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1318 ResearchArticle Received:20January2009Accepted:4June2009PublishedonlineinWileyInterscience:20July2009(www.interscience.com)DOI10.1002/jms.1614Methodsandlimitationsof‘clumped’COisotope()analysisbygas-sourceisotoperatiomassspectrometryK.W.Huntington,J.M.Eiler,H.P.Affek,W.Guo,M.Bonifacie,L.Y.Yeung,N.Thiagarajan,B.Passey, Thegeochemistryofmultiplysubstitutedisotopologues(‘clumped-isotope’geochemistry)examinestheabundancesinnaturalmaterialsofmolecules,formulaunitsormoietiesthatcontainmorethanonerareisotope(e.g.).Suchspeciesformthebasisofcarbonateclumped-isotopethermometryandundergodistinctivefractionations Correspondenceto:K.W.Huntington,DepartmentofEarthandSpaceSciences,UniversityofWashington,Seattle,WA98195,USA.E-mail:kate1@u.washington.eduDepartmentofEarthandSpaceSciences,UniversityofWashington,Seattle,WA98195,USADivisionofGeologicalandPlanetarySciences,CaliforniaInstituteofTechnology,Pasadena,CA,91125,USADepartmentofGeologyandGeophysics,YaleUniversity,NewHaven,CT,06520,GeophysicalLaboratory,CarnegieInstitutionofWashington,Washington,DC,20015,USA J.Mass.Spectrom.,1318–1329Copyright2009JohnWiley&Sons,Ltd. 1319 ‘Clumped’isotopes [6,9]butthisistherstarticletopresentdetaileddataandargumentsregardingthetheoreticalandpracticallimitsofpreci-sion,methodsofstandardization,instrumentlinearityandrelatedanalyticalissues.Wearemotivatedbythreegoals:todocumentthemethodsofanalysisofmultiplysubstitutedisotopologuesingreaterdetailthanistypicallypossibleinanappliedpaper;toguideotherswhomightattemptmeasurementsofthiskind;andtoilluminatethelessonsthesemethodsmightprovideforanalogousattemptsatexceptionallypreciseorsensitivemassspectrometricmeasurements.Althoughmanydetailsofthisarticleareofinterestonlytootherworkersattemptingcarbonatethermometry,thedatawepresentprovideamoregeneraldemonstrationofclumped-isotopegeochemistry,andthuswillguidefutureappliedusesofmultiplysubstitutedisotopologues.MassSpectrometryofMultiplySubstitutedTheabilitytoperformhigh-precisionanalysesofmolecularions(e.g.COorO)iscriticalforclumped-isotopegeochem-istry.Clumped-isotopegeochemistryprovidesuniqueconstraintsonlywhenonecandeterminehowagivenpopulationofrareisotopesisdistributedamongmolecularspecies;anyanalysisthatdisproportionatestheanalyteintoitsconstituentatomswilldestroythatinformation.Assumingitispossibletoavoidfragmentationoftheanalyte,analysesofnaturallyoccurringmul-tiplysubstitutedisotopologuesfacetwoadditionalhurdles:First,suchspeciestypicallyconstituteonly10to10ofthecom-poundofinterest,andinsomecases10orless.Thismakestheclumpedisotopicspecieseasilytherarestanalyticaltargetsconsideredbystableisotopegeochemistry.Furthermore,manyoftheprocessesofgreatestinterestproducerelativelysubtleisotopicvariations.Forexample,theexcessrelativetoastochas-ticdistributionofObondsincarbonatesislessthan1‰atroomtemperatureequilibriumandvariesbyonlyperdegreefrom0Cto50C.Therefore,onemustanalyzeabun-danceanomaliesofmultiplysubstitutedisotopologueswithpre-cisionsof10(thousandthsofpermil),rivalingthebestthathaveeverbeenachievedforanymassspectrometricmeasurement.Todate,allusefullyprecisemeasurementsofmultiplysubsti-tutedisotopologuesinnaturalmaterialshavebeenmadeusingaThermo-Finnigan253gas-sourceIRMS.Suchinstrumentsarewellsuitedtothetask,astheytypicallyanalyzemolecularionsandareequippedwithanarrayofFaradaydetectors,whichpermitsrelativelystablemulticollectionmeasurements.Introductionofsamplesusingadual-inletandchange-overvalveallowsrapid,repeatedintercomparisonsofasamplegaswithastandardgasofnominallyknownisotopiccomposition,whichenablesonetocorrectformostinstrumentalbiasesandiskeytoachievingsubtenthofpermilprecision.Additionally,suchinstrumentshavemassresolvingpowers(200)andabundancesensitivitiessufcienttoseparatecleanlytherelativelyweakbeamsofmanymultiplysubstitutedionsfromthemuchstrongerbeamsforisotopicallynormalandsinglysubstitutedions.However,severalissuespotentiallyaffectmeasurementsofmul-tiplysubstitutedisotopologuesusinggas-sourceIRMSsystems.First,themassresolutionisinsufcienttoresolvethemanyinter-ferencesthatoneencounterswhenanalyzingmolecularions.Thisisaparticularconcernforclumped-isotopemeasurements,whereevenappb-levelcontaminantthatcontributestoananalyzedionbeam(e.g.ClonO)canleadtosignicantapparentchangesinisotopiccomposition.Inaddition,thedynamicallypumpedelectronbombardmentsourcesusedinsuchinstru-mentstypicallyyieldonlyoneionperseveralhundredormoreanalytemolecules,makingitdifculttoachievethedesiredlowcounting-statisticserrorsforanalysesofrareisotopicspecies.Asaconsequence,weusecountingsystemsconsistingofaFaradaycupregisteredthrougha10resistortomeasureionbeamsofmultiplysubstitutedisotopologues.Thesehavebeenusedfortheanalysisofhydrogendeuterium(HD)buthavenotbeenshownpreviouslytobesuitableforanalysesthatdemandsubtenthpermilprecision.Finally,electronbombardmentsourcesfragmentanalytemoleculesandsomeproportionofthosefragmentsrecombinestocontributetothepopulationofdetectedions,whichmayinuencethemeasuredproportionofisotopologues.MultiplysubstitutedisotopologuesofCOClumped-isotopeanalysisusesvaluesoftodenotetheexcessofisotopologuerelativetotheamountexpectedforthestochasticdistributionofisotopesamongisotopologuesofamolecule.Forthestochasticdistribution,theabundanceofanisotopologueistheproductoftheabundancesoftheisotopesitcontains(e.g.[[13C][[16O],wheretherandomdistribution,and2isasymmetrynumberumber).Thedenesthedifferenceinabundancesintermsofpermildeviationfromthestochasticdistribution: 1000(1)istheabundanceratiooftheisotopologueofinterestrelativetotheisotopicallynormalisotopologue,andisthatratioinapoolofmoleculeshavingthesamebulkisotopiccompositionbutastochasticdistributionofisotopologues.isotopologues.Wangetalalderivedtherelationshipbetweenandthetemperature-dependentequilibriumconstant,,forisotopeexchangereactionsinvolvingonedoublysubstitutedisotopologue.InthecaseofCOforonesuchexchangereactioninvolvingthedoublysubstitutedO(i.e. ),theratio,whereistheequilibriumconstantforthestochasticdistribution,isrelatedtovaluesasfollows:1000ln((2)Omakesup97%ofmass-47CO.Hence,eventhoughexistingsectormassspectrometersareunabletodistinguishOfromitsisobars,Oand,ameasurementofthevaluecalculatedasinEqn(1),butincludingcontributionsfromallisotopologueshavinganominalcardinalmassof47,shouldbestronglyproportionaltoabundancesoffThus,fromEqns(1)and(2),thetemperature-dependentmass-47anomaly()describingtheenrichmentofOinCOrelativetothestochasticdistributionisdenedasfollows: Š1Š
R Š1Š
R whichiscalculatedas RR2RRR(R2ŠR R2RR(R2ŠR 1000(3) J.Mass.Spectrom.,1318–1329Copyright2009JohnWiley&Sons,Ltd. 1320 K.W.Huntingtonetal ThenumeratortermsinEqn(3)aremeasuredsampleabundanceratiosrelativetomass44,asderivedfromforthesample(‘SA’)referencedtoaworkinggas(‘WG’)standardofnominallyknownisotopicsotopic(Ri,SA/Ri,WG)Š1]×1000}.Thedenominatortermsarethecalculatedthatwouldoccurinthesampleifithadthestochasticdistribution,whicharebasedonthesample’smeasuredvalues.Asillustratedbythefollowingexample,onecancalculate(theabundanceratiosOandO,respectively,forthesample)becausearederivedfromthemeasuredassumingthestochasticdistribution,[10,11]isderivedassumingaspecicmass-dependentfractionation.Bydenition,[44]]12C][[16O]and[45]45]13C][[16O]+2[12C][[17O].Assumingthestochasticdistribution,[1/(1),[[16O]=1/(1)and[).Substitutingthesetermsin[45][44],wendtheratiothatwouldoccurinthesampleifithadthestochasticdistribution:.Similarly,.Valuesofdeterminedinananalogousfashionto,andcanbeusedtocalculatethemass-48andmass-49anomaliesrelativetothestochasticdistribution: Š1Š2
R 1000(4) Š1Š2
R Š1Š
R 1000(5)AnumericaldemonstrationofhowtocalculatefrommassspectrometerdataisprovidedinMATLABcodeformatinthesupportinginformation.ThefactthatOandCvaluesarecalculatedfrommeasure-mentsofbyassumingthestochasticdistribution[10,11]hastwonoteworthyimplications.First,thetermsinEqns(3)–(5)inthenumeratorareequaltounity,nity,andthusdonotcontributetothevalues.Second,aspointedoutbyEilerandSchauble,Schauble,Eqns(3)–(5)involveacircularitythatmightrequireaniterativecalculationtocircumvent.How-issosmallrelativetothatvariationsareessentiallyindependentofOandC.Indeed,measurementsperformedatYaleUniversity(usingamassspectrometeridenticaltoMS-Idescribedbelow)ofcylinderCOsamplesrepresentinga40‰variationinOandC,butequilibratedatroomtemperature(namely,havingthesameOordering)demonstratethatisindependentofOandC(Fig.s1inthesupportinginfor-mation).Carbonateclumped-isotopethermometryThemostdevelopedapplicationofclumped-isotopegeochem-istrytodateisthecarbonateclumped-isotopethermometer.IfbondingamongisotopesofcarbonandoxygeninCOgroupsincarbonatemineralswererandom,theabundanceofeachcarbonate-ionisotopologuewouldbethestochastic/combinatoryproductoftheabundancesoftheisotopesofwhichitissHowever,isotopologueabundancesarenotequaltoastochasticdistributioninthecarbonatecrystallattice;‘clumping’ofheavyisotopes(O)intobondswitheachotheristher-modynamicallyfavoredtoanincreasingdegreeastemperature[3,4]Asaconsequence,theextenttowhichacarbon-ateformedinthermodynamicequilibriumisenrichedinbonds(relativetotheamountexpectedforastochasticdistribu-tionofisotopes)canprovideameasureofthetemperatureofcarbonategrowth.Currently,itisnotpossibletomeasuredirectlyabun-dancesofCOionicgroupsincarbonateswiththeneces-saryprecisiontodetermineasample’sObondenrich-ment.Instead,thisenrichmentcanbeinferredbyisotopiccharacterizationofCOproducedbyphosphoricaciddiges-tionofcarbonate,becausetheOabundanceanomalyinproductCOisproportionaltotheabundanceanomalyinthecarbonatemineral.mineral.The
47valueofCOat25Cfrominorganic,syntheticcalcitegrownatknowntemperaturesbetween0Cand50Cisobservedtovaryasafunctionofthegrowthtemperatureaccordingtothehe
47=0.0592×106×TŠ2Š0.02(6)Aleast-squareslinearregressionthattakesintoaccountuncer-taintyineachmeasurementreportedinGhoshetalalyieldsaslightlymodiedversionofthisrelation,including1tiesonthetparameters(Fig.1;seesupportinginformationfordetailsoftheregression):016)(7)NotethisiswithinuncertaintyofEqn(6).MeasuredforCOextractedfromnaturalsurfaceanddeepwaterdwelling 10 11 12 13 14 0.5 0.6 0.7 0.8 5055
47 (‰) ° 6T-2 (K)0.50.60.70.847 (‰) Figure1.(a)Thedashedlineisthecalibrationlineformass-47anomalyversustemperatureofcarbonategrowthofGhoshetalalItisdenedbyasimplelinearregressionofmeasurementsonTforsyntheticcarbonatedata(whitesymbolswith2errorbars)grownatknowntemperaturesbetween1and50C.Thesolidblacklineisdenedbyaleast-squareslinearregressionofonT,weightedbytheuncertaintiesandT..Uncertaintiesintparameters(slopeandintercept)arecalculatedasdescribedinthesupportinginformation,and95%condencelimits(graycurves)arecalculatedbythemethodofCrowetalalThedashed(Eqn(6))andsolidblack(Eqn(7))linesagreewithinuncertainty.(b)Thesamecurveshownin(a)isplottedversusTinsteadofT,witherrorhyperbolerepresentingthe95%condencelimitsshownin(a).forcoralsamplesgrownatknowntemperatureraturefallonthecalibrationline(blacksymbolswith2errorbars). Copyright2009JohnWiley&Sons,Ltd.J.Mass.Spectrom.,1318–1329 1321 ‘Clumped’isotopes coralsgrownatknowntemperaturesbetweenCand30[3,15]approximatelyconformtothetrenddenedbythesyntheticcalcitesamples,asdoresultsformanyothernaturalcarbonatesofknownorestimatedgrowthtemperatures.[1,16]Additionofthesedatadoesnotsignicantlychangetemperatureestimates(tparametersarewithin1ofthoselistedinEqn(7)).Hence,forconsistencywithallpreviouspublications,carbonategrowthtemperaturecalculationsinthisarticleareperformedusingthepublishedinorganiccarbonatecalibrationlineofGhoshetalalAlthoughtherelationshipbetweengrowthtemperatureandforshotolithsissimilarinslopetoEqns(6)and(7),itisoffsettoslightlylower(01–0.02‰)valuesofatanygivenivenPotentialsourcesofuncertaintyinclumped-isotopeanalysisandtemperatureestimatesSeveralpotentialsourcesofuncertaintymaybeencounteredwhenapplyingclumped-isotopethermometryandotherisotopologuetechniquestoaparticularsample.Theseincludeunconstrainedisotopicfractionationsduringsamplepreparationandpuricationaswellasrandom(i.e.shotnoise)errorsandanyuncharacterizedisotopicfractionationsthatmightoccurduringmassspectrometry.Twomassspectrometricerrorsoruncertaintiesareparticularlyrelevanttoclumped-isotopeanalysesingeneral:(1)subtlebutmeasurablenonlinearityintherelationshipbetweenactualandmeasured47/44ratiosand(2)isotopicexchangeamonganalyteCOmoleculesassociatedeitherwithfragmentationandrecombinationinthesourceorinteractionwiththewallsofmetalcapillaries.Asdetailedbelow,thesephenomenamustbecorrectedforempiricallybasedonanalysesofheatedCOgases,whichhaveastochasticdistributionofisotopesamongallpossibleisotopologues(implyingavalueof[5,6]Uncertaintiesintheseempiricalrelationshipscontributetooverallanalyticaluncertainty.Analsourceofuncertaintyrelevantforclumped-isotopethermometry,inparticular,isintroducedbytheempiricalcalibrationofthethermometeritself(Eqn(6)).Thisuncertaintyissystematicratherthanrandom(i.e.itissharedbyallunknownsamples)andmaydifferfordifferentclassesofcarbonatesforunknownreasons,suchaskineticisotopeeffects[18,19]orcrystal-structuralcontrolsononCarbonateaciddigestion,COextractionandpuricationCarbondioxidewasextractedfrom5to12mgaliquotsofcar-bonatepowdersbyreactionwith2mlanhydrousHCfor8–24hfollowingthemethodsofMcCreaMcCreaandSwartetalalAfterreaction,conventionalvacuumcryogenicpurica-tionprocedureswereusedtoisolateproductCOusingtheglassvacuumapparatusdescribedbyGhoshetalalThecryogenicallypuriedCOwasthenentrainedinHecarriergasowingatarateof3ml/minandpassedthroughanAgilentTech6890Ngaschromatograph(GC)column(Supelco-Q-PLOTcolumnwithminternaldiameter,30mlong)heldatC.TheGCwasbakedoutatatemperatureof150Cbetweensamplesandat220Cfor6honceevery24h.COexitingthecolumnwascryogenicallycollectedfor40mininaglasstrapimmersedinliquidN.FollowingtheGCstep,theHecarriergaswasremovedwhilesampleCOremainedcondensedintheliquidNThisproceduredoesnotoptimizeCOcollectiontime(whichcouldbereducedifamultilooptrapwereintroduced)butpurieseffectivelywithoutfractionatingorlosingsamplegas(near100%collectionefciency).Finally,conventionalcryogenicpuri-cationprocedureswererepeatedtwicebeforetransfertothemassCarbondioxideforheatedgasnormalizationmeasure-ments(describedbelow)waspreparedinquartzbreaksealsandheatedinamufefurnaceto1000Cfor2handrapidlyquenchedatroomtemperature.Thisprocedurepre-viouslyhasbeenshowntoyieldCOthatcloselyap-proachesastochasticdistributionofisotopesamongallpos-sibleisotopologues;i.e.itsvalueoffHeatedgaseswerepuriedusingconventionalcryogenicproceduresandGCprocessinginamanneridenticaltotheprepa-rationofsamplesbeforebeingtransferredtothemassIsotopicanalysisInadditiontotheYaleUniversityinstrumentnotedabove,twodual-inletgas-sourceThermo-Finnigan253IRMSsystems,denotedMS-IandMS-II,wereusedtomeasuretheisotopiccompositionofattheCaliforniaInstituteofTechnology.TheinstrumentswereequippedwithcollectionsystemsconsistingofboththestandardsetofthreeFaradaycupsregisteredthrough3(forM/z44),(forM/z45)and10(forM/z46)resistorsandthreeadditionalFaradaycupsregisteredthrough10resistors(forM/z47,48and49),asdescribedbyEilerandSchauble.Schauble.Samplesizesweretypicallyapproximately50molwithresultingionbeamcurrentsforM/z44,45,46,47,48and49ofapproximately50nA,0.6nA,0.2nA,2pA,0.2pAand2fA,respectively.TheworkingreferencegaswasaCOstandardfromOztech(VSMOWVPDB60‰),whichwasstandardizedbycomparisonwithCOevolvedfromphosphoricacidreactionwithNBS-19standard.ValuesforCreportedVPDBandVSMOWwerestandardizedbycomparisonwiththeworkingreferencegas.TheprogramIsodat2.0wasusedtoCandOfromtheobservedisotopicabundances.ForMS-I,isotopiccompositionsweretypicallymeasuredfornineacquisitionsof10cycleseach(8sintegrationtimeeachforthereferencegasandsamplesideseachcycle),withpeakcentering,backgroundmeasurementsandpressurebalancingbetweenthereferencegasandsamplesidesmadebeforeeachacquisition.Eachacquisitionrequires20–30min,andthetotalanalysistimepersampleistypically3–4h.Measurementsaretypicallymadewithanaccelerationpotentialof9.5kV,anelectronenergy65–100V,andwiththe‘sulfurwindow’(anapertureonthesideoftheionizationchamberusedtocontrolthepressureandresidencetimeofgasinthesource)closed.ThesamecongurationwasusedforMS-II,exceptthatMS-IImeasurementsweremadeforeightacquisitionsconsistingofsevencycles(26sintegrationtimeeach),andthewidthsoftheFaradaycupsonMS-IandMS-IIdifferslightly.Forbothmachines,thecapillaryaperturewasadjustedtoyielda5Vsignalformass44forabellowpressureof50mbar.Comparisonofsamplegasestostandardsofknownisotopiccompositionandstateoforderingvalueisdenedasthedifferencebetweenthemeasuredvalueofasampleandthevalueonewouldhavemeasuredforasampleofthatsamebulkisotopiccomposition(i.e.theCandOvalues)havingthestochasticdistributionofisotopologues.Thisrequiresthatwecompareasamplegastoa J.Mass.Spectrom.,1318–1329Copyright2009JohnWiley&Sons,Ltd. 1322 K.W.Huntingtonetal referencegasthathasbothaknownbulkisotopiccompositionandaknownstateofordering(i.e.itsownvaluemustbeindependentlyknown).Thisischallengingbecausethecommonreferencematerialsonecanusetoestablishasample’sbulkcomposition(e.g.COextractedfromNBS-19carbonatestandard)donothaveindependentlyknownvalues.Inaddition,theprocedureweusetocreateheatedgaseswithnominallyknownvalues(i.e.heatingfortwoormorehoursinaquartztubetodrivetheircompositiontothestochasticdistribution)canchangetheirbulkisotopiccompositions(primarilytheOursolutiontothisproblemisasfollows:weestablishthebulkisotopiccompositionofaworkingreferencegas(‘WG’)byconventionalmeans(i.e.comparisonwithrecognizedinterlaboratorystandards).Then,weanalyzeaheatedgas(‘HG’)asasample,usingWGasthestandard.WecalculatethebulkisotopiccompositionoftheheatedgasasifboththeHGandWGhadthestochasticdistribution(i.e.usingnormalioncorrectionalgorithms).Thisassumptionwillintroduceanerroriftheworkinggashasavalueveryfarfrom0,butitisgenerallysoundforcommonnaturalmaterials(i.e.anythingotherthansyntheticmaterialsthataremixturesofexceptionallyisotopicallyenrichedordepletedcompounds)becausetheobservedrangeissmall.Wethencalculatevaluesforobservedmasses(45,46,47)asdescribedabove.Fromthese,wecomputerelativetotheworkinggasfortheHGusingEqn(3).Theprocessisrepeatedforthesample:afteranalyzingasample(‘SA’)usingtheworkinggasasthestandard,wecalculatethebulkisotopiccompositionofthesampleasifboththesampleandWGhadthestochasticdistribution.WethencalculatevaluesfortheobservedmassesandcomputetheforthesampleusingEqn(3).Finally,wecalculatethesample’smass-47enrichmentinexcessofthestochasticdistributionbysubtractingfortheheatedgasfromforthesample:[SAHG][SA.WG]]vs.WG].(NotethatarecalculatedanalogouslyusingEqns(4)and(5).)Thisnalstepmakestheapproximationthatvaluescanbeaddedandsubtractedlinearly.Becauseisnotalinearfunctionofisotopeabundance,thisis,strictlyspeaking,aconvenientbutincorrectapproximation,butforthe1‰rangeinvaluesofnaturalmaterialsitaddsnosignicanterrors.However,themassspectrometryitselfinvolvesanonlinearitybetweenmeasuredandrealvaluesthatcanintroducesignicanterrorsinvaluesifitisnotcarefullydocumentedandcorrected.[16,17]Weobservelinearcorrelationsbetweenthevaluesofheatedgasesmeasuredtheworkinggasandtheirvaluesmeasuredthatworkinggas.(WeWevs.WG]1000,aconvenientmeasureofbulkcomposition.Becauseisasmallnumber,isapproximatelyequalto(),andthusto(Thatis,ifoneanalyzestwoheatedgases,onecloselysimilarintotheworkinggasandasecondthatissubstantiallydifferent,twodifferenterentvs.WG]valueswillbeobserved.Notethattheworkingreferencegasisthesameinthesetwomeasurements,andallheatedgaseshavenominalabsolutevaluesof0;hence,intheabsenceofanymeasurementartifact,thetwomeasuredvaluesshouldbeindistinguishable.Thus,theobservedrelationshipbetweenforheatedgasesreectsasubtlenonlinearityintherelationshipbetweenactualvaluesandthemeasuredintensityratiobetweenthemass-47andmass-44ionbeams.AlthoughweobservethisnonlinearityinheatedgasmeasurementsforMS-I,MS-IIandtheYalemassspectrometer,itdiffersinthethreemachines,variesgraduallywithtimeonanygiveninstrument,andwasnotobservedininitialstudiesusingMS-I.MS-I.Hence,itmaynotbeauniversalphenomenon.Itisnotyetclearwhethertheultimatecauseofthisnonlinearitycomesfromtheperformanceofthedetectors,theresistorsthroughwhichioncurrentsaremeasuredorsomecomponentofthesourceoranalyzer.Nevertheless,anormalizationbasedontheanalysisofheatedgasesoverarangeofcompositionspaceisIfthesampleandheatedgashavethesame,then[SA.HG][SA.WG]]vs.WG].Ifthesampleandheatedgasdifferintheirvalues,thenhenvs.WG]correspondingto[SA.WG]mustbeestimatedbylinearregressionofmeasuredmeasuredvs.WG]onnvs.WG]forthetime-periodduringwhichthesamplewasanalyzed(seesupportinginformationfordetailsoftheregressionanderrorpropagation).Wendthattheslopeoftheempiricallydeterminedlineforheatedgasesinaplotofofvs.WG]isstableovertimescalesofmultipleweeksormonths,butcaninsomecaseschangesubsequenttocleaningthesourceandorreplacingthetungstenlamentorchangingtheionsourcefocusing–presumablyreectingachangeinmassspectrometerperformancethatinuencesthenonlinearitybetweenactualandvalues(Fig.2(a–c)).Inthemonthsfollowingourdiscoveryofnonlinearityinmeasurements,theinterceptsoflinestthroughdataforheatedgasesinplotsof(‘heatedgaslines’)wereessentiallyinvariant,evenoverlargerangesinslope.lope.However,subsequentanalyseshaverevealedmeasurablesecularvariationsintheinterceptsofheatedgaslines(Fig.2(d,e)).Inordertoestablishthephysicalcauseofthisphenomenon,weconductedexperimentsinwhichwevariedtheresidencetimeofgasinthesourcebyopeningandclosingthesulfurwindow.Thisproducedalargevariationintheinterceptoftheheatedgasline(Fig.2(f)),consistentwiththehypothesisthatalongresidencetimeorhighgaspressureinthesourcepromotesfragmentation/recombinationreactionsthat‘scramble’isotopesamongisotopologues,reducingthecontrastbetweensampleandstandardgases.Ifso,thenthisartifactshouldbecorrectedforbymultiplyingthemeasuredofunknownsbyafactorthatisproportionaltotheinterceptoftheheatedgasline.Inpractice,wescalealldatatoaxedinterceptoftheheatedgasline,takentobeevs.WG]8453‰(i.e.theinterceptoftheheatedgaslineusedforthecalibrationstudyofGhoshetalal).Thatis,thecorrected[SA.HG][SA.HG]compressedmpressedvs.WG]8453),whereherevs.WG]istheheatedgaslineinterceptfortheperiodduringwhichthesamplewasanalyzed.Inprinciple,thebestwaytodealwithisotopic‘scrambling’inthesourcewouldbetoopenthesulfurwindow,minimizingresidencetimeinthesource.However,theresultinglossofionintensitydramaticallydegradesmeasurementprecision.Weconcludethatthebestpracticalapproachtothisartifactisacompromise:weacceptandcorrectforacertainamountofisotopicscramblinginexchangeforthehighprecisionthatcomeswithelevatedsourcepressure.However,itispossiblethatotherinstrumentsorinstrumenttuningconditionsmightrequireadifferentapproach–oneobviouslycouldnotacceptaconditionthatresultedinsomuch‘scrambling’thatallgasesareindistinguishablein Copyright2009JohnWiley&Sons,Ltd.J.Mass.Spectrom.,1318–1329 1323 ‘Clumped’isotopes
47 = 0.0128(47) - 0.82
47 = 0.0081(47) - 0.84
47 = 0.0064(47) - 0.84 sulfur window closed
47 = 0.0072(47) - 0.77 -5010152025 47 [HG vs. WG] (‰)
47 [HG vs. WG] (‰)-0.6-0.8-1.047 [HG vs. WG] (‰)-0.6-1.047 [HG vs. WG] (‰)-0.6-0.8-1.047 [HG vs. WG] (‰) -50-40-30-20-10-10()(e)-0.5-0.6-0.8-1.0 -5010152025 47 [HG vs. WG] (‰)
47 [HG vs. WG] (‰)
47 [HG vs. WG] (‰)-0.9-0.7-0.8-1.1-1.3-0.9-1.2abcd -50101520255()5 -50101520255()5-50101520255()50Figure2.2.vs.WG]anddvs.WG](‘heatedgaslines’)areshownfordifferenttime-periodsandmassspectrometercongurations.(a–d)Theempiricalrelationshipbetweenetweenvs.WG]anddvs.WG]isapproximatelylinearfor16Vsignalheatedgasobservations()fromfourdistincttimeintervalsin2007and2008.Thesmallcirclesareindividualanalyses,andtheverticalerrorbarsrepresent2s.e.uncertaintyinmeasurements.Thehorizontalerrorbarsareofthesamemagnitudeastheverticalerrorbars.Thesolidlinesrepresenttheleast-squareslinearregressionofdataforeachtime-period,andtheshadedgrayregionindicatesthe95%condenceinterval.(e)Best-tlinesand95%condenceintervals(a–d)aresuperimposedthighlighttemporalvariationsintheheatedgasline.Heatedgaslines(a),(b)and(c)haveapproximatelythesameinterceptbutdifferentslopes.Hegasline(d)hasasignicantlydifferentintercept.(f)Themass-47heatedgaslineisshownfordifferentcongurationsofthesulfurwindow.Thesmacirclesareindividualanalyses,andtheverticalerrorbarsrepresent2s.e.uncertaintyinmeasurements.PrecisionandStabilityinIsotopeRatioInternalprecisionWecomparedmeasurementsofconductedusingMS-IandMS-II(incontinuoususesince2003and2008,respectively)tothepredictionsforprecisionattheshot-noiselimit(Fig.s2inthesupportinginformation).Theobservedprecisionforthetwomassspectrometersapproachestheshot-noiselimit.ResultsforMS-I,inparticular,indicatethattheprecisionofcanreachlevelsaslowas5partspermillion(ppm)(forlongion-currentintegrationtimes(3200s,orapproximately24hofmassspectrometertime)andlargegasloads(16Vsignal).Fortypicalmeasurementprotocol(16Vsignalandion-currentintegrationtimesof480–720s,correspondingtosixtonineacquisitionsandapproximately2–4hofmassspectrometertime),theshot-noiselimittoprecisionis0.013–0.016‰.Weintegratedioncurrentsforupto3200sforgasloadscorrespondingtosignalsbetweenapproximately4and32Vtoexaminetheeffectofsamplesizeandoftime-dependentfractionationofsampleand/orstandardgasreservoirsand/orchangesinconditionofthemassspectrometeronaccuracyofmeasurements(Fig.s2).IsotoperatioobservationsforMS-II(700sintegrationtime,fouracquisitionsofseven25scycleseach)indicatethattheprecisioninmeasurementsisattheshot-noiselimitandimproveswithincreasedsignalsize.However,theMS-Idataindicatethaterrorclimbsaftercrossingathresholdsomewherebetweenasignalof21–30V.Theseobservationssuggestthatsignalssafelybelowthisthreshold–approximately16V,correspondingto8mgofcarbonateor50molCO–areoptimalforthisinstrument.Forion-currentintegrationsofa16Vsignal,therunningaveragevaluestabilizesby320s,butclearlydriftsafterapproximately1500s,or18–19acquisitionsoften8scycleseach.WeinferthatonMS-I,precisioncanbeoptimizedbyintegrating16Vsignalsoverperiodsinexcessof320s(preferably480–720s,orsixtonineacquisitionsoften8scycleseach),butdoesnotcontinuetoimproveforintegrationtimesgreaterthanapproximately1500s.OurconclusionthatprecisionsofmeasurementsareprimarilydominatedbycountingstatisticsappliestoCO J.Mass.Spectrom.,1318–1329Copyright2009JohnWiley&Sons,Ltd. 1324 K.W.Huntingtonetal avarietyofsources,includingCOgeneratedbyphosphoricaciddigestionofcarbonates.Wecompiledtheinternalprecision(i.e.standarderror)ofisotopicmeasurementsfor21analysesoffromtheNBS-19carbonatestandardand172analysesofdifferentaliquotsof63differentcarbonatesampleunknownsperformedundertypicalconditionsfrom2004to2008(Fig.s3inthesupportinginformation).Theaveragestandarderrorforeachmeasurement(0003‰)isinagreementwiththelowerendoftheshot-noiselimitpredictedforanalysesofsixtonineacquisitions(0.013–0.018‰).TheaverageobservedstandarderrorsinOandCmeasurementsofsampleunknownsisroughlyanorderofmagnitudebetterthanthatobservedforalthoughlower-precisionoutliersupto0.005‰exist.TheinternalprecisioninmeasurementsispoorlycorrelatedwithprecisionofeitherOorCforthestandardandsampledatasets,withPearson’scorrelationcoefcients()of0.26–0.29forNBS-19and0.07–0.09forthesamples.InternalprecisioninOandCarehighlycorrelatedwithoneanother(78–083),whichisnotsurprisingbecauseunlike,bothOandCvarystronglywithmass-dependentfractionation.ractionation.Long-termsignalstabilityAslong-termdriftscanalsoaffectmeasurementprecision(i.e.inadditiontoshotnoise),weexaminedthestabilityandaccuracyofourIRMSsystembyusingamodiedformoftheAllanvariancetechnique,originallydevelopedtocharacterizeultrastableoscillators.scillators.Insteadofusingtimeastheindependentvariable,hereweuseindividualIRMSacquisitions (8)Dataarerstbinnedintobins(eachconsistingofoneormoreacquisitions),andtheaverageofeachbin,,istaken.ThedifferencebetweenadjacentbinsissquaredandthensummedbeforebeingnormalizedtocomputetheAllanvariance.Forexample,adatasetwithsixelements[]willproducethreevaluesofAllanvariancecorrespondingtobinsofone([],[],[],[],[],[]),two([],[],[])andthree([]and[])elementseach.Themaximumbinsizeisthereforehalfthetotalnumberofelementsinadataset.PlottingAllanvariancebinsize,then,convenientlypresentsbothnoise-anddrift-relatedeffectsonsingleplot.AnexampleoftheAllanvarianceforarelativelylong-durationanalysis,consistingof40acquisitionsof80ssampleintegrationeach(ten8scycles),madeonMS-IisshowninFig.3(thesearethesamedatadepictedinFig.s2(b–d)).Anidealstatistical-noise-limitedmeasurement,forwhichlong-termdriftsarenegligible,willdisplayapower–lawrelationshiptheAllanvarianceplot,where5,reectingthePoissonstatisticsgoverningtheprecisionoftheoverallmeasurement.Incontrast,ameasurementdominatedbylong-term,correlatedrandom-walkdriftswillhave5.Consequently,theoptimumnumberofmeasurementstoaveragetogetherinagivenanalysis(i.e.theoptimumbinsize)willoccurnearwheretheAllanvariancereachesaminimum,i.e.where0.Forourinstrument,measurementsseemtobedominatedbystatisticalnoisefor10acquisitions,withonlyasmallcontributionfromlong-termdrift.Thevariabilityofappearstoincreaseformeasurementsmadeinexcessofnineacquisitions(Fig.3),althoughweattributethistothesmallernumberofbinswith110100 Figure3.Allanvarianceplotofover40IRMSacquisitions.Apower–lawregressionisshownovertherstnineacquisitionsshowingindicatingthatPoissonstatistics,notlong-termdrifts,dominatetheuncertaintiesintheaverageinthisregime.greaterthannineacquisitionscontributingtotheAllanvariancecalculation.MoreprecisevaluesoftheAllanvariancewiththesenumbersofacquisitionswouldrequireamoresustainedanalyticalrunbyseveralfactorsintime.Nevertheless,theidealprecisionthatshouldbeattainableonasinglegasrunformeasurementsthatareclearlydominatedbystatisticalnoise(nineacquisitions,or720scountingtime)attheoptimalvoltage(16V)is0.013‰.ExternalPrecisionandErrorPropagationCarbonatestandardsandsampleunknownsThemoststraightforwardwaytoquantifyexternalprecisioninmeasurementsistodeterminethereproducibility(standarddeviation)ofindependentanalysesofthesamematerial.Wecompiledthestandarddeviationsinisotopemeasurementsfor92externallyreplicatedsamples(2–11replicateseach)analyzedonMS-Iandfoundthattheaverageexternalprecisionin015‰,inagreementwiththestandarddeviationofrepli-cateanalysesfortheNBS-19carbonatestandard(0.022‰;Fig.s4inthesupportinginformation).TheaverageexternalprecisioninisapproximatelytwicetheaveragestandarderrorweobserveforeachCOgasmadebyaciddigestionofcarbonates.Inaddition,thestandarddeviationforreplicateextractionsvariesoverawiderrangethandoesthestandarderrorforeachextraction.ThissuggeststhatsubstantialvariancebeyondcountingstatisticscanbeaddedtomeasurementsofCOfromsomecarbonatesamplesduetosomecombinationofsampleheterogeneityandanalyticalartifactssuchasuncontrolledfractionationsorcontaminants.Wesuspectthatsampleheterogeneitycausesthefailureofmanycarbonatematerialstoachievereproducibilityinparablewithcountingstatistics.AnexaminationofmeasurementsOandCinthesamegases(Fig.s4)revealsthatstandarddeviationsforreplicateanalysesofOandCforbothsampleunknownsandtheNBS-19standardareanorderofmagnitudelargerthantheaveragestandarderrorweobserveforeachCOgasmadebyaciddigestionofcarbonates(0.0014‰forand0.0007‰forC),wellinexcessofthelimitsimposedbycountingstatistics.SmallerrorsinOandCthatmaybeduetosampleheterogeneityleadtosmallchangesincalculatedvalues.Althoughthisreducesthereproducibilityofmentsforsamplesthatareheterogeneousinisotopiccomposition Copyright2009JohnWiley&Sons,Ltd.J.Mass.Spectrom.,1318–1329 1325 ‘Clumped’isotopes orotherwiseaffectedbyanalyticalartifacts,thevariabilityinissmallerthanvariabilityinOandCbecausechangesinareoffsetbychangesin(Eqn(3)).Nevertheless,alargenumberofsamplesexhibitstandardde-viationsforreplicateanalysesofunknownsthataremuchbetterthantheaverageandcomparablewiththelimitsimposedbycountingstatistics:49of92samplesexhibitstandarddeviationsinforreplicateextractionsof010‰,and23areThesewell-replicatedsamplesarenearlytwiceasprevalentthanwouldoccurbyrandomchanceifthetrueanalyticalerrorwere0.019‰(theaveragefortheentirepopulation).WeconcludethatmeasurementsofinCOextractedfromchemicallypure(i.e.freeororganicmatter,suldesandothersourcesofcontaminantgases)homogeneouscarbonateshaveerrorscontrolledbycount-ingstatisticsandnotsignicantlydegradedbyanalyticalartifacts.AdetailedexampleofanalyticalreproducibilityforunknownnaturalsamplesWeexaminedreplicateanalysesofasuiteofsamplesperformedoverarelativelylongintervaloftimesuchthatthestabilityofthestochasticreferenceframeisputtothetest.Thetwobiogeniccarbonatesamples(oyster95123andbivalvesp.95124)wereanalyzedpreviouslybySpencerandndandHuntingtonetalalandexhibitnoobviousevidenceofsampleheterogeneityorcontamination.Replicatemeasurementsofeachsampleincorporateuncertaintiesintheheatedgasreferenceframe(Fig.2),andpotentialanalyticalartifactsintroducedbycarbonateaciddigestion,COandpuricationprocedures.Thetwosamplesexperiencedidenticaltemperatureconditionsduringgrowthandburialandhavethesamevalue.Thus,reproducibilityoftheirmeasurementsalsoshouldreectanynoiseintroducedbysamplepreparation(cleaning,samplingandpowdering).Figure4illustratestheuseofheatedgasdatatonormalize[SA.WG]measurementsofunknownsamplestoacommonreferenceframeandtoscreenforcontaminants.Divergent[SA.WG]resultsforindependentanalysesof95123and95124carriedoutduringthethreedifferenttime-periods(Fig.4(a))collapsetothesame[SA.HG]valuewithinuncertainty(0.003–0.006‰,1s.e.)aftertheheatedgasnormalizationisapplied(Fig.4(b,c)).EilerandSchaubleSchaublefoundthatmass-48and ()11121314151616()-0.60-0.65-0.70-0.75-0.80
47 [HG vs. WG] (‰)11121314151691011 95I24 3/18/073/19/07 -5/25/073/26/07 -7/4/07 ()020406080 Figure4.Isotoperatioandclumped-isotopethermometryresultsfortwobiogeniccarbonates.(a)[SA.WG]isplottedagainst[SA.WG]forthreeindependentaciddigestionseachofsample95I23(whitecircleswith2s.e.errorbars)andsample95I24(blackcircleswith2s.e.errorbars).Eanalysisrepresents720sofintegrationtimeofa16Vsignal.(b)Heatedgasnormalizationfor95I23and95I24measurementsmadeovera5-monthperiod.Theheatedgaslinesforeachtime-periodaretakenfromFig.2,andarelabeledwiththeappropriaterangeofdates.Thedashedarrowsillustrahowthebest-ttvs.WG]valuecorrespondingtothevalueof[SA.WG]from(a)foreachanalysisisfoundusingtheheatedgaslineforthetime-periodduringwhichtheanalysiswasperformed.Thewhiteandblacksquaresindicatetheheatedgasnormalizationfactorforthreeanalysesofsample95I23and95I24,respectively.(c)Aftertheheatedgasnormalizationfrom(b)isapplied(seetext),the[SA.HG]valuesforallsixanalysesareindistinguishable.Theblacklinerepresentsazoomed-inportionofthetemperaturecalibrationlineshowninFig.1(a).Thedashedarrowillustrateshowthemeasuredvaluesareprojectedontothecalibrationlinetocalculatetemperature.(d)Mass-48measurements(crosses)forthethreeheatedgaslinesshownin(b)denetherelationshipbetweenexpectedforcleansamples.Thesamplesdonotdeviatesignicantlyfromthebest-theatedgasmass-48lines(composedofresultsforcleanCOsamples),suggestingthatthesamplesarefreeofhydrocarbon,halocarbonandsulfurcontamination.Thesymbolsarelargerthantheuncertainties. J.Mass.Spectrom.,1318–1329Copyright2009JohnWiley&Sons,Ltd. 1326 K.W.Huntingtonetal mass-49signalscanbesensitiveindicatorsofthepresenceofhydrocarbonsandchlorocarbonsinspikedanalyteCO,andGuoandEilerilerfoundevidencethatsulfur-bearingcontaminantscanalsoleadtosubstantialinterferencesonmasses48and49(presumablyfromspeciessuchas).However,wehaveobservedastrongcorrelationbetweenmass-49signalsandthepressureimbalancebetweenthebellowsthatregulatethesampleandworkinggasowintothemassspectrometersource.Valuesdonotshowthissensitivitytobellowspressure,suggestingthatmass-48measurementsaremostappropriateindicatorsofcontaminantspecies;i.e.wecanidentifyclearlycon-taminatedsamplesbynotingdifferencesbetweentheirsystematicsandthoseexhibitedbypureheatedgases.AsshowninFig.4(d),themass-48signalsforallsixanalysesplotwithintherangeofmeasuredheatedgasmass-48values,suggestingthatthesamplesarefreeofrecognizedcontaminants.If[SA.WG]foranyanalysisweresignicantlyhigherthanthanvs.WG],thiswouldprovideevidenceforimpuritiesthatleadtoisobaricin-terferenceswithinthemassrangeofCO;althoughcontaminantsclearlycouldinterferewithmass48butnot47,wesuggestthatsuchevidencediminishesthereliabilityofameasurement.AlthoughtheirOvaluesdiffer(Table1),valuesfor95I23and95I24areindistinguishable.Giventhesharedhistoryofthesesamples,weconcludethatthesesixanalysesreectapopulationofmeasurementsofsamplesthatwereindistinguishableintemperatureoflastequilibration,andthusprovideawindowintotheinternalandexternalprecisionofthetechnique.[SA.HG]resultsofallsixanalysesconvergebyapproximately40cyclesorfouracquisitions(320sintegrationtime),andprecisionapproximatelyfollowscountingstatistics(Fig.5).Averageobservedprecisioninis0.0227‰(1s.e.)atthelevelofasingleacquisition(80sintegrationtime)and0.0088‰foreachanalysis(i.e.summingoverallacquisitionsrunonthatgas,foratotalintegrationtimeof720s).Averageexternalprecisioninis0.0046‰,afterintegratingdataforallthreeextractions(i.e.atotalintegrationtimeof2160spersample).Theweightedaveragevaluesforthreeindependentanalyseseachof95I23and95I24are0006‰and0003‰,andtheexternalerroris0.0039‰ifresultsfrombothsamples(sixanalyses)arecombined.Precisioninabsolutetemperatureestimatesvariesasafunctionofboththetemperatureofcarbonategrowthandtheuncertainty(Fig.6(a);supportinginformation).Forasingleanalysisofacarbonatesamplegrownat20C(typicalprecisionin),theuncertaintyinabsolutetemperatureC(1s.e.).Ifthreereplicatemeasurementsaremade005‰precisionin),thetemperatureuncertaintyC(1s.e.).Takingadvantageofthelargenumberofisotoperatiomeasurements(inourcase,atleast90cyclesforeachanalysis),wecancalculatethe95%condencelimitontemperatureestimatesbymultiplyingthestandarderrorofthemean(1s.e.)givenbyFig.6(a)byStudent’s-factor(1.6)..Althoughweformallypropagateuncertaintiesusingthepublishedcalibrationdata,data,wenotethatgiventhelargenumberofadditionaldatainagreementwiththeoriginalcalibrationthathavebeengenerated,[1,16,28,29]actualcontributionstotemperatureuncertaintyfromthiscalibrationarelikelytobeverysmall.Theprecisionoftemperaturedifference(T)estimatesislimitedbytheprecisionoftheleast-precisesamplemeasurementandtheprecisionoftheslope(i.e.temperaturedependence)ofthecalibrationdata(Fig.6(b)).IftheabsolutetemperatureestimatesforsamplesAandBare30CandC,respectively(1s.e.intemperaturefortypicalsamples010‰precisioninfromFig.4(a)),thetemperaturedifference()wouldbe10C(Fig.4(b)),ontheorderoftherootofthesumofthesquareduncertaintiesinandTTprecisionisslightlyworsethantheprecisionofabsolutetemperatures,buttheerrorisrelativelyinsensitivetothemagnitudeofthetemperaturedifferenceFig.4(b).Ouranalysisconrmsthatitispossibletomeasureverysubtlevariations–routinelywith1‰precision–intheabundanceofextremelyrarespeciesforclumped-isotopeanalysisusingexistingtechnology(Fig.s4).Forclumped-isotopecarbonatethermome-try,precisionof1–2Ccanbeachieved,dependingprimarilyontheintegrationtimeoftheanalysis,andsecondarilyonthenumberofcalibrationdatatakenintoconsideration.Theseisotopologue Table1.SummaryofcarbonandoxygenisotopicdatafortwobiogeniccarbonatesamplesshowninFigs.s4and4.Heatedgas-normalizedvaluesarereportedwithuncertaintiespropagatedformallyasdescribedinthesupportinginformation.Notethattheheatedgasnormalizationcontributeslittleuncertaintybecauseofthelargenumberofindependentmeasurementsusedtodenethebest-tline(Fig.2)(month/date/year)carb(‰)water(‰)47,sample47,sample47,sample47,sample47,HG Sample95I23 1.840.8720.0820.008312.6870.00830.6610.5790.00850.00951.860.3960.1470.008112.5520.00820.7420.5940.00820.00951.861.0410.1870.008112.4820.00810.7640.5770.00830.0103Sampleaverage:05830005640Sample95I24 0.981.4990.0560.007714.0860.00780.6430.5870.00790.00911.010.8110.1400.008114.0200.00790.7300.5900.00820.00971.001.4740.1760.007513.9490.00760.7550.5790.00780.0101Sampleaverage:05850003339Formationaverage:05840002940 Withoutuncertaintyfromheatedgasnormalitation.Includinguncertaintyfromheatedgasnormalitation. Copyright2009JohnWiley&Sons,Ltd.J.Mass.Spectrom.,1318–1329 1327 ‘Clumped’isotopes 95I23_1 95I23_1 95I23_2 95I23_2 95I23_2 95I23_3 95I23_3 95I23_3 95I24_1 95I24_1 95I24_2 95I24_2 95I24_2 95I24_3 95I24_3 95I24_3 8s cycles
47 [SA vs. HG] running average 1030507090 0.450.50 acquisitions (10 x 8s cycles)
47 [SA vs. HG] running average 8s cycless.e. 47 [SA vs. HG] 1030507090 levelavg. s.d.avg. s.e.acquisition0.071710 8s cycles0.0227analysis0.02649 acqs.0.0088sample0.00803 analyses0.0046unit0.00952 samples0.0039 Figure5.Summarizedresultsforsixindependentanalyses(threepersample)forthetwobiogeniccarbonatesamplesshowninFig.4.(a)Thelinesshowtherunningaverageof[SA.HG]plottedversusthenumberof8scyclesaveraged.Thethreeanalysesforsample95I23areshowninblack,andthethreeanalysesforsample95I24areshowningray.(b)Therunningaverageisshownasin(a),butheretheresultsarebinnedbyacquisition(ten8scycles).(c)1s.e.of[SA.HG]measurementsfortheanalysisshownin(a)and(b)versuscyclenumber.Insettableshowstheaveragestandarddeviation(avg.s.d.)andstandarderror(avg.s.e.)in‰,foreachlevelofanalysisofthetwosamples.measurementsapproachtheshot-noiselimitofprecision(Fig.s2),indicatingthatfurtherimprovementswillrequireadditionalmeth-odsand/orinstrumentdevelopmentthatincreasetheintensityofanalyzedionbeamsorextendthepracticalperiodofanaly-sesofeachsample.Althoughourdatacompilationindicatesthatexternalprecisionforanalysisofrelativelypure,apparentlyho-mogeneouscarbonatesfollowscountingstatisticstothe0.005‰level,manyothermaterialsfailtoreachthislevelofexternalpre-cision.Insomecases,wecanattributepoorprecisiontosampleinhomogeneity,whereasinothercasesthecauseisnotobvious.Poormassresolutionisanoutstandinglimitationofthemassspectrometersweusedthatlimitsourabilitytoexaminepossiblecontaminantsorotherartifactsthatmaybetoblameforpoorexternalreproducibilityinmeasurements.Poormassresolutionresultsinaninabilitytoresolvemolecularioninterfer-encesthatmayhavealargeimpactonapparentisotopologueabundances.Nevertheless,itappearsthatcomparingsamplemass-48anomalieswiththoseofcleanheatedgasesmayprovideameanstoscreenforcertaincontaminantsthatmayaffecttheisotopologuesignalofinterest.Themostimportantlimitationofcurrentmassspectrometertechnologyisthetrade-offbetweenionyieldpermoleculeofanalytegasandtheoccurrenceoffragmentation/recombinationreactionsinthesource,or‘scrambling.’Oursulfurwindowexperiments(Fig.2(f))illustratethatwhiletheefciencywithwhichadynamicallypumpedsourceionizesanalytemoleculescanbeimprovedbyincreasingthegaspressure,increasedpressureincreasesscrambling.Asscramblinginuencesthemeasuredproportionofisotopologuesbydrivingtheanalytetowardthestochasticdistribution,thedynamicallypumpedsourcedesignfundamentallylimitsthenumberofionsthatcanbeproducedandcountedinagiventimeinterval.Encouragingly,ouranalysisindicatesreasonablestabilityandlinearityatlevelsofthousandthsofpermilofionbeamsofinterestcollectedinaFaradaycupregisteredthrougha10resistor(Figs.s1,3).Oneconsequenceofstabilityisthatwecanintegratesmallioncurrentsoververylongtime-periods J.Mass.Spectrom.,1318–1329Copyright2009JohnWiley&Sons,Ltd. 1328 K.W.Huntingtonetal 010203040500101520Figure6.Formalerrorintemperatureestimatesandtemperaturediffer-ences(T)deducedfrom.(a)Thecontoursrepresent,theformalstandarderrorinabsolutetemperatureestimatesinC,asafunctionoftem-peratureandstandarderrorofmeasurements.Formeasurementprecisionof01‰,thestandarderrorinTis2–3C.(b)Thecontoursrepresent,theformalstandarderrorinT(estimatedaroundanaverageof20C)inC,asafunctionoftemperatureandstandarderrormeasurements.Formeasurementprecisionof01‰,thestandarderrorinTaroundanaverageof20CisC,regardlessofthemagnitudeofthetemperaturedifference.toimproveprecision(Fig.3).However,diminishingreturnsonprecisionwithtimeandthepossibilitythattheaccuracyofisotopologuemeasurementmayeventuallydecrease(Fig.s2)suggestthatverylongcountingtimes(inexcessof720s)maynotbeadvantageous.Instead,machinetimewouldbespentbetteronanalysisofindependentlypreparedreplicates,whichenableexternalprecisiontobecharacterized.Perhapsmostimportantly,ourexampleshighlightthedependenceofpreciseclumped-isotopeanalysisonaheatedgasreferenceframe.Unlikestandardisotopicanalyses,whicharereferencedtoanarbitraryvalue(i.e.theVSMOWtheheatedgasreferenceforclumpedisotopeshasauniquephysicalmeaning–bydenitionof0‰meansastochasticdistribution.Theuseofsuchan‘absolute’referenceframeisascriticalforpracticalconsiderations(i.e.removingthesubtlenonlinearityobservedintherelationshipbetweenactualvaluesandthemeasuredintensityratiobetweenthemass-47and44ionbeamsandremovingtheeffectsofscalecompressionduetoisotopic‘scrambling’inthesource)asitiselegant.WerecommendanalyzingaheatedgaseachdaysampleunknownsareanalyzedandCOextractedfromacarbonatestandardsuchasNBS-19occasionallytoestablishthe0‰referenceframepreciselyandmonitorpossiblechangesinmachineconditions.SummaryandOutlookOurdatacompilationindicatesthatuseofaThermo-FinniganMAT253dual-inletgas-sourceIRMSroutinelyyieldssubtenthofapermilprecisioninmeasurements.Forrelativelypure,apparentlyhomogeneouscarbonates,precisionfollowscountingstatistics,andfurtherimprovementwouldrequirehardwaremodications.Tothebestofourknowledge,ourstudyprovidestherstdetailedexaminationofthestabilityandlinearityofacountingsystemconsistingofaFaradaycupregisteredthrougha10atlevelsofthousandthsofpermil.Wendthestabilityofresponseofthissystemtobesufcientforprecisequantitativeanalyses,butcarefulstandardizationisrequiredtocorrectforsubtlenonlinearity.WeoutlineamethodbywhichheatedCOgaseswithastochasticdistributionofisotopesamongallpossibleisotopologues(0‰)areusedtocorrectfor(1)subtlenonlinearityintherelationshipbetweenactualandmeasured47/44ratiosand(2)scalecompressionduetoisotopicexchangeamonganalyteCOmoleculesinthesourceorcapillaries.Measurableimprovementsintheprecisionofisotopologueanalysesmaybepossiblewithinstrumentandmethodsdevel-opments.Incrementaladvancesinmethoddevelopmentcouldincludeincreasingtheioncurrentbyreducingtheresistancethroughwhichtheionbeamsareregisteredorimprovingtheextractionefciency.Wearenotoptimisticabouttheuseofcarriergasintroductionbecauseitseffectsonexchangeamongana-lyteCOmolecules(‘scrambling’),linearity,stabilityofionizationandextractionefciencyareunknown.Majoradvancesinpreci-sionwouldrequiresubstantialhardwaredevelopmenttoachievehighermassresolution(),lowercurrentioncounting,animprovedion-countingsystem,orpotentiallyanimprovedvacuumsystemandsourcedesign.Untilsuchimprovementsarerealized,subtenthofapermilprecisioninremainsatthelimitofmassspectrometermeasurements.ThisworkwassupportedbytheNationalScienceFoundationandbytheDivisionofGeologicalandPlanetarySciencesandtheDavidowFundattheCaliforniaInstituteofTechnology.H.P.A.thankstheEarthSystemCenterforStableIsotopeStudiesoftheYaleInstituteforBiosphericStudies.TheauthorsalsothankJohnHayesandananonymousreviewerforinsightfulcommentsthatimprovedthisarticle.SupportinginformationSupportinginformationmaybefoundintheonlineversionofthis[1]J.M.Eiler.‘‘Clumped-isotope’’geochemistry-Thestudyofnaturally-occurringmultiply-substitutedisotopologues.EarthandPlanetaryScienceLetters,309. 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