Frontiers Clumped-isotope geochemistry The study of ... · Stable isotope geochemistry is rooted in the land-mark discoveries in physical chemistry made during the 1920s and 30s.

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Earth and Planetary Science Letters 262 (2007) 309–327www.elsevier.com/locate/epsl

Frontiers

“Clumped-isotope” geochemistry—The study of naturally-occurring,multiply-substituted isotopologues

John M. Eiler

Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, United States

Accepted 13 August 2007

Available onli

Editor: A.N. Halliday

ne 28 August 2007

Abstract

Clumped isotope geochemistry is concerned with the state of ordering of rare isotopes in natural materials. That is, it examinesthe extent to which rare isotopes (D, 13C, 15N, 18O, etc.) bond with or near each other rather than with the sea of light isotopes inwhich they swim. Abundances of isotopic ‘clumps’ in natural materials are influenced by a wide variety of factors. In most cases,their concentrations approach (within ca. 1%, relative) the amount expected for a random distribution of isotopes. Deviations fromthis stochastic distribution result from: enhanced thermodynamic stability of heavy-isotope ‘clumps’; slower kinetics of reactionsrequiring the breakage of bonds between heavy isotopes; the mass dependence of diffusive and thermo-gravitational fractionations;mixing between components that differ from one another in bulk isotopic composition; biochemical and photochemicalfractionations that may reflect combinations of these simpler physical mechanisms; and, in some cases, other processes we do notyet understand. Although clumped isotope geochemistry is a young field, several seemingly promising applications have alreadyemerged. Most importantly, it appears that proportions of 13C–18O bonds in carbonate minerals are sensitive to their growthtemperatures, independent of bulk isotopic composition. Thus, ‘clumped isotope’ analysis of ancient carbonates can be used as aquantitative paleothermometer that requires no assumptions about the δ18O of waters from which carbonates grew. This approachhas been used to reconstruct marine temperatures across the Phanerozoic (reaching back to the Silurian), terrestrial groundtemperatures across the Cenozoic, thermal histories of aqueously altered meteorites, among other applications. Clumped isotopegeochemistry is also placing new constraints on the atmospheric budget and stratospheric photochemistry of CO2, and should becapable of placing analogous new constraints on the budgets of other atmospheric gases. Finally, this field could be extended toencompass sulfates, volatile hydrocarbons, organic moieties and other materials.© 2007 Elsevier B.V. All rights reserved.

Keywords: isotopes

1. Introduction

For most of the history of stable isotope geochemistryit has focused, knowingly or implicitly, on the con-centrations of isotopic species containing one rareisotope. For example, when discussing the 18O content

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0012-821X/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.epsl.2007.08.020

of meteoric water, one generally means the relativeabundances of H2

18O vs. H216O; the 18O contained in

other isotopic variants of water (e.g., HD18O andD218O)

is neglected or deduced based on a few simple andgenerally unverified assumptions.

There are good reasons for this neglect. Speciescontaining two or more rare isotopes typically constitute10's of parts per million or less of a given population of

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http://dx.doi.org/10.1016/j.epsl.2007.08.020

Table 1Stochastic abundances of isotologues of common gases

Mass a Isotopologue Relative abundance

N2b

28 14N2 99.30%29 15N14N 0.73%30 15N2 13.4 ppm

O2c

32 16O2 99.50%33 17O16O 756 ppm34 18O16O 0.40%

17O2 0.144 ppm35 18O17O 1.52 ppm36 18O2 4.00 ppm

CO2d

44 12C16O2 98.40%45 13C16O2 1.11%

12C17O16O 748 ppm46 12C18O16O 0.40%

13C17O16O 8.4 ppm12C17O2 0.142 ppm

47 13C18O16O 44.4 ppm12C17O18O 1.50 ppm13C17O2 1.60 ppb

48 12C18O2 3.96 ppm13C17O18O 16.8 ppb

49 13C18O2 44.5 ppba Nominal cardinal mass in AMU.b Asuming a 15N/14N ratio equal to atmospheric N2.c Assuming 17O/16O and 18O/16O ratios equal to the VSMOW

standard.d Assuming 17O/16O and 18O/16O ratios equal to the VSMOW

standard and 13C/12C ratio equal to the PDB standard.

310 J.M. Eiler / Earth and Planetary Science Letters 262 (2007) 309–327

molecules (Table 1). Therefore, they generally have nomeaningful impact on bulk isotopic compositions (anexception is the δD of water, which can be measurablyimpacted by variations in D2O abundance; (Polyakovet al., 2005; Rolston and Gale, 1982). Moreover, untilrecently it was not clear how any of the speciescontaining two or more rare isotopes could be analyzedin natural materials with meaningful precision, nor whatpurpose such data would serve if they could be obtained.

However, there are also good reasons to think thatthese rare, neglected isotopic species could be anuntapped resource for geochemistry. First, they aremore diverse than their isotopically normal and singly-substituted relatives. For example, of the twelvenaturally occurring isotopic variants of CO2, eightcontain two or more rare isotopes (Table 1). Second,just as singly-substituted molecules have physical andchemical properties distinct from isotopically normalmolecules, each of the species containing multipleisotopes is in some sense unique (i.e., in bond vibrationfrequencies, zero point energies, near-infra-red absorp-tion spectra, etc.). Therefore, these multiply-substitutedspecies should exhibit diverse and distinctive fractio-nations, and studies of their distributions in naturemight reveal new and useful information. Finally, thesespecies, whatever their ultimate usefulness, constituteone of geochemistry's last large, unmapped realms.The urge to discover new things demands that it beexplored.

This Frontiers article provides an overview of therecent development of a field of geochemistryconcerned with measurements of abundances in naturalmaterials of molecules containing two or more rareisotopes. The methods of these measurements and theirapplications to-date are detailed in a series of papers andabstracts published over the last three years (Schauble etal., 2003, 2006; Eiler and Schauble, 2004; Wang et al.,2004; Affek et al., 2005, in press; Guo and Eiler, 2005;Affek and Eiler, 2006; Ghosh et al., 2006a,b, 2007; Eileret al., 2006; Eiler, 2006a,b; Came et al., in press; Guoand Eiler, submitted for publication). These studiesinvolved a large number of authors from severaldifferent institutions; therefore, sections of this paperwritten in the active voice use plural pronouns inrecognition of the contributions of these colleagues.Rather than systematically reviewing all of the pub-lished work, our purpose here is to provide a broadercontext of related prior research, an overview of thephysical and chemical principles that are common to allwork on such isotopic species, a description of the stateof this nascent field, and a preview of the likelydirections of its future growth. Our subject makes use a

variety of unfamiliar terms; please see the accompa-nying “Jargon Box” for their definitions.

2. Background

2.1. The chemistry of isotopes

Stable isotope geochemistry is rooted in the land-mark discoveries in physical chemistry made during the1920s and 30s. The most relevant of these was thatisotopic substitution of a heavy for a light isotope (e.g.,D for H) in a chemical bond reduces the vibrationfrequencies of that bond and, therefore, its zero-pointenergy (Urey, 1947; Bigeleisen and Mayer, 1947;Fig. 1). For this reason, isotopic substitution influencesthermodynamic stabilities of molecules and rates ofmany kinetically-controlled reactions.

Bonds between two heavy isotopes (e.g., the D–Dbond in doubly substituted molecular hydrogen) areslower-vibrating and lower in energy than equivalent

Box 1

The jargon of clumped isotope geochemistry

Isotopologues are two ormorevariants of amolecule that differ in the isotopic identityof one ormoreof their constituent atoms. For example, 14N2,

15N14N and 15N2 are the three naturally-occurringisotopologues of molecular nitrogen. We also use this term to refer to isotopic variants of organicmoieties or mineral structural units (e.g., the isotopologues of the carbonate ion include 12C16O3

−2,13C16O3

−2, 12C18O16O2−2, etc.).

Multiply-substituted isotopologues are isotopologues that contains two or more rare isotopes. Thisterm is precise but sufficiently awkward that we also use the term clump as a short-hand for thesespecies (i.e., they are produced by ‘clumping’ two rare isotopes together).

Isotopomers are structural variants of an isotopologue that differ in the symmetrically non-equivalentlocation of an isotopic substitution. For example, 14N–15N–16O and 15N–14N–16O (where ‘– ‘ denotesthe location of a bond between two isotopes) are isotopomers of one another; both are nitrous oxideisotopologues containing one 15N atom, but in two different and symmetrically non-equivalentpositions within the molecule. 18O–12C–16O and 16O–12C–18O are not isotopomers of one anotherbecause they are symmetrically equivalent and thus constitute a single kind of CO2 isotopologue. Theanalytical methods that form the basis of most of this paper are unable to distinguish betweenisotopomers, and so we focus our discussion on relative abundances of isotopologues (although theprinciples that guide the work presented here could be extended to the study of naturally occurring,multiply-substituted isotopomers, assuming one could develop a sufficiently precise method for theiranalysis).

Stochastic distribution refers to a state in which all the stable isotopes in a given population ofmolecules are randomly distributed among all possible isotopologues. For example, in a population ofwater molecules inwhich [D] is the fraction of all hydrogen atoms that are deuterium (i.e., [D]=D/(D+H)) and [16O] is the fraction of all oxygen atoms that are 16O (i.e., [16O]=16O/(16O+17O+18O)), thenthe stochastic abundance of D2

16O is equal to: [D]2 ·[16O]. We use the stochastic distribution as areference frameand focusourattentionon thecauses and significanceofdeviations from that referenceframe.

Δivaluesmeasure thedifference, in permil, between themeasured abundanceof isotopologue i (or allisotopologues of mass i) and the abundance of that isotopologue expected for the stochasticdistribution for that sample. A key concept is that absolute abundances of multiply-substitutedisotopologues vary with bulk isotopic composition, but Δi values do not. Rather, they measure thepropensityof rare isotopes to clump togethermore (for positiveΔi values) or less (for negativeΔi values)than would occur by random chance.

311J.M. Eiler / Earth and Planetary Science Letters 262 (2007) 309–327

bonds between a heavy and a light isotope (e.g., H–D)which are, in turn, slower vibrating and lower in energythan equivalent bonds between two light isotopes (e.g.,H–H; Fig. 1). It is commonly assumed that the change inbond energy associated with double heavy isotopesubstitution (i.e., the difference in energy between theH–H bond and the D–D bond) is exactly twice thatassociated with heavy-isotope substitution of onlyone atom (i.e., the difference in bond energy betweenthe H–H bond and the H–D bond); this assumption issometimes called the ‘rule of the geometric mean’ orsimply the ‘rule of the mean’ (Bigeleisen, 1955).

The rule of the mean implies that there is no energeticpreference for grouping heavy isotopes into bonds with

each other as opposed to distributing them into a largernumber of bonds with light isotopes (i.e., a systemcontaining a H2 and a D2 has the same total vibrationalenergy as a system containing two HD's). Stated interms of classical thermodynamics, the rule of the meanassumes that compounds containing two or moreisotopologues are ideal; i.e., there is no enthalpy ofmixing associated with mixing two or more isotopolo-gues of the same compound (Bigeleisen, 1955).However, the rule of the mean is more of a simplifyingapproximation than a rule. Its statistical-mechanicaljustification arises from an approximation to the series-expansion form of the equation for the partition function(the statistical mechanical variable that describes the

Fig. 1. Illustration of the energy content of a molecular hydrogen bond (E, in kcal/mol) as a function of bond distance, (r–re, in angstroms, where re isthe minimum-energy bond distance). The solid curve represents the Morse potential for H2. Horizontal lines indicate the energy levels correspondingto the quantum states of bond vibration, n=0, 1, 2, …. The lowest accessible quantum state, n=0, is referred to as the zero point energy, or ZPE. Theinset illustrates the effect of isotopic substitution on the energy of the n=0 quantum state. Note that the zero point energy is reduced with a singleheavy isotope substitution and reduced further with a second heavy isotope substitution. Distances ΔE’ and ΔE’’ indicate these energy changes.Based on (Urey, 1947; Bigeleisen and Mayer, 1947).


vibrational, rotational and translational energies ofmolecules) and is not accurate except at the hightemperature limit (Urey, 1947; Bigeleisen, 1955). Infact, decreases in vibrational energy associated withdouble heavy-isotope substitution often slightly exceedtwice that of a single heavy-isotope substitution.Departures from the rule of the mean arise from thehigher-order terms to the series expansion form of theequation describing partition functions (Urey, 1947;Bigeleisen, 1955); alternatively, one can think of thesedepartures as a consequence of the fact that there is asmall but observable enthalpy of mixing associated withmixtures of two or more isotopologues of mostcompounds. One can reach a more intuitive understand-ing of these departures by considering some of thestructural features of molecules that might lead topreferential concentration of isotopes into one atomicsite vs. another. For example, in N2O (N–N–O) thebonding environment for the terminal N differs fromthat for the central N, which leads to a difference in 15Ncontent between the two sites. Similarly, the vibrationenergies of C–O bonds differ slightly between the 18O–C–16O and 16O–C–16O isotopologues of CO2, and thisdifference gives rise to a preferential partitioning of 13Cinto the former at the expense of the latter (this exampleis discussed in greater detail below).

For our purposes, the important thing about thefailures of the rule of the mean is that there is athermodynamic driving force that often promotes‘clumping’ of heavy isotopes into multiply-substitutedisotopologues at the expense of singly-substitutedisotopologues. This effect can be described in terms ofthe equilibrium constant for a homogeneous isotopeexchange reaction involving only isotopologues of asingle molecule, such as:

2d HD ¼ H2 þ D2 Reaction ð1Þ

Such reactions are also sometimes referred to as‘isotopic disproportionation reactions’ (e.g., Polyakovet al., 2005). If the stochastic distribution prevails, theequilibrium constant for this reaction, K1, is a simplefunction of the symmetry numbers and stoichiometrycoefficients of reactant and product molecules: K1=([H2] · [D2])/[HD]

2 = ([H]2 · [D]2)/(2 · [H] · [D])2 =0.25.But, because D2 is slightly more stable than one wouldpredict based on the rule of the mean, there is athermodynamic propensity to drive Reaction (1) to theright, raising K1. This driving force is balanced by theeffect of isotopic distribution on the entropy of thesystem, such that the random distribution of rare isotopesamong all possible isotopic species is increasingly

Fig. 2. Temperature dependence of the equilibrium constants for thehomogeneous isotope exchange reactions, Reactions (1) and (2). Theheavy horizontal line indicates the value of the equilibrium constantthat corresponds to a stochastic distribution (0.25). Note thatthermodynamic driving forces promote higher-than-stochastic valuesof Keq, corresponding to larger proportional abundances of multiply-substituted isotopologues (D2 and D2O) at ambient temperatures, and agradual approach toward the stochastic distribution with increasingtemperature. Equilibrium curves are taken from (Richet et al., 1977).

Fig. 3. Enrichments or depletions in relative abundances ofisotopologues of ozone, in units of per mil, normalized to a unitchange in 16O3, produced during photochemical experiments onO2–O3

mixtures (Mauersberger et al., 1993). Note that all asymmetricisotopologues of ozone are anomalously enriched, and all symmetricisotopologues are relatively depleted. These results are representativeof a large body of experimental work on the kinetic isotope effectsaccompanying gas-phase reactions, which collectively constitute thelargest single source of observational data on the chemical properties ofmultiply-substituted isotopologues.


favored with increasing temperature. And, the enthalpiesof isotope exchange reactions are temperature dependent(generally decreasing in absolute value with increasingtemperature). These two factors lead to a temperaturedependence of equilibrium constants for homogeneousisotope exchange reactions, such that K1 is significantlymore than 0.25 at room temperatures and approaches0.25 with increasing temperature. Reaction (1) and asimilar homogeneous isotope exchange reaction involv-ing isotopologues of water:

2dHD16O ¼ H216O þ D2

16O Reaction ð2Þ

are among the few that were explored by experiments andstatistical thermodynamic theory (e.g., Pyper et al., 1967)prior to our recent work on such problems (Fig. 2;significant previous work has also be done on similarreactions for hydrogen sulfide and ammonia; seePolyakov et al., 2005; Richet et al., 1977 for reviewsand primary references).

2.2. Anthropogenic isotopic enrichments and labelingexperiments

There are several uses of isotopes in engineering andthe natural sciences that can be thought of as inadvertentclumped-isotope geochemistry. Isotopic enrichmentprocedures used for nuclear weapons, energy andmedicine yield materials that must contain abundancesof multiply-substituted isotopologues many orders of

magnitude greater than those found in nature, simplybecause their exceptionally high concentrations of rareisotopes increase the probability that two or more willform bonds with one another. Similarly, many branchesof the natural sciences use isotopically enrichedmaterials as tracers for movement of atomic andmolecular species. Examples include labeled nutrientsfed to microbial communities (Chang et al., 2005) orisotopically labeled dopants in chemical diffusionexperiments (Elphick et al., 1991). These studiesgenerally involve mixing of materials that contraststrongly in their abundances of multiply substitutedisotopologues. In Section 4 of this paper we illustrate theeffects of such mixing on abundances of clumpedisotopic species, and discuss how these effects might beexploited.

2.3. Physical chemistry experiments on enrichedmaterials

Multiply substituted isotopologues are of interest tophysical and organic chemistry because of their distinc-tive kinetics in unidirectional reactions (e.g., photolysis orenzymatically controlled reactions). There is a rich historyand high current rate of experimental studies of suchisotope effects, generally conducted on materials that areartificially enriched in rare isotopes. The purpose of suchwork is to probe the physical mechanisms behind poorly-understood chemical reactions. A recent example is thestudy of the isotope effects that accompany ozone


production and consumption by photochemical reactionsin O2-rich atmospheres (Mauersberger et al., 1993). In thisstudy, Mauersberger et al. demonstrate that the distinctive‘mass independent’ enrichment in 18O and 17O inatmospheric ozone (Mauersberger, 1981) reflects enhancedproduction of the asymmetric isotopologues (18O16O2,17O16O2,

18O216O, 18O2

17O, etc.; Fig. 3). This obser-vation underlies theoretical advances in our understandingof the physical chemistry responsible for this isotope effect(Gao and Marcus, 2001).

2.4. Half-steps towards applied clumped-isotopegeochemistry

The previous research on multiply-substituted iso-topologues summarized above constitutes a broad andimportant body of work in physical and biochemistry.But, it is not geochemistry in the full sense of the wordbecause it does not involve the analysis and interpretationof these rare species in nature. There have been severalprevious studies that more closely approached, but did notquite achieve, a real ‘clumped isotope’ geochemistry.

The largest body of such work involves attempts tomeasure isotopic compositions of specific atomic siteswithin larger molecules or condensed phases; e.g.,analyses of the oxygen isotope composition of hydroxylgroups in hydrous minerals (Hamza and Epstein, 1980),position-specific carbon isotope analysis of organicmolecules (Monson and Hayes, 1982), or measurementsof the distribution of 15N between central and terminalpositions in N2O (Brenninkmeijer and Rockmann, 1999).These are not clumped isotope geochemistry because theyconsider only singly-substituted isotopic species. How-ever, they are motivated by an understanding that rareisotopes are not randomly distributed within molecules,organic moieties and mineral structures, and this is a keyconcept behind clumped isotope geochemistry.

It has been shown that conventional measurements ofδ13C in CO2 potentially contain small but observablesystematic errors due to the failure to account correctly forthe fraction of 13C contained in 13C18O16O (Zyakun,2003). While this study recognized that natural variationsin thismultiply-substituted isotopologue could exist, it didnot attempt to measure these variations. Similarly, (Kaiseret al., 2003) presented theoretical arguments for theconsequences of photochemical reactions on the abun-dance of atmospheric 15N15N16O. This study also did notpresent measurements of these species (and, in fact,concluded that such measurements would likely containlittle distinctive information).

Mroz et al. (1989) presented what are, to the best ofour knowledge, the first attempted measurements of a

‘clumped’ isotopic species at natural abundances. Theyexamined the mass spectrum of methane from Antarcticair, finding abundances of 20 AMU species (presumablysome combination of 12CD4 and 13CHD3) up to 500times higher than expected for the stochastic distributionof methane. This report was immediately followed bypublication of a model demonstrating that such extremeenrichments are inconsistent with the experimentally-constrained atmospheric lifetimes of these species (Kayeand Jackman, 1990). This inconsistency has never beensatisfactorily resolved, but presumably reflects somecombination of analytical error in the atmosphericmeasurements and/or misconceptions about the budgetof atmospheric methane (e.g., unrecognized anthropo-genic sources of 12CD4).

2.5. The relationship between ‘clumped isotope’ and‘mass independent’ isotope geochemistry

On first glance, clumped isotope geochemistry mightappear to be a subset of mass-independent isotopegeochemistry\the field of isotope geochemistryconcerned with the study of the mass dependence ofisotopic fractionations in systems having three or moreisotopes (e.g., 18O, 17O and 16O). The most obvious pointof similarity between these two fields is that both reportdata using ‘Δ’ values. In the case of clumped isotopemeasurements, Δ values refer to deviations from astochastic distribution, whereas mass-independent iso-tope geochemistry useΔ values to denote deviations froma specific mass-dependant fractionation law. However,beyond this superficial similarity in nomenclature, thefields have little in common. Mass-independent isotopegeochemistry generally considers bulk isotope composi-tions of materials, and thus primarily reflects variations inthe relatively abundant singly-substituted isotopologues.In contrast, clumped isotope geochemistry is concernedwith the organization, or state of ordering, of isotopesamong all possible isotopologues, independent of bulkisotopic composition. In this sense, clumped isotopegeochemistry is just as different from mass-independentisotope geochemistry as it is from conventional isotopegeochemistry. Also, because most natural processes ofisotopic fractionation have a simple mass dependence,mass-independent isotope geochemistry generally focus-es on the search for rare anomalies that signify unusualprocesses (e.g., the signatures of photochemical reactionsonΔ17O values of atmospheric O3, O2 and CO2). This isbecause the strongest mass-independent isotopic fractio-nations stem from symmetry-based isotope effects thatoccur only in a few species and environments (e.g.,Mauersberger, 1981; Mauersberger et al., 1993). In


contrast, essentially all processes of isotopic fractionation(diffusion, isotope exchange reactions, irreversible reac-tions, etc.) lead to distinctive clumped isotope variationsand so clumped isotope geochemistry is applicable to awider variety of problems (note however, that studiesattempting to characterize subtle variations in the slopesof mass-dependent fractionations more closely resembleclumped isotope geochemistry in this regard). Perhaps themost meaningful similarity between these two fields is inthe ways in which they can be used: both adddimensionality and specificity to isotopic measurementsthat complement conventional isotopic data and enhanceour ability to recognize the processes responsible forisotopic fractionation.

3. Analytical approaches—real and imaginable

The basic demands of clumped-isotope analysis are:high abundance sensitivity (because the target speciesmake up small fractions of the analyzed gas; e.g.,Table 1); high precision (typically 10−5; because isotopesignals of interest are often less than 10−3); high samplepurity or excellent mass resolving power (becauseinterferences can easily lead to small variations ofapparent abundances of rare species); and, mostimportantly, integrity of the original bonds in the analyte(because re-distribution of isotopes among isotopolo-gues during analysis will render the measurementsmeaningless). Our recent work demonstrates that gas-source isotope ratio mass spectrometry can meet thesedemands for some compounds of interest (Eiler andSchauble, 2004; Guo and Eiler, 2005; Affek and Eiler,2006; Ghosh et al., 2006a; Eiler, 2006b). In this section,we review the principles and limitations of thisapproach, and then discuss possible alternatives thatshould be explored in the future.

3.1. Gas-source mass spectrometry

Gas-source isotope ratio mass spectrometry is anattractive analytical approach to clumped isotope geo-chemistry for two reasons: (1) the multiple-Faradaycollection arrays used by such instruments can achieveexceptionally high precision inmeasured isotope ratios (asgood as ca. 10−5 to 10−6; e.g., Severinghous et al., 1998);and (2) analyses are routinely made on molecular ions,which potentially retain information on the distribution ofisotopologues. Disadvantages include: analytes must begasses at ambient conditions; noise levels in the Faraday-based collectors used in these instruments generallypreclude meaningful analyses of the lowest-abundancesspecies (e.g., 13C18O2; Table 1); themass-resolving power

of such instruments (typically corresponding to M/ΔMvalues of ca. 500) is insufficient to discriminate amongisotopologues having the same cardinal mass (e.g.,13C18O16O and 12C18O17O), or between analyte mole-cules and some isobaric interferences; and, analytemolecules typically undergo fragmentation and recombi-nation during ionization, possibly leading to redistributionof isotopes among the various analyzed isotopologues.Experiments on mixtures of isotopically labeled gasesdemonstrate that this last factor can be reduced tonegligible levels for CO2 (Eiler and Schauble, 2004),CO (Guo and Eiler, 2005) and O2 (unpublished data) but itmight be limiting for other species.

The only instruments that have been used to makepublished, high-precision clumped-isotope measure-ments are a pair of modified Thermo-Finnegan 253'shoused in the Caltech laboratories for stable isotopegeochemistry (Schauble et al., 2003, 2006; Eiler andSchauble, 2004; Wang et al., 2004; Affek et al., 2005, inpress; Guo and Eiler, 2005; Affek and Eiler, 2006;Ghosh et al., 2006a,b, 2007; Eiler et al., 2006; Eiler,2006a,b; Came et al., in press; Guo and Eiler, in press).These instruments have collector arrays consisting ofeight Faraday cups, four of which are registered through1012 Ohm resistors. We suspect other instruments ofbroadly similar design and capability could be simi-larly effective at such measurements. Most publishedanalyses using these instruments have been made usinga dual-inlet system for sample introduction, whichmaximizes the amount of gas available for measurementand assures stable analytical conditions for relativelylong times (tens of minutes or longer). A smaller numberof published measurements have been made using amicro-volume inlet, which maintains acceptably highsource pressures with ca. 1 μm-sized samples (Guo andEiler, in press), but at the cost of poorer signal stabilityand shorter analytical durations. We also imagine thesemeasurements could be made in a similar way usingtechniques of carrier-gas mass spectrometry (Matthewsand Hayes, 1978), although it likely will be difficult toachieve 10−5-level external precisions.

Because clumped-isotope species make up little ofmost natural gases (ca. 10−5 and less; Table 1) yet oftenmust be analyzed with unusually high precision (oforder 10−5), extraordinarily large samples and/or longcounting times often are required. Fig. 4 illustrates theshot-noise limits to precision in measurements of Δ47 ofCO2 (primarily a measure of the departure of 13C18O16Oabundances from the stochastic distribution; see the endof this section for a more complete definition) as afunction of the integrated charge collected for the majorisotopologue of CO2 (

12C16O2). Precisions approaching

Fig. 4. Shot-noise limit to the external precision of a measurement ofthe mass-47 to mass-44 ratio in natural CO2, in units of per mil, as afunction of the integrated charge of mass-44 collected during a massspectrometric analysis. The heavy solid line indicates the precisioncalculated according to the methods of (Merritt and Hayes, 1994). Thehorizontal dashed line indicates a typical ‘target’ precision forapplications, and the vertical dashed lines indicate the amounts ofcharge typically collected during dual-inlet and carrier-gas massspectrometric analyses (assuming standard analytical protocols). Oneto two orders of magnitude more charge than is commonly collectedmust be obtained before a clumped isotope analysis becomes usefullyprecise.


a few hundredths of per mil (the ‘price of entry’ formany applied problems) are not reached until onecollects ca. 10x the amount of charge normally collectedin a dual inlet measurement. Exceptional precisions ofca. 0.01‰ or better (required for high-precisioncarbonate paleothermometry; see Section 5, below)demand nearly 100x the amount of charge collected fora typical dual inlet measurement.

Finally, even nominally pure gases prepared onconventional vacuum lines can contain significant (i.e.,ppb and higher) abundances of volatile trace gases (e.g.,organics, organic halides, and sulfides), some of whichcan undergo fragmentation and/or recombination reac-tions in the mass spectrometer source to produce isobaricinterferences (e.g., the 12C35Cl+ fragment from methylchloride interferes with 13C18O16O+ in CO2). Thisproblem calls for the most stringent sample purificationprocedures, often involving repeated cryogenic separa-tions, gas chromatography, and/or exposure to reactive‘getters’ (such as silver phosphate to remove sulfidecontamination) (Eiler and Schauble, 2004; Affek andEiler, 2006; Eiler, 2006b; Guo and Eiler, in press).

3.2. Possible alternatives

Spectroscopic methods could form an ideal basis formeasurements of multiply-substituted isotopologues be-

cause isotopologues have unique near-infra-red spectro-scopic features that could be used to discriminated themfrom their relatives— even those having identical cardinalmass (Perevalov et al., 2006). And, such methods can beexceedingly sensitive, potentially permitting analysis ofisotopologues containing three or more rare isotopes (e.g.,13C18O17O; Table 1). Spectroscopic measurements ofstable isotope composition have achieved precisions onthe order of 10−4 for singly-substituted isotopologues(Bergamaschi et al., 1994). However, we are not aware ofany evidence that these methods could generate precisionon the order of 10−5 for the less abundant multiply-substituted isotopologues. Nevertheless, progress on thisfront would constitute a genuine breakthrough in ourability to study multiply-substituted isotopologues, andeven existing instruments and methods might be adequatefor study of multiply-deuterated water or methane(which likely exhibit relatively large departures from thestochastic distribution).

Modern thermal ionization mass spectrometersemploy multiple-Faraday collector arrays and routinelyachieve precisions in isotope ratio measurements in therange of 10−5 and 10−6 (Caro et al., 2003). Moreover,many species can be analyzed as molecular ions, andthus potentially preserve information regarding thedistribution of isotopes among the various possibleisotopologues of those molecules. For these reasons, thisapproach is an attractive possibility for studying theclumped isotope geochemistry of solids that cannot beeasily converted into gases (e.g., sulfides, oxides,silicates and halides). However, thermal ionizationoccurs at high temperatures from a condensed substrate,and may promote substantial isotopic redistributionduring analysis. This exchange will have to beminimized and/or carefully controlled in order to makeprecise and meaningful measurements.

Secondary ion mass spectrometry yields high relativeabundances of molecular ions from many materials andcan, in some cases, achieve precisions for isotope ratioanalysis on the order of 10−4 (Kita et al., 2007); therefore,it potentially provides a means of making in-situmeasurements of clumped isotope species in solids.However, this approach faces considerable challenges.Most fundamentally, while molecular ions are emittedfrom solids during ion sputtering, an unknown, but likelylarge proportion of them form by fragmentation/recom-bination rather than through direct emission of dimmersand higher-order clusters containing the same interatomicbonds that existed in the pre-sputtered sample. Thisphenomenon will have to be understood and controlledbefore sputtering could be used as a quantitative analyticaltool for clumped isotope geochemistry. Furthermore, ion


probe measurements seem unlikely to ever achieve 10−3

and better precisions for low-abundance multiply-substi-tuted molecular ions, and thus this approach, even ifphysically feasible, may be limited to isotopicallyenriched, synthetic materials, elements that exhibit strongdepartures from the stochastic distribution (e.g., H) andelements having sub-equal abundances of two or moreisotopes (and thus relatively high abundances of clumpedisotopic species; e.g., Cl).

3.3. Precise definition of the Δi value

Clumped isotope analyses use values of Δi to denotethe excess or deficit of isotopologue i relative to theamount expected if a material conforms to the stochasticdistribution. This is a straightforward concept, but it isnot obvious on inspection just how a Δi value relates tothe properties one can measure in a gas sample. In thissection we explain in detail how this is done for the mostcommonly measured value of Δi\the Δ47 value forCO2 (which largely reflects variations in abundance of13C18O16O). This example is adapted from moredetailed discussions of this subject found in references(Eiler and Schauble, 2004; Wang et al., 2004; Affek andEiler, 2006). TheΔ47 value of CO2 can be calculated as:

D47 ¼ R47

R47*� 1

� �� R46

R46*� 1

� �� R45

R45*� 1

� ��

� 1000

where R47, R46, R45 are abundance ratios of masses 47,46 and 45 relative to mass 44; i.e., the 47/44, 46/44, 45/44 ratios, respectively. These Ri values are determinedby comparison with a standard having an acceptedcomposition (this is usually CO2 gas of known bulkisotopic composition that has been intensely heated todrive its isotopic distribution to the stochastic distribu-tion). R47⁎, R46⁎, R45⁎ are the corresponding ratios thatwould occur in the sample if it had a stochasticdistribution. These are calculated using the equations:

R45⁎ ¼ R13 þ 2 � R17

R46⁎ ¼ 2 � R18 þ 2 � R13 � R17 þ R17� �2

R47⁎ ¼ 2 � R13 � R18 þ 2 � R17 � R18 þ R13 � R17� �2

where R13, R17 and R18 are the abundance ratios13C/12C, 17O/16O and 18O/16O for the sample. R13 andR18 are derived from the measured δ13CPDB andδ18OVSMOW values of the sample and R17 is calculatedfrom R18 by assuming that the sample lies on a specificmass-dependent fractionation line in dimensions of R17

vs. R18. Note that this approach requires iteration if theΔ47 value is more than a few per mil different from 0because R13, R17 and R18 values initially calculatedbased on measured δ13C and δ18O values usingstandard assumptions will contain small errors.

4. Fractionating processes—principles and examples

The processes that lead to familiar fractionations ofbulk isotopic compositions (e.g., diffusion, exchangeequilibria, evaporation, photolysis, etc.) generally alsolead to fractionations of relative abundances of multiply-substituted isotopologues. For example, just as the dif-ference in vapor pressures between HD16O and H2

16Oleads to fractionations of D/H ratios during evaporation ofwater (Horita andWesolowski, 1994), differences betweenthe vapor pressures of D2

16O and H216O [Polyakov et al.,

2005 and references therein] must lead to fractionations ofthese species from one another during evaporation ofwater. The important thing, in the context of ourdiscussion, is to identify and understand fractionatingprocesses that result in departures from the stochasticdistribution, because it is these departures that convey newinformation distinct from that learned by conventionalmeasurements of bulk isotopic composition. The follow-ing paragraphs review the principles and systematics ofsome of the more common and potentially useful clumpedisotope fractionations.

4.1. Thermodynamically-controlled fractionations

As was explained in Section 2, chemical systems atequilibrium are generally expected to group heavyisotopes into bonds with each other in abundancesgreater than expected for a stochastic distribution, anddo so more strongly with decreasing temperature (e.g.,Fig. 2). Recent theoretical and experimental studieshave examined, at 10−5 levels of precision, the size andtemperature-dependence of homogeneous isotope ex-change equilibria analogous to Reactions (1) and (2), butfor isotopologues of N2, O2, CO, NO, CO2, N2O(Schauble et al., 2003; Eiler and Schauble, 2004; Wanget al., 2004; Guo and Eiler, 2005) and carbonate iongroups in calcite, aragonite, magnesite, dolomite, andcarboxylic acids (Ghosh et al., 2006a, 2007; Schaubleet al., 2006; Eiler, 2006a; Came et al., in press). Data weintend to publish soon will extend these calculations andmeasurements to include sulfates, compounds ofuranium, methane and dissolved inorganic carbon (i.e.,CO2aq, H2CO3, HCO3

−, CO3−2). In this section we

consider some of the general trends revealed by thesetheoretical calculations and experimental data.

Fig. 6. Temperature dependences of Δi values, in units of per mil, forrepresentative multiply-substituted isotopologues of common molec-ular gases, as calculated by reduced partition function theory (all aretaken from Wang et al., 2004). Panel A shows calculated trends formolecules that show a typical ca. T−2 temperature dependence of Δi

values. Panel B shows calculated trends for example species showinganomalous temperature dependences of Δi values.

Fig. 5. Values of Δi (i.e., enrichments relative to the stochasticdistribution, in per mil) expected for representative multiplysubstituted isotopologues in thermodynamically equilibrated popula-tions of H2, N2 and UO2 at 298 K. Note that values of Δi for theclumped isotopic species are relatively large (ca. 100‰) for moleculeswith low reduced mass, moderate (ca. 1‰) for those with reducedmass comparable to common atmospheric gases, and small (ca.0.02‰) for molecules with high reduced mass. The value of Δi for D2

was taken from (Richet et al., 1977), that for N2 is from (Wang et al.,2004), and that for 238U18O16O was calculated by E. Schauble(personal communication).


For bonds of generally similar type, the equilibriumconstants for homogeneous equilibria involvingclumped isotopic species vary inversely with reducedmass (Fig. 5). This phenomonon reflects the fact thatzero-point-energy effects scale with bond vibrationfrequency, which in turn depend strongly on reducedmass (Urey, 1947; Bigeleisen and Mayer, 1947).

Most thermodynamically-controlled deviations fromthe stochastic distribution exhibit a simple temperaturedependence:Δi values of the multiply-substituted speciesclosely approach 0 at temperatures in excess of ca. 500 K,and increase with decreasing temperature following atrend that is nearly linear with T−2 at temperatures ofinterest to most problems (Fig. 6A). However, someequilibria of this kind have more complex temperaturedependences. For example, Δi values of 15N2

16O,15N2

17O and 15N218O in thermodynamically equilibrat-

ed populations of N2O molecules vary non-linearly withT−2 and exhibit inflection points (i.e., changes in thesign of ∂Δi/∂T) and negativeΔi values (Fig. 6B). Thesephenomena are indirect consequences of differences instability between the isotopomers of singly-substitutedN2O molecules (e.g., 15N14N18O vs. 14N15N18O).

Finally, there are several second-order effects on thesizes ofΔi values for multiply-substituted isotopologuesresulting from homogenous isotope exchange equilibria:Within a given molecule type (e.g., CO2), the highest Δi

values are observed for isotopologues that have bondsbetween heavy isotopes, and smaller Δi values for

isotopologues that have two or more heavy isotopes innon-adjacent positions. For example, even though12C18O2 (structure:

18O–12C–18O) has a higher molec-ular mass than 13C18O16O (structure: 18O–13C–16O),the Δi value of the former is only about half that of thelatter at any given temperature (Wang et al., 2004). Also,among broadly similar types of bonds there aresystematic correlations between Δi values and bondorder. For example, clumping of 13C with 18O incompounds containing C–O bonds is strongest at anygiven temperature for CO (triple bond), weaker for CO2

(double bond) and weakest for compounds containingCO3

−2 (average bond order 4/3) (Schauble et al., 2006).Finally, for molecules of a given type, there may be veryweak dependences ofΔi values involving one given bondon the nature of other bonds in that molecule. For

Fig. 7. Illustration of a typical diffusive fractionation of multiply-substituted isotopologues. The three-dimension panel (A) shows the surface of thestochastic distribution for CO2 in dimensions of δ13CPDB vs. δ18OVSMOW vs. R47 (the abundance ratio of mass-47 isotopologues to mass 44isotopologues). Deviations above and below that surface correspond to positive and negative values ofΔ47, respective. Dashed lines show contours ofconstant R47 value. The solid arrow in this panel shows the vector followed by Knudsen diffusion fractionation (calculated following Gibbs, 1928).Note that the diffusive vector is closer to horizontal than is the surface of the stochastic distribution (which is almost, but not exactly, flat over thisrange of δ13C and δ18O values). The two-dimensional panel (B) projects the Knudsen diffusion vector into dimensions of Δ47 (departure from thestochastic distribution) vs. δ18O, where we assume the initial gas (before diffusive fractionation) has values of 0 for both variables.


example, formation of 13C–18O bonds in carbonate ions ispredicted to vary slightly at any given temperature withthe identity of the cation to which the carbonate ion bonds(e.g., Δ(13C

18O16

O2

−2) in calcite is predicted to be0.004‰ greater than in dolomite at 298 K) (Schaubleet al., 2006).

4.2. Vapor pressure isotope effects

Vapor-pressure isotope effects are thermodynamically-controlled differences in isotopic composition betweenvapor and a condensed phase. In thermodynamicallyequilibrated system containing a vapor and a condensedphase, relative abundances of the various possibleisotopologues in each phase can be described by thehomogeneous isotope exchange equilibria discussedin the preceding section. For example, Keq for Reaction(2) (‘K2’) in water vapor is the same in vapor only andvapor+liquid systems. In this sense, clumped isotope

abundances in systems containing a condensed phaseand a vapor are just a special case of equilibriumfractionations and follow all the rules and general trendsoutlined above.

However, it is important to note that the homoge-neous equilibria that control clumped isotope abun-dances need not have identical equilibrium constantsin the condensed and vapor phases (e.g., K2 for watervapor is greater than that for liquid water at any giventemperature; Polyakov et al., 2005), and differencesbetween the two might, in some circumstances, lead todistinctive clumped isotope fractionations duringphase changes. For example, if liquid water is ableto continuously maintain equilibrium with respect tothe D2

16O-forming homogeneous isotope exchangereaction but the vapor does not (e.g., because collisionfrequency is too low to promote efficient intermolec-ular exchange), then H2O irreversably evaporatedfrom the liquid could ‘inherit’ the ΔD2

16O value of the


liquid, lower than that expected for equilibrated vapor.One can imagine using such an isotope effect tocomplement the information content of conventionalstable isotope data, much as the ‘deuterium excess’ (ameasure of the deviation from the meteoric water line)has been used in studies of water vapor and meteoricprecipitation.

4.3. Kinetic fractionations associated with unidirectionalreactions

Many natural systems are influenced by unidirec-tional reactions that manifest kinetically-controlledisotopic fractionations arising from differences inreaction rate between isotopologues. Common exam-ples of such processes include: photo-oxidation ofmethane (Saueressig et al., 2001) and other gas-phasereactions (Mauersberger et al., 1993), biosynthesis (e.g.,photosynthesis; Guy et al., 1993), and various hydra-tion, oxidation, sorption and solvation reactions in-volved in chemical weathering of minerals (Cole andChakraborty, 2001).

Bulk isotopic fractionations associated with manykinetically controlled reactions have been studiedextensively, but rates of reaction for multiply-substitutedisotopologues are generally only well known forphotolytic and other gas-phase reactions (e.g., Mauers-berger et al., 1993; Saueressig et al., 2001). With a fewexceptions (Methane and N2O; Kaiser et al., 2003; Mrozet al., 1989; Kaye and Jackman, 1990), these data havenot been considered in light of their implications forclumped isotope analyses of natural materials. We areaware of no data that usefully (i.e, at per-mil and betterlevels of precision) constrain relative reaction rates formultiply-substituted isotopologues in condensed-phasereactions. Until such data become available, transition-state theory can provide some guidance as to thedirections and orders of magnitude of clumped-isotopefractionations expected to accompany unidirectional,condensed-phase reactions. Briefly, given a detaileddescription of the atomic-scale structure of reactants andtransition states in chemical reactions, one can predictthe relative rates of reaction for different isotopologuesbased on the effects of isotopic substitution on zero-point energies of those reactants and transition states(much as zero point energies can be used to predictequilibrium isotope fractionations; (Urey, 1947; Bige-leisen and Mayer, 1947). In the near future, we intend topublish studies using this approach to model isotopicfractionations accompanying hydration of CO2, disso-ciation of carbonic acid, and reaction of carbonate withphosphoric acid (W. Guo, pers. com.).

4.4. Diffusion

Isotopic fractionations caused by diffusion-limitedtransport are well known for gas- and liquid-phaseprocesses (e.g., exchange of CO2 across leaf stomata orthrough leaf water; Jahne et al., 1987; Gibbs, 1928).Diffusion rates generally have mass-dependences thatlead to fractionations of isotopologues between diffusedand residual reservoirs that lead to deviations from astochastic distribution; therefore, diffusion can lead tochanges in Δi values (Eiler and Schauble, 2004).

Diffusive fractionations of Δi values are somewhatcounter-intuitive. For example, CO2 diffused through asmall orifice (i.e., Knudsen diffusion) is 11‰ lower inδ13C, but 0.49‰ higher in Δ47, than residual gas (Eilerand Schauble, 2004). Similar effects occur for gas-phaseinterdiffusion and are expected for liquid-phase diffusion.These effects can be understood in the following way:The stochastic distribution for CO2 can be depicted as atwo-dimensional surface in the three-dimensional spaceof δ18O vs. δ13O vs. the abundance of mass-47isotopologues (mostly 13C18O16O; Fig. 7). This surfaceis curved, but for much of its area (and all of that relevantto natural materials), it is very nearly a flat plane. Thatplane has a slope that is steeper than the vector thatdescribes the diffusive fractionation in these dimensions.Therefore, when a gas is fractionated by diffusion, thediffused portion moves along the vector of the diffusivefractionation toward lower δ13C, lower δ18O and higherΔ47, whereas the residual portion moves along that vectortoward higher δ13C, higher δ18O and lower Δ47.

4.5. Fractionations caused by gravitational potentialand thermal diffusion

The kinetic theory of gases predicts that a static gasphase (i.e., one not subjected to convective mixing) in agravitational or thermal gradient will develop isotopicgradients characterized by high abundances of heavymolecules in regions that are cold and have a lowgravitational potential energy, and visa versa (Gibbs,1928; Grachev and Severinghaus, 2003).

The kinetic theory of gases also predicts thatgravitational separation should lead to distinctive varia-tions in Δi values of multiply substituted species (Gibbs,1928). Gravitational fractionations are proportional toabsolute mass difference; e.g., fractionation of 15N2 from14N2 (2 AMU per molecule mass difference) should betwice as strong as fractionation of 15N14N from 14N2

(1 AMU per molecule mass difference). Thus, for a givenincrease in bulk δ15N (almost entirely controlled by15N14N), one should see a 2x larger increase in 15N2

Fig. 8. Effects of mixing between materials of natural isotopiccomposition and highly enriched materials, in dimensions of aΔi valuefor a multiply-substituted isotopologue vs. a δ value describing a bulkisotopic composition. Panel A illustrates the effects of mixing betweenwater vapor having the isotopic composition of the VSMOW standardand pure D2O, as might occur if ‘heavy water’ mixed with naturalatmospheric water vapor. Panel B illustrates the effects of mixingbetween natural uranium metal and weapons-grade uranium (assumed90 at.% 235U), as could occur during ‘blending’ or other mixingprocesses. Note that in both cases relatively subtle variations in bulkcomposition and small mixing ratios of the enriched end member leadto remarkably large enrichments in Δi values for multiply substitutedisotopologues. This reflects the fact that the stochastic distribution isgenerally curved in dimensions of isotopologue abundance vs. bulkcomposition (e.g., [D2] vs. [D]) whereas mixing lines in thosedimensions are straight. One implication of these trends is thatclumped isotopic analyses could greatly enhance the sensitivity fordetecting enriched materials (e.g., by factors of ca. 100 for weapons-grade U, and of ca. 6000 for heavy water), assuming clumped isotopicspecies can be measured with precision comparable to bulk isotopiccompositions (which is true in at least some cases, given sufficientmaterial and effort; e.g., Eiler and Schauble, 2004; Affek and Eiler,2006; Ghosh et al., 2006a,b; Came et al., in press).


concentration. But, the stochastic distribution predictsthat [15N2] should increase as the square of [15N]. Thus,gas at the bottom of a non-convecting, gravitationallyfractionated column should have a relative deficit inΔ15

N2(and the gas at the top of that column a relative

Δ15N2excess). For example, gravitational fractionation of

nitrogen gas in a static column 10 km long at 273.15 Kand under a gravitational acceleration of 9.81 ms−2 leadsto enrichments of 43.2‰ in 14N15N and 86.4‰ in 15N2,

but 1.71‰ lower Δ15N2, at the bottom of the column

relative to the top. However, for environments of interestto natural applications, the predicted change in Δ15

N2is

negligible: for a 100 m column, similar to the thickness ofglacial firn, the contrast inΔ15

N2between top and bottom

is only 0.0002‰—likely un-measurable (note Δ15N2

isnot linearly proportional to column length because ofcurvature in the relationship between [15N] and [15N2] forthe stochastic distribution).

Isotopic fractionations caused by thermal gradients areusually calculated using empirical factors derived fromlaboratory study of gas mixtures subjected to extremetemperature gradients (because theoretical estimates ofsuch fractionations cannot easily account for interactionsbetween molecules other than ideal gases; Grachev andSeveringhaus, 2003). Fractionations in a temperaturegradient have been measured for both the 15N2/

14N2 and15N14N/14N2 ratio, but the overlapping data are insuffi-ciently precise to yield a meaningful prediction offractionations in Δ15N2 across thermal gradients (seeGrachev and Severinghaus, 2003 for a review andprimary references). If we turn to the theoretical mass-scaling law for fractionations in a thermal gradient (whichpredicts that α varies as (M1−M2)/(M1+M2); (Grachevand Severinghaus, 2003, and references therein)), thenwepredict that a thermal gradient sufficient to create a 1‰increase in δ15N will lead to a −0.035‰ decrease inΔ15N2. This is small but measurable. Because thermalfractionations lead to largerΔi changes for a given changein bulk composition than do gravitational fractionations,clumped isotopemeasurementsmay be able to distinguishgravitational from thermal fractionations in gases trappedin glacial ice and therefore refine the interpretation of suchdata as constraints on past climate change (Severinghouset al., 1998).

4.6. Mixing

Generally speaking, one cannot tell whether the bulkisotopic composition of a given material (e.g., the δDvalue of water vapor) reflects isotopic fractionation thatchanged it from some previous, different composition(e.g., by condensation of rain from vapor), or mixingbetween two isotopically distinct reservoirs to yield anintermediate hybrid (e.g., mixing water vapor from airmasses that originally differ in isotopic composition).There are instances in which ancillary information mightbe used to help make this distinction (e.g., under somecases, one can tell fractionations of water-vapor-isotopes due to condensation from isotopic variationsdue to mixing by plotting the water-vapor mixing ratiovs. δD value). But, these are special cases — there is no

Fig. 9. Dependence of the Δ47 value of CO2 produced by phosphoricacid digestion of carbonate on the growth temperature of that carbonate.Data are shown for inorganic calcite grown under controlled conditionsin the laboratory (Ghosh et al., 2006a), various biogenic carbonatescollected in nature and having known or estimated growth temperatures(Ghosh et al., 2006a, 2007; Came et al., in press), and a natural soilcarbonate collected from a location with known mean annualtemperature. See the legend for further details. The line is fitted tothe data for inorganic calcite from (Ghosh et al., 2006a) (this line issolid where interpolated and dashed where extrapolated). Note that allcarbonates approximately conform to the inorganic trend (excepting aca. 0–2 °C offset for the data for otoliths—possibly attributable tosystematic error in estimated growth temperatures of free-living fishes;Ghosh et al., 2007).


universal ‘finger print’ of bulk isotopic compositionsthat result from mixing.

However, because two-component mixing followslinear vectors in isotopic composition space but thestochastic distribution is generally a curved surface inthat space, mixing can lead to large, predictable andinterpretable deviations from the stochastic distribution.Subtle (per mil level) mixing effects of this kind havebeen observed experimentally for CO2 (Eiler andSchauble, 2004), and much more extreme ones areexpected for mixing involving anthropogenicallyenriched materials. For example, accidental or inten-tional release of ‘heavy water’ (nominally D2O) to theatmosphere, or ‘blending’ of weapons grade uranium(ca. 90% 235U) with natural uranium (ca. 0.72% 235U),assuming each end member conforms to the stochasticdistribution, will produce mixtures that have positive Δi

values for clumped isotopic species (Fig. 8). For thesecases, mixing produces changes in Δi values hundredsor thousands of times greater than changes in bulkisotopic composition for a given mixing ratio of endmembers. Thus, clumped isotope analyses couldprovide greatly increased sensitivity for detectingenriched components and a means of distinguishingmoderate anthropogenic enrichments vs. mixturesbetween natural and highly enriched components.

5. Demonstrated uses

Clumped isotope geochemistry is a new disciplinewith few practitioners. So, while it seems likely to usthat the field will grow and diversify, at present there arejust a few applications with demonstrated ‘stayingpower’. In this section, we briefly review theseemerging areas of applied research. We refer readersto the primary publications of these studies for details(Schauble et al., 2003, 2006; Eiler and Schauble, 2004;Wang et al., 2004; Affek et al., 2005, in press; Guo andEiler, 2005; Affek and Eiler, 2006; Ghosh et al., 2006a,b, 2007; Eiler et al., 2006; Eiler, 2006a; Eiler, 2006b;Came et al., in press; Guo and Eiler, in press); here wefocus on methods, goals and principles of interpretationshared by them all.

5.1. Carbonate paleothermometry

Perhaps the most useful recognized application ofclumped isotope geochemistry is a carbonatepaleothermometer based on the formation of carbonateion groups containing both 13C and 18O (Ghosh et al.,2006a,b, 2007; Eiler et al., 2006; Schauble et al., 2006;Came et al., in press; Guo and Eiler, in press). At

thermodynamic equilibrium, carbonate minerals areexpected to contain abundances of 13C18O16O2

– 2 ionicgroups defined by the homogeneous equilibrium:

M12C18O16O2 þM13C16O3

¼ M13C18O16O2 þM12C16O3 Reaction ð3Þ

(where M is a metal such as Ca; Schauble et al., 2006).This reaction is analogous to those for molecular hydro-gen and water discussed above (i.e., Reactions (1) and(2)). The equilibrium constant for Reaction (3) (K3)approaches the stochastic distribution at high tempera-ture, and increases, driving the reaction to the right(forming super-stochastic abundances of 13C–18Obonds) with decreasing temperature. Thus, by analyzinga carbonate mineral for its relative abundances of all thereactant and product isotopologues that appear inReaction (3), one could directly constrain the carbonatemineral growth temperature (assuming equilibriumgrowth and an appropriate calibration of the temperaturedependence of K3). We refer to this approach as‘carbonate clumped isotope thermometry’.


There is a critical difference between carbonateclumped isotope thermometry and conventional oxy-gen-isotope carbonate-water paleothermometry(McCrea, 1950; Epstein et al., 1953; Kim and O'Neil,1997; Veizer et al., 1999): conventional carbonate-waterpaleothermometry is based on a heterogeneous equilib-rium that fractionates 18O between carbonate and water.Therefore, temperature is only rigorously constrained ifthe δ18O values of both phases are known. However, formuch of the geological (and meteoritical) record, wehave few direct constraints on the oxygen isotopecompositions of waters from which carbonates grew.For this reason, many applications of the carbonate-water thermometer are in some sense compromised byassumptions regarding the isotopic composition ofwater. In contrast, the carbonate clumped isotopethermometer is based on a homogeneous equilibrium,and all of the information needed to reconstruct theequilibrium constant for that reaction is preserved withinthe carbonate mineral itself.

In practice, because existing methods of preciseclumped isotope analysis require gas as an analyte, thecarbonate clumped isotope thermometer is actuallycalibrated by comparing the Δ47 value of CO2 (whichis dominated by variations in 13C18O16O) released fromcarbonate by phosphoric acid digestion to the growthtemperature of that carbonate (Ghosh et al., 2006a). Thiscalibration includes a significant but apparently well-behaved acid-digestion fractionation (much as formeasurements of δ18O in carbonate by phosphoricacid digestion; Swart et al., 1991). Ongoing theoreticaland experimental research on this effect suggests it is aconsequence of a kinetic isotope effect associated withdissociation of H2CO3 to release CO2 gas (W. Guo, pers.com.). Whatever its cause, it varies little with reactiontemperature (ca. 1 ppm per °C) and appears to beindistinguishable among various carbonate types. Wehave experimentally or empirically calibrated thecarbonate clumped isotope thermometer for syntheticinorganic calcite (Ghosh et al., 2006a), natural inorganiccalcite from a soil (previously unpublished), aragoniticotoliths (Ghosh et al., 2007), aragonitic corals (Ghoshet al., 2006a), aragonitic mollusks and calcitic brachio-pods (Came et al., in press) (Fig. 9). Ongoing research isextending this calibration to include foraminifera andsynthetic aragonite and dolomite. The uniformity of theresults to-date suggests that vital effects and othermaterial-specific isotopic fractionations (a commoncomplexity to conventional stable isotope thermometry)are relatively unimportant for this system. This uni-formity is expected based on theoretical models of iso-topic clumping in various kinds of carbonate minerals

(Schauble et al., 2006). Nevertheless, it will beimportant to continue expanding the breadth of thiscalibration to include other carbonate types.

Given the best external precisions achieved foranalyses of Δ47 in CO2 from carbonate (ca. ±0.005‰;Came et al., in press) and the temperature sensitivityimplied by the data in Fig. 9, the carbonate clumpedisotope thermometer has uncertainties in temperature ofca.±1 °C at earth-surface temperatures (more at highertemperatures).

Perhaps the most useful thing about the carbonateclumped isotope thermometer is its lack of dependenceon the isotopic composition of water (or any other phasewith which carbonate might co-exist). Moreover, thisthermometer is based on a thermodynamically con-trolled process that apparently differs little amongvarious kinds of biological and inorganic carbonates,and so can be used equally well in many different sortsof materials (although some caution is required on thispoint until we gain more experience with it in applieduse). In this respect, it is potentially broader in its usethan the various empirical thermometers developed forCenozoic marine climate records (e.g., alkenoneabundances or various biodiversity or physiognomictemperature proxies). For these reasons, the carbonateclumped isotope thermometer can be particularly usefulfor reconstructing temperatures in times and locationswhere the isotopic composition of water is unknown andthe various empirical thermometers are inapplicable oruncalibrated. Examples include pre-Cenozoic marinesediments, terrestrial sediments and meteorites.

Another important characteristic of the carbonateclumped isotope thermometer is that it provides a meansof rigorously constraining the δ18O of ancient waters.That is, once one has determined the growth temperatureof a carbonate using the clumped isotope approach, onecan then combine the δ18O value of that carbonate(measured at the same time and on the same material asthe clumped isotope measurement) with the knowntemperature-dependent fractionation of oxygen isotopesbetween carbonate and water (McCrea, 1950; Epsteinet al., 1953; Kim and O'Neil, 1997) to calculate the δ18Ovalue of the water from which carbonate grew. There aremany problems for which the δ18O of water is of equal orgreater importance than carbonate growth temperature(e.g., water-rock reaction in the crust; aqueous alterationof meteorites; some aspects of terrestrial climate changeand paleoaltimetry; e.g., Ghosh et al., 2006b). We expectthat clumped isotope thermometry will play an importantrole in advancing such problems.

It is important to establish how well the carbonateclumped isotope thermometer resists post-depositional


resetting through diagenesis, burial metamorphism,weathering and other processes. These sorts of compli-cations affect all methods of paleothermometry togreater or lesser degrees, and generally can beunderstood only through applied study in a wide rangeof settings (because experiments at laboratory time-scales generally fail to capture the complexity of therelevant mechanisms, especially at low temperatures).Experience to-date with soil carbonates of varying ageand burial depth (Eiler et al., 2006), Precambrianlimestones (Eiler, 2006a and unpublished), marbles(Ghosh et al., 2006a) and Phanerozoic fossils (Cameet al., in press) suggests that the carbonate clumpedisotope thermometer preserves primary temperaturesthrough subsequent heating over geological time scalesup to temperatures of ca. 200 °C, provided thatcarbonate does not undergo dissolution and reprecipita-tion. This last clause is key: if carbonate dissolves andre-precipitates at any temperature, the relatively rapidkinetics of oxygen exchange between water anddissolved inorganic carbon (Kim and O'Neil, 1997)will promote isotopic re-distribution. For this reason,carbonate clumped isotope temperatures should bedetermined only after one has established the primarycharacter of the sample through textural, structural and/or trace-metal studies (e.g., Veizer et al., 1999).

5.2. Budgets of atmospheric gases

Clumped isotope measurements can contribute to thestudy of atmospheric gases because they provide new,independent constraints on gas budgets that often sufferfrom under-constraint (e.g., concentration and δ13C andδ18O values of atmospheric CO2 are insufficient touniquely define its budget). Moreover, it is relativelystraightforward to extract and analyze atmosphericgases without redistribution of isotopes, so this isamong the simplest uses of clumped isotope geochem-istry from a purely practical standpoint.

We have significant experience with Δ47 measure-ments of atmospheric CO2, including field experiments,regional studies and nominally ‘clean’ background air(Eiler and Schauble, 2004; Affek et al., 2005, in press;Affek and Eiler, 2006). To-date, such data have beenused to constrain the mixing ratios of combustionproducts in urban air (Affek and Eiler, 2006) and haveresulted in two unexplained but potentially importantobservations: (1) the Δ47 value of CO2 in nominallyclean air varies seasonally with surprisingly highamplitude (ca. 0.2‰) and in a way that is not consistentwith purely thermodynamic control (i.e., Δ47 values arelower in the winter than in the summer, opposite the

direction predicted for equilibrium) (Affek et al., 2005,in press). We suspect this seasonal trend reflects thetrade-off of respiration and photosynthesis and kineticcontrols on theΔ47 value of respired CO2. However, thishypothesis awaits laboratory and field tests. And, (2) theΔ47 value of stratospheric CO2 rises strongly (by morethan 0.5‰) with increasing photochemical exchange ofCO2 with O(1D) (as measured by the Δ17O value ofCO2) (Affek et al., 2005). This phenomenon is oppositeto the expected trend because the CO2+O(1D) ex-change reaction is highly energetic and should promoteisotopic ‘scrambling’ (driving CO2 toward the stochasticdistribution). Nevertheless, the observations are clearand appear to indicate something counter-intuitive aboutthe photochemical processing of stratospheric CO2. Weare currently examining this issue further throughlaboratory photochemical studies.

We can imagine many uses of clumped isotopegeochemistry analogous to those summarized above.Particularly attractive targets include: Studies of multi-ply-deuterated methane and molecular hydrogen, whichcould precisely define the residence times of these gaseswith respect to atmospheric photo-oxidation (Mroz et al.,1989; Kaye and Jackman, 1990); studies of 18O2 and18O17O, which could help de-convolve the competingeffects of photosynthesis, respiration and photochemistryon the isotopic budget of O2; and studies of 15N2, whichcould potentially constrain the N2 budget.

5.3. Mechanisms of isotopic fractionation

As was mentioned above, there is a long history ofmechanistic studies of the physical and biochemistry ofisotopically substituted species through laboratory andfield experiments on artificially enriched materials. Theadvent of precise clumped isotope measurementssuitable for work on natural abundances of these speciescreates the possibility that studies of this kind could beperformed on natural systems. Such data could be usedto relate physical, chemical and biosynthetic processesthat are well-understood from laboratory studies onenriched materials to natural processes and budgets, orto discover new and unexpected mechanisms of isotopicfractionation through exploration of the clumped iso-tope compositions of natural things. For example, it hasbeen suggested that vital effects controlling the bulk Cand O isotope composition of some biogenic carbonatesreflect fractionation between seawater and animal bodywater combined with equilibrium partitioning duringprecipitation of carbonate from body water (Adkinset al., 2003). Clumped isotope geochemistry could testthis hypothesis because it predicts that all biogenic


carbonates, regardless of the impact of vital effects ontheir bulk isotopic compositions, will have clumped-isotope compositions consistent with equilibrium attheir temperatures of growth.

Our work to-date has provided several instances inwhich clumped-isotope measurements revealed mech-anistically significant information (although some,such as the anomalous Δ47 enrichments in stratospher-ic CO2 cited above (Affek et al., 2005), will requireadditional experimental work before it is fully under-stood). The simplest example is a study of the stableisotope systematics of CO2 in car exhaust, whichdemonstrated that its oxygen isotope and clumpedisotope composition reflects equilibration with co-emitted water vapor at ca. 200 °C (presumably thetemperature at which the cooling exhaust stream‘quenches’ its internal isotope exchange equilibria;(Affek and Eiler, 2006)).

5.4. Future Challenges

At present, clumped isotope geochemistry is morenoteworthy for its novelty and promise than for itsaccomplishments, and there are a number of pressingchallenges that must be met before it can advance.

Most importantly, the community of practitioners ofthis field must grow. Spread of the analytical approachesand applied work described here to other labs will spurtechnical and conceptual innovation, diversify thefamily of problems that are addressed, and more quicklyfill in the many gaps in our knowledge of clumpedisotope chemistry and distributions in nature. Clumpedisotope analyses can be performed in any modern stableisotope laboratory, but are sufficiently challenging thatthey are unlikely to become widespread until technicalinnovation makes them simpler, less time consumingand more reliable. Automation of sample preparationdevices will help in this regard.

A second fundamental advance that is sorelyneeded is development of analytical instruments thatare more suitable to the needs of clumped isotopemeasurements. These analyses are currently made oncommercially-available gas-source isotope ratio massspectrometers that were only modestly modified forthis purpose. These instruments have relatively poormass resolving power, preventing mass-resolution ofthe most common trace contaminants, and areinsufficiently sensitive for analyzing exceedingly rarespecies, such as triply-substituted isotopologues. Amajor step forward in analytical capabilities wouldresult from development of a gas source massspectrometer with enhanced mass resolving power

(M/ΔM of ca. 2000–5000 would be sufficient) and thecapability to use ion counters (e.g., electron multi-pliers) to collect some species.

The scope of clumped isotope geochemistry couldalso be greatly expanded by developing a class ofinstruments for near-infra-red absorption spectroscopythat are optimized for precise isotope ratio measurementsof the clumped isotopic species. Even if such measure-ments required purified samples and highly controlledconditions, this would allow for resolved analysis ofspecies having the same cardinal mass (e.g., 12C17O18Ofrom 13C18O16O, or 17O17O from 18O16O)—somethingthat will likely remain impossible for magnetic sectormass spectrometers.

Existing thermal ionization mass spectrometers maybe suitable for clumped isotope analysis of some solids,and we strongly encourage that this be explored by oneof the existing appropriately equipped laboratories.

Even baring creation of new classes of analyticalinstruments, the scope of clumped isotope geochemistrycould be expanded significantly by developing newmethods for extracting analyte gases from currentlyinaccessible materials. For example, we have attemptedseveral approaches to extracting CO from organic matter(all unsuccessful) and have plans to prepare SO2 fromsulfates for clumped isotope analysis. Such methodo-logical innovations face significant hurdles because asuccessful technique must not redistribute isotopesduring extraction of analyte gas and, if it fractionatesisotopologues from one another it must do so reproduc-ibly (e.g., as for phosphoric acid digestion of carbonatesGhosh et al., 2006a).

Finally, even if we restrict ourselves to the analytesthat have been demonstrated to be reliably measurable(CO2 from carbonates and air), there are several pressingneeds. First, our theoretical understanding of equilibri-um fractionations (i.e., the equilibrium constants forhomogeneous isotope exchange equilibria) and fractio-nations arising from simple physical processes (e.g.,diffusion) are relatively sound, but only a few suchfractionations have been studied by experiment (Schau-ble et al., 2003; Eiler and Schauble, 2004; Ghosh et al.,2006a, 2007; Came et al., in press). The foundation ofthis field will not be firm until we have thoroughlyexamined more of these fractionations through directobservation. Our understanding of kinetic isotopeeffects associated with unidirectional, condensed-phasereactions is even poorer, and demands focused anddetailed studies of clumped isotope fractionationsaccompanying processes such as photosynthesis, respi-ration and other metabolic processes, and a-biologicalprocesses such as air-sea gas exchange.


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Dr. John Eiler received his Ph.D. inGeology from the University of Wisconsinin 1994, after which he moved to theCalifornia Institute of Technology as apostdoctoral fellow. He joined the faculty atCaltech in 1998, where he is currently aProfessor of Geochemistry. He is director ofCaltech's Microanalysis Center and super-vises a laboratory for stable isotope geochem-istry that pursues research in petrology,

meteoritics, climate reconstruction, environmental science and thephysical- and biochemistry of isotopes.

Frontiers Clumped-isotope geochemistry The study of ... · Stable isotope geochemistry is rooted in the land-mark discoveries in physical chemistry made during the 1920s and 30s.

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