et al., 1999)suggests that volume effects are the dominant component of nuclearfield shift fractionation, but it is possible such shape effects are moreimportant for some elements and materials. Third, a quantitative oreven semi-quantitative theory of magnetic-isotope fractionationis needed. At present there is no tractable framework for predictingthese fractionations, even though they apparently dominate Hg-isotopeMIF. Fourth, we are aware of no attempts to incorporate nuclear fieldshift effects into transition state theory. This means that our understand-ing of kinetic processes of mass-independent fractionation in heavyelements is largely empirical and phenomenological, despite the criticalimportance of chemical–kinetic isotope effects in geochemistry (above).Finally, disagreements between calculated Hg-isotope fractionationsand experiments have highlighted uncertainties in tabulated nuclearcharge radii (e.g., Schauble, 2007; Ghosh et al., 2008; Estrade et al.,2009;Wiederhold et al., 2010; Ghosh et al., 2013), indicating for instancethat the Fricke and Heilig (2004) tabulation is more accurate than Angeli(2004). This suggests that careful measurement of nuclear field shiftfractionation is a potential tool for determining nuclear structureparameters of high-Z isotopes.

0

10

20

30

a) Speleothems

b) Corals

c)

Deep-sea

Surface

0 1 2 3 4

-1

1

2

3

4

5

6

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-6

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Clu

mpe

d Is

otop

e A

ppar

ent T

empe

ratu

re (

˚C)

δ18Oobserved –δ18Oexpected

δ13C

obse

rved

– δ

13C

expe

cted

Fig. 10. Isotopic compositions of representative speleothems (a and c, red symbols), deep-sea codeviate from expected equilibriumwith coexisting waters for all three materials, but (c) whereexpected equilibrium values, deep-sea corals conform to equilibrium. Data from Adkins et al.,Saenger et al., 2012; Kluge and Affek, 2012; and Affek, 2012.

8. Clumped isotope geochemistry of carbonate species

Recent advances in isotope ratio mass spectrometry make it feasibleto precisely determine the abundances of doubly-substitutedisotopologues at their low natural abundances, leading to a new fieldof isotope studies — clumped isotope geochemistry (Eiler andSchauble, 2004; Eiler, 2007, 2013). The most notable tool to emergefrom this young field is ‘carbonate clumped isotope thermometry’(Eiler, 2011), which is based on the fact that abundances of doublysubstituted isotopologues of carbonate ions containing both a 13C andone 18O (i.e., 13C18O16O2

−2) in equilibrated systems are controlled by ahomogeneous equilibrium:

13C16O3−2þ12C18O16O2

−2¼13C18O16O2−2þ12C16O3

−2

The equilibrium constants for reactions of this form are a function oftemperature, and thus provide the basis of a peleothermometer (Ghoshet al., 2006; Schauble et al., 2006; Eiler, 2011); perhaps themost impor-tant feature of thismethod of paleothermometry is that it can be used toconstrain temperatures without knowing the δ18O of waters fromwhich carbonate minerals grew.

One significant challenge faced by carbonate clumped isotope ther-mometry is the possibility that kinetic fractionations, including both‘vital effects’ and abiological processes, might disturb the homogeneousequilibrium onwhich themethod is based. Both speleothems and coralsshow significant deviations from equilibrium with co-existing waters,for both carbon and oxygen isotope compositions (Fig. 10a and b). Inthe case of speleothems and surface corals, these are accompanied byclumped isotope compositions that also differ markedly from equilibri-um at known growth temperatures, yet for deep-sea corals similarlyprofound ‘vital effects’ in δ13C and δ18O are accompanied by equilibriumclumped isotope compositions (Fig. 10c). Here we discuss recentattempts to understand kinetic isotope effects in these carbonatematerials, focusing on two questions: (1) Under what circumstances isisotopic ‘clumping’ in carbonate controlled by kinetics rather thanequilibrium? And, (2) what do these examples teach us about thechemistry of dissolved inorganic carbon and carbonate minerals?More generally, the studies discussed below present the first well-

10 20 30

Deep-sea corals

Speleothems

Surface corals

Environmental Temperature (˚C)

rals (blue, b and c) and surface corals (yellow, b and c). Values of δ18O and δ13C of both (a, b)as speleothems and surface corals deviate strongly in clumped isotope compositions from2003; Mickler et al., 2004; Affek et al., 2008; Daeron et al., 2011; Thiagarajan et al., 2011;

CO32-

OH-

H+

H2O

CO2 HCO3- H+

hydration

dehydration

hydroxylation

dehydroxylation

OH-

Ca2+

CaCO3

precipitation

Ca2+

precipitation

Fig. 11. Schematic illustration of important reactions affecting the isotopic composition ofdissolved inorganic carbon.


developed example in which complex, kinetically controlled clumpedisotope fractionation has been examined from several perspectives —experimental, theoretical and as expressed in natural materials.

8.1. Speleothems and degassing of DIC solutions

Carbonate clumped isotope analyses of modern speleothems typi-cally yield apparent temperatures significantly higher than knowngrowth temperatures (i.e. assuming a calibration of the thermometerbased on nominally equilibrated calcite)— herewe use the term ‘appar-ent’ temperature to mean the clumped-isotope derived temperaturethat may or may not relate to the actual formation temperature. Thesedifferences can be up to ~22 °C, and are typically on the order of~10 °C (Fig. 10c). Speleothem precipitation is driven by the fact thatdrip waters (calcium bicarbonate solutions) are exposed to high partialpressures of CO2 as they percolate through soil and rock, but once theyenter a ventilated cave they encounter the relatively low pCO2 of air.Dissolved CO2 in the drip water outgasses in response to this drop inpCO2. As CO2 leaves the solution, bicarbonate decomposes by dehydrox-ylation (and, similarly, the small amount of carbonic acid dehydrates).This decrease in dissolved inorganic carbon at constant total alkalinityincreases the carbonate saturation state, driving growthof calcite or ara-gonite from the drip water (a simpler way to describe this process isthat the reaction, Ca2+ + 2xHCO3

− = CaCO3 + CO2 + H2O, is drivento the right when pCO2 decreases). The δ13C and δ18O values ofspeleothem carbonates commonly deviate fromexpected compositions,given their temperatures of growth and compositions of their parentwaters, indicating that this process involves kinetic isotope effects,and proceeds more rapidly than re-equilibration with water. Forthis reason, it has been hypothesized (anddemonstrated in some detail)that the failure of carbonate clumped isotope compositions torecord equilibrium at the known growth temperature reflects the influ-ences of kinetic isotope effects associated with dehydroxylation ofbicarbonate.

Solution to this problem required a combination of theoretical, ex-perimental, and field-based approaches. Guo et al. (2007) and Guo(2009) use first principle transition state calculations to simulate the ki-netic fractionations of all isotopologues of HCO3

− during dehydroxyl-ation, and predicted these fractionations would lead to a lowerproportion of 13C–18O substituted isotopologues in the residual HCO3

−

as compared to that expected at equilibrium, and thus to overestima-tions of carbonate growth temperatures based on carbonate clumpedisotope thermometer. These calculations also predict HCO3

− dehydrox-ylation will lead to increases in the δ18O of residual DIC species, whichis also passed on to speleothems; thus, there should be a correlation be-tween anomalously low abundances of clumped isotope species andanomalously high δ18O values, with a slope of ~−0.025 at 25 °C.These theoretical predictions are broadly consistent with the experi-mental observations in modern speleothems, and have been used tocorrect measured compositions of natural speleothems for these kineticeffects (Guo et al., 2007; Guo, 2009; Wainer et al., 2011). However, themodel-predicted correlation between clumped isotope depletion andoxygen isotope enrichment is significantly smaller, by a factor of ~2,thanwhat is observed inmodern speleothems. This indicates that eitherthe kinetic model of HCO3

− dehydration and dehydroxylation reactionsadopted in Wainer et al. (2011) and similar recent work containssome systematic error, or that kinetic processes other thandegassing re-actions, such as kinetic isotope effects associated with precipitation ofdissolved carbonate (Nielsen et al., 2012), also affect the clumped iso-tope composition of speleothems.

8.2. Corals

The clumped isotope composition of deep-sea corals exhibit noapparent deviations from expected equilibrium values, despite havingwell documented and large vital effects in their carbon and oxygen

isotope compositions (Fig. 10b and c; Thiagarajan et al., 2011). Incontrast, surface corals appear to exhibit pronounced enrichments in13C–18O ‘clumps’ relative to expected proportions for their knowngrowth temperatures (and thus apparent temperatures lower thanknown growth temperatures; Saenger et al., 2012; Fig. 10c).

The lack of a kinetic signature in clumped isotope temperatures ofdeep-sea corals appears to be most consistent with the pH model ofstable isotope vital effects in biogenic carbonates, which hypothesizesthat they arise due to differences between the equilibrium stableisotope compositions of CO3

−2 and HCO3− ions and the differences in

pH between environmental and body waters from which biomineralsprecipitate (Zeebe, 1999; Adkins et al., 2003; Guo et al., 2009;Thiagarajan et al., 2011). Dissolved HCO3

− and CO32− in an equilibrated

solution differ in δ18O by ~6.8‰ at 25 °C (Beck et al., 2005), such thatbasic solutions (pH N9), which are dominated by carbonate ion, tendto precipitate low δ18O carbonate, whereas higher pH solutions (pHfrom ~6 to 9), which are dominated by bicarbonate ion, grow higherδ18O carbonate. Thus, an organism that increases the pH of its bodywaters to induce carbonate precipitation will tend to exhibit a negative‘vital effect’ in δ18O (Fig. 10b).

Guo et al. (2008) and Guo et al. (2012) predict a subtle difference of~0.04‰ between the equilibrium clumped isotope compositions ofbicarbonate and carbonate ions (also at 25 °C), using first principlequantum mechanical calculations of isotope effects on the vibrationalenergies of HCO3

−·(H2O)n and CO32−·(H2O)n clusters. Based on these

predictions, Guo et al. concluded that modest variations in pH couldlead to observable changes in δ18O (permil level)when the correspond-ing changes in clumped isotope composition remain similar to analyti-cal errors (~0.01–0.02‰). These expectations are generally consistentwith initial experiments constraining the difference in Δ47 betweenHCO3

− and CO32− (Guo et al., 2012) and with later theoretical calcula-

tions by Hill et al. (2014). However, a larger experimental data setpresented by Tripati et al. (in press) suggests a somewhat larger effect(0.06 ± 0.02‰). These effects are just strong enough that theymay well lead to observable vital effects in clumped isotopes and/orequivalent differences in temperature dependence of Δ47 for inorganiccarbonates grown from high and low pH solutions. It is possiblethat this effect plays some role in explaining discrepancies betweensome calibrations of the carbonate clumped isotope thermometer(e.g., Ghosh et al., 2006 vs. Dennis et al., 2010).

The non-equilibrium enrichment in isotopic ‘clumps’ in surfacecorals is less well understood at present, and might reflect diffusionof CO2 across cell membranes, chemical kinetics of the hydrationand hydroxylation of aqueous CO2 (Saenger et al., 2012; see alsoMcConnaughey, 1989; Cohen and McConnaughey, 2003) or, perhaps,


the equilibrium fractionation factors between solutions and the distinc-tive surface layers of growing grains (Watson, 2004; see Fig. 11).There are currently no experimental constraints on the clumped isotopeeffects associated with hydration and hydroxylation of CO2. Guo et al.(2007) and Guo (2009) made first-order theoretical estimates of theseprocesses, assuming no isotope effects on the forward reactions (i.e., Ofrom water is added to CO2 unfractionated), and predicted that thisprocess should yield bicarbonate species with clumped isotope compo-sitions significantly higher than the expected equilibrium values, atleast in the direction of the kinetic isotope effects observed in surfacecorals (Saenger et al., 2012). If this process is responsible for the surfacecoral vital effect, it could be thought of as a mirror image of the kineticeffect in speleothems; i.e., whereas speleothems are depleted in13C–18O clumps due to rapid dehydroxylation of bicarbonate anddegassing of CO2, enrichments in those clumps in surface corals aredue to rapid hydration of excess CO2.

An essential process that must influence whether or not kineticisotope effects can be manifested in the clumped isotope compositionsof DIC species is the rate of their isotope exchange with water. I.e., ifchemical or physical fractionations drive the DIC pool out of equilibriumwith respect to the homogeneous equilibria that control clumping,exchange with co-existing water may allow a return to the equilibriumstate. This may be an important factor that mitigates the effect of CO2

degassing on the isotopic compositions of speleothems (and thus per-haps explains the range in offsets between apparent and independentlyknown temperatures; Fig. 10c). Although the kinetics of oxygen isotopeexchange of DIC species have been well constrained by experimentalstudies (Beck et al., 2005), only recently has there been any such datafor clumped isotope equilibria (Affek, 2013).


The greatest gaps in our understanding of the clumped isotope geo-chemistry of carbonateminerals and related dissolved species is the rel-ative paucity of experimental constraints on the exchange equilibriaand kinetics of all the relevant species (Fig. 11). Particularly importantgoals include: (1) establishing whether pH effects arising from differ-ences between carbonate and bicarbonate ions influence the tempera-ture dependence of Δ47 values for biogenic carbonates and previousattempts to calibrate the method by inorganic experiments; (2)constraining the kinetic fractionations associated with CO2 hydrationand hydroxylation reactions; (3) studies of clumped isotope effects as-sociatedwith variations in solid growth rates, whichmay inform kineticisotope effects associated with the solution/solid interface (Fig. 1,above); and (4) kinetics of clumped isotope exchange between DICspecies and water. And, it will be important that this work considersthe effects of carbonic anhydrase or other catalysts (Uchikawa andZeebe, 2011).

Afinalmore general point to keep inmind is that all clumped isotopestudies examine second-order isotope effectsmore subtle than those re-sponsible for most stable isotope signals. It has recently been shownthat the theories commonly used to predict and interpret chemicalisotope effects (i.e., models of vibrational isotope effects based on Ureytheory) lead to small but analytically significant errors due to approxi-mations in the handling of anisotropy and ro-vibrational coupling(Webb and Miller, 2014). It may be important for the future growthof this field that higher-level theory (e.g., Feynman path integralapproaches) be brought to bear on these problems.

9. Position-specific and clumped isotope effects in organics

Isotopic measurements of organic compounds are generallyapproached usingmethods that constrain only the bulk isotopic compo-sition of an element of interest, averaged across allmolecular sites in theanalyte. This is because these methods generally convert complexmolecules to simpler gases such as CO2, CO, H2, O2, SO2, and SF6.

However, each distinctive ‘site’ in the molecule need not have thesame isotopic composition. For example, acetate (CH3COO−) has twodistinct carbon containing groups, a methyl group (CH3) and carboxylgroup (COO−) which differ in the 13C/12C ratio by up to 20‰ in naturalsamples (Blair et al., 1985). Additionally, clumping in organic moleculeshas been both predicted (Ma et al., 2008) and demonstrated in syntheticand natural compounds (Stolper et al., 2012; Clog et al., 2013; Stolperet al., 2014, submitted for publication). Much of the potential richnessin the isotope geochemistry of organic compounds arises from thisfact that isotopic tracers and fractionations can be tied to specific atomicsites in complex molecular structures.

There have been several attempts to measure natural-abundanceisotopic compositions at the site-specific level in organic compounds,motivated by the constraints such measurements could provide onchemical, biological and environmental processes, and their potentialas forensic tracers of foods, elicit drugs, explosives and other materials.This sub-discipline of isotope chemistry has been contemplated in someform since the 1930's, but only recent advances in analytical instru-ments and methods have made it tractable. Eiler (2013) reviews thehistory of approaches to this subject. Here, we focus on three emergingmethods: NMR, high-resolution sector mass spectrometry, and IRabsorption spectroscopy.

9.1. Natural abundance NMR (‘SNIF-NMR’)

Nuclear Magnetic Resonance (NMR) has several characteristics thatmake it a promising technique for site-specific isotope analysis. First, theNMR effect (i.e., coupling of nuclear spin with an applied oscillatingmagnetic field) provides a measurement of the electronic structure,and thus chemical environment, of atoms in a molecule. NMR spectradistinguish, for example, between saturated and unsaturated carbons,and members of rings vs. side branches, based on the magnitude ofthe energy shift that is measured by an NMR analysis. Thus NMR isinherently ‘site specific’. Second, NMR experiments are sensitive to iso-topic composition because the NMR effect is proportional to magneticmoment, which varies among some isotopes. This feature of NMR effec-tively removes problems of interferences present in mass spectrometryand reduces the importance of abundance sensitivity (i.e., difficultyobserving a rare species against the background created by someother, more abundant species). On the other hand, no NMR shift is ob-served when both the number of protons and neutrons in a nuclideare even; i.e., H, D, 13C and 17O are ‘seen’; 12C, 16O and 18O are not.Thus, an NMR measurement may be used to directly compare relativeconcentrations of 13C in two sites of a molecule, but 13C/12C ratios ineach site generally require some sort of additional constraint, such asa known bulk isotope ratio for the molecule.

NMR has long been used to analyze the site-specific isotopic compo-sitions of artificially enriched materials, or of the products of reactionsthat have been driven to high extents of completion, such that theunreacted residues manifest exceptionally large heavy-isotope enrich-ments (Singleton and Thomas, 1995). This is a relatively routine analysisthat could bemade by a large number of laboratories. However, makingsuch measurements on materials with natural isotope abundances andat the precisions necessary for geochemical studies requires exceptionalstability and extraordinary signal integration times (‘site-specificnatural isotope fractionation (SNIF)-NMR’ techniques). The basic tech-nologies used by SNIF-NMR are available in many NMR facilities, butonly a very few have established the methodologies to do it in practice.

SNIF-NMRhas beendeveloped for both site-specific δDand δ13C, andhas been used sporadically for nearly 30 years to study the forensics ofagricultural products and illicit drugs and mechanisms of metabolicpathways (Caer et al., 1991; Hays et al., 2000; Schmidt et al., 2003).This work has increased in pace and taken significant steps towardbroader geochemical use with the demonstration that site-specific δDof cellulose may be a paleoclimate archive (Betson et al., 2006) and

Fig. 12. Carbon isotope budgets of the reagents and products of DMMP produced by theArbuzov reaction process. Note C is transferred without net bulk fractionation, buta large position-specific isotope effect is created at the P–C bond. White = hydrogen;gray = carbon; red = oxygen; orange = phosphorous; Previously unpublished data ofT. Larson.


with the characterization of site-specific C isotope anatomies of sugarsand alkanes of different origins (Gilbert et al., 2012, 2013).

As an example of the potential of site-specific carbon isotope mea-surements for forensic studies we present results from an experimentone of us (T. Larson) recently performed to study the isotopic structureof dimethyl methylphosphonate (DMMP), a common precursor forchemical weapons (Fig. 12). We examined the carbon isotope composi-tion of phosphorous-bound carbon in dichlor synthesized by theArbuzov reaction (i.e. the reaction of a trialkyl phosphate with an alkylhalide to produce an alkyl phosphonate). The δ13C of the wholeDMMP molecule, as determined by conventional combustion followedby IRMS of CO2, is identical to the starting reagent CH3OH (δ13CPDB =−45.9). However, when the two methoxyl groups of DMMP arechemically removed, leaving only the single carbon on phosphorus,the δ13C value of the remaining methyl phosphonic acid (MPA)becomes −84.0‰; i.e., the isotope effect associated with forming theP\C bond is observed. This effect was demonstrated by relativelylaborious chemical decompositions of DMMP. However, it should bemeasurable by SNIF-NMR because that method differentiates the C\Pfrom C\O bonds; i.e., it provides a site-specific measurement thatshould reveal the exceptionally low 13C/12C ratio diagnostic of theP\C bond when it is formed by the Arbuzov reaction. If, as we suspect,other methods of DMMP synthesis do not exhibit this distinctive site-specific isotopic fractionation, it is easy to imagine using a SNIF-NMRmeasurement to recognize the specific methods used to synthesizethis chemical weapons agent.

9.2. High-resolution gas source mass spectrometry

It is imaginable that mass spectrometry could produce a general(or at least very broad) approach to studies of position specific andmultiply substituted isotopologues in organics. Electron bombardmentof organic molecules yields a wide range of fragmentation products,separate analysis of which could be used to constrain site-specific isoto-pic compositions (much as analysis of N2O+ and NO+ can yield site-specific 15N composition of N2O; Yoshida et al., 2000). And, massspectrometry is the only well demonstrated method for analysis ofmultiply substituted isotopologues at their low natural abundances(but see the discussion of spectroscopy below).

However, any such approach must contend with the existence of acomplex family of isobaric interferences at nearly every cardinal massin the mass spectra of many organic molecules. As the number ofatoms in a molecule increases, so do the number of species (bothisotopologues and species that differ in stoichiometry) with the samecardinal mass. Unambiguous analyses of these species can only be

made if these isobaric interferences are resolved or somehow correctedfor (e.g., the H3

+ correction that is commonly made to determine HD/H2

ratios by gas source mass spectrometry). Fragmentation and other ionsource reactions complicate this problem. For example, resolving the12CDH3 isotopologue of methane from 13CH4 requires a mass resolvingpower of more than 5800 (M/ΔM), an order of magnitude higher thantypical commercial gas source isotope ratio mass spectrometers; alsoseparating these species from the adduct 12CH5

+ requires a formalmass resolution of nearly 11,000 (and, to cleanly separate all thesespecies, something closer to 20,000 is preferred).

These problems were recently overcome using a prototype highmass resolution gas-source mass spectrometer (Eiler et al., 2012). Thisinstrument, the Thermo 253 Ultra, combines the inlet system and ionsource of a conventional gas source isotope ratio mass spectrometer(it most resembles the Thermo 253) with a double focusing analyzerand multi-collector array (resembling the Thermo Neptune ICPMS andTriton TIMS). Most importantly, it achieves mass resolutions up to~27,000 (M/ΔM), can be easily re-configured for a wide range analytesfrom 1 to 300 amu (because it possesses moveable collectors with botha faraday cup or SEMdetector at every position), and has relatively goodabundance sensitivity (as good as a few times 10−12). This prototypeinstrument was installed at Caltech at the end of 2011 and remainsthe only machine of its kind; however, several more of broadly similarconstructions are in development by Thermo and Nu Instruments andwe expect that several laboratories will be making measurementswith such machines in the coming years.

High resolution gas sourcemass spectrometrywill be used to study abroad range of site-specific and multiply-substituted isotopologues oforganics and other molecules. A simple representative application isthe doubly substituted isotopologues of methane, which is already thebasis of a calibrated ‘clumped isotope’ thermometer (Stolper et al.,2012, 2014, submitted for publication; Fig. 13). Methane is importantcommercially and as a greenhouse gas (Lelieveld et al., 1998) and is akey metabolite in some microbial ecosystems. The sources and geo-chemical and biochemical budgets of methane are often poorlyconstrained (Mroz, 1993; Walter et al., 2006), in part because bulkisotopic measurements (δ13C and δD values and 14C abundances)often have non-unique interpretations. Measurements of one or moreof the multiply substituted isotopologues of methane (the most abun-dant of which is 13CH3D) could contribute to this problem by providinga thermometer that distinguishes high temperature, thermogenicsources from low temperature sources from biological sources orserpentinization (much as carbonate “clumped isotope”measurementshave contributed to paleoclimate research; see Eiler, 2011 and above).The basis for this approach is the temperature dependence of equilibriumconstants for reactions such as:

13CH4þ12CH3D ¼13CH3Dþ12CH4

The temperature sensitivity of this reaction is such that usefulgeothermometry calls for measurements of the equilibrium constantwith errors of a few tenths of per mil or better. Also note that, just asfor the clumped isotope geochemistry of CO2 and carbonate, there isevery reason to suspect that kinetic isotope effects, physical fraction-ations and mixing effects will compromise the interpretation of suchmeasurements, and the ‘blocking temperature’ of the system mayinterfere with the attainment and/or preservation of environmentallymeaningful temperatures. Current applied research with this tool isjust beginning to come to grips with these complexities.

Themethane clumped isotope thermometer was recently calibratedby experimental equilibration over Ni catalyst at elevated temperatures(200–500 °C), and the first exploratory applications to natural gassamples and cultured methanogens are underway. Fig. 13 presents asummary of some of these first results (from Stolper et al., 2014,submitted for publication).

7

0

6

5

4

3

2

1

Δ18(‰)

0 100 200 300 400 500 600 700

Temperature (˚C)

Fig. 13. Calibration of amethane clumped isotope thermometer based on theory (DFT andUrey–Bigeleisen methods; gray curve), equilibration of methane gas with catalysts atelevated temperatures (red), methane formed by cracking higher order hydrocarbons(yellow), and natural methane having well known formation temperatures (blue). Thevertical axis reflects the enrichment, in per mil, of doubly substituted isotopologues(~98% of which is 13CH3D) with respect to a stochastic distribution. These ‘clumps’ arefavored at low temperatures, and a random distribution is favored at high temperatures.Data from Stolper et al., 2012, 2014, submitted for publication.


At present it appears that straightforward first-principle models ofthe temperature dependent excesses of 13CH3D are accurate (or atleast indistinguishable from experimental data at the present ~0.2‰errors), that suspected natural thermogenic gases yield apparent tem-peratures in the range ~150–250 °C (within what is conventionallyregarded as the ‘gas window’ for petroleum deposits), and that naturalbiogenic methane yields apparent temperatures consistent with itsknown growth conditions. Taken together, these results suggest thatnatural methane commonly forms in equilibriumwith respect tometh-ane clumping reactions and preserves the composition correspondingto that formation temperature over geological time-scales and throughsampling and sample processing. Nevertheless, previous experimentson photochemical lifetimes of isotopologues of methane stronglysuggest that atmospheric samples will deviate from this equilibriumcondition, perhaps in ways that will offer new constraints on the oxida-tion reactions that destroy methane in air (Kaye and Jackman, 1990).And, the most recent data for cultured methanogens suggest they arecapable of manifesting kinetic isotope effects under some conditions,artificially raising apparent temperature (D. Stolper, pers. com), andsuggesting some the clumped isotope geochemistry of some naturalenvironments could be more complex than suggested by work to date.

The Ultra is also being used to develop novel measurements ofother previously unexplored isotopologues of higher-order alkanes,including 13C2H6 and preferential distribution of 13C between thecentral and terminal positions of propane (i.e., 12CH3–

13CH2–12CH3 vs.

13CH3–12CH2–

13CH3; a simple form of position-specific isotope effect;Clog et al., 2013; Piasecki et al., 2012; similar work demonstrates the ca-pabilities of this instrument for multiple isotopologues of N2O; Magyaret al., 2012).While there are thermodynamic effects that lead to distinc-tive predicted fractionations of these and related species, it is unlikelythat the carbon isotope anatomies of metastable organic compoundssuch as these consistently display equilibrium isotopic distributions.Rather, we suspect that multiple 13C substitutions and position specific13C distributions in hydrocarbons are inherited from the biosyntheticreactions that create their source organic matter, modified by ‘cracking’reactions that generate components of gas and oil, and perhaps alsomodified by chemical and physical processes after these componentsare generated (e.g., biological consumption, secondary cracking ordiffusion through pores).

9.3. Absorption spectroscopy

Infrared absorption spectroscopy is emerging as a powerful tool forhigh-precision isotope ratio measurements of gases. These methods

are best known for their field portability, applicability to natural, unpro-cessed samples of air andwater, and their relatively low cost and simpleoperation (at least, as compared with conventional mass spectrometricdevices). To-date, most of themeasurements enabled by these technol-ogies are conventional in the sense that they probewell-known isotopicproperties of molecules (e.g., the δ13C of CO2 or δD of water; Griffis,2013). However, continued innovations (particularly extending the fre-quency range of light sources into the regions of the infraredwith strongmolecular absorptions in compounds of interest) are giving rise to anew generation of devices for measuring position-specific and clumpedisotope compositions. To-date, the only instrument of this kind that isdemonstrated to achieve useful precision at natural isotope abundancesis one for measuring position-specific 15N in N2O (i.e., distinguishing15N14O16O from 14N15N16O; Waechter et al., 2008). However, severalrecent papers and abstracts have explored the possibility that thesemethods could lead to a useful measurement of 13CH3D (Ma et al.,2008; Tsuji et al., 2012; Ono et al., 2013a, 2013b).


The low signal-to-noise ratio of NMR resonances, a result of lownuclear spin polarization, is a major factor limiting the precision andsensitivity of quantitative NMR (Saito et al., 2004). This low sensitivityis the principal reason why SNIF-NMR methods are limited to just afew research groups, and in all cases require very large samples andlong integration times. This factor also currently prevents the use ofNMR to study multiply substituted isotopologues at their low naturalabundances. In the long run this may be the greatest limitation ofSNIF-NMR techniques because it removes from consideration most ofthe isotopic diversity of organic molecules. This field could be dramati-cally expanded by new techniques that improve the signal to noise ratioof NMR.

It seems likely that infrared absorption spectroscopy could emergeas an important tool in clumped- and position-specific isotope geo-chemistry: its great potential for sensitivity and freedom from isobaricinterferences make it ideally suited to the study of low abundanceisotopologues of molecular gases. However it isn't clear yet whetherthesemethods can be extended beyond the small family of vibrationallysimple room-temperature gases. And, such devices are generally capa-ble of analyzing only a few isotopic absorption features, so thesemethods may not be well suited to the study of molecules with diverseisotopologues (e.g., propane and higher order hydrocarbons). Finally,many clumped isotope measurements call for exceptional precisionand accuracy across a wide range of bulk compositions, because anom-alies are frequently sub-per-mil departures from a random distributionfor isotopologues that vary in abundance by hundreds of per mil. Itremains to be seen whether spectroscopic devices can be calibrated tothis level of accuracy.

We suspect that continued development of these and related tech-nologies, and experience with their application to natural organics,will lead to a wide variety of novel geochemical tools. For example,recent experiments combining data from the Ultra with other novelmass spectrometric methods demonstrate that we may be close tohaving measurements that precisely constrain proportions of literallydozens of isotopologues of semi-volatile organic compounds (alkanes,derivatives of amino acids, etc.; Eiler et al., 2013b). The constituents oforganic matter contain diverse enzymatically formed and modifiedcarbon–carbon bonds, whose 13C–13C and 13C\D clumping andposition-specific fractionations may provide signatures of metabolicpathways, environmental conditions (e.g., temperature) or state ofbiological stress during biosynthesis (see the recent review by Eiler,2013). If so, such measurements may let us recognize the evolutionaryhistory of metabolic strategies through time, or could provide novelbiosignatures that will aid the search for life in extreme environmentsor (dare to dream!) extraterrestrial samples. And, the very large num-ber of independent compositional variables that characterize the full


isotopic structures of organic molecules may permit applications to fo-rensics with an unprecedented level of specificity. Perhaps the greatestchallenge of this field may be understanding this compositional com-plexity; as John Hayes so succinctly put it: “It often seems that isotopicfractionations provide toomuch information about toomany processes,combining it all in a package that is unmanageably intricate” (2001).

10. Future prospects

This review has wandered widely through the subjects of stableisotope geochemistry — from chemistry to geology to forensics; frommetals to gases to organic mater; from theory to experiment to hard-ware. But we have tried to wander with a few unifying goals: to illumi-nate the areas where this field is breaking new ground, and point toproblems that presently prevent fundamental understanding of newdiscoveries, and to catalyze a new generation of interdisciplinary collab-oration among chemists and earth and environmental scientists to solvethese problems. Four of the most prominent threads that link thesubjects of this paper are:

10.1. A diversifying landscape of analytical technologies

Twenty years ago, an aspiring stable isotope geochemist was facedwith only one core analytical technology: low-resolution, multi-collector, gas-source sector mass spectrometry. A zoo of preparatorydevices were invented to feed simple molecular gases to thesemachines — vacuum lines, carrier gases, preparatory GC, laser ablation —

but the isotopic measurements themselves were not greatly differentfrom those made in the 1940's and 50's. Today a person in this fieldcould consider, in addition to this, multi-collector plasma source massspectrometers, absorption spectroscopy, the emerging high-resolutionmulti-collector gas source mass specs, and natural abundance NMRtechniques. And, we could have easily added to these a section of thispaper on high-precision ion microprobe techniques for stable isotopeanalysis (Kita et al., 2009). Understanding, and the ability to innovatewith, advanced analytical instruments is perhaps more important nowthan at any time since the birth of stable isotope geochemistry.

10.2. Exploration of novel isotopic properties

The recent emergence of the study of mass laws of isotopic fraction-ation, position-specific isotope effects, and clumped isotope geochemis-try have tremendously expanded the potential to describe the isotopiccompositions of natural things. One of the simplest but most importantactivities of geochemistry is to explore compositional diversity,searching for the signatures that will be the foundations of new tools.The ‘space’ we are at least potentially able to explore has expandedgreatly in recent years, but most of the discoveries that must followare still waiting to be made. Some particularly obvious open playingfields include the 17O anomalies of past waters (through high precisionΔ17O measurements of carbonates and other minerals), the expansionof clumped and position specific isotope geochemistry into methaneand other organic compounds, and themass independent geochemistryof heavy metals.

10.3. Limits of conventional theories of fractionation

The frontier of stable isotope geochemistry, taken as a whole, hassurprisingly little understanding of what it is doing at the moment.For more than half a century, the kinetic theory of gases and the chem-ical physics of the 1930's and 40's served as adequate guides to mostknown stable isotope fractionations. Those few exceptions—mass inde-pendent oxygen isotope fractionations of meteorites and ozone—wererare beasts, confined to a few exotic settings. But the subjects of the lastdecade of work at the frontiers of this subject — mass independentisotope variations in S and various heavy metals; subtle variations in

mass laws of S and O isotopes; clumped isotope compositions of solids,solutions and gases; position-specific isotopic fractionations — involveeither poorly understood chemical physics (photochemical, magneticand nuclear volume effects) or poorly understood aspects of theconventional chemical isotope effects we thought we knew (secondaryisotope effects; sorption; etc.). There is a great need in these rapidlygrowing sub-disciplines of stable isotope geochemistry for predictive,quantitative and fundamental models of the physical causes of thesenovel forms of isotopic fractionations.

10.4. First-principle computational tools

One motivation for this paper (and the workshop from which itgrew) is the recognition that the computational tools for first-principle chemical models of isotope effects (e.g., DFT and MD simula-tions) have become so advanced and so widespread that it is realisticto imagine integrating them with experimental and applied stable iso-tope geochemistry studies. The community that develops and routinelyworks with these tools generally is not involved in applied isotopegeochemistry and so is unaware of many of this field's emerging focusareas. And, the models themselves are sufficiently complex and imper-fect that uneducated users from the geochemistry community are likelyto create nothing but confusion unless they get help or invest effort inlearning the relevant tools. Nevertheless, application of first principletheoretical models could advance our understanding of many novelstable isotope measurements, particularly subtle variations in masslaws for S and O, isotopic ‘clumping’, and position specific effects inchemical reactions and equilibria. These are instances where the chem-ical physics, stripped to its most fundamental level, is known, yet themanifestations of that physics are challenging because they involvesecond-order isotope effects, dynamics of surfaces or solvated com-pounds, or other structural complexities. Finally, it will be essentialthat such theoretical studies carefully consider the approximationsand errors inherent in their methods, and broaden their scope toencompass alternate visions of how such problems could be (perhapsshould be) approached (e.g., Webb and Miller, 2014).

Acknowledgments

This paper is an outgrowth of a workshop, “The Chemistry of NovelIsotope Effects in the Geosciences”, organized and supported by theDepartment of Energy office for Basic Energy Sciences, and in particularby the Geosciences section of DOE's Chemistry division. We thankeveryone involved in that program, and its administrative staff in partic-ular, for helping us organize and run this productive workshop. Thispaper is significantly influenced by the talks and discussions at thatworkshop given by the participants in addition to the authors, including:Michael Bender, Joel Blum, Bill Casey, Don DePaolo, David Johnston, AbbyKavner, Boaz Luz, Shuhei Ono, Alison Piasecki, Jim Rustad, Alex Sessions,Gary Sposito and Mark Thiemens. Finally, this paper is dedicated to thememory of Jake Bigeleisen, whose seven-decade career of creativity andvision is an inspiration to the field of isotope geochemistry.

References

Abe, M., Suzuki, T., Fujii, Y., Hada, M., 2008a. An ab initio study based on a finite nucleusmodel for isotope fractionation in the U(III)–U(IV) exchange reaction system.J. Chem. Phys. 128, 144309.

Abe, M., Suzuki, T., Fujii, Y., 2008b. An ab initio molecular orbital study of the nuclearvolume effects in uranium isotope fractionations. J. Chem. Phys. 129, 164309.

Adkins, J.F., Boyle, E.A., Curry, W.B., Lutringer, A., 2003. Stable isotopes in deep-sea coralsand a new mechanism for “vital effects”. Geochim. Cosmochim. Acta 67, 1129–1143.

Affek, H.P., 2012. Clumped isotope paleothermometry: Principles, applications, and chal-lenges. In: Linda, C., Ivany, Huber, Brian (Eds.), Reconstructing Earth’s Deep-Time Cli-mate – The State of the Art in 2012. Paleontological Society Papers, 18, pp. 101–114.

Affek, H.P., 2013. Clumped isotopic equilibrium and the rate of isotope exchange betweenCO2 and water. Am. J. Sci. 313, 309–325.

Ali, S.M., Samanta, A., Ghosh, S.K., 2002. A microscopic theory of tracer diffusivity:crossover to the hydrodynamic limit. Chem. Phys. Lett. 357, 217–222.

http://refhub.elsevier.com/S0009-2541(14)00088-6/rf1345
















Anbar, A.D., Rouxel, O., 2007. Metal stable isotopes in paleoceanography. Annu. Rev. EarthPlanet. Sci. 35, 717–746.

Angeli, I., 2004. A consistent set of nuclear rms charge radii: properties of the radiussurface R(N, Z). At. Data Nucl. Data Tables 87, 185–206.

Aupiais, J., 2011. Electrophoretic mobilities of the isotopes of chloride and bromide ions inaqueous solution at 25 °C and infinite dilution. J. Solution Chem. 40, 1629–1644.

Balan, E., Cartigny, P., Blanchard, M., Cabaret, D., Lazzeri, M., Mauri, F., 2009. Theoreticalinvestigation of the anomalous equilibrium fractionation of multiple sulfur isotopesduring adsorption. Earth Planet. Sci. Lett. 284, 88–93.

Bao, H.M., Thiemens, M.H., Farquhar, J., Campbell, D.A., Lee, C.C.-W., Heine, K., Loope, D.B.,2000. Anomalous 17O compositions in massive sulfate deposits on the Earth. Nature406, 176–178.

Bao, H., Fairchild, I.J., Wynn, P.M., Spötl, C., 2009. Stretching the envelope of past surfaceenvironments: Neoproterozoic Glacial Lakes from Svalbard. Science 323, 119–122.

Barkan, E., Luz, B., 2005. High precision measurements of 17O/16O and 18O/16O ratios inH2O. Rapid Commun. Mass Spectrom. 19, 3737–3742.

Barkan, E., Luz, B., 2007. Diffusivity fractionations of H216O/H2

17O and H216O/H2

18O in air andtheir implications for isotope hydrology. Rapid Commun. Mass Spectrom. 21,2999–3005.

Barkan, E., Luz, B., 2012. High-precision measurements of 17O/16O and 18O/16O ratios inCO2. Rapid Commun. Mass Spectrom. 26, 2733–2738.

Baroni, M., Thiemens, M.H., Delmas, R.J., Savarino, J., 2007. Mass-independent sulfurisotopic compositions in stratospheric volcanic eruptions. Science 315, 84–87.

Baroni, M., Savarino, J., Cole-Dai, V., Thiemens, M.H., 2008. Anomalous sulfur isotopecompositions of volcanic sulfate over the last millennium in Antarctic ice cores.J. Geophys. Res. - Atmos. 113, D20112.

Baskaran, M., 2011. Handbook of Environmental Isotope Geochemistry. Advances inIsotope Geochemistry, vol. 1. Springer-Verlag, Berlin.

Beck, W.C., Grossman, E.L., Morse, J.W., 2005. Experimental studies of oxygen isotopefractionation in the carbonic acid system at 15° 25° and 40 °C. Geochim. Cosmochim.Acta 69, 3493–3503.

Becke, A.D., 1993. A new mixing of Hartree–Fock and local density-functional theories.J. Chem. Phys. 98, 1372–1377.

Beekman, H.E., Eggenkamp, H.G.M., Appelo, C.A.J., 2011. An integrated modeling approachto reconstruct complex solute transport mechanisms –Cl and δ37Cl in pore waterof sediments from a former brackish lagoon in The Netherlands. Appl. Geochem. 26,257–268.

Bergquist, B.A., Blum, J.D., 2007. Mass-dependent and independent fractionation of Hgisotopes by photoreduction in aquatic systems. Science 318, 417–420.

Bergquist, R.A., Blum, J.D., 2009. The odds and evens of mercury isotopes: applications ofmass-dependent and mass-independent isotope fractionation. Elem. 5, 353–357.

Betson, T.R., Augusti, A., Schleucher, J., 2006. Quantification of deuterium isotopomersof tree-ring cellulose using nuclear magnetic resonance. Anal. Chem. 78,8406–8411.

Bhattacharya, S.K., Savarino, J., Thiemens, M.H., 2000. A new class of oxygen isotopicfractionation in photodissociation of carbon dioxide: potential implications froatmospheres of Mars and Earth. Geophys. Res. Lett. 27, 1459–1462.

Bhattacharyya, S., Bagchi, B., 2000. Power law mass dependence of diffusion: a modecoupling theory analysis. Phys. Rev. E. 61, 3850–3856.

Bigeleisen, J., 1949. The relative velocities of isotopic molecules. J. Chem. Phys. 17,675–678.

Bigeleisen, J., 1965. Chemistry of isotopes. Science 147, 463–471.Bigeleisen, J., 1996a. Temperature dependence of the isotope chemistry of the heavy

elements. Proc. Natl. Acad. Sci. 93, 9393–9396.Bigeleisen, J., 1996b. Nuclear size and shape effects in chemical reactions. Isotope

chemistry of the heavy elements. J. Am. Chem. Soc. 118, 3676–3680.Bigeleisen, J., Mayer, M.G., 1947. Calculation of equilibrium constants for isotopic

exchange reactions. J. Chem. Phys. 15, 261–267.Bigeleisen, J., Wolfsberg, M., 1958. Theoretical and experimental aspects of isotope effects

in chemical kinetics. Adv. Chem. Phys. 1, 15–76.Black, J.R., John, S., Young, E.D., Kavner, A., 2010. Effect of temperature and mass transport

on transitionmetal isotope fractionation during electroplating. Geochim. Cosmochim.Acta 74, 5187–5201.

Blair, N., Leu, A., Munoz, E., Olsen, J., Kwong, E., Desmarais, D., 1985. Carbon isotopicfractionation in heterotrophic microbial metabolism. Appl. Environ. Microbiol. 50,996–1001.

Blunier, T., Barnett, B., Bender, M.L., Hendricks, M.B., 2002. Biological oxygen productivityduring the last 60,000 years from triple oxygen isotope measurements. GlobalBiogeochem. Cycles 16 (Art. # 1029).

Blunier, T., Bender, M.L., Barnett, B., von Fisher, 2012. Planetary fertility during the past400 ka based on the triple isotope composition of O2 in trapped gases from theVostok ice core. Clim. Past 8, 1509–1526.

Boering, K.A., Jackson, T., Hoag, K.J., Cole, A.S., Perri, M.J., Thiemens, M.H., Atlast, E., 2004.Observations of the anomalous oxygen isotopic composition of carbon dioxide in thelower stratosphere and the flux of the anomaly to the troposphere. Geophys. Res.Lett. 31, L03109.

Böttcher, M.E., Neubert, N., von Allmen, K., Samankassou, E., Dellwig, O., Nägler, T.F., 2011.Barium isotope fractionation during formation of anhydrous barium carbonate(witherite): influence of experimental conditions. Geophys. Res. Abstr. 13(EGU2011-4982-1).

Bourg, I.C., Sposito, G., 2007. Molecular dynamics simulations of kinetic isotope fraction-ation during the diffusion of ionic species in liquid water. Geochim. Cosmochim.Acta 71, 5583–5589.

Bourg, I.C., Sposito, G., 2008. Isotopic fractionation of noble gases by diffusion in liquidwater: molecular dynamics simulations and hydrologic applications. Geochim.Cosmochim. Acta 72, 2237–2247.

Bourg, I.C., Sposito, G., 2011. Molecular dynamics simulations of the electrical double layeron smectite surfaces contacting concentrated mixed electrolyte (NaCl–CaCl2)solutions. J. Colloid Interface Sci. 360, 701–715.

Bourg, I.C., Sposito, G., Bourg, A.C.M., 2008. Modeling the diffusion of Na+ in compactedwater-saturated Na-bentonite as a function of pore water ionic strength. Appl.Geochem. 23, 3635–3641.

Bourg, I.C., Richter, F.M., Christensen, J.N., Sposito, G., 2010. Isotopic mass dependence ofmetal cation diffusion coefficients in liquid water. Geochim. Cosmochim. Acta 74,2249–2256.

Bowring, S.A., Schmidz, M.D., 2003. High-precision U–Pb zircon geochronology and thestratigraphic record. Zircon. Rev. Mineral. Geochem., vol. 53, pp. 305–326.

Boyd, S.R., Pillinger, C.T., Milledge, H.J., Mendelssohn, M.J., Seal, M., 1988. Fractionation ofnitrogen isotopes in a synthetic diamond of mixed crystal habit. Nature 331,604–607.

Buchachenko, A.L., 2001. Magnetic isotope effect: nuclear spin control of chemicalreactions. J. Phys. Chem. A 105, 9995–10011.

Buchachenko, A.L., Ivanov, V.L., Roznyatovskii, V.A., Artamkina, G.A.G.A., Vorob ev, A.K.,Ustynyuk, Y.A., 2007. Magnetic isotope effect for mercury nuclei in photolysis ofbis(p-trifluoromethylbenzyl)mercury. Dokl. Phys. Chem. 413, 39–41.

Caer, V., Trierweiler, M., Martin, G.J., Martin, M.L., 1991. Determination of site-specific car-bon isotope ratios at natural abundance by carbon-13 nuclear magnetic resonancespectroscopy. Anal. Chem. 63, 2306–2313.

Car, R., Parrinello, M., 1985. Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55, 2471–2474.

Casciotti, K.L., 2009. Inverse kinetic isotope fractionation during bacterial nitrite oxidation.Geochim. Cosmochim. Acta 73, 2061–2076.

Casey, W.H., 1991. On the relative dissolution rates of some oxide and orthosilicateminerals. J. Colloid Interface Sci. 146, 586–589.

Casey, W.H., Westrich, H.R., 1992. Control of dissolution rates of orthosilicate minerals bydivalent metal–oxygen bonds. Nature 355, 157–159.

Casey, W.H., Rustad, J.R., Spiccia, L., 2009. Minerals as molecules — Use of aqueous oxideand hydroxide clusters to understand geochemical reactions. Chem. Eur. J. 15,4496–4515.

Chackraborty, S., Davis, R.D., Ahmed, M., Jackson, T.L., Thiemens, M.H., 2012. Oxygenisotope fractionation in the vacuum ultraviolet photodissociation of carbonmonoxide: wavelength, pressure, and temperature dependency. J. Chem. Phys. 137(art. # 024309).

Chandan, P., Ghosh, S., Bergquist, B.A., 2014. Mercury isotope fractionation duringaqueous photo-reduction of monomethylmercury in presence of dissolved organicmatter. Environ. Sci. Technol. (submitted for publication).

Chapman, S., Cowling, T.G., 1960. The Mathematical Theory of Non-Uniform Gases, 2nded. Cambridge University Press, Cambridge.

Chen, J.B., Hintelmann, H., Feng, X.B., Dimock, B., 2012. Unusual fractionation of both oddand even mercury isotopes in precipitation from Peterborough, ON, Canada.Geochim. Cosmochim. Acta 90, 33–46.

Cheng, S., Lechman, J.B., Plimpton, S.J., Grest, G.S., 2011. Evaporation of Lennard–Jonesfluids. J. Chem. Phys. 134, 224704.

Clayton, R.N., 1993. Oxygen isotopes in meteorites. Ann. Rev. Earth Planet. Sci. 21, 115–149.Clayton, R.N., Grossman, L., Mayeda, T.K., 1973. Component of primitive nuclear composi-

tion in carbonaceous meteorites. Science 182, 485–488.Clog, M., Eiler, J., Guzzo, J., Moraes, E., Souza, I., 2013. Doubly 13C-substituted ethane.

Abstract presented at the 2013 Goldschmidt conference, Florence Italy.Cobert, F., Schmitt, A.-D., Bourgeade, P., Labolle, F., Badot, P.-M., Chabaux, F., Stille, P., 2011.

Experimental identification of Ca isotopic fractionations in higher plants. Geochim.Cosmochim. Acta 75, 5467–5482.

Cohen, A.L., McConnaughey, T.A., 2003. Geochemical perspectives on coral mineralization.Rev. Mineral. Geochem. 54, 151–187.

Cooper, G.W., Thiemens, M.H., Jackson, T.L., Chang, S., 1997. Sulphur and hydrogenisotope anomalies in meteorite sulfonic acids. Science 277, 1072–1074.

Corry, B., Chung, S.-H., 2006. Mechanisms of valence selectivity in biological ion channels.Cell. Mol. Life Sci. 63, 301–315.

Daeron,M., Guo,W., Eiler, J., Genty, D., Blamart, D., Boch, R., Drysdale, R., Maire, R.,Wainer,K., Zanchetta, G., 2011. 13C18O clumping in speleothems: observations from naturalcaves and precipitation experiments. Geochim. Cosmochim. Acta 75, 3303–3317.

Danielache, S.O., Eskebjerg, C., Johnson, M.S., Ueno, Y., Yoshida, N., 2008. High-precisionspectroscopy of S-32, S-33 and S-34 sulfur dioxide: ultraviolet absorption crosssections and isotope effects. J. Geophys. Res. - Atmos. 113, D17314.

Dansgaard, W., 1964. Stable isotopes in precipitation. Tellus 16, 436–468.deBoer, R.B., 1977. Influence of seed crystals on the precipitation of calcite and aragonite.

Am. J. Sci. 277, 38–60.Deines, P., 2003. A note on intra-elemental isotope effects and the interpretation of non-

mass-dependent isotope variations. Chem. Geol. 199, 179–182.Demers, J.D., Blum, J.D., Zak, D.R., 2013. Mercury isotopes in a forested ecosystem:

implications for air-surface exchange dynamics and the global mercury cycle. Glob.Biogeochem. Cycles 27 (1), 222–238.

Dennis, K., Schrag, D., 2010. Clumped isotope thermometry of carbonatites as an indicatorof diagenetic alteration. Geochim. Cosmochim. Acta 74, 4110–4122.

DePaolo, D.J., 2004. Calcium isotope variations produced by biological, kinetic, radiogenic,and nucleosynthetic processes. Rev. Mineral. Geochem. 55, 255–288.

DePaolo, D.J., 2011. Surface kinetic model for isotopic and trace element fractionationduring precipitation of calcite from aqueous solutions. Geochim. Cosmochim. Acta75, 1039–1056.

DeWitt, H.L., Hasenkopf, C.A., Trainer, M.G., Farmer, D.K., Jimenez, J.L., McKay, C.P., Toon,O.B., Tolbert, M.A., 2010. The formation of sulfate and elemental sulfur aerosolsunder varying laboratory conditions: implications for earth Earth. Astrobiology 10,773–781.

































































































































































































Dickson, J.A.D., 1991. Disequilibrium carbon and oxygen isotope variations in naturalcalcite. Nature 353, 842–844.

Dole, M., Jenks, G., 1944. Isotopic composition of photosynthetic oxygen. Science 100, 409.Dove, P.M., Czank, C.A., 1995. Crystal chemical controls on the dissolution kinetics of the

isostructural sulfates: celestite, anglesite, and barite. Geochim. Cosmochim. Acta 59,1907–1915.

Dreisner, T., Ha, T.-K., Seward, T.M., 2000. Oxygen and hydrogen isotope fractionation byhydration complexes of Li+, Na+, K+, Mg2+, F−, Cl−, and Br−: a theoretical study.Geochim. Cosmochim. Acta 64, 3007–3033.

Eggenkamp, H.G.M., Coleman, M.L., 2009. The effect of aqueous diffusion on the fraction-ation of chlorine and bromine stable isotopes. Geochim. Cosmochim. Acta 73,3539–3548.

Eigen, M., 1963. Fast elementary steps in chemical reaction mechanisms. Pure Appl.Chem. 6, 97–115.

Eiler, J.M., 2007. “Clumped isotope” geochemistry — the study of naturally-occurring,multiply-substituted isotopologues. Earth Planet. Sci. Lett. 262, 309–327.

Eiler, J.M., 2011. Paleoclimate reconstruction using carbonate clumped isotope thermometry.Quat. Sci. Rev. 30, 3575–3588.

Eiler, J.M., 2013. The isotopic anatomies of molecules and minerals. Annu. Rev. Earth Planet.Sci. 41, 411–441.

Eiler, J.M., Schauble, E., 2004. 18O13C16O in Earth's atmosphere. Geochim. Cosmochim.Acta 68, 4767–4777.

Eiler, J., Clog, Magyar, P., Piasecki, A., Sessions, A., Stolper, D., Deerberg, M., Schlueter, H.-S.,Schwieters, J., 2012. A high-resolution, gas-source isotope ratio mass spectrometer.Int. J. Mass Spectrom 335, 45–56.

Eiler, J., Cartigny, P., Hofmann, A.E., Piasecki, A., 2013a. Non-canonical mass laws inequilibrium isotopic fractionations: empirical evidence from the vapor pressureisotope effect of SF6. Geochim. Cosmochim. Acta 107, 205–219.

Eiler, J.M., Krumwiede, D., Schlueter, H.-J., 2013b. Mass spectrometric measurements ofthe isotopic anatomies of molecules. Abstract presented at the 2013 Fall AGUmeeting.

Epstein, S., Buchsbaum, R., Lowenstam, H.A., Urey, H.C., 1951. Carbonate-water isotopictemperature scale. Geol. Soc. Am. Bull. 62, 417–426.

Estrade, N., Carignan, J., Sonke, J.E., Donard, O.F.X., 2009. Mercury isotope fractionationduring liquid–vapor evaporation experiments. Geochim. Cosmochim. Acta 73,2693–2711.

Eyring, H., Cagle Jr., F.Wm., 1952. The significance of isotopic reactions in rate theory.J. Phys. Chem. 56, 889–892.

Fantle, M.S., DePaolo, D.J., 2007. Ca isotopes in carbonate sediment and pore fluid fromODP Site 807A: the Ca2+(aq)-calcite equilibrium fractionation factor and calciterecrystallization rates in Pleistocene sediments. Geochim. Cosmochim. Acta 71,2524–2546.

Farquhar, J., Wing, B.A., 2003. Multiple sulfur isotopes and the evolution of theatmosphere. Earth Planet. Sci. Lett. 213, 1–13.

Farquhar, G.D., Ehleringer, J.R., Hubick, K.T., 1989. Carbon isotope discrimination andphotosynthesis. Annu. Rev. Plant Physiol. Plant Mol. Biol. 40, 503–537.

Farquhar, J., Thiemens, M.H., Jackson, T., 1998. Atmosphere–surface interactionson Mars: Δ17O measurements of carbonate from ALH 84001. Science 280,1580–1582.

Farquhar, J., Savarino, J., Jackson, T.L., Thiemens, M.H., 2000a. Evidence of atmosphericsulphur in the martian regolith from sulphur isotopes in meteorites. Nature 400,50–52.

Farquhar, J., Bao, H.M., Thiemens, M.H., 2000b. Atmospheric influence of Earth's earliestsulfur cycle. Science 289, 756–758.

Farquhar, J., Savarino, J., Airieau, S., Thiemens, M.H., 2001. Observation ofwavelength-sensitive mass-independent sulfur isotope effects during SO2

photolysis: implications for the early atmosphere. J. Geophys. Res. SolidEarth Planets 106, 32829–32839.

Farquhar, J., Peters, M., Johnston, D.T., Strauss, H., Masterson, A., Wiechert, U., Kaufman,A.J., 2007. Isotopic evidence for Mesoarchaean anoxia and changing atmosphericsulphur chemistry. Nature 449, 706–709.

Finnegan, S., Bergmann, K., Fischer, W.W., Jones, D.S., Fike, D.A., Hughes, N.C., Tripati, A.,Eiler, J.M., 2011. Constraints on the duration and magnitude of Late Ordovician–Early Silurian glaciation. Science 331, 903–906.

Fricke, G., Heilig, K., 2004. Landolt–Bornstein: Num. Data and Funct. Relat. Science andTech. New Series, Group I: Elem. Part., Nuclei and Atoms., vol. 20.

Fujii, Y., Nomura, M., Okamoto, M., Onitsuka, H., Kawakami, F., Takeda, K.Z., 1989. Ananomalous isotope effect of 235U in U(IV)–U(VI) chemical exchange. Z. Naturforsch.A 44, 395–398.

Fujii, T., Moynier, F., Albarède, F., 2006. Nuclear field vs. nucleosynthetic effects as cause ofisotopic anomalies in the early Solar System. Earth Planet. Sci. Lett. 247, 1–9.

Fujii, T., Moynier, F., Albarede, F., 2009. The nuclear field shift effect in chemical exchangereactions. Chem. Geol. 267, 139–156.

Gao, Y.Q., Marcus, R.A., 2001. Strange and unconventional isotope effects in ozoneformation. Science 293, 259–263.

Gao, X., Thiemens, M.H., 1991. Systematic study of sulphur isotopic composition in ironmeteorites and the occurrence of excess 33S and 36S. Geochim. Cosmochim. Acta 55,2671.

Gehler, et al., 2012. Really Gehler 2011?? pale, 17O.Geissler, P.L., Dellago, C., Chandler, D., 1999. Kinetic pathways of ion pair dissociation in

water. J. Phys. Chem. B 103, 3706–3710.Ghosh, P., Adkins, J., Affek, H., Balta, B., Guo, W.F., Schauble, E.A., Schrag, D., Eiler, J.M.,

2006. 13C–18O bonds in carbonate minerals: a new kind of paleothermometer.Geochim. Cosmochim. Acta 70, 1439–1456.

Ghosh, S., Xu, Y., Humayun, M., Odom, L., 2008. Mass-independent fractionation ofmercury isotopes in the environment (G3: Q03004).

Ghosh, S., Schauble, E.A., Couloume, G.L., Blum, J.D., Bergquist, B.A., 2013. Estimation ofnuclear volume dependent fractionation of mercury isotopes in equilibrium liquid–vapor evaporation experiments. Chem. Geol. 336, 5–12.

Gilbert, A., Silvestre, V., Robins, R.J., Remaud, G.S., Tcherkez, G., 2012. Biochemical andphysiological determinants of intramolecular isotope patterns in sucrose from C3,C4 and CAM plants accessed by isotopic 13C NMR spectrometry: a viewpoint. Nat.Prod. Rep. 29, 476–486.

Gilbert, A., Yamada, K., Yoshida, N., 2013. Exploration of intramolecular 13C isotopedistribution in long chain n-alkanes (C11–C31) using isotopic 13C NMR. Org. Geochem.62, 56–61.

Gómez-Gallego, M., Sierra, M.A., 2011. Kinetic isotope effects in the study of organometallicreaction mechanisms. Chem. Rev. 111, 4857–4963.

Gratz, L.E., Keeler, G.J., Blum, J.D., Sherman, L.S., 2010. Isotopic composition and fraction-ation of mercury in Great Lakes precipitation and ambient air. Environ. Sci. Technol.4, 7764–7770.

Griffis, T.J., 2013. Tracing the flow of carbon dioxide and water vapor between the biosphereand atmosphere: a review of optical isotope techniques and their application. Agric. For.Meteorol. 174, 85–109.

Griffis, T.J., Baker, J.M., Sargent, S.D., Tanner, B.D., Zhang, J., 2004. Measuring field-scaleisotopic CO2 fluxes with tunable diode laser absorption spectroscopy andmicromete-orological techniques. Agric. For. Meteorol. 124, 15–29.

Griffith, E.M., Schauble, E.A., Bullen, T.D., Paytan, A., 2008. Characterization of calciumisotopes in natural and synthetic barite. Geochim. Cosmochim. Acta 72, 5641–5658.

Guo, W., 2009. Carbonate clumped isotope thermometry: application to carbonaceouschondrites and effects of kinetic isotope fractionation. (Dissertation (Ph.D.)) CaliforniaInstitute of Technology (http://resolver.caltech.edu/CaltechETD:etd-12182008-115035).

Guo, W., Niles, P., Daeron, M., Eiler, J.M., 2007. Isotope fractionations associated withdegassing of CO2 aqueous solutions and its implications for carbonate clumpedisotope thermometry. Eos Trans. AGU Fall Meet. Suppl. (Abstract PP43B-1276.).

Guo,W., Daeron,M., Niles, P., Genty, D., Kim, S.T., Vonhof, H., Affek, H.,Wainer, K., Blamart,D., Eiler, J., 2008. 13C–18O bonds in dissolved inorganic carbon: implications forcarbonate clumped isotope thermometry. Geochim. Cosmochim. Acta 72, A336.

Guo, W., Kim, S.T., Thiagarajan, N., Adkins, J., Eiler, J.M., 2009. Mechanisms for “vitaleffects” in biogenic carbonates: new perspectives based on abundances of 13C–18Obonds. EOS Trans. AGU 90 (52) (Fall Meet. Suppl., Abstract PP34B-07).

Guo, W., Kim, S.T., Yuan, J., Farquhar, J., Passey, B., 2012. 13C–18O bonds in dissovledinorganic carbon: toward a better understanding of clumped isotope thermometerin biogenic carbonates. Abstract submitted to 2012 Goldschmidt meeting.

Gussone, N., Eisenhauer, A., Heuser, A., Dietzel, M., Bock, B., Böhm, F., Spero, H.J., Lea, D.W.,Bijma, J., Nägler, T.F., 2003. Model for kinetic effects on calcium isotope fractionation(δ44Ca) in inorganic aragonite and cultured planktonic foraminifera. Geochim.Cosmochim. Acta 67, 1375–1382.

Gussone, N., Langer, G., Thoms, S., Nehrke, G., Eisenhauer, A., Riebesell, U., Wefer, G., 2006.Cellular calcium pathways and isotope fractionation in Emiliania huxleyi. Geology 34,625–628.

Guy, B.M., Ono, S., Gutzmer, J., Kaufman, A.J., Lin, Y., Fogel, M.L., Beukes, N.J., 2012. A multiplesulfur and organic carbon isotope record from non-conglomeratic sedimentary rocks oftheMesoarcheanWitwatersrand Supergroup, South Africa. Precambrian Res. 216, 208–231.

Halevy, I., 2013. Production, preservation, and biological processing of mass-independentsulfur isotope fractionation in the Archean surface environment. Proc. Natl. Acad. Sci.U. S. A. 110, 17644–17649.

Halevy, I., Johnson, D.T., Schrag, D., 2010. Explaining the structure of the Archean mass-independent sulfur isotope record. Science 329, 204.

Halliday, A.N., Lee, D.C., Christensen, J.N., Walder, A.J., Freedman, P.A., Jones, C.E., Hall,C.M., Yi, W., Teagle, D., 1995. Recent developments in inductively-coupled plasmamagnetic-sectormultiple collectormass-spectrometry. Int. J.Mass Spectrom. 146, 21–33.

Hansen, J.P., McDonald, I.R., 1986. Theory of Simple Liquids, 2nd ed. Academic Press,London.

Hays, P.A., Remaud, G.S., Jamin, E., Martin, Y.L., 2000. Geographic origin determination ofheroin and cocaine using site-specific isotopic ratio deuterium NMR. J. Forensic Sci.45, 552–562.

Heidenreich, J.E., Thiemens, M.H., 1983. A non-mass-dependent isotope effect in theproduction of ozone from molecular oxygen. J. Chem. Phys. 78, 892–895.

Hendricks, M.B., Bender, M.L., Barnett, B.A., Strutton, P., Chavez, F.P., 2005. Triple oxygenisotope composition of dissolved O2 in the equatorial Pacific: a tracer of mixing,production, and respiration. J. Geophys. Res. 110, C12021.

Hill, P.S., Schauble, E.A., 2008. Modeling the effects of bon environment on equilibriumiron isotope fractionation in ferric aquo-chloro complexes. Geochim. Cosmochim.Acta 72, 1939–1958.

Hill, P.S., Schauble, E.A., Young, E.D., 2010. Effects of changing solution chemistry onFe3+/Fe2+ isotope fractionation in aqueous Fe–Cl solutions. Geochim. Cosmochim.Acta 74, 6669–6689.

Hill, P.S., Tripati, A.K., Schable, E.A., 2014. Theoretical constraints on the effects of pH, sa-linity, and temperature on clumped isotope signatures of dissolved inorganic carbonspecies and precipitating carbonate minerals. Geochim. Cosmochim. Acta 125,610–652.

Hirth, J.P., Pound, G.M., 1960. Coefficients of evaporation and condensation. J. Phys. Chem.64, 619–626.

Hoag, K.J., Still, C.J., Fung, I.Y., Boering, K.A., 2005. Triple oxygen isotope composition oftropospheric carbon dioxide as a tracer of terrestrial gross carbon fluxes. Geophys.Res. Lett. 32, L02802.

Hofmann, A.E., Bourg, I.C., Depaolo, D.J., 2012. Ion desolvation as a mechanism for kineticisotope fractionation in aqueous systems. Proc. Natl. Acad. Sci. U. S. A. 109,18689–18694.

Hulston, J.R., Thode, H.G., 1965. Variations in S33, S34 and S36 contents and their relationto chemical and nuclear effects. J. Geophys. Res. 70, 3475–3484.





































































































































http://resolver.caltech.edu/CaltechETD:etd-12182008-115035







































































Jahn, S., Wunder, B., 2009. Lithium speciation in aqueous fluids at high P and T studied byab initio molecular dynamics and consequences for Li-isotope fractionation betweenminerals and fluids. Geochim. Cosmochim. Acta 73, 5428–5434.

Jähne, B., Heinz, G., Dietrich, W., 1987. Measurement of the diffusion coefficients ofsparingly soluble gases in water. J. Geophys. Res. 92, 10767–10776.

Johnson, C.M., Beard, B.L., Albarède, F., 2004. Geochemistry of Non-Traditional Stable Iso-topes. Rev. Mineral., vol. 55. Mineralogical Society of America, Geochemical Society.

Johnston, D.T., 2011. Multiple sulfur isotopes and the evolution of Earth's surface sulfurcycle. Earth-Sci. Rev. 106, 161–183.

Johnston, D.T., Farquhar, J., Canfield, D.E., 2007. Sulfur isotope insights into microbial sul-fate reduction: when microbes meet models. Geochim. Cosmochim. Acta 71,3929–3947.

Jouzel, J., Froehlich, K., Schotterer, U., 1997. Deuterium and 18O in present-day precipita-tion: data and modeling. J. Hydrol. Sci. 42, 747–763.

Kaufman, A.J., Johnston, D.T., Farquhar, J., Masterson, A.L., Lyons, T.W., Bates, S., Anbar,A.D., Arnold, G.L., Garvin, J., Buick, R., 2007. Late Archean biospheric oxygenationand atmospheric evolution. Science 317, 1900–1903.

Kaye, J.A., Jackman, C.J., 1990. Detection of multiply deuterated methane in the atmo-sphere — comments. Geophys. Res. Lett. 17, 659–660.

Kelly, K.K., Hirschi, J.S., Singleton, D.A., 2009. Newtonian kinetic isotope effects. Observa-tion, prediction, and origin of heavy-atom dynamic isotope effects. J. Am. Chem. Soc.131, 8382–8383.

Kerisit, S., Parker, S.C., 2004. Free energy of adsorption of water and metal ions on the10–14 calcite surface. J. Am. Chem. Soc. 126, 10152–10161.

Kerisit, S., Rosso, K.M., 2009. Transition path sampling of water exchange rates and mech-anisms around aqueous ions. J. Chem. Phys. 131. http://dx.doi.org/10.1063/1.3224737 (art. #114512).

Kiczka, M., Wiederhold, J.G., Frommer, J., Kraemer, S.M., Bourdon, B., Kretzschmar, R.,2010. Iron isotope fractionation during proton- and ligand-promoted dissolution ofprimary phyllosilicates. Geochim. Cosmochim. Acta 74, 3112–3128.

Kim, K., Lee, X., 2011. Isotopic enrichment of liquid water during evaporation from watersurfaces. J. Hydrol. 399, 364–375.

Kita, N.T., Ushikubo, T., Fu, B., Valley, J.W., 2009. High precision SIMS oxygen isotope anal-ysis and the effect of sample topography. Chem. Geol. 264, 43–57.

Klinman, J.P., 2010. A newmodel for the origin of kinetic hydrogen isotope effects. J. Phys.Org. Chem. 23, 606–612.

Kluge, T., Affek, H.P., 2012. Quantifying kinetic fractionation in Bunker cave speleothemsusing Δ47. Quaternary Science Reviews 49, 82–94.

Knudsen, M., 1911. Die molekulare wärmeleitung der gase und derakkomodationskoeffizient. Ann. Phys. 34, 593–656.

Knyazev, D.A., Myasoedov, D.F., 2001. Specific effects of heavy nuclei in chemical equilib-rium. Sep. Sci. Technol. 36, 1677–1696.

Knyazev, D.A., Semin, G.K., Bochkarev, A.V., 1999. Nuclear quadrupole contribution to theequilibrium isotope effect. Polyhedron 18, 2579–2582.

Kolb, C.E., Cox, R.A., Abbatt, J.P.D., Ammann, M., Davis, E.J., Donaldson, D.J., Garrett, B.C.,George, C., Griffiths, P.T., Hanson, D.R., et al., 2010. An overview of current issues inthe uptake of atmospheric trace gases by aerosols and clouds. Atmos. Chem. Phys.10, 10561–10605.

Kolmodin, K., Luzhkov, V.B., Aqvist, J., 2002. Computational study of the influence of sol-vent on 16O–18O equilibrium isotope effects in phosphate deprotonation reactions.J. Am. Chem. Soc. 124, 10130–10135.

Kotaka, M., Okamoto, M., Bigeleisen, J., 1992. Anomalousmass effects in isotopic exchangeequilibria. J. Am. Chem. Soc. 114, 6436–6445.

Kowacz, M., Putnis, C., Putnis, A., 2007. The effect of cation:anion ratio in solution on themechanism of barite growth at constant supersaturation: role of the desolvation pro-cess on the growth kinetics. Geochim. Cosmochim. Acta 71, 5168–5179.

Kowalski, P.M., Jahn, S., 2011. Prediction of equilibrium Li isotope fractionation betweenminerals and aqueous solutions at high P and T: an efficient ab initio approach.Geochim. Cosmochim. Acta 75, 6112–6123.

Lacan, F., Francois, R., Ji, Y., Sherrell, R.M., 2006. Cadmium isotopic composition in theocean. Geochim. Cosmochim. Acta 70, 5104–5118.

Laio, A., Parrinello, M., 2002. Escaping free-energyminima. Proc. Natl. Acad. Sci. U. S. A. 99,12562–12566.

Landais, A., Barkan, E., Yakir, D., Luz, B., 2006. The triple isotopic composition of oxygen inleaf water. Geochim. Cosmochim. Acta 70, 4105–4115.

Landais, A., Barkan, E., Luz, B., 2008. Record of δ18O and 17O-excess in ice from VostokAntarctica during the last 150,000 years. Geophys. Res. Lett. 35, L02709.

Landais, A., Risi, C., Bony, S., Vimeux, F., Descroix, L., Falourd, S., Bouygues, A., 2010. Com-bined measurements of 17Oexcess and d-excess in African monsoon precipitation:implications for evaluating convective parameterizations. Earth Planet. Sci. Lett.298, 104–112.

Langmuir, I., 1913. The vapor pressure of metalic tungsten. Physics Reviews 2, 329–342.Lasaga, A.C., Otake, T.,Watanabe, Y., Ohmoto, H., 2008. Anomalous fractionation of sulfur iso-

topes during heterogeneous reactions. Earth Planet. Sci. Lett. 268, 225–238.Lavastre, V., Jendrzejewski, N., Agrinier, P., Javoy, M., Evrard, M., 2005. Chlorine transfer

out of a very low permeability clay sequence (Paris Basin, France): 35Cl and 37Clevidence. Geochim. Cosmochim. Acta 69, 4949–4961.

Lelieveld, J., Crutzen, P.J., Dentener, F.J., 1998. Changing concentration, lifetime andclimate forcing of atmospheric methane. Tellus 50, 128–150.

Luz, B., Barkan, E., 2010. Variations of 17O/16O and 18O/16O in meteoric waters. Geochim.Cosmochim. Acta 74, 6276–6286.

Luz, B., Barkan, E., Bender, M.L., Thiemens, M.H., Boering, K.A., 1999. Triple-isotope composi-tion of atmospheric oxygen as a tracer of biosphere productivity. Nature 400, 547–550.

Luz, B., Barkan, E., Yam, R., Shemesh, A., 2009. Fractionation of oxygen and hydrogenisotopes in evaporating water. Geochim. Cosmochim. Acta 73, 6697–6703.

Lyons, J.R., 2007. Mass-independent fractionation of sulfur isotopes by isotope-selectivephotodissociation of SO2. Geophys. Res. Lett. 34, L22811.

Lyons, J.R., 2009. Atmospherically-derived mass-independent sulfur isotope signatures,and incorporation into sediments. Chem. Geol. 267, 164–174.

Lyons, J.R., Stark, G., Blackie, D., Pickering, J.C., 2010. High-resolution xSO2 spectra, andsulfur MIF due to SO2 photolysis. Geochim. Cosmochim. Acta 74, A648.

Ma, Q., Wu, S., Tang, Y., 2008. Formation and abundance of doubly-substituted methaneisotopologues (13CH3D) in natural gas systems. Geochim. Cosmochim. Acta 72,5446–5456.

Maggi, F., Riley, W.J., 2009. Transient competitive complexation in biological kineticisotope fractionation explains nonsteady isotopic effects: theory and application todenitrification in soils. J. Geophys. Res. 114, G04012.

Magyar, P., Kopf, S., Orphan, V., Eiler, J., 2012. Measurement of nitrous oxide isotopologuesand isotopomers by the MAT 253 Ultra. Presented at Goldschmidt Conf., June 24–29,Montreal.

Martin, G.J., Martin, M.L., 1981. Deuterium labeling at the natural abundance level asstudied by high-field quantitative 2H NMR. Tetrahedon Lett. 22, 3525–3528.

Masterson, A.L., Farquhar, J., Wing, B.A., 2011. Sulfur mass-independent fractionationpatterns in the broadband UV photolysis of sulfur dioxide: pressure and third bodyeffects. Earth Planet. Sci. Lett. 306, 253–260.

Matsuhisa, Y., Goldsmith, J.R., Clayton, R.N., 1978. Mechanisms of hydrothermalcrystallization of quartz at 250 °C and 15 kbar. Geochim. Cosmochim. Acta42, 173–182.

Matthews, A., Zhu, X.-K., O'Nions, K., 2001. Kinetic iron stable isotope fractionation be-tween iron (−II) and (−III) complexes in solution. Earth Planet. Sci. Lett. 192, 81–92.

Mauersberger, K., 1987. Ozone isotope measurements in the stratosphere. Geophys. Res.Lett. 14, 80–83.

Mauersberger, K., Erbacher, B., Krankowsky, D., Gunther, J., Nickel, R., 1999. Ozone isotopeenrichement: isotopomer-specific rate coefficients. Science 283, 370–372.

McConnaughey, T., 1989. 13C and 18O isotopic disequilibrium in biological carbonates .1.Patterns. Geochim. Cosmochim. Acta 53, 151–162.

McEwing, C.E., Rees, C.E., Thode, H.G., 1983. Sulfur isotope effects in the high-temperatureoxidation of troilite. Geochim. Cosmochim. Acta 47, 2059–2061.

Merlivat, L., 1978. Molecular diffusivities of H216O, HD16O, and H2

18O in gases. J. Chem. Phys.69, 2864–2871.

Miller, M.F., 2002. Isotopic fractionation and the quantification of 17O anomalies in theoxygen three-isotope system: an appraisal and geochemical significance. Geochim.Cosmochim. Acta 66, 1881–1889.

Mills, R., 1973. Self-diffusion in normal and heavy water in the range 1–45. J. Phys. Chem.77, 685–688.

Mroz, E.J., 1993. Deuteromethanes — potential fingerprints of the sources of atmosphericmethane. Chemosphere 26, 45–53.

Mucci, A., Morse, J.W., 1983. The incorporation of Mg2+ and Sr2+ into calcite over-growths: Influences of growth rate and solution composition. Geochim. Cosmochim.Acta 47, 217–233.

Nielsen, L.C., Druhan, J.L., Yang, W., Brown, S.T., DePaolo, D.J., 2011. Calcium isotopes astracers of biogeochemical processes. In: Baskaran, M. (Ed.), Handbook of Environ-mental Isotope Geochemistry, pp. 105–124.

Nielsen, L.C., DePaolo, D.J., De Yoreo, J.J., 2012. Self-consistent ion-by-ion growth modelfor kinetic isotopic fractionation during calcite precipitation. Geochim. Cosmochim.Acta 86, 166–181.

Nomura,M., Higuchi, N., Fujii, Y., 1996. Mass dependence of uranium isotope effects in theU(IV)–U(VI) exchange reaction. J. Am. Chem. Soc. 118, 9127–9130.

Nowlan III, D.T., Gregg, T.M., Davies, H.M.L., Singleton, D.A., 2003. Isotope effects and thenature of selectivity in rhodium-catalized cyclopropanations. J. Am. Chem. Soc. 125,15902–15911.

O'Leary, M.H., 1984. Measurement of the isotope fractionation associatedwith diffusion ofcarbon dioxide in aqueous solution. J. Phys. Chem. 88, 823–825.

Oduro, H., Harms, B., Sintim, H.O., Kaufman, A.J., Cody, G., Farquahr, J., 2011. Evidence ofmagnetic isotope effects during thermochemical sulfate reduction. Proc. Natl. Acad.Sci. U. S. A. 108, 17635–17638.

Oduro, H., Van Alstyne, K.L., Farquhar, J., 2012. Sulfur isotope variability of oceanic DMSPgeneration and its contributions to marine biogenic sulfur emissions. Proc. Natl. Acad.Sci. U. S. A. 109, 9012–9016.

Ohlin, C.A., Villa, E.M., Rustad, J.R., Casey, W.H., 2009. Dissolution of insulating oxidematerials at the molecular scale. Nat. Mater. 9, 11–19.

Ohmoto, H., Watanabe, Y., Ikemi, H., Poulson, S.R., Taylor, B.E., 2006. Sulphur isotopeevidence for an oxic Archaean atmosphere. Nature 442, 908–911.

Oi, T., Taguma, N., Kakihana, H., 1985. Calculations of thermodynamic sulfur isotope effect.J. Nucl. Sci. Technol. 22, 818–832.

Ono, S., Eigenbrode, J.L., Pavlov, A.A., Karecha, P., Rumble, D., Kasting, J.F., Freeman, K.H.,2003. New insights into Archean sulfur cycle from mass-independent sulfur isotoperecords from the Hamersley Basin, Australia. Earth Planet. Sci. Lett. 213, 15–30.

Ono, S., Wing, B.A., Johnston, D.T., Farquhar, J., Rumble, D., 2006. Mass-dependent frac-tionation of quadruple stable isotope system as a new tracer of sulfur biogeochemicalcycles. Geochim. Cosmochim. Acta 70, 2238–2252.

Ono, S., Whitehill, A.R., Lyons, J.R., 2013a. Contributions of isotopologue self-shielding tosulfur mass-independent fractionation during sulfur dioxide photolysis. J. Geophys.Res. Atmos. 118, 2444–2454.

Ono, S., Sherwood Lollar, B., Harris, E., McManus, B., Zahniser, M., Nelson, D., 2013b.Clumped methane isotopologue (13CH3D) thermometry of geological methane bytunablemid-infrared laser spectroscopy. Abstract presented at the 2013 Goldschmidtconference, Florence Italy.

Otake, T., Lasaga, A.C., Ohmoto, H., 2008. Ab initio calculations for equilibrium fraction-ations in multiple sulfur isotope systems. Chem. Geol. 249, 357–376.

























http://dx.doi.org/10.1063/1.3224737

http://dx.doi.org/10.1063/1.3224737
















































































































































































Pack, A., Gehler, A., Süssenberger, A., 2013. Exploring the usability of isotopically anoma-lous oxygen in bones and teeth as paleo-CO2-barometer. Geochim. Cosmochim. Acta102, 306–317.

Panagiotopoulos, A.Z., 1987. Direct determination of phase coexistence properties offluids by Monte Carlo simulation in a new ensemble. Mol. Phys. 61, 813–826.

Paris, G., Sessions, A.L., Subhas, A.V., Adkins, J.F., 2013. MC-ICP-MS measurement of 34Sand Δ33S in small amounts of dissolved sulfate. Chem. Geol. 345, 50–61.

Patterson, C., Tilton, G., Inghram, M., 1955. Age of the Earth. Science 121, 69–75.Pavlov, A., Kasting, J.F., 2002. Mass-independent fractionation of sulfur isotopes in

Archean sediments: strong evidence for an anoxic Archean atmosphere. Astrobiology2, 27–41.

Philippot, P., van Zuilen, M., Rollion-Bard, C., 2012. Variations in atmospheric sulphurchemistry on Earth linked to volcanic activity. Nat. Geosci. 5, 668–674.

Piana, S., Gale, J.D., 2006. Three-dimensional kinetic Monte Carlo simulation of crystalgrowth from solution. J. Cryst. Growth 294, 46–52.

Piasecki, A., Eiler, J.M., 2012. Direct mass spectrometric analysis of position-specific 13C inorganics. Abstract presented at the 2012 Goldschmidt Conference, Montreal.

Rees, C.E., Thode, H.G., 1977. A 33S anomaly in Allende meteorite. Geochim. Cosmochim.Acta 41, 1679–1682.

Reinhard, C.T., Pianavsky, N.J., Lyons, T.W., 2013. Long-term sedimentary recycling of raresulphur isotope anomalies. Nature 497, 100–103.

Remaud, G.S., Martin, Y.L., Martin, G.G., Martin, G.L., 1997. Detection of sophisticatedadulterations of natural vanilla flavors and extracts: application of the SNIF-NMRmeth-od to vanillin and p-hydroxybenzaldehyde. J. Agric. Food Chem. 45, 859–866.

Richens, D.T., 2005. Ligand substitution reactions at inorganic centers. Chem. Rev. 105,1961–2002.

Richter, F.M., 2004. Timescales determining the degree of kinetic isotope fractionation byevaporation and condensation. Geochim. Cosmochim. Acta 68, 4971–4992.

Richter, F.M., Davis, A.M., DePaolo, D.J., Watson, E.B., 2003. Isotope fractionation by chem-ical diffusion between molten basalt and rhyolite. Geochim. Cosmochim. Acta 67,3905–3923.

Richter, F.M., Mendybaev, R.A., Christensen, J.N., Hutcheon, I.D., Williams, R.W., Sturchio,N.C., Beloso Jr., A.D., 2006. Kinetic isotope fractionation during diffusion of ionicspecies in water. Geochim. Cosmochim. Acta 70, 277–289.

Richter, F.M., Janney, P.E., Mendybaev, R.A., Davis, A.M., Wadhwa, M., 2007. Elementaland isotopic fractionation of Type B CAI-like liquids by evaporation. Geochim.Cosmochim. Acta 71, 5544–5564.

Richter, F.M., Watson, E.B., Mendybaev, R.A., Teng, F.-Z., Janney, P.E., 2008. Magnesiumisotope fractionation in silicate melts by chemical and thermal diffusion. Geochim.Cosmochim. Acta 72, 206–220.

Richter, F.M., Dauphas, N., Teng, F.-Z., 2009. Non-traditional fractionation of non-traditional isotopes: evaporation, chemical diffusion and Soret diffusion. Chem.Geol. 258, 92–103.

Ripperger, S., Rehkämper,M., Porcelli, D., Halliday, A.N., 2007. Cadmium isotope fractionationin seawater— A signature of biological activity. Earth Planet. Sci. Lett. 261, 670–684.

Risi, C., Landais, A., Bony, S., Jouzel, J., Masson‐Delmotte, V., Vimeux, F., 2010. Understand-ing the 17O excess glacial‐interglacial variations in Vostok precipitation. J. Geophys.Res. Atmos. 115, D10112.

Risi, C., Landais, A., Winkler, R., Vimeux, F., 2012. What controls the spatio-temporaldistribution of D-excess and 17O-excess in precipitation? A general circulationmodel study. Clim. Past Discuss. 8, 5493–5543.

Rolison, J.M., Landing, W.M., Luke, W., Cohen, M., Salters, V.J.M., 2013. Isotopic composi-tion of species-specific atmospheric Hg in a coastal environment. Chem. Geol. 336,37–49.

Romero, A.B., Thiemens, M.H., 2003. Mass-independent sulfur isotopic compositions inpresent-day sulfate aerosols. J. Geophys. Res. Atmos. 108, 4524. http://dx.doi.org/10.1029/2003JD003660.

Rumble, D., Miller, M.F., Franchi, I.A., Greenwood, R.C., 2007. Oxygen three-isotopefractionation lines in terrestrial silicate minerals: an inter-laboratory comparison of hy-drothermal quartz and eclogitic garnet. Geochim. Cosmochim. Acta 71, 3592–3600.

Rustad, J.R., 2001. Molecular models of surface relaxation, hydroxylation, and surfacecharging at oxide-water interfaces. Rev. Mineral. 44, 169–272.

Rustad, J.R., Casey, W.H., 2012. Metastable structures and isotope exchange reactions inpolyoxometalate ions provide a molecular view of oxide dissolution. Nat. Mater.http://dx.doi.org/10.1038/NMAT3203.

Rustad, J.R., Casey, W.H., Yi, Q.-Z., Bylaska, E.J., Felmy, A.R., Bogatko, S.A., Jackson, V.E.,Dixon, D.A., 2010. Isotopic fractionation of Mg2+(aq), Ca2+(aq), and Fe2+(aq)with carbonate minerals. Geochim. Cosmochim. Acta 74, 6301–6323.

Saenger, C., Affek, H.P., Felis, T., Thiagarajan, N., Lough, J.M., Holcomb, M., 2012. Carbonateclumped isotope variability in shallow water corals: temperature dependence andgrowth-related vital effects. Geochim. Cosmochim. Acta 99, 224–242.

Saito, T., Nakaie, S., Kinoshita, M., Ihara, T., Kinugasa, S., Nomura, A., Maeda, T., 2004.Practical guide for accurate quantitative solution state NMR analysis. Metrologia 41,213–218.

Schauble, E.A., 2007. Role of nuclear volume in driving equilibrium stable isotope fraction-ation of mercury, thallium, and other very heavy elements. Geochim. Cosmochim.Acta 71, 2170–2189.

Schauble, E.A., 2011. First-principles estimates of equilibrium magnesium isotopefractionation in silicate, oxide, carbonate, and hexaaquamagnesium(2+) crystals.Geochim. Cosmochim. Acta 75, 844–869.

Schauble, E.A., Ghosh, P., Eiler, J.M., 2006. Preferential formation of 13C–18O bonds incarbonate minerals, estimated using first-principles lattice dynamics. Geochim.Cosmochim. Acta 70, 2510–2529.

Scheppele, S.E., 1972. Kinetic isotope effects as a valid measure of structure–reactivityrelationships. Isotope effects and nonclassical theory. Chem. Rev. 72, 511–532.

Schmidt, H.L., Werner, R.A., Eisenreich, W., 2003. Systematics of 2H patterns in naturalcompounds and its importance for the elucidation of biosynthetic pathways.Phytochem. Rev. 2, 61–85.

Sharif, S., Denisov, G.S., Toney, M.D., Limbach, H.H., 2006. NMR studies of solvent-assistedproton transfer in a biologically relevant Schiff base: toward a distinction of geometricand equilibrium H-bond isotope effects. J. Am. Chem. Soc. 128, 3375–3387.

Sherman, L.S., Blum, J.D., Johnson, K.P., Keeler, G.J., Barres, J.A., Douglas, T.A., 2010. Mass-independent fractionation of mercury isotopes in Arctic snow driven by sunlight.Nat. Geosci. 3, 173–177.

Singleton, D.A., Thomas, A.A., 1995. High-precision simultaneous determination of multi-ple small kinetic isotope effects at natural abundance. J. Am. Chem. Soc. 117,9357–9358.

Skaron, S., Wolfsberg, M., 1980. Anomalies in the fractionation by chemical-equilibrium of18O/16O relative to 17O/16O. J. Chem. Phys. 72, 6810–6811.

Sonke, J.E., 2011. A global model of mass independent mercury stable isotope fraction-ation. Geochim. Cosmochim. Acta 75, 4577–4590.

Sposito, G., 2004. The Surface Chemistry of Natural Particles. Oxford University Press.Stack, A.G., Raiteri, P., Gale, J.D., 2012. Accurate rates of the complex mechanisms for

growth and dissolution of minerals using a combination of rare-event theories.J. Am. Ceram. Soc. 134, 11–14.

Stirling, C.H., Andersen, M.B., Potter, E.-K., Halliday, A.N., 2007. Low-temperature isotopicfractionation in uranium. Earth Planet. Sci. Lett. 264, 208–225.

Stolper, D.A., Sessions, A.L., Eiler, J.M., 2012. Measurement of intact methaneisotopologues, including 13CH3D. Presented at Goldschmidt Conf., June 24–29,Montreal.

Stolper, D.A., Sessions, A.L., Ferreira, A.A., Santos Neto, E.V., Schimmelmann, A., Shusta, S.S.,Valentine, D.L., Eiler, J.M., 2014a. Combined 13C–D and D–D clumping in methane:Methods and preliminary results. Geochim. Cosmochim. Acta 126, 169–191.

Stolper, D.A., Lawson, M., Davis, C.L., Ferreira, A., Santos Neto, E.V., Ellis, G.S., Lewan, M.D.,Martini, A.M., Sessions, A.L., Eiler, J.M., 2014. The formation temperature of methanein natural environments. Science (submitted for publication).

Stumm, W., Morgan, J.J., 1996. Aquatic Chemistry, 3rd ed. Wiley.Sun, T., Bao, H., 2011. Thermal-gradient-induced non-mass-dependent isotope fraction-

ation. Rapid Commun. Mass Spectrom. 25, 756–773.Tcherkez, G.G.B., Farquhar, G.D., Andrews, T.J., 2006. Despite slow catalysis and confused

substrate specificity, all ribulose bisphosphate carboxylases may be nearly perfectlyoptimized. Proc. Natl. Acad. Sci. U. S. A. 103, 7246–7251.

Teng, F.-Z., Dauphas, N., Helz, R.T., Gao, S., Huang, S., 2011. Diffusion-driven magnesiumand iron isotope fractionation in Hawaiian olivine. Earth Planet. Sci. Lett. 308,317–324.

Thiagarajan, N., Adkins, J., Eiler, J., 2011. Carbonate clumped isotope thermometry ofdeep-sea corals and implications for vital effects. Geochim. Cosmochim. Acta 75,4416–4425.

Thiemens, M.H., Heidenreich, J.E., 1983. The mass-independent fractionation ofoxygen — A novel isotope effect and its possible cosmochemical implications.219, 1073–1075.

Thiemens, M.H., Jackson, T., Mauersberger, K., Schueler, B., Morton, J., 1991. Oxygenisotope fractionation in stratospheric CO2. Geophys. Res. Lett. 18, 669–672.

Thiemens, M.H., Brearly, A., Jackson, T., Bobias, G., 1994. Detection of a 33S excess in anoldhamite separate from Norton County. Meteoritics 29, 540–541.

Thiemens, M.H., Jackson, T., Zipf, E.C., Erdman, P.W., van Egmond, C., 1995. Carbon dioxideand oxygen isotope anomalies in the mesosphere and stratosphere. Science 270,969–972.

Thiemens, Mark H., 2006. History and applications of mass-independent isotope effects.Annual Review of Earth and Planetary Sciences 34, 217–262 CODEN: AREPCIISSN:0084-6597. AN 2006:594478 CAPLUS (Copyright (C) 2006 ACS on SciFinder(R)).

Thiemens, M.H., Chackraborty, S., Dominguez, G., 2012. The physical chemistry of mass-independent isotope effects and their observation in nature. Annual Reviews inPhysical Chemistry., 63, pp. 155–177.

Tripati, A.K., Hill, P.S., Eagle, R.A., Schauble, E.A., Eiler, J.M., Zeebe, R.E., Uchikawa, J., 2014.13C–18O bond ordering and 18O/16O ratios in dissolved inorganic carbon speciesand their potential to be preserved in the solid phase. Geochim. Cosmochim. Acta(in press).

Tsuji, K., Teshima, H., Sasada, H., Yoshida, N., 2012. Spectroscopic isotope ratio measurementof doubly-substituted methane. Spectrochim. Acta A Mol. Biomol. Spectrosc. 98, 43–46.

Tsuruta, T., Nagayama, G., 2004. Molecular dynamics studies on the condensation coeffi-cient of water. J. Phys. Chem. B 108, 1736–1743.

Uchikawa, J., Zeebe, R.E., 2011. An experimental study on the effect of carbonicanhydrase on the oxygen isotope exchange kinetics and equilibrium in the car-bonic acid system. Abstract PP41A-1730 presented at 2011 Fall Meeting, AGU,San Francisco, Calif., 5–9 Dec.

Uemura, R., Abe, O., Motoyama, H., 2010. Determining the 17O/16O ratio of water usinga water–CO2 equilibration method: application to glacial–interglacial changes in17O-excess from the Dome Fuji ice core Antarctica. Geochim. Cosmochim. Acta 74,4919–4936.

Ueno, Y., Johnson, M.S., Danielache, S.O., Eskebjerg, C., Pandey, A., Yoshida, N., 2009.Geological sulfur isotopes indicate elevated OCS in the Archean atmosphere, solvingfaint young sun paradox. Proc. Natl. Acad. Sci. U. S. A. 106, 14784–14789.

Urey, H.C., 1947. The thermodynamic properties of isotopic substances. J. Chem. Soc.562–581.

Varma, S., Rempe, S.B., 2006. Coordination numbers of alkali metal ions in aqueoussolutions. Biophys. Chem. 124, 192–199.

Vineyard, G.H., 1957. Frequency factors and isotope effects in solid state rate processes.J. Phys. Chem. Solids 3, 121–127.





























































http://dx.doi.org/10.1029/2003JD003660






http://dx.doi.org/10.1038/NMAT3203































































































































Waechter, H., Mohn, J., Tuzson, B., Emmenegger, L., Sigrist, M.W., 2008. Determination ofN2O isotopomers with quantum cascade laser based absorption spectroscopy. Opt.Express 16, 9239–9244.

Wainer, K., Genty, E., Blamart, D., Daeron, M., Bar-Matthews, M., Vonhof, H., Dublyansky,Y., Pons-Branchu, E., Thomas, L., van Calsteren, P., Quinif, Y., Caillon, N., 2011.Speleothem record of the last 180 ka in Villars cave (SW France): investigation of alarge δ18O shift between MIS6 and MIS5. Quat. Sci. Rev. 30, 130–146.

Walter, K.M., Zimov, S.A., Chanton, J.P., Verbyla, D., Chapin, F.S., 2006. Methane bubblingfrom Siberian thaw lakes as a positive feedback to climate warming. Nature 443,71–75.

Wang, J., Davis, A.M., Clayton, R.N., Mayeda, T.K., 1994. Kinetic isotope fractionationduring the evaporation of the iron oxide from liquid state. Lunar Planet. Sci., vol.25. The Lunar and Planetary Institute, Houston, pp. 1459–1460.

Wasserburg, G.J., Lee, T., Papanastassiou, D.A., 1977. Correlated O and Mg isoto-pic anomalies in Allende inclusions 2 Magnes. Geophys. Res. Lett. 4,299–302.

Watanabe, Y., Farquhar, J., Ohmoto, H., 2009. Anomalous fractionations of sulfur isotopesduring thermochemical sulfate reduction. Science 324, 370–373.

Watkins, J.M., DePaolo, D.J., Huber, C., Ryerson, F.J., 2009. Liquid composition-dependenceof calcium isotope fractionation during diffusion in molten silicates. Geochim.Cosmochim. Acta 73, 7341–7359.

Watkins, J.M., DePaolo, D.J., Ryerson, F.J., Peterson, B.T., 2011. Influence of liquid structureon diffusive isotope separation in molten silicates and aqueous solutions. Geochim.Cosmochim. Acta 75, 3103–3118.

Watson, E.B., 2004. A conceptual model for near-surface kinetic controls on the trace-element and stable isotope composition of abiogenic calcite crystals. Geochim.Cosmochim. Acta 68, 1473–1488.

Webb, M.A., Miller III, T.F., 2014. Position-specific and clumped stable isotope studies:comparison of the Urey and Path-Integral approaches for carbon dioxide, nitrousoxide, methane and propane. J. Phys. Chem. (in press).

Weyer, S., Anbar, A.D., Gerdes, A., Gordon, G.W., Algeo, T.J., Boyle, E.A., 2008. Naturalfractionation of 238U/235U. Geochim. Cosmochim. Acta 72, 345–359.

Whitehill, A.R., Ono, S., 2012. Excitation band dependence of sulfur isotope mass-independent fractionation during photochemistry of sulfur dioxide using broadbandlight sources. Geochim. Cosmochim. Acta 94, 238–253.

Wiederhold, J.G., Cramer, C.J., Daniel, K., Infante, I., Bourdon, B., Kretzschmar, R., 2010.Equilibrium mercury isotope fractionation between dissolved Hg(II) species andthiol-bound Hg. Environ. Sci. Technol. 44, 4191–4197.

Winkler, R., Landais, A., Sodemann, H., Dümbgen, L., Prié, F., Masson-Delmotte, V., Stenni,B., Jouzel, J., 2012. Deglaciation records of 17O-excess in East Antarctica: reliablereconstruction of oceanic relative humidity from coastal sites. Clim. Past Discuss. 7,1845–1886.

Wunder, B., Meixner, A., Romer, R.L., Jahn, S., 2011. Li-isotope fractionation betweensilicates and fluids: pressure dependence and influence of the bonding environment.Eur. J. Mineral. 23, 333–342.

Yamaji, K., Makita, Y., Watanabe, H., Sonoda, A., Kanoh, H., Hirotsu, T., Ooi, K., 2001.Theoretical estimation of lithium isotope reduced partition function ratio for lithiumions in aqueous solution. J. Phys. Chem. A 105, 602–613.

Yoshida, N., Toyoda, S., 2000. Constraining the atmospheric N2O budget from intramolec-ular site preference in N2O isotopomers. Nature 405, 330–334.

Young, E.D., Galy, A., Nagahara, H., 2002. Kinetic and equilibriummass-dependent isotopefractionation laws in nature and their geochemical and cosmochemical significance.Geochim. Cosmochim. Acta 66, 1095–1104.

Yu, Y., Hewins, R.H., Alexander, C.M.O'D, Wang, J., 2003. Experimental study of evapora-tion and isotopic mass fractionation of potassium in silicate melts. Geochim.Cosmochim. Acta 67, 773–786.

Zachos, J., Pagani, M., Sloan, L., Thomas, E., Billups, K., 2001. Trends, rhythms andaberrations in global climate 65 Ma to present. Science 292, 686–693.

Zahnle, K., Claire, M., Catling, D., 2006. The loss of mass-independent fractionation of sulfurdue to a Paleoproterozoic collapse of atmospheric methane. Geobiology 4, 271–283.

Zeebe, R.E., 1999. An explanation of the effect of seawater carbonate concentration onforaminiferal oxygen isotopes. Geochim. Cosmochim. Acta 63, 2001–2007.

Zheng, W., Hintelmann, H., 2009. Mercury isotope fractionation during photoreduction in nat-ural water is controlled by its Hg/DOC ratio. Geochim. Cosmochim. Acta 73, 6704–6715.

Zheng, W., Hintelmann, H., 2010. Nuclear field shift effect in isotope fractionation ofmercury during abiotic reduction in the absence of light. J. Phys. Chem. A 114,4238–4245.

Zhu, X.K., Guo, Y., Williams, R.J.P., O'Nions, R.K., Matthews, A., Belshaw, N.S., Canters, G.W.,de Waal, E.C., Weser, U., Burgess, B.K., Salvato, B., 2002. Mass fractionation processesof transition metal isotopes. Earth Planet. Sci. Lett. 200, 47–62.

Zink, S., Schoenberg, R., Staubwasser, M., 2010. Isotopic fractionation and reaction kineticsbetween Cr(III) and Cr(VI) in aqueous media. Geochim. Cosmochim. Acta 74,5729–5745.

Zmolek, P., Zu, X.P., Jackson, T., Thiemens, M.H., Trogler, W.C., 1999. Large mass indepen-dent sulfur isotope fractionations during the photopolymerization of (CS2)–12C and(CS2)–13C. J. Phys. Chem. A 103, 2477–2480.


















































































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