, 2 2 N 15 O, 18 O nia Institute of 18 b O, 2 aInstituteofTechnology, 16 g O 18 C 2009 John Wiley & Sons, Ltd. 13 gineering, Califor c ¨ eron s, University of Washington, Seattle, de l’Environnement, NRS/CEA/UVSQ, itution of Washington, Washington, DC, on, Department of Earth and Space ines the abundances in natural netarySciences,Californi M. Da M. Bonifacie, d b,f measurements of heterogeneous natural nt technical limit to precision intrinsic to our carbonate clumped- thermometry of W. Guo, e thermometry and undergo distinctive fractionations c A. Tripati, DepartmentofGeology andGeophysics,YaleUniversity,NewHaven,CT,06520,USA Geophysical Laboratory, Carnegie Inst Division of Chemistry and Chemical En Correspondence to: K. W. Huntingt Sciences, University of Washington, Seattle, WA 98195,E-mail: USA. [email protected] Department of Earth and SpaceWA 98195, Science USA DivisionofGeologicalandPla Pasadena, CA, 91125, USA 20015, USA Technology, Pasadena, CA, 91125, USA Department of Earth Sciences, University ofUK Cambridge, Cambridge, CB2 3EQ, Laboratoire des Sciences duFrance Climat et University of Texas at Austin, JacksonUSA School of Geosciences, Austin, TX 78712, f b c ∗ a e g h d b al limits of precision, methods of standardization, instrument -inlet gas-source isotope ratio mass spectrometry (IRMS). We ssible isotopologues, we document and correct for (1) isotopic ed-isotope’ geochemistry) exam n in 47/44 ratios for counting systems consisting of a Faraday O, 16 O 18 Methods C H. P. Affek, 13 b B. Passey, [5–8] 2009 John Wiley & Sons, Ltd. . b 2 More generally, c [3,4] O form bonds with each 18 Such species participate 5 parts per million (ppm), whereas precisions of J. M. Eiler, resistor on three Thermo-Finnigan 253 IRMS systems. Based on the analyses of heated CO ∼ ) analysis by gas-source isotope O bonds) and follow counting statistics. The prese 01‰ are routinely achieved for measurements of the mass-47 anomaly (a measure mostly of [1] . . ∗ molecules and (2) subtle nonlinearity in the18 relationship between actual and measured 47/44 0 Cand − 10 ppm (both 1 s.e.). These correspond to errors in a 2 2 ∼ C- ∼ 13 2 12 47 O 13 16 O , 1318–1329 Copyright 18 N. Thiagarajan, 44 C h , e 13 C, respectively. Copyright ◦ 4 . 2009 or The most developed of these is the thermody- 2 ). Such species form the basis of carbonate clumped-isotop ± − 2 [2] 2

carbonate thermometry; isotopologues; mass 47; clumped ; precision N 2 15 O isotopologues critical for carbonate clumped-isotope

16

Cand 2 ◦ O O,

2 17 18 . This article describes the methods and limitations of analyses C O

1 ratio mass spectrometry ratios. External precisions of the abundance anomaly of thermometry. Our subject has been addressed in the sections and appendices of previous applied studies in this of multiply substituted isotopologues by gas-sourcemass isotope spectrometry ratio (IRMS), with particular focusof on measurement CO during a variety of naturaldetailed data processes, and but arguments regarding initial the theoretical reportslinearity and have practic and provided related few issues for detailsdemonstrate clumped-isotope of long-term analysis their by stability analysis. dual and Incup subtenth this registered per study, through mil we a precisio present 10 J. Mass. Spectrom. materials of molecules, formula units or moieties that contain more than one rare isotope (e.g. 18 Introduction The geochemistrycolloquially, of ‘clumped-isotope’ multiplyabundances in geochemistry natural substituted – examines materialsmoieties that of isotopologues contain – the more molecules, than formula one rare units isotope; e.g. or gases, which have a stochastic distribution of isotopes among po 13 and R. Came The geochemistry of multiply substituted isotopologues (‘clump K. W. Huntington, L. Y. Yeung, exchange among analyte CO Methods and limitations of ‘clumped’ CO isotope ( (www.interscience.com) DOI 10.1002/jms.1614 Research Article Received: 20 January 2009 Accepted: 4 June 2009 Published online in Wiley Interscience: 20 July 2009 these species undergo distinctive fractionationsof processes during (diffusion, a photolysis, variety irreversible reactions,potentially etc.) provide unique and independent constraints on the origins and budgets of natural materials. The best-developed applications of this sort concern the budget of atmospheric CO other in the lattices of carbonate minerals. namically based carbonate clumped-isotope thermometer, which examines the extent to which methods and instrumentation is in temperature-dependentreactions homogeneous that can be isotope usedconstrain as temperature exchange based that on rigorously thephase isotopic composition alone. of one Keywords: Supporting information may be found in the online version of this article. materials are more typically ±

1318 1319 , 2 2 + [2] [2] . (2) O O. 16 ). The 16 et al O 1000 O 2 [6] denotes 1000 (3) O 18 OinCO 18 ∗ × C 16 is that ratio C 16 × C ∗ i 13 13 O   Wang 13 R K 1 1 2 18 ) to denote the ,ameasurement C [2] + − O 2 17 i − 13 R O ∗ 16 ( 17 O O], where 45 O 17 45 R 2 .Hence,eventhough 16 R × 16 R C 2 2 18 O values as follows: 45 and the temperature- C  i 13 13 18 + R O][ C R i 12 1000 (1) − 18 13 · 12 + + R   C][ 2 1 Oand is the equilibrium constant for 18 1 ,forisotopeexchangereactions − O 13 − R ∗ 18 − K resistor to measure ion beams of 2 − 16 2[ K O 47 ) O × ∗ C R i ∗ 16 i 46 17 17 46 = R O 17 13 R R R C R 12 ( ∗ R 18 relative to the amount expected for  12 2  C + O] i 13 = + , where − 16 97% of mass-47 CO www.interscience.wiley.com/journal/jms 17 i ∗ O(i.e. R O  18 ∼ K 16 1 / R 46 = 18 × O K R ) C − × ∗ 18 13 13 K ∗ C R 13 / 47 2 47 ) describing the enrichment of R 13 K R R 2 47 + defines the difference in abundances in terms of per  i is the abundance ratio of the isotopologue of interest  18 value calculated as in Eqn (1), but including contributions Omakesup Ofromitsisobars, = i R i ), the ratio = R 2 16 16 2 47 1000 ln( O O O − 47 − 16 18 18 C C C multiply substituted isotopologues. These have beenanalysis used for of the hydrogen deuteriumpreviously (HD) to but be have suitable not formil been analyses precision. shown that Finally, demand subtenth electronanalyte per bombardment molecules sources fragment andrecombines to some contribute proportionwhich to may influence of the the measured those population proportion of of isotopologues. fragments detected ions, relative to the isotopically normal isotopologue, and which is calculated as mil deviation from the stochastic distribution: existing sector mass spectrometers are unable to distinguish for one such exchange reaction involving the doubly substituted isotopologue from all isotopologuesshould having be a strongly nominal proportional to cardinal abundances mass of of 47, changes in isotopicpumped composition. electron In bombardment addition,ments sources typically the yield used dynamically onlyanalyte in one molecules, ion such making per it instru- severalcounting-statistics difficult hundred to errors or for achieve analyses more the ofa desired consequence, rare low we isotopic use species. counting As cup systems registered consisting through of a a 10 Faraday the stochastic distribution ofa isotopes molecule. For among the isotopologues stochasticisotopologue of distribution, is the the abundance product ofit of contains an (e.g. the [ abundances of the isotopes excess of isotopologue the random distribution, and 2 is a symmetry number in a pool of molecules havingbut the same bulk a isotopic composition stochastic distribution of isotopologues. where dependentequilibrium constant, involving one doubly substituted isotopologue. In the case of CO relative to the stochastic distribution is defined as follows: derived the relationship between 12 13 13 Thus, from Eqns (1) and (2),anomaly the ( temperature-dependent mass-47 Experimental Multiply substituted isotopologues of CO Clumped- uses values of of the the stochastic distribution, is related to variable 2009 John Wiley & Sons, Ltd. 005‰ c . 0 ∼ of the com- 6 − or less. This makes to 10 8 200) and abundance 5 − − ∼ m / m O) can lead to significant apparent 16 C. Therefore, one must analyze abun- O ◦ 18 O bonds in carbonates is less than 1‰ , 1318–1329 Copyright C 18 44 13 , C- ) is critical for clumped-isotope geochem- Cto50 13 ◦ + 2 2009 Cl on (thousandths of per mil), rivaling the best that have 35 6 C or O − 12 + but this is the first article to present detailed data and 2 [6,9] To date, all usefully precise measurements of multiply substi- However, several issues potentially affect measurements of mul- ‘Clumped’ isotopes per degree from 0 arguments regarding the theoretical andsion, practical methods limits of of standardization, preci- instrument linearityanalytical and related issues. We are motivatedthe by methods three of goals: toin analysis document greater of detail multiply thanto substituted guide is isotopologues others typically who possibleand might in to attempt an illuminate measurements the of appliedanalogous this lessons paper; attempts kind; these at methodsspectrometric might exceptionally provide precise measurements. for or Althougharticle sensitive are of many mass interest only to detailsthermometry, other workers of the attempting carbonate this datademonstration of we clumped-isotope geochemistry, presentguide future and applied provide thus uses of will multiply a substituted isotopologues. more general istry. Clumped-isotope geochemistry provides unique constraints only when one canisotopes determine is how distributed athat among given disproportionates population molecular of the species;will rare analyte any destroy analysis into thatfragmentation information. its of the Assuming analyte, constituent analyses it of atoms tiply naturally is substituted occurring mul- possible isotopologues face to twosuch additional avoid hurdles: species First, typically constitute only 10 dance anomalies of multiply substitutedcisions isotopologues of with 10 pre- the clumped isotopic speciesconsidered easily by the stable rarest isotopeof analytical geochemistry. targets the Furthermore, processes many isotopic of variations. For greatest example, interest thetic excess produce distribution relative relatively to of a subtle stochas- J. Mass. Spectrom. The ability to perform(e.g. high-precision analyses CO of molecular ions Mass Spectrometry ofIsotopologues Multiply Substituted field, at room temperature equilibrium and varies by only tuted isotopologues in natural materials haveThermo-Finnigan been 253 made gas-source using IRMS. a Such instrumentssuited are well to the task,are as equipped they with an typicallyrelatively array analyze of stable molecular Faraday ions multicollection detectors, and samples measurements. which using permits Introduction a of dual-inletrepeated and intercomparisons change-over of a valveof sample allows gas nominally rapid, with known ato standard isotopic correct gas composition, for which mostsubtenth instrumental enables of biases one and perhave is mil key mass to precision. resolving achieving powers Additionally, ( such instruments ever been achieved for any mass spectrometric measurement. sensitivities sufficient tobeams of separate many multiply substituted cleanly ionsbeams from for the the isotopically much normal stronger relatively and singly substituted weak ions. tiply substituted isotopologues usingFirst, the gas-source mass IRMS resolution is systems. insufficientferences that to one resolve encounters the when many analyzing molecular inter- is ions. a This particular concern for clumped-isotope measurements,even where a ppb-level contaminant that contributesbeam to (e.g. an analyzed ion pound of interest, and in some cases 10 . O The 14 18 data et al C- 47 values [14] . 13 yields a 50 55 47 , with error extracted 2 uncertain- 016) (7) [3] et al . It is defined . for synthetic , 1318–1329 − 2 0 σ 2 45 44 [3] − . 13 , ± et al O bond enrich- et al 02 (6) 40 18 . 031 fall on the calibration 2009 . 0 C- (0 K. W. Huntington − 13 [15] TinsteadofT 35 − 2 O abundance anomaly value of CO C is observed to vary 12 − 2 ◦ 18 T error bars) grown at known − , weighted by the uncertainties 47 2 T (K) 30 C- C) versus × σ − cted for a stochastic distribu- -2 ° 13 6 × T 6 6 measurements on T T ( on T 10 25 10 The 10 47 C. The solid black line is defined by a 47 × ◦ J. Mass. Spectrom. 11 × Cand50 20 ◦ [12] produced by phosphoric acid diges- O) into bonds with each other is ther- error bars). 0592 18 . 2 σ 0 15 0014) . C, 0 = 13 ionic groups in carbonates with the neces- 10 is proportional to the abundance anomaly ± 10 47 − 2 2 Uncertainties in fit parameters (slope and intercept) are 3 As a consequence, the extent to which a carbon- 5 0605 [13] . [3,4] (0 (a) The dashed line is the calibration line for mass-47 anomaly 0 extracted from natural surface and deep water dwelling 9 [3] = C from inorganic, synthetic calcite grown at known 2 and T. ◦ temperature of carbonate growth of Ghosh

0.8 0.7 0.6 0.5 0.8 0.7 0.6 0.5

47

47

47 (‰) 47 47 (‰) 47 ∆ ∆ Currently, it is not possible to measure directly abun- (a) (b) Note this is within uncertainty of Eqn (6). Measured A least-squares linear regressiontainty that in takes each into measurement account reported uncer- in Ghosh in the carbonate mineral. slightly modified version of this relation, including 1 temperatures between 1 and 50 carbonate data (white symbols with 2 dances of CO bonds (relative to the amounttion expe of isotopes) cancarbonate growth. provide a measure of the temperature of tion of carbonate, because the ment. Instead,characterization this of enrichment CO can be inferred by isotopic dashed (Eqn (6)) and(b) solid The black same curve (Eqn shown (7)) in (a) lines is plotted agree within uncertainty. calculated as described in the supporting information, and 95%limits confidence (gray curves) are calculated by the method of Crow sary precision to determine a sample’s hyperbole representing the 95% confidence limits shown in (a). Figure 1. versus line (black symbols with 2 at 25 in product CO least-squares linear regression of of heavy isotopes ( ate formed in thermodynamic equilibrium is enriched in as a functionrelation: of the growth temperature according to the by a simple linear regression of in temperatures between 0 for samples grown at known temperature for CO modynamically favored to andecreases. increasing degree as temperature ties on the fitdetails parameters of (Fig. the 1; regression): see supporting information for 2 ∗ ), C, 49 47 [2] O] by 46 13 are 12 and R 16 R ∗ ionic 2009 John Wiley & Sons, Ltd. [10,11] , 46 2 C/ ∗ ) C, but 49 + R c − O][ R 13 2 47 and 17 13  , and can 3 16 R δ R ∗ 1 /(1 ( is derived values. As C. Indeed, 48 47 C][ and 13 and − 13 + R R δ 17 45 , ). Substituting 12 ∗ ∗ [ δ R 45 that variations 17 45 47 18 48 45 = R R R R R and Copyright Oand R = 1000 (4) O]. Assuming the 46 13 that would occur ∗ C] + . The denominator 18  R and R and } 17 δ × 46 13 2 Oand 17 ∗ − R 45 R , 46 R 18 O][ ), [ + ∗   δ δ + in Eqn (3) are measured and 1000 1 1 16 13 45 , 18 [10,11] R R values. Second, as pointed , we find the ratio that R − − 47 × /(1 45 C][ .Valuesof 45 i and ∗ δ 2 R 2 + R ∗ ∗ 17 ) 12 1] 46 46 R 46 46 46 = 17 2[ (the abundance ratios R R [44] R R = R − R / ( ∗ 1/(1 and C (Fig. s1 in the supporting infor- Eqns (3)–(5) involve a circularity ) O ordering) demonstrate that ∗   , + 18 O] 46 13 13 R 2 2 18 = 47 46 R R for the sample (‘SA’) referenced to WG δ 17 [5] , C values are calculated from measure- i R R O] [45] C- − − R C] + , 13 45 / 16 13 in the numerator are equal to unity, δ   δ and 12 47 18 = 1 1 SA , .Bydefinition,[44] R i R )and[ O][ 46 Oand 17 R − − by assuming the stochastic distribution 18 O, respectively, for the sample) because ∗ R 17 18 R 16 [( R 18 and R R ∗ ∗ 16 45 , δ 46 Oand 2 R 49 48 C][ . Similarly, R 49 48 + = 13 O/ 46 R R 18 R R and R 13 + δ 17 ι δ 17 [ 1000 (5) 18 and δ R , are derived from the measured R { However, isotopologue abundances are not equal to 18 45 and   × 47 = R + R + 17 [1] δ assuming a specific mass-dependent fractionation 18 is so small relative to 45 = = R 13 from R R 13 R ∗ R are essentially independent of ∗ 49 48 18 1/(1 2 47 R Oand R 45 = = 47 = R measurements performed at Yale University (using a mass 16 and ∗ ∗ O] The fact that 47 O/ 45 47 13 16 terms are the calculated equilibrated at roomtemperature-dependent temperature (namely, having the same that might require anever, iterative calculation to circumvent. How- sample abundance ratiosmeasured relative to mass 44, as derived from spectrometer identical to MS-I described below) of cylinder CO in the samplebased if on it the had sample’s the measured stochastic distribution, which are illustrated by the following example, one can calculate determined in an analogous fashion to be used to calculate theto mass-48 the and stochastic mass-49 distribution: anomalies relative www.interscience.wiley.com/journal/jms is independent of samples representing a 40‰ variation in has two noteworthy implications. First,containing the terms in Eqnsand (3)–(5) thus do not contribute to the from mass spectrometer data is providedin in the MATLAB supporting code information. format and 17 The numerator terms groupsincarbonatemineralswererandom,theabundanceofeach carbonate-ion isotopologue would be the stochastic/combinatory product ofcomposed. the abundances of the isotopes of which it is Carbonate clumped-isotope thermometry The most developed applicationistry of to clumped-isotope date geochem- isbonding the among carbonate isotopes clumped-isotope of thermometer. carbon If and oxygen in CO mation). a stochastic distribution in the carbonate crystal lattice; ‘clumping’ and [45] [ these terms in A numerical demonstration of how to calculate from R out by Eiler and Schauble, R assuming the stochastic distribution, in ments of a working gascomposition (‘WG’) standard of nominally known isotopic stochastic distribution, [ between would occur in theR sample if it had the stochastic distribution:

1320 1321 O = 18 δ Heated Sample 2h and VSMOW [5] > O [5] (for M/z 44), resistors (for 18 δ 0‰. 8 VPDB and Cfor 10 12 that closely ap- ◦ ≡ × 2 versus 47 mol with resulting ion µ 9.5 kV, an electron energy ca (for M/z 46) resistors and three value one would have measured C reported 47 11 13 R δ 60‰), which was standardized by standard from Oztech ( . 3 2 www.interscience.wiley.com/journal/jms O from the observed isotopic abundances. evolved from phosphoric acid reaction with =− 2 18 δ O values) having the stochastic distribution of 18 VSMOW were standardized by comparison with δ VPDB C Cand 13 (for M/z 45) and 10 13 δ versus δ Cand value is defined as the difference between the measured 13 10 47 δ effectively without fractionating or losing sample gas (near 65–100 V, and with the ‘sulfur window’ (an aperture on the at the California Institute of Technology. The instruments were 10 value of a sample and the 96‰, 2 2 ∼ . Carbon dioxide for heated gas normalization measure- × 47 comparison with CO of side of the ionization chamberresidence time used of gas to in the source) control closed. The thewas same used configuration pressure for MS-II, and except that MS-II measurementseight were acquisitions made consisting for of seven cycles (26each), s and integration the time widths of theslightly. Faraday For cups both on machines, MS-I the and capillary MS-II apertureyield differ was a adjusted 5 to V signal for mass 44 for a bellow pressure of 50 mbar. Comparison of sample gases tocomposition and standards state of of ordering known isotopic The M/z 47, 48 and 49), as described by Eiler and Schauble. NBS-19 standard. Values for 24 for a samplesame of that same bulk isotopic composition (i.e. the reported isotopologues. This requires that we compare a sample gas to a equipped with collection systems consisting ofset both of the three Faraday standard cups registered through 3 R rapidly quenched atviously room has temperature. This been procedure shown pre- to yield CO 3 proaches a stochasticsible distribution isotopologues; of isotopes i.e. among its all pos- value of additional Faraday cups registered through 10 ments (described below)and was heated prepared in in quartz a break muffle seals furnace to 1000 100% collection efficiency). Finally, conventional cryogeniccation purifi- procedures were repeated twice before transfer tospectrometer. the mass For MS-I, isotopic compositions wereacquisitions typically of measured for 10 nine cyclesreference each gas (8 and s sample integration sidesbackground each time measurements cycle), each and with pressure for peak balancing the centering, reference between the gas and sampleEach acquisition sides requires made 20–30 beforeper min, sample each and is the acquisition. total typicallywith analysis 3–4 time an h. acceleration Measurements are potential typically of made CO sizes were typicallybeam currents approximately for M/z 44, 50 45, 46, 47,nA, 48 0.6 and 49 nA, of 0.2 approximately nA, 50 2reference pA, 0.2 gas pA and was 2 fA, a respectively. The CO working gases were purifiedand using conventional GC cryogenicration processing procedures of inspectrometer. samples a before manner being identical transferred toIsotopic analysis to the prepa- theIn mass addition to thedual-inletgas-sourceThermo-Finnigan253IRMSsystems,denoted Yale University instrumentMS-I noted and above, MS-II, were two used toCO measure the isotopic composition of the working reference gas.calculate The program Isodat 2.0 was used to 2 ). O 47 at [3] . 18 4 [3,15] [5,6] trap. 2009 John Wiley & Sons, Ltd. C C- ◦ et al 2 c PO 13 3 0‰ and Swart C. The GC ≡ ◦ Addition of at any given [20] 47 10 using the glass Cand30 ◦ − 2 47 [1,16] The cryogenically 5 ∼ [3] . collection time (which C between samples and exiting the column was et al ◦ 2 2 2 ml anhydrous H ∼ extraction and purification 2 of those listed in Eqn (7)). Hence, σ , 1318–1329 Copyright 01–0.02‰) values of . 44 or crystal-structural controls on , 0 remained condensed in the liquid N ∼ 2 2009 [18,19] was then entrained in He carrier gas flowing at [17] molecules associated either with fragmentation and 2 [4] 2 . Following the GC step, the He carrier gas was removed After reaction, conventional vacuum cryogenic purifica- C for 6 h once every 24 h. CO 2 ◦ m internal diameter, 30 m long) held at [21] µ . C for 8–24 h following the methods of McCrea ◦ ‘Clumped’ isotopes purified CO Carbon dioxide was extractedbonate from powders 5 by to reaction 12 mg with aliquots of car- ‘clumping’. vacuum apparatus described by Ghosh was baked out at a temperature of 150 temperature. recombination in themetal source capillaries. or Asbe interaction detailed corrected with for below, the empirically these walls based phenomena of on analyses must of heated CO J. Mass. Spectrom. Carbonate acid digestion, CO gases, which have aall possible stochastic isotopologues distribution (implying of a isotopes value among of Potential sources of uncertainty inand temperature clumped-isotope estimates analysis Severalpotentialsourcesofuncertaintymaybeencounteredwhen applying clumped-isotope thermometry and othertechniques isotopologue to a particularisotopic sample. fractionations during sample These preparation and include purification unconstrained as well as random (i.e. shotisotopicfractionationsthatmightoccurduring noise) errors and massspectrometry. any uncharacterized Two mass spectrometric errorsrelevant or to uncertainties clumped-isotope are analysesmeasurable particularly in nonlinearity general: (1)and in subtle measured but the 47/44analyte relationship ratios CO and between (2) isotopic actual exchange among Although the relationship between growth temperaturefor and fish otoliths isto similar slightly in slope lower to ( Eqns (6) and (7), it is offset approximately conform tocalcite the samples, trend as do definedof results by for known many the or other synthetic natural estimated carbonates growth temperatures. coralsgrownatknowntemperaturesbetween at 220 et al 25 Uncertainties in these empirical relationships contribute toanalytical overall uncertainty. A finalclumped-isotope source thermometry, of uncertainty inthe relevant particular, for empirical is calibrationThis introduced of by uncertainty the isshared thermometer by systematic all itself ratherclasses unknown (Eqn than (6)). of samples) random carbonates andisotope (i.e. may for effects differ it unknown for is reasons, different such as kinetic tion procedures were used to isolate product CO cryogenically collected forliquid 40 min N in a glass trap immersed in while sample CO This procedure does not optimize CO these data does not(fit significantly change parameters temperature are estimates within 1 for consistency with all previoustemperature publications, calculations carbonate in growth thispublished article inorganic are carbonate performed calibration using the line of Ghosh could be reduced if a multiloop trap were introduced) but purifies a rate of 3gas ml/min chromatograph and (GC) passed column530 through (Supelco-Q-PLOT an column Agilent with Tech 6890N . . 47 vs [SA [SA et al 47 47 .WG] values [HG vs .WG]is 47 47 .WG]for vs = , 1318–1329 vs 8453‰ (i.e. . [HG 0 44 ,then 47 , [HG 47 .HG] [HG δ 47 vs 47 =− 2009 [SA However, subsequent .WG].Ifthesample K. W. Huntington 47 vs .WG] [3] 8453), where . versus vs 0 − 47 [HG / δ values, then [HG .WG]on 0 47 47 vs 47 δ (‘heated gas lines’) were essentially J. Mass. Spectrom. .WG] − . WG] must be estimated by linear [HG 47 vs vs 47 δ . .WG] [HG 47 [SA vs 47 Hence,itmaynotbeauniversalphenomenon. 47 versus δ ( [5] 47 [SA δ ). That is, the corrected × 47 [3] . values (Fig. 2(a–c)). 47 R et al = compressed between sample and standard gases. If so, then this artifact is the heated gas line intercept for the period during which 47 0 In principle, the best way to deal with isotopic ‘scrambling’ in If the sample and heated gas have the same In the months following our discovery of nonlinearity in .HG] .HG] thesourcewouldbetoopenthesulfurwindow,minimizing residence time inion the intensity dramatically source. degradesconclude However, measurement precision. that the We the resultingcompromise: best loss we practical of approach acceptisotopic to and scrambling this correct artifact in forcomes is exchange a with a for certain elevatedthat amount source the other pressure. of high instruments However,require precision or a it instrument that different is tuning approach –condition possible conditions one that obviously might resulted could in not soindistinguishable much accept in ‘scrambling’ a that all gases are the sample was analyzed. the intercept of the heated gasof line Ghosh used for the calibration study should be corrected for by multiplying the measured corresponding to stable over timein scales some of cases multiple changeor weeks subsequent replacing or to the months, tungsten cleaningfocusing but – filament the presumably can or source reflecting a changing and changeperformance the that in influences ion mass the spectrometer source nonlinearity betweenobserved actual and and heated gas differ in their regression of measured measurements, the intercepts of lines fitgases through in plots data of for heated invariant, even over large ranges in slope. vs vs It is not yet clearcomesfromtheperformanceofthedetectors,theresistorsthrough whether the ultimate cause ofwhich this ion nonlinearity currentssource are or measured analyzer. or Nevertheless,analysis some a of normalization component heated based of gasesstraightforward. on the over the a range of composition space is the time-period duringsupporting which information the for samplepropagation). details We find of that was the slope the of analyzed the empiricallyline regression determined (see for and heated error gases in a plot of WG] spectrometer, it differs inwith time the on any given three instrument, and machines,studiesusingMS-I. was not varies observed in gradually initial analyses have revealedintercepts of heated measurable gas lines secular (Fig. 2(d,e)).physical In cause variations order of this to phenomenon, establish in we the conducted experimentswhich in the we varied the residence time of gas inand the source by closing opening the sulfurin window. the This intercept produced of the athe hypothesis heated large that gas variation a line long (Fig. residencethe 2(f)), time source promotes or consistent fragmentation/recombination high reactions with gas that pressure‘scramble’ in isotopes among isotopologues, reducingin the contrast of unknowns by a factor that is proportionalheated to gas the line. intercept In of practice, the we scalethe all heated data gas to line, a taken fixed to be intercept of ∗ i O 47 47 vs. R δ O).) 18 and / i δ 2009 John Wiley & Sons, Ltd. 18 R δ [SA 45, 46, 48 c for the 47 + = 47 relative to i C 47 13 range is small. δ value must be 47 for heated gases values of natural the working gas Copyright 47 47 1000, a convenient 47 δ · is a small number, 1) values.Inaddition,the that working gas. (We versus 47 and values can be added and − 47 for the sample: 47 47 . WG]. (Note that WG values that can introduce ), and thus to ( 47 vs 47, 46 versus R 47 δ / . WG] values will be observed. is not a linear function of isotope R vs + [HG HG 47 1‰ range in 47 47, 45 ∼ δ R ( [HG values for observed masses ( values if it is not carefully documented 47 − values should be indistinguishable. Thus, ∗ i = 47 extracted from NBS-19 carbonate standard) R 47 2 / We observe linear correlations between the i R .WG] .WG] vs value very far from 0, but it is generally sound values measured [16,17] vs 47 47 [SA δ [HG 47 for the heated gas from 47 δ 47 , two different values (i.e. heating for two or more hours in a quartz values of heated gases measured are calculated analogously using Eqns (4) and (5).) This final 47 = values and the measured intensity ratio between the mass-47 to the working gas and a second that is substantially different δ Our solution to this problem is as follows: we establish However, the mass spectrometry itself involves a nonlinearity The process is repeated for the sample: after analyzing a sample 47 49 47 47 47 and their the observed relationship between measure of bulk composition. Because significant errors in and corrected. abundance, this is, strictlyapproximation, speaking, but a for convenient the but incorrect 47) as described above. From these, we compute values). the bulk(‘WG’) isotopic by conventional composition meansinterlaboratory of (i.e. standards). comparison Then, a with weas analyze recognized working a a heated sample, reference gas usingisotopic (‘HG’) composition WG gas of the as heated the gashad as standard. the if both stochastic We the distribution calculate HGalgorithms). and This (i.e. the assumption WG using will bulk introduce normal an errorgas ion if the has correction working a step makes the approximation that tube to drivecan their change composition their bulk to isotopic the compositions stochastic (primarily the distribution) HG] www.interscience.wiley.com/journal/jms values of 0; hence,the in two the measured absence of any measurement artifact, is approximately equal to ( values for the observed masses and compute the reference gas that hasand both a a known known bulk state isotopic of composition ordering (i.e. its own for common natural materials (i.e.materials anything that other are than mixtures synthetic ofor exceptionally depleted compounds) isotopically because the enriched observed That is, if oneδ analyzes two heated gases, one closely similar in materials it adds no significant errors. between measured and real Note that the workingmeasurements, and reference all gas heated gases is have the nominal same absolute in these two independently known). This is challengingreference because the materials common onecomposition (e.g. can CO use to establish a sample’s bulk sample using Eqn (3). Finally,enrichment in we excess calculate of the the stochastic sample’sthe distribution mass-47 by subtracting define the working gas for the HG using Eqn (3). (‘SA’) using thebulk working isotopic gas composition as of theand WG the standard, had sample we the as stochastic calculate distribution. if the We both then the calculate sample subtracted linearly. Because in and mass-44 ion beams.in Although heated we gas observe measurements this for nonlinearity MS-I, MS-II and the Yale mass We then calculate reflects a subtle nonlinearityR in the relationship between actual procedure we use to create heated gases with nominally known do not have independently known

1322 1323 ll o ated from –are 320 s, 2 or each 2 ∼ measurements. mol CO 0 µ 47 )fromfourdistinct n measurements are 47 measurements is at the 47 value stabilizes by 21–30 V. These observations 47 signals over periods in excess ∼ V 44 signal of ) - 0.84 8 mg of carbonate or 50 V ) - 0.77 47 ∼ [HG vs. WG] (‰) [HG vs. WG] (‰) [HG vs. WG] (‰) www.interscience.wiley.com/journal/jms 44 δ 47 5 5 δ 47 47 47 δ δ δ signal heated gas observations ( V 44 eriods and mass spectrometer configurations. (a–d) The sulfur window open sulfur window closed = 0.0081( = 0.0072( 47 measurements. 47 3/19/2007 - 5/25/2007 (n=28) 3/19/2007 - 5/25/2007 ∆ l error bars represent 2 s.e. uncertainty in 2/26/2008 - 5/21/2008 (n=29) ∆ 47 measurements (Fig. s2). Isotope ratio observations for -5 0 10 15 20 25 -50 10152025 -50 -40 -30 -20 -10 47 signal, the running average

-0.7 -0.8 -0.9 -1.0 -1.1 -1.2 -1.3 -0.4 -0.6 -0.8 -1.0 -0.4 -0.6 -0.8 -1.0

Our conclusion that precisions of

47 [HG vs. WG] (‰) WG] vs. [HG 47 47 [HG vs. WG] (‰) WG] vs. [HG 47 47 [HG vs. WG] (‰) WG] vs. [HG 47 V ∆ ∆ ∆ suggest that signals safely below16 V, this corresponding threshold to – approximately of 320 s (preferably 480–7208 s s, cycles or each), but six does totimes not greater nine continue than to acquisitions approximately improve 1500 of for s. integration ten 44 primarily dominated by counting statistics applies to CO optimal for this instrument. For ion-current integrations of a 16 V but clearly drifts after approximately 1500 s,of or 18–19 ten acquisitions 8 soptimized cycles by each. integrating 16 We V infer that on MS-I, precision can be MS-II (700 s integration time, four acquisitionseach) of indicate seven 25 that s cycles the precision in shot-noise limit and improves with increased signal size.the However, MS-I data indicate that errorsomewhere between climbs a after crossing a threshold fractionation of samplechanges and/or in standard condition gas ofthe reservoirs the mass and/or spectrometer on accuracy of (d) (b) (f) l. (e) Best-fit lines and 95% confidence intervals (a–d) are superimposed t gas line is shown for different configurations of the sulfur window. The sma (b) and (c) have approximately the same intercept but different slopes. He V 44 b 2009 John Wiley & Sons, Ltd. c 005‰) . c 0 ± . WG] is approximately linear for 16 V a vs signal and ion- measurements V [HG 47 44 47 s are individual analyses, and the vertica conducted using MS-I and ) - 0.82 ) - 0.84 .WG]and [HG vs. WG] (‰) [HG vs. WG] (‰) [HG vs. WG] (‰) 47 47 . WG] (‘heated gas lines’) are shown for different time-p 47 5 5 5 δ δ vs 47 47 47 vs δ δ δ [HG [HG d 47 47 δ = 0.0128( = 0.0064( 47 , 1318–1329 Copyright 47 5/25/2007 - 7/4/2007 (n=17) ∆ 1/01/2007 - 3/18/2007 (n=29) 1/01/2007 - ∆ signals between approximately 4 and 32 V 44 , V -50 10152025 -50 10152025 precision at the shot-noise limit (Fig. s2 in the -50 10152025 44 47 .WG]and

-0.4 -0.6 -0.8 -1.0 -0.7 -0.9 -0.4 -0.6 -0.8 -1.0 -0.5 -0.6 -0.8 -1.0 2009

vs

47 [HG vs. WG] (‰) WG] vs. [HG 47 47 [HG vs. WG] (‰) WG] vs. [HG 47 47 [HG vs. WG] (‰) WG] vs. [HG 47 ∆ ∆ ∆ (c) (e) (a) [HG 47 δ We integrated ion currents for up to 3200 s for gas loads ‘Clumped’ isotopes signal). For typical measurement protocol (16 V can reach levels asfor low long as 5 ion-current parts integration24 per times h million (3200 of s, (ppm) mass or ( spectrometer approximately time) and large gas loads (16 V MS-II (in continuous use since 2003predictions and for 2008, respectively) to the time intervals in 2007 and 2008. The small circle circles are individual analyses, and the vertical error bars represent 2 s.e. uncertainty in The horizontal error bars are of the same magnitude as the vertical error bars. The solid lines representgas the line least-squares (d) linear has regression of a data significantly f different intercept. (f) The mass-47 heated time-period, and the shaded gray regionhighlight indicates temporal the 95% variations confidence in interva the heated gas line. Heated gas lines (a), J. Mass. Spectrom. Internal precision We compared measurements of Precision and Stability in Isotope Ratio Measurements Figure 2. current integration times ofnine 480–720 acquisitions and s, approximately corresponding 2–4time), to h the of six shot-noise mass limit to to spectrometer precision is 0.013–0.016‰. corresponding to supporting information). The observed precision for thespectrometers two approaches mass the shot-noisein limit. particular, Results for indicate MS-I, that the precision of to examine the effect of sample size and of time-dependent empirical relationship between . 2 ∗ is O 47, 47 . 18 R 47 0 et al δ com- / 47 47 =− R measure- α , 1318–1329 47 44 , Cforbothsample 2009 13 C that may be due to δ 13 K. W. Huntington δ Oand Oand 18 from some carbonate samples δ 18 2 -0.47 δ over40IRMSacquisitions.Apower–law J. Mass. Spectrom. in this regime. 47 47 (x)=0.029x 2 C), well in excess of the limits imposed by σ 13 δ C in the same gases (Fig. s4) reveals that standard 13 gas made by acid digestion of carbonates. In addition, δ 2 1 10 100 number of IRMS acquisitions (80 s counting time each) number of IRMS acquisitions 015‰,inagreementwiththestandarddeviationofrepli- . Allanvarianceplotof 0.1 0 0.01

0.001

± Oand

measurements is to determine the reproducibility (standard ) Allan variance ( variance Allan is approximately twice the average standard error we observe

σ 18 2 δ We suspect that sample heterogeneity causes the failure of 47 47 019 . cate analyses for the NBS-19 carbonatein standard the (0.022‰; supporting Fig. information). s4 The average external precision in indicating that Poissonuncertainties in the statistics, average not long-term drifts, dominate the many carbonate materials to achieve reproducibility in due to some combination of sampleartifacts heterogeneity such and as analytical uncontrolled fractionations or contaminants. deviation) of independentcompiled analyses the of standard deviations the92 in externally same replicated isotope samples material. measurements (2–11on We for MS-I replicates each) and analyzed found that the average external precision in ments for samples that are heterogeneous in isotopic composition and 0.0007‰ for parable with counting statistics. An examination of measurements of deviations for replicate analyses of unknowns and the NBS-19larger standard than are the an average order standard error of we magnitude observe for each CO gas made by acid digestion of carbonates (0.0014‰ for values. Although this reduces the reproducibility of External Precision and Error Propagation Carbonate standards and sample unknowns The most straightforward way to quantify external precision in Figure 3. greater than nine acquisitions contributingcalculation. to More the precise Allan values variance ofnumbers of the acquisitions would Allan require variance a more with sustainedrun analytical these by several factorsthat in should time. be attainable Nevertheless,that on the are a ideal clearly single precision dominated gas byor run 720 statistical for s noise counting measurements time) (nine at acquisitions, the optimal voltage (16 V) is 0.013‰. regression is shown over the first nine acquisitions showing the standard deviationwider range for than does replicate the standardsuggests error extractions that for each substantial varies extraction. variance This beyond overbe counting added statistics a to can measurements of CO for each CO counting statistics. Small errors in sample heterogeneity lead to small changes in calculated 0 , in 47 (8) α 2009 John Wiley & Sons, Ltd. ] will Care ]) and 6 Cx 6 c 13 x x δ , = , 5 5 x 2 0. For our x , σ 4 ], [ ≈ x 2 : 4 Oand  ,istaken.The Cvarystrongly , x x i i 3 83), which is not   , 18 13 . Copyright x dx 3 x x δ δ  x , 2 α/ appears to increase x − ], [ d 2 , 2 78–0 1 . x 1 + σ i , x 0 5, reflecting the Poisson Oand  . 1 x x 0 generated by phosphoric = 18   δ r 2 [22] bin size, then, conveniently ) of 0.26–0.29 for NBS-19 and 5. Consequently, the optimum i r . =− inated by long-term, correlated  0 α 003‰) is in agreement with the = 1) ]), two ([ . ,both ]) elements each. The maximum bin 6 0 6 α x 47 − bins (each consisting of one or more versus 1 x Allan variance for a relatively long- , ± N N ], [ 5 5 Instead of using time as the independent x 2( x 47 , C measurements of sample unknowns is 4 009 . [23] x ], [ = 13 4 C for the standard and sample datasets, with ) δ x x 13 ( δ ], [ measurements is poorly correlated with precision 10 acquisitions, with only a small contribution 3 ]and[ x 2 Allan 3 47 x σ < Oand ], [ , Oor 2 2 18 x N x 18 δ , δ 1 ], [ x 1 x from the NBS-19 carbonate standard and 172 analyses of measurement (0 2 Plotting Allan variance 47 lower end of the shot-noisenineacquisitions(0.013–0.018‰).Theaverageobservedstandard limit predicted for analyseserrors of in six to surprising because unlike acquisitions), and the average of each bin, statistics governing theIn precision contrast, of a measurement therandom-walk dom overall drifts will have measurement. number of measurements to average together(i.e. in a the given analysis optimumvariance bin reaches a size) minimum, will i.e. occur where near where the Allan of either variable, here we use individual IRMS acquisitions although lower-precision outliers up to 0.005‰ exist.precision The in internal highly correlated with one another ( roughly an order of magnitude better than that observed for Data are first binned into presents both noise-An and example drift-related of effects the on single plot. size is therefore half the total number of elements in a data set. acid digestion of carbonates. We(i.e. compiled standard the error) internal precision ofCO isotopic measurements for 21 analyses of 0.07–0.09 for the samples. Internal precision in Pearson’s correlation coefficients ( www.interscience.wiley.com/journal/jms Long-term signal stability As long-term driftsin can also addition affectaccuracy measurement to of precision shot our (i.e. Allan IRMS noise), system variance we by technique,ultrastable using oscillators. originally examined a developed modified the to form stability characterize of the and a variety of sources, including CO with mass-dependent fractionation. different aliquots ofperformed 63 under typical different conditions from carbonatethe 2004 supporting sample to information). 2008 unknowns The (Fig. average s3 standard in error for each three ([ for measurements madealthough in we excess attribute of this nine to acquisitions the (Fig. 3), smaller number of bins with produce three values ofone Allan ([ variance corresponding to bins of duration analysis, consistingintegration of each (ten 40 8 acquisitions s(these cycles), of made are on 80 s MS-I the isstatistical-noise-limited sample shown same measurement, in for data Fig. which 3 long-termare depicted drifts negligible, will in display a Fig. power–law s2(b–d)). relationship An ideal difference between adjacent binsbefore is squared being and normalized thenexample, summed to a data compute set the with Allan six elements variance. [ For the Allan variance plot, where instrument, measurements seem tonoise be for dominated by statistical from long-term drift. The variability of

1324 1325 te 47 47 δ ach es how .WG]for vs extraction 2 [SA 47 δ found that mass-48 and and exhibit no obvious [5] 3/19/07 - 5/25/07 . HG] values for all six analyses are [25] . vs 3/26/07 - 7/4/07 . HG] value within uncertainty vs et al [SA ge of dates. The dashed arrows illustra 47 . WG] is plotted against [SA vs 47 www.interscience.wiley.com/journal/jms [SA value. Thus, reproducibility of their ed gas normalization factor for three analyses of 47 47 [HG vs. WG] (‰) 48 [HG vs. WG] (‰) 47 δ δ 1/01/07 - 3/18/07 . WG] results for independent analyses of 95123 and and Huntington vs . WG] measurements of unknown samples to a common sp. 95124) were analyzed previously by Spencer and 0 20406080 [24] [SA 11 12 13 14 15 16 vs 0 5 47 25 20 15 10 ature. (d) Mass-48 measurements (crosses) for the three heated gas measurements of each sample incorporate uncertainties in

[SA -0.60 -0.65 -0.70 -0.75 -0.80

Figure 4 illustrates the use of heated gas data to normalize

48 [HG vs. WG] (‰) WG] vs. [HG 48 47 47 (‰) WG] vs. [HG 47

∆ ∆ . WG] from (a) for each analysis is found using the heated gas line for the s.e. error bars) and sample 95I24 (black circles with 2 s.e. error bars). E reference frame and to screen for contaminants. Divergent 95124 carried out during the three different time-periods (Fig.collapse 4(a)) to the same and purificationidentical procedures. temperature conditions The duringhave growth two the and burial samples same and experienced (0.003–0.006‰, 1 s.e.)applied (Fig. after 4(b,c)). Eiler the and Schauble heated gas normalization is of thetwo stochastic biogenic reference carbonateanomia frame samples is (oysterPatchett put 95123 to and the bivalve test. The evidence of sample heterogeneity or contamination. Replicate measurements also should reflect any noise introducedpreparation by sample (cleaning, sampling and powdering). and the heated gas referenceartifacts frame introduced (Fig. by 2), carbonate and acid potential digestion, analytical CO (b) (d) re labeled with the appropriate ran vs [SA emperature calibration line shown in Fig. 1(a). The dashed arrow illustrat 47 47 δ 2009 John Wiley & Sons, Ltd. c 005‰. . expected for clean samples. The samples do not deviate significantly from the best-fit 0 samples), suggesting that the samples are free of , and sulfur 95I23 95I24 (Eqn (3)). 48 ≤ 2 ∗ 45 signal. (b) Heated gas normalization for 95I23 and 95I24 measurements made over a 5-month R / V and 44 45 (K) 48 R δ -2 med. The white and black squares indicate the heat T C because changes in 6 and 13 ∗ 10 δ 46 R / 010‰, and 23 are d47 [SA vs. WG] (‰) . 46 c) After the heated gas normalization from (b) is applied (see text), the 0 R Oand ≤ 18 extracted from chemically pure (i.e. δ 2 91011 11 12 13 14 15 16 , 1318–1329 Copyright . WG] value corresponding to the value of in CO 0.7 0.6 0.5 0.4 0.8 44 vs

, 0.00

-0.05 -0.10 -0.15 -0.20 -0.25

47

47 [SA vs. HG] (‰) HG] vs. [SA 47 47 [SA vs. WG] (‰) WG] vs. [SA 47 ∆ ∆ [HG values are projected onto the calibration line to calculate temper (c) (a) 47 2009 47 are offset by changes in Isotope ratio and clumped-isotope thermometry results for two biogenic carbonates. (a) ∗ 47 for replicate extractions of R / Nevertheless, a large number of samples exhibit standard de- 47 47 ‘Clumped’ isotopes These well-replicated samples are nearlywould twice occur as by prevalent random than 0.019‰(the chance average if for the the entire true population).measurements We analytical of conclude error that were viations for replicate analyses ofthan unknowns that the are average muchcounting better and statistics: 49 comparable of 92 with samples exhibit standard the deviations in limits imposed by analysis represents 720 s of integration time of a 16 V three independent acid digestions each of sample 95I23 (white circles with 2 heated gas mass-48 lines (composed of results for clean CO A detailed example of analytical reproducibilitynatural samples for unknown We examined replicate analyses ofover a suite a of relatively samples performed long interval of time such that the stability free or organic matter, sulfides andgases) homogeneous other carbonates sources have of errors contaminant controlled bying count- statistics and not significantly degraded by analytical artifacts. contamination. The symbols are larger than the uncertainties. period. The heated gas lines for each time-period are taken from Fig. 2, and a R J. Mass. Spectrom. Figure 4. is smaller than variability in or otherwise affected by analytical artifacts, the variability in lines shown in (b) define the relationship between time-period during which the analysissample 95I23 was and perfor 95I24, respectively. ( indistinguishable. The black line represents a zoomed-in portion of the t how the best-fit the measured . 47 [27] 47 6 0 6 C) . . . ◦ et al ( 1seT Cand 010‰ ◦ . 0 5 21 42 91 . . . . C) T ± 2 ◦ ( , 1318–1329 ± T) estimates 44 , 0 -factor (1.6). . C (Fig. 4(b)), on 47 b t ◦ 3 . (‰) 2009 3 1se K. W. Huntington C(typical ± ◦ 0 47 a . 0029 40 0056 40 0033 39 . . . (‰) 1se ), the temperature uncertainty from Fig. 4(a)), the temperature 47 47 47 584 0 583 0 585 0 . . . actualcontributionstotemperature 1‰ precision – in the abundance of (‰) J. Mass. Spectrom. . 0 < )wouldbe10 B T 47,HG (‰) 0.764 0.577 0.0083 0.0103 0.755 0.579 0.0078 0.0101 0.742 0.594 0.0082 0.0095 0.730 0.590 0.0082 0.0097 0.661 0.579 0.0085 0.0095 0.643 0.587 0.0079 0.0091 C can be achieved, depending primarily on [1,16,28,29] − ◦ we note that given the large number of − − − − − − A T ), the uncertainty in absolute temperature [3] 47 = T precision is slightly worse than the precision of T 47,sample 005‰ precision in (‰) C, respectively (1 s.e. in temperature for typical samples . δ . ◦ 0 B C (1 s.e.). If three replicateC measurements (1 s.e.). are Taking made advantage of the large number of 010‰ precision in Sample average: 0 Sample average: 0 2 . ◦ ◦ ± . 1se (Fig. 6(a); supporting information). For a single analysis 0 2 2 4 Formation average: 0 . . ± 47 2 1 ± and T 0 ∼ ± Precision in absolute temperature estimates varies as a function The precision of temperature difference ( . A of both the temperature of carbonate growthin and the uncertainty precision in of a carbonate sample grown at 20 additional data in agreementhavebeengenerated, with the original calibration that uncertainty from this calibration are likely to be very small. is limited by the precision of the least-precise sample (typical isotope ratio measurementsfor each (in analysis), ouron we temperature case, can estimates at calculate bythemean(1s.e.)givenbyFig.6(a)byStudent’s multiplying least the the 95% 90 standard confidence error cycles limit of absolute temperatures, but the error is relativelymagnitude insensitive of to the the temperature difference Fig. 4(b). Discussion Our analysis confirms thatvariations it – routinely is with possible to measure very subtle Althoughweformallypropagateuncertaintiesusing thepublished calibration data, measurement and thedependence) precision of of the thetemperature calibration slope estimates for data (i.e. samples (Fig. temperature A 6(b)). and B If are 30 the absolute extremely rare species for clumped-isotope analysis usingtechnology existing (Fig. s4). For clumped-isotopetry, carbonate precision of thermome- 1–2 with is difference ( the order of theT root of the sum of the squared uncertainties in 20 is the integration time of the analysis, and secondarily on theof number calibration data taken into consideration. These isotopologue (‰) 47,sample δ d in the supporting information. Note that the heated gas normalization 48 - 2009 John Wiley & Sons, Ltd. .WG] .WG], 48 c vs 47,sample δ vs (‰) ndependent measurements used to define the best-fit line (Fig. 2) ,andGuo 2 [SA 1se 48 [HG 48 values for 95I23 Copyright 47 (‰) 0.187 0.0081 12.4820.176 0.0081 0.0075 13.949 0.0076 0.147 0.0081 12.5520.140 0.0082 0.0081 14.020 0.0079 0.082 0.0083 12.6870.056 0.0083 0.0077 14.086 0.0078 47,sample ). However, we have is 0.0227‰ (1 s.e.) at − − − − − − − 47 O ; although contaminants 2 16 S 32 SMOW 003‰, and the external error is O . 0 18 water (‰) ± 585 . PDB C 1.86 1.041 1.00 1.474 1.86 0.396 1.01 0.811 1.84 0.872 0.98 1.499 13 − − − − − − δ carb(‰) O values differ (Table 1), 18 δ do not show this sensitivity to bellows pressure, . HG] results of all six analyses converge by vs 006‰ and 0 found evidence that sulfur-bearing contaminants 48 . 0 Summary of carbon and oxygen isotopic data for two biogenic carbonate samples shown in Figs. s4 and 4. Heated gas-normalized ± [26] [SA 47 and 583 . values for three independent analyses each of 95I23 and 95I24 is 0.0046‰, after integrating data for all three extractions (i.e. a 48 Including uncertainty from heated gas normalitation. Without uncertainty from heated gas normalitation. δ Although their 47 47 Sample 95I24 7/2/07 7/2/07 3/22/07 3/24/07 a b 2/12/07 Sample 95I23 2/12/07 contributes little uncertainty because of the large number of i Date (month/date/year) Table 1. values are reported with uncertainties propagated formally as describe 0.0039‰ if results from both samples (six analyses) are combined. and 95I24 are indistinguishable. Given thesamples, shared we history conclude of that these these sixof analyses reflect measurements a population oftemperature of samples last thatinto equilibration, were and the thus indistinguishableThe internal provide in a and window external precision of the technique. thelevelofasingleacquisition(80 sintegrationtime)and0.0088‰for each analysis (i.e. summing over all acquisitionsfor run on a that total gas, integration time of 720 s). Average external precision in this would provide evidence for impurities thatterferences lead within to the isobaric mass in- range of CO total integration time of 2160 s per sample). The weighted average can also lead to(presumably substantial from interferences species on such masses as 48 and 49 approximately 40 cyclestime), or four and acquisitions precision(Fig. (320 5). approximately s Average integration follows observed precision counting in statistics for any analysis were significantly higher than and Eiler www.interscience.wiley.com/journal/jms systematics and those exhibited byin pure Fig. heated 4(d), gases. the As mass-48 shown signalsrange for of all measured six analyses heated plotthe gas samples within are the mass-48 free of values, recognized contaminants. If suggesting that mass-49 signals can behydrocarbons and sensitive chlorocarbons in indicators spiked analyte of CO the presence of are 0 suggesting that mass-48indicators measurements of contaminant are species; i.e. we mosttaminated can samples identify appropriate clearly by con- noting differences between their clearly could interfere with masssuch evidence 48 diminishes but the not reliability of 47, a we measurement. suggest that observed a strong correlationpressure between imbalance between mass-49 the signals bellows that and regulate theand the sample working gas flow intoof the mass spectrometer source. Values

1326 1327 12 yses for sample 95I23 are shown in black, and www.interscience.wiley.com/journal/jms t here the results are binned by acquisition (ten cycle number. Inset table shows the average standard n versus Encouragingly, our analysis indicates reasonable stability and The most important limitation of current mass spectrometer resistor (Figs. s1,can 3). integrate One small consequence ion of currents stability over is very that long we time-periods linearity at levelsinterest of collected in thousandths a of Faraday per cup registered mil through of a 10 ion beams of technology is the trade-offanalyte gas between and ion the occurrence yieldreactions of per fragmentation/recombination in molecule of theexperiments (Fig. source, 2(f)) or illustratewhich a that ‘scrambling.’ dynamically while pumped Ourcan source the sulfur be ionizes efficiency analyte window improvedpressure with molecules by increases increasing scrambling.measured the proportion As of gas scramblingtoward isotopologues pressure, influences the by increased driving the stochasticsource design the distribution, fundamentally analyte limits thebe the produced number and dynamically of counted in ions a pumped that given time can interval. a means to screenisotopologue for signal of certain interest. contaminants that may affect the 8s cycles 8s cycles 2009 John Wiley & Sons, Ltd. c acquisitions (10 x 8s cycles) 123456789 levelacquisitionanalysissample 0.0717unit 10 8s cycles avg. s.d. 0.0227 0.0264 9 acqs. 0.0080 3 analyses 0.0095 0.0046 0.0088 2 samples avg. s.e. 0.0039 10 30 50 70 90 10 30 50 70 90 s (three per sample) for the two biogenic carbonate samples shown in Fig. 4. (a) The lines show thenumberof8scyclesaveraged.Thethreeanal ay. (b) The running average is shown as in (a), bu 95I24_1 95I24_3 95I23_3 95I24_2 95I23_1 95I23_2 versus )in‰,foreachlevelofanalysisofthetwosamples. 95I23_3 95I24_1 95I23_1 95I24_3 95I23_2 measurements. Poor mass 95I24_2 95I23_2 95I23_1 95I23_3 95I24_2 95I24_3 95I24_1 47

0.20 0.15 0.10 0.05 0.00 0.65 0.60 0.55 0.50 0.45 0.65 0.60 0.55 0.50 0.45

47 47 47

[SA vs. HG] running average running HG] vs. [SA [SA vs. HG] running average running HG] vs. [SA s.e. s.e. [SA vs. HG] vs. [SA ∆ ∆ ∆ . HG] plotted (c) (a) (b) . HG] measurements for the analysis shown in (a) and (b) vs vs analysis of relatively pure, apparently ho- [SA , 1318–1329 Copyright [SA 47 47 44 47 , 2009 Summarized results for six independent analyse Poor mass resolution is an outstanding limitation of the ‘Clumped’ isotopes the running average of J. Mass. Spectrom. measurements approach the shot-noise limit of precisionindicating (Fig. that s2), further improvements will require additional meth- ods and/or instrument developmentof that analyzed increase ion the beams intensity ses or of each extend sample. the Although our practicalexternal data precision for period compilation indicates of that analy- Figure 5. deviation (avg. s.d.) and standard error (avg. s.e. mogeneous carbonates follows counting statistics to thelevel, 0.005‰ many other materials fail tocision. reach In this some level cases, of we externalinhomogeneity, pre- can whereas in attribute other poor cases the precision cause to is sample not obvious. mass spectrometers we usedpossible that contaminants limits or our otherfor ability poor artifacts external to reproducibility that in examine may be to blame resolution results in an inability toences resolve that molecular may ion interfer- haveabundances. a large Nevertheless, impact it onmass-48 anomalies appears apparent with those isotopologue that of clean heated comparing gases may sample provide the three analyses for sample8 s 95I24 cycles). are (c) shown 1 in s.e. of gr . 2 et al resistor , 1318–1329 12 44 , Earth and Planetary remains at the limit 2009 0‰ reference frame 47 K. W. Huntington = 47 ), lower current ion counting, 3 ochemistry-The study of naturally- 10 ∼ J. Mass. Spectrom. m , 309. / 262 0‰) are used to correct for (1) subtle m , extracted from a carbonate standard such as ≡ 2 molecules in the source or capillaries. measurements. For relatively pure, apparently 2007 2 47 47 molecules (‘scrambling’), linearity, stability of ionization 2 Science Letters occurring multiply-substituted isotopologues. [1] J. M. Eiler. ‘‘Clumped-isotope’’ ge Measurable improvements in the precision of isotopologue analyses may be possibleopments. with Incremental instrument advances and ininclude methods method increasing devel- development the could through ion which current the by ionextraction efficiency. reducing We beams are not are the optimistic about registered thegas resistance use or of introduction carrier improving because the lyte its CO effects on exchange among ana- and extraction efficiency are unknown.sion would Major require advances substantial in hardware development preci- higher to mass achieve resolution ( homogeneous carbonates, precision followsand further counting improvement statistics, would require hardwareTo the modifications. best of our knowledge, ourexamination study provides of the first the detailed stabilityconsisting of and a linearity Faraday of cup registered a through counting a system 10 nonlinearity in the47/44 relationship ratios between and (2) actual scaleamong compression and analyte due CO measured to isotopic exchange an improved ion-countingvacuum system, system or and source potentially design.realized, Until an subtenth of such a improved improvements per are mil precision in at levels ofresponse thousandths of this of systemanalyses, per to but be mil. sufficient careful We forsubtle standardization precise nonlinearity. find is quantitative We required the outline a to stability method correct of by for which heated CO of mass spectrometer measurements. Acknowledgements This work wasand supported by the by Division the ofDavidow Geological National and Fund Planetary Science Sciences at and Foundation the thanks the the California Earth Institute System CenterYale of for Institute Technology. Stable for Isotope Biospheric H.P.A. Studies Studies.Hayes The of and authors the an also anonymous thank reviewer John improved for this article. insightful comments that Supporting information Supporting information may be found in thearticle. online version of this due to isotopic ‘scrambling’recommend analyzing in a the heated source) gasare analyzed each as and CO day it sample is unknowns elegant. We References Summary and Outlook Our data compilation indicates that use of a253 Thermo-Finnigan MAT dual-inlet gas-source IRMS routinelymil yields precision in subtenth of a per gases with a stochastic distribution of isotopesisotopologues among all ( possible NBS-19 occasionally to establish the precisely and monitor possible changes in machine conditions. 47 R 2009 John Wiley & Sons, Ltd. value), c 01‰, the . C 0 ,theformal ° T ∼ measurement σ VSMOW 47 O C, regardless of the C. (b) The contours 18 Copyright ◦ ◦ δ 3 C, as a function of tem- ◦ ∼ T (estimated around an Cis ◦ of 0‰ means a stochastic C) ° 47 T ( measurements. For C), around mean T of 20 ° 47 measurement precision of .(a)Thecontoursrepresent 47 47 5 C, as a function of temperature and standard error ◦ T difference ( T around an average of 20 01‰, the standard error in T is 2–3 . C) in , the formal standard error in ◦ 0 T ∼ 0 1020304050 0101520 σ Formal error in temperature estimates and temperature differ- T) deduced from measurements. For

0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000

47

standard error of of error standard 47 measurement (‰) measurement 47 standard error of of error standard 47 measurement (‰) measurement 47 ∆ ∆ Perhaps most importantly, our examples highlight the (a) (b) standard error in average of 20 distribution. The useas of critical such for annonlinearity practical ‘absolute’ considerations observed (i.e. reference in removing frame the the is relationship subtle between actual of perature and standard error of www.interscience.wiley.com/journal/jms values and theand measured 44 intensity ion beams ratio and removing between the effects the of mass-47 scale compression to improve precisionprecision (Fig. 3). with However, time diminishingisotopologue returns and measurement on the maysuggest that possibility eventually very long decrease that counting times (inbe (Fig. the excess advantageous. of s2) 720 accuracy Instead, s) may machine of not on time analysis would of be independently spentexternal better prepared precision to replicates, be which characterized. enable dependence of precisegas clumped-isotope reference analysis frame. onare Unlike a referenced standard heated to isotopic an analyses, arbitrary value which (i.e. the Figure 6. ences ( precision of the heated gasphysical reference meaning – for by definition clumped isotopes has a unique standard error in absolute temperature estimates in represent magnitude of the temperature difference.

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