Introduction to clumped isotopes

Ivan Prokhorov

Empa / Air Pollution and Environmental Technologies / Emissions and Isotopes

1 Today I will present ...

... fundamental principles of clumped isotopes (example of CO2)

... current and emerging analytics

... selected applications of CO2 and CH4

2 Example of CO2 molecule

O C O ISOTOPOLOGUE - a molecular entity that differs only in isotopic composition 99.76% 16 12 98.9% 18 isotopic combinations (4 symmetric) 12 isotopologues

0.2% 18 13 1.1% no heavy isotopes - principal isotopologue

1 heavy isotope - singly-substituted 0.04% 17 14 < 1 ppt 2 and more heavy isotopes - clumped or multiply-substituted

3 Random distribution of isotopes

Assumption: isotopes are randomly (stochastically) distributed among isotopologues.

[isotopologue] = П [isotopes] x statistical factor

Example:

13C16O2 = 13C x (16O)2 12C16O18O = 12C x 16O x 18O x 2

R13C = 13C/12C

δ13C = R13C/R13Cref - 1

R*(13C16O18O) = R13C x 1 x R18O

Isotopologue ratio assuming random distribution of isotopes 1Formulae

16 13 16 R 13 =R O R C R O O CO ⇥ ⇥ Abundance of CO2 isotopologues 18 12 16 R 18 =2 R O R C R O OCO ⇥ ⇥ ⇥

18 13 16 R⇤18 13 =2 R O R C R O O CO ⇥ ⇥ ⇥

R 18O13CO =(1+)R⇤18O13CO

K 44 ppm OCO + 17O13CO 1 O13CO + 17OCO ! K OCO + 17OC17O 2 2 17OCO ! K OCO + 18O13CO 3 O13CO + 18OCO ! K OCO + 17OC18O 4 17OCO + 18OCO ! K 2OCO+ 17O13C17O 5 O13CO + 2 17OCO ! 44 45 46 45 47 46 48 47 46K49 48 47 OCO + 18OC18O 6 2 18OCO Mass / mu ! ∆ - deviation from random distribution of isotopesK among isotopologues 2OCO+ 17O13C18O 7 O13CO + 17OCO + 18OCO ! 5 K 2OCO+ 18O13C18O 8 O13CO + 2 18OCO !

K 16O12C16O+16O13C17O 1 16O13C16O+16O12C17O ! K 16O12C16O+17O12C17O 2 2 16O12C17O ! K 16O12C16O+16O13C18O 3 16O13C16O+16O12C18O ! K 16O12C16O+17O12C18O 4 16O12C17O+16O12C18O ! K 2 16O12C16O+17O13C17O 5 16O13C16O+216O12C17O ! K 16O12C16O+18O12C18O 6 2 16O12C18O ! K 2 16O12C16O+17O13C18O 7 16O13C16O+16O12C17O+16O12C18O ! K 2 16O12C16O+18O13C18O 8 16O13C16O+216O12C18O !

1 How big is ∆ ?

Note: 1‰ = 1/1000 Published data: Affek2005, Came2014, Halevy2011, Kluge2015, Mekler2011, Yeung2009 6 www.nature.com/scientificreports/ www.nature.com/scientificreports

www.nature.com/scientificreports identifed with the isotopologue specifc enrichment or fractionation values (CO2 denoting any particular iso- topologue in the following equation)

[CO] [C12 16O] ∆ = 2 2 − + ∆ (CO)2 ⁎ / 12 16 ⁎ 1ln(1(CO2)), [CO]2 [CO]2 (3) commonly used for the quantifcation of isotopomers21 or multiply substituted isotopologues22,23: www.nature.com/scientificreports/ ⎛ 13 16 18 12 16 ⎞ www.nature.com/scientificreports⎛ 13 16 18 ⎞ ⎛ 12 16 18 ⎞ ⎛ K ⎞ [COO] [CO] ⎟ [COO] ⎟ [COO] ⎟ −ln⎜ 1 ⎟ = ln⎜ 2 ⎟ = ln⎜ ⎟ − ln⎜ ⎟. ⎜ ⁎ ⎟ ⎜ 13 16 12 16 18 ⎟ ⎜ 13 16 ⎟ ⎜ 12 16 ⎟ ⎝⎜K1 ⎠ ⎝⎜ [CO]2 [COO] ⎠ ⎝⎜ [CO]2 ⎠ ⎝⎜ [CO]2 ⎠ (4) identifed withT thee right isotopologue hand side expression specifc enrichment is applicable or to fractionation the optical measurement, values (CO which2 denoting provides any theparticular two particular iso- isotopo- topologue loguein the ratios following as independent equation) observables. As evident from Eq. (4), the temperature information contained in the equi- librium constant does only depend on two12 16 concentration ratios, that may be regrouped diferently. ln (K1) is completely [CO] [CO] 17 OPEN independent of∆ the(C bulkO) =isotope 2composition./ 2 Consequently,− 1l n(1( the+ ∆ OCO isotopic)), composition does not at all afect the Optical2 clumped⁎ 12 16 ⁎ isotope2 determination of the equilibrium[CO]2 constant.[C BulkO]2 isotopic compositions are only introduced when isotopologue(3) concen- ∆ ⁎⁎12 16 18 13 16 ⁎ trations are replaced by values as21 defined in Eq. (3). Using K1 ==1[22,23 COO] [CO]2 / commonly used12 16 for the⁎ 13 quanti16 18fcation⁎ of isotopomers or multiply substituted isotopologues : thermometry([ CO2 ][ COO] ) and keeping only the of leading termscarbon in the Taylor series expansiondioxide on both sides, one obtains ⎛ ⎞ ⎛ 13 16 18 12 16 ⎞ ⎛ 13 16 18 ⎞ ⎛ 12 16 18 ⎞ ⎜ K1 ⎟ ⎜[COOK ] [CO]2 ⎟ ⎜[COO] ⎟ ⎜[COO] ⎟ −ln⎜ ⎟ = ln⎜ 1 −∆1( 13CO16⎟ =18O)ln⎜−∆(C13 16O)⎟ −−∆ln⎜(C12 16OO18 ), ⎟. Ivan⎜ P⁎r⎟okhor⎜ov 13 1,2,316 ⁎ 12 16K18luge⎟1,2 & Christof⎜ 13 16 Jans2⎟sen ⎜ 1,312 16 ⎟ ⎝K1 ⎠ ⎝ [CKO]1,2 Tobias[C OO] ⎠ ⎝ [CO]2 ⎠ ⎝ [CO]2 ⎠ (4) (5) Te rightSwhereimultaneous hand the side expression sign analysis indicates is applicable of the carbon approximative to dioxidethe optical isotopologuescharacter measurement, of the which relation.involved provides T inis the equation, the isotope two particular which exchange may isotopo also between- be derived the Received: 4 September 2018 22 logue ratiosdoublydirectly as independent substitutedfrom Eq. observables. (24) 13 ofC Wang16O 18AsO et evident moleculeal. , is from very and Eq. similar 12(4C),16 the toO thetemperature has commonly become information usedan exciting defnition contained new of ∆tool in47 inthe for clumped equi geochemical,- isotope librium constant does only depend on two14,24 concentration ratios, that may2 be regrouped diferently. ln (K ) is completely Accepted: 22 February 2019 atmosphericmass spectrometry and paleoclimaticof CO2 , research with applications ranging from stratospheric1 chemistry to independent of the bulk isotope composition. Consequently, the 17O isotopic composition does not at all afect the Published: xx xx xxxx carbonate-based geothermometry studies.47 Full exploitation46 of45 this isotope proxy and thermometer is determination of the equilibrium constant. Bulk∆47 isotopic= ∆−(C compositionsO)2 ∆−(C areO) only2 introduced∆(CO)2 when, isotopologue concen- (6) limited due to time consuming and costly analysis using mass⁎⁎ spectrometric12 16 18 instrumentation.13 16 ⁎ Here, we trations are replaced by ∆ values as defined in Eq. (3). Using K1 ==1[COO] [CO]2 / 12 16 ⁎where13 16 isotopologues18 ⁎ are replaced by m/z signals, because they cannot be measured individually. Comparison of ([ CO][presentCO anO] all) opticaland keeping clumped only the C Oleading2 isotopologue terms in the thermometer Taylor series expansion with capability on both sides, for onerapid obtains analysis and 2 ⁎ simplifedEqs (5) and sample (6) leads preparation. to the identif Thecation current of ∆−47 developmentKK11/1 with also the provides relative deviationthe option of forthe analysisequilibrium of con- 24 stant K1 from Kits1 statistical value.13 16 It 18has been argued13 16 that the last12 two1816 18terms on the right hand side are zero , but additional multiply-substituted−∆1( CO isotopologues,O) −∆(CO) such−∆ as(C C OOO2. Since), the instrument unambiguously ⁎ 2 ∆ 22 this premise isK not completely consistent12 16with the13 de16fnition18 of13 16 in Eq. 12(3) 16and18 thermodynamic calculations measuresLaser all isotopologues1 Fiber ofDetector the C O 45+ C O O 46 C O + C O O exchange, its(5 equilibrium) 4439 nm 2 2 that respectively yield −4 and −11 ppm for ∆( CO2) and ∆( CO2) for CO2 equilibrated at 300 K. Te reason for where the constantthe sign con indicatesficting and theresults the corresponding approximative is that in the onecharacter temperature case approximate of the arerelation. measured but Tpreciselyis equation, directly. measurable which Being mayand essentially inalso the be other derived independent case exact but of Laser 4329 nm 22 directly fromtheonly Eq. isotope approximatively (24) of composition Wang et accessible al. , ofis verythe atomic calibrationsimilar isotope to the gas, ratios commonly an are uncalibrated used used in de thefnition calculations working of ∆ 47reference inof clumpedthe statistical is sufcientisotope abundances. and usage 14,24 mass spectrometryofNonetheless, international of CO the2 so calibration de, fned ∆ 47standards is overwhelmingly is obsolete. infuenced Other byisotopologues the frst of the andthree molecules terms, which can in be turn accessed is to a 9 cm Detector usinglarge extent the methodology, (97%, see Table opening 1) dominated up new by the avenues 13C16O 18inO isotope isotopologue. research. Here we demonstrate the high- 10 m 47 46 45 Unlike the direct ∆measurement47 = ∆−(C O)of2 ln (K∆−1)(C accordingO)2 to∆ (CEq. (O)42), ,mass spectrometer determinations(6) of ∆47 not precisionReference performanceGas of the instrument with frst gas temperature measurements of carbon dioxide only require measurementhandling of heavyVacuum isotopologue abundances. Te ‘absolute’ or bulk isotope composition must samplesSample from unitgeothermal sources. where isotopologuesalso be known are replaced in order byto m/zdetermine signals, the because statistical they abundance cannot be measuredof the m/z individually. = 47 signal. ComparisonTis implies determiningof 13 12 18 16 17 16 ⁎ 13 18 17 Eqs (5) andatomic (6) leads C/ to C,the identiO/ Of cationor O/ ofO ∆− ratios47 KK (traditionally11/1 with quanti the relativefed in deviationterms of δ ofC, the δ equilibriumO and δ O convalues),- neces- 24 stant K1 fromsitating its statistical that international value. It has standard been argued substances that the are last used two and terms that on assumptions the right hand on side the are17O zero isotope, but content are 22 this premiseMassmade. isFigure not spectrometry In completelythis 2. wayScheme systematic of consistent of multiply the home biases withsubstituted built of the dual-laser up de tof 40isotopologuesnition system.ppm of are Lasers∆ introduced in Eq.or are clumped ( connected3) 24and. Equally thermodynamic isotopes to the important, optical has become cell calculationsmass via optical an spectrometers extremely fibres and powerful optical can elements. An off-axis parabolic mirror45 focusses the exiting46 light from the multi-pass cell on the photo-detector. The light of the that respectivelytoolonly inapproximately yield the natural−4 and −accesssciences.11 ppm the for Demonstratedclumped ∆( CO 13C2)16 andO 18applications ∆O (isotopologueCO2) for which CO (also2 equilibrated investigated due to an ation-source carbon300 K. T dioxide, dependente reason methane, for scrambling nitrous single pass is projected on a second detector without further focussing. The cell is filled with sample and reference gases via a the confictingoxide,efect) results molecularusing is the that m/z hydrogenin the= 47 one signal andcase and oxygenapproximate a corresponding range but from precisely scalingtectonic measurable factor history must and and be evolution, inapplied the other1,14 .geobiology case exact butand atmospheric custom-built inlet system and it can be evacuated using a second gas connection. only approximativelychemistryUsing the over accessible equilibrium the investigation atomic constant isotope of of non-equilibrium anratios isotope are used exchange in processes the (or calculations isomerisation) with correction of the reaction statistical procedures, with abundances. a particular diagenesis working studies, the Nonetheless,investigationgas the as a so thermometer, def nedof mineral ∆47 istemperature overwhelmingly formation is conditions, directly infuenced measured the byassessment theas a f thermodynamicrst of of the hydrothermal three terms, variable. whichfow T systemse inequilibrium turn andis to paleo-evolution a constant of 13 16 18 large extenttoan (97%, paleothermometry; isotopeDuplicate see exchange Table mass 1) dominatedreaction spectrometer and there isDoubly linkedby measurements are the many toC thesubstitutedO morereaction haveO isotopologue. beenpotential free performed enthalpyisotopologue applications using ∆F the of ThermoFischer1that,2. T reactione most prominent MAT253PlusK = exp(−∆ uses instrumentF/(kT are)) linked25 at–27 IUP, to Unlikethe wherethe oxygen Heidelberg,direct k is themeasurement isotope Boltzmann that has exchange been of constant equipped ln reaction(K1) andaccording with wherebetween an additional weto Eq. thehave m( main4/ adopted),z =mass 47isotopologue.5 spectrometer acup per and molecule 10 13andW determinationsresistors therather 13C- than on18Om / acontainingz per =of 47 ∆mole47 49not de massspecies fnition cups. of of The CO reactants products 2 only requireenergies. measurementm/z = T47e.5 freeis usedof energy heavy for continous of isotopologue the gas baseline is linked abundances. monitoring to the gas’ of TK resistance moleculare ‘absolute’ for partition clumped or bulk isotopefunction,isotope analysis. composition which Details sums must ofover this all setup energy will be also be knownstatespublished. in ε order taking25 to Thedegeneracies determine analysis followsthe d12 statisticalinto16 accepted account++ abundance13 procedures. and16 18counting 13of, 14 the13 internalm/z16 = 47 energy signal.12 16 states T18 is .implies from the determining lowest or zero-point 13 12 18 i 16 17 16 i CO2 COOCOC2 13 18OO 17 (R1) atomic C/energyC, O/(ZPE)O or ε stateO/ ofO theratios molecule (traditionally quantifed in terms of δ C, δ O and δ O values), neces- 0 17 sitating that internationalReaction2.2 Equilibrium (R1 standard) involves constant, substances onlyD47 aand single are approximations used chemicaldoubly and that compound, assumptions but on could the notO isotope be exploited content scientifically are until main levels εε24 singly substituted made. In thisrecently. wayThe equilibriumsystematic Tis is because constantbiases oftheirK up1 of veryto the 40 isotope lowppm natural are exchangesubstituted introduced abundance−− reactioni . (EquallyR1 hampers) is strictly important, 0the proportional study mass of multi-substituted tospectrometers the product of can absorption isotopic signals mole- 13 16 18 1 13 16 118Qd==eQkT QekT13. 18 only approximatelycules,A = sucha 13accessC as16O a Cthe12CO16 clumpedO18O,Oa containing12 16 Ca13O 16 Otwo18 isotopologue, or which∑ morei therefore rare (also isotopes allows trdueansi to for (e.g.nt an the ion-source opticalC and measurement O)dependent simultaneously. via scrambling When compared 2 C O2 C O O "clumped" (7) = 12 16 i −4 1,14 efect) usingto the m/zmain isotopologue47 signal and a correspondingC O2, these are scaling well factor below must 10 be (see applied Table 1.). At the same time, the measurement Equilibrium constant 13 16 12 16 18 Using the equilibriumIn the Eq. (7 constant) we have of made an isotope the usual exchange separation (orC isomerisation)O of theC centreO O reaction of mass withmotion a particular (trans) from working the molecular techniques needed to attain extremely highK = accuracy2 levels of a few= S0.01‰A, (~tens of ppm) in order to trace(2) the gas as a thermometer, temperatureof isotope is directly exchange measured 1 as a12 thermodynamic16 13 16 18 variable. Te equilibrium constant of 9 naturalinternal variability degrees of offreedom the corresponding (int). Since the isotopologue equilibriumC O2 and constantC a dynamicO O is given range⇥ as a onproduct the order of partition of about functions 10 or better of is reaction: 26⇥,27 ⇤⇥ ⇤ 25–27 an isotopetherefore reactantexchange ( reactrequired. reaction) and is Soproduct linked far, only to (prod the mass )reaction molecules spectrometer free enthalpy instruments ∆F of that are reaction capable Kof = ful exp(flling−∆ theseF/(kT criteria)) , and clumped ⇥ 1 ⇤⇥1 ⇤ where k is the whereBoltzmann the scaling constant factor andS = wheres12 16 wes 13have16 18adopteds13 16 a1 sper,212 16molecule18 depends rather on thethan13 involved a per mole molecular defnition line strengths. of Lacking CO2 has not yet been measuredC byO 2opticalC O methodsO C O . CDoublyO O substituted CH3D methane, which shows higher energies. Te free energy of the gas is linked to⎛ the gas’ molecular⎞3/2 2 partition ⎛function, which− sums over⎞ all energy fractionationthe required values, accuracy, however,∏ currentQprod data has base been∏ valuesM investigatedprod cannot⎟ ∏ beQ in usedusingtp, ro ford laser-based determining∑ εε0,pr Sinstruments.od, which∑ best0,re isac Tt determinede frst laser experimentally spectrometer by states ε taking degeneraciesK d= into account= and⎜ counting⎟ internal energyexp,⎜ states− from the lowest or⎟ zero-point i exploiting3 the temperaturei dependence⎜ of K1 or⎟ its logarithm (see Fig.⎜ 3). The latter is widely used,⎟ because deviations from setup for clumped methane∏ Qreac isotopologuest ⎝⎜∏ Mreact based⎠ ∏ onQkin ditr, eafcterence⎝ frequency Tgeneration⎠⎟ (DFG) still sufered from energy (ZPE) the ε0 state statistical of the value molecule(K? = 1, where the ?-symbol indicates the13 high temperature limit) are small and4 it can be expressed(8) by uncertainties in the 20‰1 range which exceeds natural CH3D variability of about 8‰ . Nevertheless, a more three individual logarithmic terms, which can be identified with5 the isotopologue specific enrichment or fractionation values recentit is amenable diode laser to quantum study on statistical doublylevels substituted mechanicsεε andmethane computational has successfully chemistry demonstrated methods. Here that we optical have followed systems can −−i 0 (CO2 denoting any particular isotopologue in the following equation) wellthe usual approach simpli thefcation necessary toQd evaluate== requirements.∑ theieQ ratiokT T of etrtranslational anachievedsiQent kT precision. partition level functions of 200 toppm, ratios however, of molecular remains masses still well 26 M . Te only non-trivial factors arei the total internal partition functions thatH. Urey,need to 1934 be evaluated7 (7 separately.) If above the commonly accepted threshold of[CO 100] ppm12 (orC16 0.1‰)O required for the study of clumped isotope frac- one is mainly interested in isotopeD fractionation(CO )= 2efects, it is convenient2 1 ln to(1 normalise+ D(CO )), the equilibrium constant by(3) In the tionationEq. (7) we in have non-hydrogenated made the usual separationmolecules.2 [ofCO the]? centre12 16of mass? motion' (trans) 2from the molecular dividing through its classical high temperature 2limiting ⇥ C valueO2 ⇤ K , which is given as the product of the classical internal degrees of freedom (int). Since the equilibrium constant is given as* a product of partition functions of symmetry numbers of product and reactant molecules: reactant (reactcommonly) and product used for(prod the) quantificationmolecules26,27 of isotopomers26 or⇥ multiply⇤ substituted isotopologues:27, 28

1 133/216 18 12 16 13 16 18 12 16 218 Institute of EnvironmentalK1⎛ Physics,⎞C HeidelbergO O CUniversity,O⎛2 εε 69120,− CHeidelberg,O O ⎞ Germany.C O HeidelbergO Graduate SCIENTIFIC REPORTS | (2019) 9:4765 | https://doi.org/10.1038/s41598-019-40750-z∏ Qprlnod ⎜ ∏=Mlnprod ⎟ ∏ Qintp, rod ⎜ ∑ =0,prlnod ∑ 0,react ⎟ ln . 5(4) School Kof =Fundamental =K? Physics,⎜ Heidelberg⎟13C16O University,12C16exOp,18⎜−O 69120, Heidelberg,13C16O ⎟ Germany. 12 3CLERMA-IPSL,16O Sorbonne ∏ Q ✓ 1⎝⎜◆∏ M ⇥ ⎠⎟ ∏ Qk2 ⇤ ⇥ ⎝⎜ ⇤ ! ⇥T 2 ⇤⎠⎟! ⇥ 2 ⇤! Université, CNRS,re Observatoireact re acdet Paris, PSLintr, eaUniversité,ct 75005, Paris, France. Correspondence(8 and) requests for The right hand side expression corresponds⇥ most⇤ ⇥ to the optical⇤ measurement,⇥ which⇤ provides the⇥ two particular⇤ isotopologue it is amenablematerials to quantum should statisticalbe addressed mechanics to C.J. (email:and computational [email protected] chemistry methods.) Here we have followed ratios as independent observables. As immediately evident from this Eq. (4), the temperature information contained in the the usual simplifcation to evaluate the ratio of translational partition functions to ratios of molecular masses 26 equilibrium constant does only depend on two concentration ratios, that may be regrouped differently. ln(K1) is completely M . Te only non-trivial factors are the total internal partition functions17 that need to be evaluated separately. If SCIENTIFIC REPORTS | (2019) 9:4765independent | https://doi.org/10.1038/s41598-019-40750-z on the bulk isotope composition. Consequently, the O isotopic composition, for example, does not at all enter. 1 one is mainly interestedBulk isotopic in compositionsisotope fractionation are only introduced efects, it when is convenient isotopologue to concentrationsnormalise the are equilibrium replaced by constantD values definedby in Eq. (3). dividing through its classical high temperature? limiting? value K ?, which is given? as the product of the classical Using K? = 1 = 12C16O18O 13C16O 12C16O * 13C16O18O and keeping only the leading terms in the Taylor symmetry numbers of1 product and reactant molecules:2 2 series expansion on⇥ both hand⇤ sides,⇥ one obtains⇤ .⇣⇥ ⇤ ⇥ ⇤ ⌘

K1 13 16 18 13 16 12 16 18 SCIENTIFIC REPORTS | (2019) 9:4765 | https://doi.org/10.1038/s41598-019-40750-z? 1 D C O O D C O2 D C O O , 5 (5) K1 ' ⇣ ⌘ ⇣ ⌘ ⇣ ⌘

4/13 www.nature.com/scientificreports

OPEN Optical clumped isotope thermometry of carbon dioxide Ivan Prokhorov 1,2,3, Tobias Kluge1,2 & Christof Janssen 1,3

Simultaneous analysis of carbon dioxide isotopologues involved in the isotope exchange between the Received: 4 September 2018 13 16 18 12 16 doubly substituted C O O molecule and C O2 has become an exciting new tool for geochemical, Accepted: 22 February 2019 atmospheric and paleoclimatic research with applications ranging from stratospheric chemistry to Published: xx xx xxxx carbonate-based geothermometry studies. Full exploitation of this isotope proxy and thermometer is limited due to time consuming and costly analysis using mass spectrometric instrumentation. Here, we present an all optical clumped CO2 isotopologue thermometer with capability for rapid analysis and simplifed sample preparation. The current development also provides the option for analysis of 12 18 additional multiply-substituted isotopologues, such as C O2. Since the instrument unambiguously 12 16 13 16 18 13 16 12 16 18 measures all isotopologues of the C O2 + C O O C O2 + C O O exchange, its equilibrium constant and the corresponding temperature are measured directly. Being essentially independent of the isotope composition of the calibration gas, an uncalibrated working reference is sufcient and usage of international calibration standards is obsolete. Other isotopologues and molecules can be accessed using the methodology, opening up new avenues in isotope research. Here we demonstrate the high- precision performance of the instrument with frst gas temperature measurements of carbon dioxide samples from geothermal sources.

Mass spectrometry of multiply substituted isotopologues or clumped isotopes has become an extremely powerful tool in the natural sciences. Demonstrated applications which investigated carbon dioxide, methane, nitrous oxide, molecular hydrogen and oxygen range from tectonic history and evolution, geobiology and atmospheric chemistry over the investigation of non-equilibrium processes with correction procedures, diagenesis studies, the investigation of mineral formation conditions, the assessment of hydrothermal fow systems and paleo-evolution to paleothermometry; and there are many"Clumping" more potential effect applications1,2. Te most prominent uses are linked to 13 18 the oxygen isotope exchange reaction between the main isotopologue and the C- O containing species of CO2

12 16 13 16 18 13 16 12 16 18 CO2 ++COOC OC2 OO. (R1) Cold Reaction (R1) involves only a single chemical compound,Warm but could not be exploited scientifically until recently. Tis is because their very low natural abundance hampers the study of multi-substituted isotopic mole- cules, such as 13C16O18O, containing two or more rare isotopes (e.g. 13C and 18O) simultaneously. When compared 12 16 Bond− of4 heavy isotopes is to the main isotopologue C O2, these are well below 10 (see Table 1). At the same time, the measurement techniques needed to attain extremely high accuracy levelsslower of vibrating a few 0.01‰ and lower (~tens in of ppm) in order to trace the natural variability of the corresponding isotopologue andenergy a dynamic than equivalent range on of the light order of about 109 or better is therefore required. So far, only mass spectrometer instrumentsisotopes. are capable of fulflling these criteria and clumped 1,2 13 CO2 has not yet been measured by optical methods . Doubly substituted CH3D methane, which shows higher fractionation values, however, has been investigated usingClumping laser-based is energetically instruments. Te frst laser spectrometer setup3 for clumped methane isotopologues based on dipreferential.ference frequency generation (DFG) still sufered from 13 4 uncertainties in the 20‰ range which exceeds natural CH3D variability of about 8‰ . Nevertheless, a more recent diode laser study on doubly substituted methane5 has successfully demonstrated that optical systems can well approach the necessary requirements. Te achieved precision level of 200 ppm, however, remains still well above the commonly accepted threshold of 100 ppm (or 0.1‰) requiredH. for Urey, the study19348 of clumped isotope frac- tionation in non-hydrogenated molecules.

1Institute of Environmental Physics, Heidelberg University, 69120, Heidelberg, Germany. 2Heidelberg Graduate School of Fundamental Physics, Heidelberg University, 69120, Heidelberg, Germany. 3LERMA-IPSL, Sorbonne Université, CNRS, Observatoire de Paris, PSL Université, 75005, Paris, France. Correspondence and requests for materials should be addressed to C.J. (email: [email protected])

SCIENTIFIC REPORTS | (2019) 9:4765 | https://doi.org/10.1038/s41598-019-40750-z 1 Clumped isotope thermometry

-5 / Kelvin

∆ 10 -6 / Kelvin 5x10

Prokhorov2019 9 Take away message

1. isotopes are never randomly (stochastically) distributed among isotopologues, 2. small variations of clumped isotope are temperature dependent, 3. these variations are always in favour of clumped isotope formation, 4. clumped isotope excess is independent of bulk isotopic composition and other clumped isotope species, 5. All this is true for thermodynamic equilibrium.

10 Today I will present ...

... fundamental principles of clumped isotopes (example of CO2)

... current and emerging analytics

... selected applications of CO2 and CH4

11 Analytical challenges

Isotopes are rare, Clumped isotopes are but clumped isotopes are (rare)2 thermodynamically active systems

Sensitivity Scaling (precision) (accuracy)

12 O13CO + 18OCO K 18O13CO + OCO !

18 13 Q 18O13COQOCO [ O CO] [OCO] R 18O13CO Isotope RatioK= Mass Spectrometry= 13 18 = QO13COQ 18OCO [O CO] [ OCO] RO13COR 18OCO

K DualR 18O 13inletCO : switchingR 18OCO betweenR O13CO ln =ln ln ln K⇤! R⇤reference18O13CO! and R sample⇤18OCO! gas RO⇤ 13CO!

Ri i = 1 Ri⇤ measured R47 47 = 1 R⇤ 47 calculated R47 47 = 2 1 2R13R18 +2R17R18 + R13R17

ref Ri =(1+) Ri

K 18O13CO = ln K⇤! [18O13CO] [OCO] K = [O13CO] [18OCO] 13

K ⇠⇠: 0 ⇠⇠: 0 18 13 18⇠⇠ ⇠13 ⇠ ln = O CO ⇠⇠OCO ⇠⇠O CO K⇤!

[18O13CO] [18OCO] K = 13 [O CO] , [OCO]

3 www.nature.com/scientificreports/ www.nature.com/scientificreports Isotope Ratio Mass Spectrometry

Isotopologue i a No Symbol Mass (u) Rel. abundance ni/Σjnj (mol/mol) Rel. contribution to mass (%) Note 12 16 −1 1 C O2 44 9.842 ⋅ 10 100.000 13 16 −2 2 C O2 45 1.100 ⋅ 10 93.636 3 12C16O18O 46 3.947 ⋅ 10−3 99.785 4 12C16O17O 45 7.478 ⋅ 10−4 6.364 b 5 13C16O18O 47 4.413 ⋅ 10−5 96.710 6 13C16O17O 46 8.361 ⋅ 10−6 0.211 12 18 −6 7 C O2 48 3.957 ⋅ 10 99.578 c 8 12C17O18O 47 1.500 ⋅ 10−6 3.286 12 17 −7 9 C O2 46 1.421 ⋅ 10 0.004 13 18 −8 10 C O2 49 4.424 ⋅ 10 100.000 11 13C17O18O 48 1.676 ⋅ 10−8 0.422 13 17 −9 12 C O2 47 1.588 ⋅ 10 0.003

Table 1. Typical relative abundance of stable CO2 isotopologues in decreasing order. Abundance values are based on assumingMAT a 253 statistical Plus distributionMAT253 of oxygen Ultra and carbonisobar isotopes free in international 13C16O18O standard materials (VSMOW for O and VPDB for C: 13R = 11056/988944, 17R = 3790/9976206, 18R = 20004/9976206)53. aAtomic b 10,11 12 M/mass∆M constant. Can900 only be measured afer 40,000conversion into O2 or using56,000 isotope exchange techniques . cSignal used to detect contaminant species, such as hydrocarbons or halogenated compounds14.

14 While mass spectrometers excel in the achieved precision of about 10 to 20 ppm6,7, the instruments have to cope with inherent drawbacks. Not only are they relatively costly and heavy, thus not permitting in-feld opera- tion; they also require time consuming measurements and careful sample preparation in order to avoid contam- ination of the measurement signal. With current mass spectrometric procedures, preparation and analysis of a carbonate sample take about 3 to 6 h8. Importantly, only the largest and most sophisticated instruments can reach 9 the mass resolution required to resolve isobaric interferences in CO2 . Typical operation conditions are around 13 16 12 16 17 13 16 18 ∆M/M ~ 40000 or lower, which is insufcient to separate C O2 from C O O at m/z = 45 or C O O from 12C17O18O at m/z = 47, for example. In order to resolve these masses, a resolving power of above 52000 is needed – so far only accessible for large radius instruments in ‘non-normal operation’ mode9. Tis makes multiply sub- stituted isotopologue analysis by mass spectrometry a very exclusive technology that will remain limited to only a handful of highly specialised laboratories worldwide, likely also constraining industrial or commercial use. Note 12 16 13 18 that only two ( C O2 and C O2) out of twelve stable CO2 isotopologues can be detected entirely free from iso- 13 16 12 16 18 13 16 18 baric interference using a mass spectrometer (see Table 1). Te four isotopologues C O2, C O O, C O O, 12 18 and C O2, strongly dominate (>90%) a cardinal mass signal. Tey can thus well be assessed by the same tech- 12 18 nology except C O2, whose quantifcation sufers from distorting background signals. For minor contributions to a cardinal mass, such as 12C16O17O however, more advanced sample preparation or conversion technologies10–12 must be employed at the cost of prolonged measurement time and reduced precision. Simple counting statistics prevent using current mass spectrometer technology for the analysis of CO2 iso- topologues below the relative abundance level of 10−5, even if these provide the main contribution to a cardi- nal mass. Assuming the measurement uncertainty being limited by Poisson statistics, the 10 ppm precision is reached afer about 3 or 4 h of measurement on m/z = 47 (13C16O18O)13. In order to obtain the same precision for 12 18 16 13 16 18 12 18 2 the C O2 isotopologue on m/z = 48, a (n( C O O)/n( C O2)) ~ 100 times longer analysis time would be required, thus about two weeks. Even measurement times of two days are impractical and contrary to common practice. Demonstrations of ppm level instrument stabilities over such long time periods are lacking too. Te m/z = 48 and 49 signals can therefore only be used as an indicator for sample contamination (hydrocarbons, 1,14,15 12 18 13 18 halocarbons, sulphur monoxide) and must remain useless in exploiting C O2 or C O2 as isotopic tracers with mass spectrometry. Despite the pioneering achievements of mass spectrometry in rare multi-isotope research, it is evident that alternative technologies are needed to overcome several of the aforementioned limitations. In this paper, we will present the frst optical multi-isotopologue analyser for CO2 that is not infuenced by most of these limitations, most notably the isobaric interference problem. Te instrument achieves a measurement accuracy well below the 100 ppm level in the measurement of 13C16O18O and the technique has the capacity of assessing new tracers 12 18 such as C O2 that likely provide new and complementary information. In principle the developed method is calibration free and has strong potential of becoming a breakthrough technology, because it provides great isotopologue selectivity at reduced time, size and cost factors, which makes it well suited for widespread scien- tifc, laboratory and commercial applications. Te paper focusses on the measurement of carbon dioxide and the isotope exchange in the gas phase and we present the analysis of CO2 from thermal sources in the Upper Rhine Valley. Te results will be compared to duplicate mass spectrometer measurements of CO2 from the same source. Apart from direct studies of gaseous carbon dioxide, current applications are concerned with multiply-substituted isotopologues in carbonates. Because carbonate isotopologues are obtained from measurements of gaseous CO2 released during the acid digestion of the carbonates, they can be investigated using the same analysis systems. Te direct application of carbon dioxide isotopologue analysis to carbonates is further facilitated by the fact that the 6 carbonate clumped isotope scale has been directly tied into the equilibrium CO2 gas scale .

SCIENTIFIC REPORTS | (2019) 9:4765 | https://doi.org/10.1038/s41598-019-40750-z 2 Isotope Ratio Mass Spectrometry

Popa, et al. 2018 Stolper, et al., 2016 If isobaric interferences can not be avoided, clumped isotopes are quantified as variation of mass signal, e.g.

Popa2018, Stolper2015 15 Laser Absorption Spectroscopy

Prokhorov2019 16 Laser Absorption Spectroscopy

Precision on the level of 10-5

• No isobaric, but spectral interferences • Detection in gas mixtures is possible Demonstrated for IR active • Faster, but not necessarily more precise than IRMS molecules: CO2, N2O, CH4

Prokhorov2019 17 Calibration and reference scale

Heated gas 1000˚C (sealed quartz tubes)

2O(l)

(g) + H Equilibrated2 gas

Pure CO (sealed glass tubes)

Is thermodynamic equilibrium reached ?

Kinetic isotope effects, mixing of isotopes from different sources, diffusion and bond formation -> drivers of isotope exchange reaction

Prokhorov2019, Ono2014 18 Take away message

1. LAS and IRMS offer precise and accurate measurements of clumped isotopes at 10-5 level, 2. isobaric interferences are the main limitations of IRMS, 3. LAS is faster but less stable, emerging technique with potential to replace IRMS 4. for both methods, calibration schemes are based on thermodynamic re- equilibration of isotopes

19 Today I will present ...

... fundamental principles of clumped isotopes (example of CO2)

... current and emerging analytics

... selected applications of CO2 and CH4

20 Carbonate clumped isotope paleothermometer

18O exchange between water and carbonate during carbonate formation - classical δ18O-thermometer, however...... δ18O of initial water is unknown

Future applications

Kinetic fractionation

Equilibrium

22 Clumped isotopes to distinguish methane sources

Gonzales2019 Summary

1. small variations ∆ of clumped isotopes (multiply-substituted isotopologues) are temperature driven in equilibrium, 2. temperature dependence is independent of bulk isotopic composition, 3. IRMS and LAS are two major method to analyse ∆ at sub-permill level, 4. clumped isotopes augment classical isotope methods

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