Of the six stable isotopic variants of O2, only three are measured routinely. Observations of natural variations in 16O18O/16O16O and 16O17O/16O16O ratios have led to insights in atmospheric, oceanographic, and paleoclimate research. Complementary measurements of the exceedingly rare 18O18O and 17O18O isotopic variants might therefore broaden our understanding of oxygen cycling. Here we describe a method to measure natural variations in these multiply substituted isotopologues of O2. Its accuracy is demonstrated by measuring isotopic effects for Knudsen diffusion and O2 electrolysis in the laboratory that are consistent with theoretical predictions. We then report the first measurements of 18O18O and 17O18O proportions relative to the stochastic distribution of isotopes (i.e., Δ36 and Δ35 values, respectively) in tropospheric air. Measured enrichments in 18O18O and 17O18O yield Δ36 = 2.05 ± 0.24‰ and Δ35 = 1.4 ± 0.5‰ (2σ). Based on the results of our electrolysis experiment, we suggest that autocatalytic O(3P) + O2 isotope exchange reactions play an important role in regulating the distribution of 18O18O and 17O18O in air. We constructed a box model of the atmosphere and biosphere that includes the effects of these isotope exchange reactions, and we find that the biosphere exerts only a minor influence on atmospheric Δ36 and Δ35 values. O(3P) + O2 isotope exchange in the stratosphere and troposphere is therefore expected to govern atmospheric Δ36 and Δ35 values on decadal timescales. These results suggest that the ‘clumped’ isotopic composition of atmospheric O2in ice core records is sensitive to past variations in atmospheric dynamics and free-radical chemistry.
 Measurements of 18O18O and 17O18O in atmospheric O2 could offer independent isotopic constraints on O2budgets. For instance, the isotopic signature of atmosphere-biosphere interactions could potentially be resolved from that of the hydrosphere because the tendency for18O-18O and 17O-18O bonds to form upon photosynthesis should be insensitive to the isotopic composition of the source water. Water has no O-O bonds to pass on, so photosynthetic chemistry alone should determine the extent to which18O and 17O ‘clump’ together during photosynthesis. In addition, the mass dependence of respiration for 18O18O and 17O18O could be used in concert with well-known mass dependences for16O18O and 16O17O with 16O16O to understand oxygen consumption mechanisms in terrestrial and marine environments.
 While 18O18O and 17O18O are exceedingly rare (4 ppm and 1.6 ppm, respectively, in O2; see Table 1), recent advances in gas-source mass spectrometry suggest that their variations can be measured with “normal” (i.e., low-resolution) isotope-ratio mass spectrometers (IRMS). The routine analysis of rare ‘clumped’ isotopic variants of CO2 to high precision (i.e., ≤0.02‰ in 16O13C18O, which is 46 ppm in CO2 [Eiler and Schauble, 2004; Eiler, 2007; Huntington et al., 2009; Eiler, 2011]) suggests that variations in 18O18O and 17O18O could be measured with a precision of order ±0.1‰ using existing technology. The presence of 36Ar in air at 37 times the natural abundance of 18O18O (also at mass 36), however, poses a significant analytical challenge for low-mass-resolution instruments.
Table 1. Properties of O2 Isotopologues in Air
7.8 × 10−4
1.6 × 10−5
4.1 × 10−3
8.6 × 10−4
1.5 × 10−7
3.2 × 10−8
1.6 × 10−6
3.4 × 10−7
4.2 × 10−6
8.8 × 10−7
 Here we describe a method to measure natural variations in 18O18O and 17O18O and we report the first measurements of 18O18O and 17O18O in tropospheric air. These analyses were made possible by (i) an apparatus for quantitative separation of O2 from Ar in large samples, (ii) the development of a standardization method based on the reversible decomposition of BaO2, and (iii) characterization of the extent of isotopic reordering during sample preparation. We demonstrate the accuracy of our methods with two sets of laboratory experiments in which O2 is subjected to either Knudsen diffusion or electrolysis. The results of those experiments are consistent with theoretical predictions. Last, we report the proportions of 18O18O and 17O18O in tropospheric air with a 1σ precision of ±0.1‰ and ±0.2‰, respectively, and interpret these results using a box model of the atmosphere.
2. Clumped-Isotope Systematics of O2
18O18O and 17O18O distributions are reported against the stochastic (random) distribution of isotopes as defined by the following relationships:
in accordance with the recent recommendations by Coplen  and conventions for reporting ‘clumped’ isotope distributions [Huntington et al., 2009; Dennis et al., 2011]. Enrichments and deficits in Δn-notation, reported in per mil (‰), reflect proportional deviations from a canonical relationship derived from the bulk isotopic composition, similar to the way in which Δ17O or 17Δ values are derived from δ18O and δ17O values [Miller, 2002; Young et al., 2002]. In this case, the canonical relationship is the random occurrence of isotopes in a molecular species.
 Conceptually, Δn quantifies the abundances of rare isotopic variants relative to those predicted by chance for a given collection of stable isotopes: Δn = 0 represents the random distribution of isotopes, whereas a nonzero Δnvalue represents on over- or under-abundance of the indicated rare isotopologue relative to the random distribution. In many instances, this over- or under-abundance of rare isotopologues can be thought of as an excess or deficit in bond ordering, i.e., the tendency of two (or more) rare isotopes to occur as neighbors on the same bond. This definition of Δn as an ordering parameter can be misleading, however, when variations in Δn occur not through intramolecular bond scission or synthesis, but rather by fractionation of isotopologues. In the latter case, bond ordering is unchanged, but the expected stochastic distribution (e.g., 36Rstochastic) is altered by changing the overall (bulk) isotopic composition of the ensemble (e.g., 18R) [Eiler, 2007].
 In effect, Δn can change either by altering bond ordering in molecules or by altering the reference stochastic composition. The Δnvalues so defined are not conserved quantities precisely because the stochastic distribution changes with bulk isotopic composition. Apparent isotopic bond ordering can therefore be modified by both bond-altering processes and bond-preserving processes. Atmospheric budgets are affected by mechanisms that fall into both categories [Affek and Eiler, 2006; Affek et al., 2007; Yeung et al., 2009], so we will discuss the isotopic systematics of O2 separately in each context.
2.2. Bond-Ordering Equilibrium: Breaking and Making Bonds, but Preserving Atomic Abundances
 The familiar carbonate clumped-isotope paleothermometer [Eiler, 2011] relies on the change in isotopic bond ordering resulting from a bond-breaking/bond-making process: carbonate mineral growth at equilibrium. In that case, intraphase isotope-exchange equilibrium, when achieved [Wang et al., 2004; Ghosh et al., 2006; Eagle et al., 2010], results in a bond-ordering signature that is independent of the isotopic mass balance between the carbonate and its source water. Bond ordering in the carbonate mineral system, consequently, would then depend only on the temperature of equilibration, and thus would be independent of bulk isotopic composition. These equilibrium bond-ordering values are typically enrichments of up to one per mil in Δn because heavy isotopes usually prefer to bond with each other at low temperatures [Wang et al., 2004].
 The relevant intraspecies isotopic equilibrium state for O2in the atmosphere is gas-phase O2 + O2isotope-exchange equilibrium wherein the bulk isotopic composition (and therefore the stochastic distribution) is constant. Bond re-ordering during isotope exchange leads only to changes in Δ36 and Δ35 values. Theoretical equilibrium Δ36 and Δ35 values are 1.5–3.0‰ for Δ36 and 0.8–1.6‰ for Δ35, between 300 and 200 K [Wang et al., 2004]. Thus, any process that breaks and re-forms O-O bonds without consuming or producing O2 could, in principle, drive Δ36 and Δ35 toward equilibrium values with no measurable change in δ18O and δ17O. Possible mechanisms resulting in equilibration include the reversible decomposition of alkali-earth peroxides (Section 3.2), catalytic isotope exchange on zeolites (Section 3.3) [Starokon et al., 2011], and gas-phase O(3P) + O2 isotope exchange reactions (Section 4.2) [Kaye and Strobel, 1983].
2.3. Physical Fractionation: Preserving O-O Bonds
 The simplest bond-preserving process relevant to the atmosphere is two-component mixing. The isotopic composition (e.g.,18R and 36Rmeasured) varies linearly with mixing fraction, yet the stochastic distribution, i.e., 36Rstochastic = (18R)2, varies nonlinearly with mixing fraction. So, even if a mixture consists of two gases with the same initial Δn values, mixing yields Δn anomalies; Δn is not conserved. Mixing equal parts O2 with δ18O ∼ 0 (e.g., ocean water) and δ18O ∼ 25‰ (e.g., atmospheric O2), both starting with Δ36 = 0, yields an anomaly of +0.15‰ in Δ36 (see Figure 1). This feature of Δn notation has been demonstrated in previous work on CO2 [Eiler and Schauble, 2004]. Only in rare cases, such as when the mixing end-members have the same bulk isotopic composition, are Δnvalues conserved upon mixing. Mixing-based budgets for atmospheric Δn values are therefore less straightforward than traditional budgets based solely on bulk isotopic δ-notation.
 An intuitive relationship between isotopologue fractionation and Δn values for O2for bond-preserving processes can be derived from the familiar parlance of mass-dependent isotope effects. Here, we follow the practice of describing fractionation factorsα related by mass dependences β [Young et al., 2002]:
where the numerical subscripts describe fractionation factors between different O2 isotopologues of mass mi and mj and 16O16O (m = 31.989829). In equation (3), a fractionation that preserves Δ36 and Δ35 has mass dependences of β36/34 = 0.500 and β35/34 ≈ 0.66, respectively. While β36/34 = 0.500 preserves Δ36 as a natural consequence of its definition, β35/34 values that preserve Δ35 vary somewhat with β34/33 due to the presence of two different rare stable isotopes in 17O18O. We derive these relationships in Appendix A. Graphically, Δnvalues are approximated by horizontal excursions on a triple-isotopologue plot relative to the mass-dependent relationship for the stochastic distribution, i.e.,δ36 excursions relative to a β36/34 = 0.500 line on a δ34 versus δ36 plot (see Figure 2). Examples of these mass dependences can be found in gravitational fractionation and Knudsen diffusion.
 A stagnant air column in a gravitational potential will have a higher partial pressure of heavy isotopologues at the base. This fractionation depends on mass according to the barometric formula. For a species of mass m, its partial pressure P at a height Z and temperature T can be related to the surface partial pressure P0 by the equation:
where g is the acceleration due to gravity (9.81 m s−2) and RG is the gas constant. This equation can be recast to reflect isotopic ratios:
where m32 is the mass of 16O16O. One can now recognize that because the mass difference between 16O18O and 16O16O, (m34 − m32), is exactly half the mass difference between 18O18O and 16O16O, (m36 − m32), we have (α34)2 = α36. Therefore, α34 = (α36)0.5, or β36/34 = 0.5, and gravitational fractionation has a negligible effect on Δ36 (even when including the contribution from 17O17O; see Appendix A). A similar argument can be made to show that β35/34 = 0.666, resulting in no fractionation for Δ35. This behavior for Δ36 and Δ35is distinct from the bulk-isotope fractionations of 0.1–1‰ in natural systems [Craig et al., 1988; Severinghaus et al., 1996].
 Knudsen diffusion, in contrast, leads to changes in both Δ36 and Δ35. Graham's law of effusion states that the flux of gas through an orifice smaller than the mean free path of that gas will be inversely proportional to the square root of its mass. For pure O2 gas, the isotopic fractionation factor is:
Mass dependences for effusion can be derived from these α values to be β36/34 = 0.515 and β35/34 = 0.676 (see Table 1), which lead to Δ36 and Δ35 increases in the isotopically lighter diffused population: O2 that has leaked through a critical orifice from an infinite reservoir is lower in δ18O and δ17O by 29.9‰ and 15.3‰, respectively, but higher in Δ36 and Δ35 by 1.7‰ and 0.9‰, respectively, than the reservoir. This fractionation is a classic example of ‘clumped’ isotope signatures changing due to shifts in the stochastic reference frame (i.e., the bulk isotopic composition of the gas).
 In a finite system, the residue population will be fractionated in the opposite direction: Higher in δ18O and δ17O, but lower in Δ36 and Δ35 (see Figure 2). Furthermore, this closed system has β values that are slightly larger than those of the infinite system due to the effective α values derived from Rayleigh fractionation relationships:
where f represents the fraction of the initial gas remaining, and α for the Rayleigh system is defined by Rdiffused/Rinitial [Young et al., 2002]. β36/34 and β35/34 values, defined by connecting the Rdiffused and Rresidue corresponding to a single f value, range from 0.515–0.522 and 0.676–0.681, respectively, depending on f. We explore these particular systematics experimentally in Section 4.1.
 To analyze 18O18O and 17O18O in O2, argon was first removed from samples using gas chromatography at sub-ambient temperatures. Next, the purified O2 was analyzed against a working reference gas on an IRMS, where the residual Ar content was also measured (as a m/z= 40 voltage ratio). Then, standard gases with similar bulk isotopic composition, but a ‘clumped-isotope’ composition near the stochastic distribution, were prepared and analyzed over a range of Ar concentrations. Reported Δ36 and Δ35 values correspond to the excesses or deficits in 18O18O/16O16O and 17O18O/16O16O ratios relative to the stochastic distribution of isotopes after correction for the residual Ar signals and deviations from a purely stochastic distribution in the reference gases (see Appendix B).
3.1. Sample Handling and Purification
 O2 samples (150–200 μmol O2) were transferred to and from a gas chromatographic system through two glass U-traps at −196°C on a high-vacuum glass line pumped by a diaphragm-backed turbomolecular pump (Pfeiffer HiCube), which had a typical baseline pressure of ∼5 × 10−6 mbar. Purified O2 samples were adsorbed for 10 min onto small glass fingers filled with molecular sieve 5A pellets at −196°C before analysis on the IRMS.
 The gas chromatographic (GC) system, which was designed to separate O2 from Ar and N2, consisted of a reconditioned HP 5890 Series II GC capable of cryogenic cooling with liquid nitrogen and thermal conductivity detection. First, samples were adsorbed onto degassed silica gel pellets in a U-trap at −196°C for ∼30 min. The U-trap was then immersed in warm water (∼60°C) while an ultra-high-purity helium carrier gas (>99.9995%; Grade 5.5) flowed through it to desorb the sample. The desorbed sample was then injected onto the GC column (3 m, molecular sieve 5A, 80/100 mesh; Restek) using two 4-way VICI/Valco switching valves. As an additional precaution against atmospheric leaks, the switching valves were isolated in He-flushed “jackets.” The eluent from the GC column was collected on a second silica gel U-trap downstream from the GC column at −196°C. Air samples were passed through the GC system a second time to remove residual Ar remaining from the first pass. A diagram of the vacuum/GC extraction and purification system is shown inFigure 3.
 Baseline separation of Ar, O2, and N2 was achieved at T ≤ −65°C, and routine separations were carried out at −80°C. The volumetric flow rate was 25 mL min−1 (∼23 psi He carrier). Argon typically eluted near 30 min, while O2 eluted near 38 min (see Figure 3); collection of O2 lasted 23–25 min, starting near minute 37. After collection of O2, the column temperature was raised to 200°C and the He pressure was raised to 40 psi to elute N2.
 The conditions for O2/Ar separation were chosen to minimize both residual Ar and total sample preparation time. Higher O2/Ar elution temperatures decreased the O2/Ar peak resolution and also increased the amount of Ar in the purified product. For instance, raising the temperature to 25°C after the Ar peak eluted, which reduced the O2 collection time to ∼15 min, actually increasedthe Ar content relative to a 25-min collection at −80°C. Furthermore, using a 6-m molecular sieve 5A column yielded no improvements in O2/Ar separation efficiency due to on-column dispersion and a longer O2collection time. However, installing a U-trap to purify the helium carrier filled with molecular sieve 5A and a 6-ft silica gel column (45–60 mesh; SRI International), both at −196°C, resulted in a twofold improvement in Ar removal. Consequently, we believe that Ar impurities in the helium stream ultimately limited O2 purity in the current system. Typical air preparations with two passes through our system resulted in 1–5 ppm 40Ar (i.e., 3–17 ppb 36Ar) in O2. Additional small ion corrections at m/z= 36 were necessary for high-precision measurements of18O18O (see Appendix B).
 The use of a stochastic reference frame for O2 isotopologue abundances requires that one develop methods to generate laboratory standards with known Δ36 and Δ35 values over a range of bulk isotopic composition [Huntington et al., 2009; Dennis et al., 2011]. High-temperature standards, reflecting Δ36 ∼ Δ35 ∼ 0, are a convenient reference close to the stochastic distribution. We utilized the reversible decomposition of BaO2to generate Ar-free O2at high-temperature isotopic equilibrium:
Argon can be pumped out at low temperatures so O2 will evolve exclusively from the lattice when the peroxide is heated above 600°C [Tribelhorn and Brown, 1995]. The oxygen atoms in each product O2 molecule originate from different peroxide groups in the mineral lattice [Tribelhorn and Brown, 1995], and the process is reversible, so BaO2decomposition at high temperatures should produce a ‘clumped-isotope’ distribution in the evolved O2reflecting high-temperature equilibrium; experimental studies indicate that equilibrium can be maintained at T < 1000°C at low heating/cooling rates [Tribelhorn and Brown, 1995; Jorda and Jondo, 2001]. This method is general to alkali-earth peroxides, and is similar to that used byAsprey  to synthesize pure F2 gas from the reversible decomposition of solid K2NiF6·KF, i.e., 2(K2NiF6·KF)solid ⇌ 2(K3NiF6)solid + F2.
 To estimate the clumped-isotope composition of O2 derived from BaO2decomposition, theoretical models for bond-ordering in O2 and BaO2 were used. A comparative model of isotopologue ordering in O2 was calculated using the same method and data as Wang et al. , using the harmonic frequency of 16O16O [Huber and Herzberg, 1979]. Vibrational frequencies of isotopologues were determined from their reduced masses, and the resulting estimate was essentially identical to the harmonic model of Wang et al. . We note that Wang et al.  showed that inclusion of anharmonic terms has a minor effect on ordering equilibria for O2, <0.01‰ at room temperature.
 BaO2 is predicted to be much less enriched in multiply substituted isotopologues than O2 is at all temperatures (see Figure 4 and Appendix C). It is also predicted to have lower 18O/16O and 17O/16O ratios. Above 600°C, Δ36 and Δ35 are both predicted to be <0.01‰ in BaO2, whereas they are predicted to be ≤0.08‰ in O2. As with the C-O bonding system, there appears to be a strong correlation between equilibrium constants and bond order, with double-bonded species (e.g., CO2 and O2) showing larger enrichments in multiply substituted isotopologues than species with lower-order bonds (e.g., C–O bonds in carbonate and bicarbonate and O–O bonds in peroxide) [Wang et al., 2004; Schauble et al., 2006; Eagle et al., 2010].
 To decompose BaO2 in the laboratory, BaO2 powder was first loaded into 1/4″ OD quartz tubes and pumped to 10−6–10−5 mbar overnight. Afterwards, the quartz tubes were sealed with a torch and placed in a tube furnace at 800°C for 2.5 h (calculated Δ36 = 0.03‰ and Δ35 = 0.02‰). Hot breakseals were quenched immediately when plunged into cold water. As a test of the breakseal method, we also performed experiments in which BaO2was heated to 800°C for 2.5 h in an evacuated 9-mm ID quartz-and-glass tube that extended from the interior of the tube furnace to an aliquot volume. In this arrangement, the evolved O2 was allowed to equilibrate with BaO and BaO2only at high temperatures, unlike the breakseal-quenching process, in which some low-temperature isotope exchange might be present. We did not observe significant differences beyond typical experimental scatter in the resulting Δ36 and Δ35 values measured (±0.1–0.3‰, depending on the isotopologue), consistent with the breakseal method yielding O2at high-temperature equilibrium.
 A second method for generating high-temperature O2 standards in breakseals was also developed. In that method, O2 was collected into breakseals with molecular sieve 5A and Platinum wire and heated to 1000°C (expected Δ36 = 0.02‰ and Δ35 = 0.01‰). Hot breakseals were again quenched immediately by plunging them into cold water. While we cannot rule out a lower ‘blocking’ temperature for gases prepared in this manner, high O2 concentrations should passivate platinum when T < 500°C [Brewer, 1953], where Δ36 = 0.11‰ and Δ35 = 0.06‰, so O2 standards prepared in this manner are still expected to be near the stochastic distribution, and nearly indistinguishable from it within the analytical uncertainty. We note that this method altered the bulk isotopic composition of O2, probably by isotopic exchange with the molecular sieve and/or quartz, but the bulk isotopic fractionation was relatively consistent.
3.3. Other Sources of Isotopic Reordering
 While the oxygen-oxygen bond in O2 is not easily broken (bond dissociation enthalpy 118 kcal mol−1), any isotopic reordering during sample preparation and analysis will result in an alteration of Δ36 and Δ35. Thus, we performed experiments with O2 samples enriched in 18O18O to quantify the extent of isotopic reordering in our sample preparation scheme.
 The extent of isotopic reordering in the source of the IRMS was determined by measuring the isotopic composition of our O2 standard gas “spiked” with an aliquot of ≥97% 18O18O (Cambridge Isotope Labs). Significant isotopic reordering in the IRMS source would result in a significant increase in δ34 (500–600‰ for our 18O18O spike size), with little change in δ36 relative to the unspiked O2, due to fragmentation-recombination reactions such as
Zero isotopic reordering would yield (i) no change in δ18O beyond any 16O18O present in the ≥97% 18O18O gas and (ii) a large change in the m/z = 36 voltage. In our experiment, we observed only a small change in δ34 (∼9‰) and a relatively large change in δ36 (3.4 × 105‰), indicating that the extent of O2 isotopic reordering in the IRMS source was small. We further quantified the extent of isotopic reordering in the IRMS source by the method of standard additions (see Figure 5). The results were consistent with only 1% of the bonds being reordered toward an (probably high-temperature) isotope-exchange equilibrium in the IRMS source.
 Similar 18O18O spike-reordering tests were performed with molecular sieve adsorbents because O2can exchange isotopes with the molecular sieves and/or reorder its isotopes on the surface of molecular-sieve zeolites at low temperatures [Starokon et al., 2011]. Adsorption of O2 onto the molecular sieve 5A at −196°C, followed by desorption at 240°C for 30 min, resulted in ∼1% isotopic reordering. Passing gas through the GC system only reordered isotopes in O2 after the column was baked with a helium flow at 350°C overnight (∼12h). In that case, the bond ordering resembled equilibrium at the GC temperature, −80°C. During a typical air preparation, O2 was exposed to molecular sieve four times (twice through the GC and twice in a sample finger), which would result in a reduction in Δ36 signal magnitude of ∼4% (i.e., ∼0.08‰ for Δ36= 2‰) We observed some evidence for isotopic reordering (2–3%) upon exposure to a pressure gauge that had both Pirani-type and inverted magnetron capabilities (Edwards WRG-S; perhaps due to the tungsten electrode exposed to vacuum), so we isolated the gauge from O2 during our sample preparation.
4.1. Knudsen Diffusion: Mass Fractionation While Preserving O-O Bonds
 We performed experiments to induce shifts in Δ36 and Δ35 by Knudsen diffusion of O2. These experiments provide a useful test of our analytical methods because the changes in Δ36 and Δ35 due to diffusion are readily calculable. We showed, in Section 2.3, that fractionation factors α for O2 diffusion through a critical orifice lead to measured effective β36/34 and β35/34values of between 0.515–0.522 and 0.676–0.681, respectively, for a system subject to Rayleigh fractionation. In a laboratory setting, back-diffusion through the critical orifice can also alter effectiveα and βvalues: Because the “downstream” volume is never ideal (finite size and pressure), gas can travel “upstream” into the high-pressure volume. This back-diffusion is subject to the same isotopic fractionation described inequations (6)–(8), but with a time-dependentRinitial value corresponding to the changing Rdiffused in a Rayleigh system; Benedict showed that the resulting fractionation factors could be described by the equation [Benedict, 1947; Naylor and Backer, 1955]:
where Pds/Pus is the ratio of pressures in the downstream and upstream volumes.
 Assuming no back diffusion, i.e., Pds/Pus = 0, and f = 0.5, the difference in δ18O, δ17O, Δ36 and Δ35 between the diffused and residue populations is calculated to be −41.9‰, −21.4‰, +2.7‰, and +1.4‰ respectively. For Pds/Pus = 0.1 and f= 0.5, the difference between the diffused and residue populations is calculated to be −37.7‰, −19.2‰, +2.5‰, and +1.3‰, respectively. Because the mass dependence of diffusion governs both forward and back-diffusion,β36/34 and β35/34 values do not change appreciably for f = 0.5 (i.e., β36/34 = 0.5170 versus 0.5174 for Pds/Pus= 0 versus 0.1, respectively). Thus, back-diffusion mainly reduces the bulk isotopic fractionation relative to the unidirectional Rayleigh limit.
 In our pinhole diffusion experiment, we allowed O2gas to diffuse from a 5-L glass bulb through an orifice of known diameter into a vacuum. We measured the isotopic composition of both the diffused and residue populations. The initial pressure in the 5-L bulb was 1.0 mbar, resulting in a mean free path,λ, of 100 μm. Molecular oxygen diffused through a laser-drilled orifice (Lenox Laser) with a diameter,D, of 75 ± 7.5 μm. It then passed through a length of flexible bellows tubing and a second 5-L bulb and two U-traps at −196°C (total volume ∼5.1 L) before being collected onto a silica gel trap at −196°C for purification on the GC system. The purpose of the second 5-L bulb was to reduce back-diffusion through the critical orifice, as adsorption of O2 onto silica gel is a slow process. The steady state pressure on the “diffused” side of the apparatus was ≤10−1 mbar during the experiment. After 3 h of diffusion, both bulbs were isolated from the critical orifice, and the diffused population was allowed to adsorb onto the silica gel trap for another 60 min. Both the diffused and residue population were analyzed on the IRMS.
 The results of the diffusion experiment are shown in Figure 6 and Table 2. As predicted for a diffusion-limited system, the diffused gas exhibited decreases inδ18O and δ17O and increases in Δ35 and Δ36. In addition, using equation (12) with Pds/Pus = 0.2 yields good agreement between theory and experiment. The measured isotopic fractionations yield a β36/34 value of 0.517 ± 0.002 (1σ), consistent with the predicted β36/34of 0.518. An assumption of no back-diffusion, i.e.,Pds/Pus= 0, instead predicts bulk- and clumped-isotope fractionations that are smaller, and anf value that is larger, than the measured values.
Table 2. Results of Knudsen-Diffusion Experiment
Measured f = 0.50 ± 0.05
f = 0.591, Rayleigh
f = 0.529, Pds/Pus= 0.2, Plus Back-Diffusion
Diffused – Residue
1.0 ± 0.6
−0.3 ± 0.6
1.3 ± 0.7
1.39 ± 0.16
−0.74 ± 0.29
2.13 ± 0.33
 Back-diffusion of order 20% is possible given the relatively slow O2 adsorption rate onto silica gel, which resulted in the relatively high steady state downstream pressure of ≤10−1 mbar. However, the size of our critical orifice (λ/D = 1.33) also yielded gas flow properties in the transition region between purely molecular (Knudsen) and purely viscous (Poiseuille) flows. Because viscous flow does not fractionate isotopologues, while Knudsen diffusion fractionates isotopologues according to Graham's law, a small amount of viscous flow probably reduces Graham's law fractionations with a scaling factor on (α− 1) similar to the effect of back-diffusion inequation (12). Furthermore, theoretical calculations by Wahlbeck  suggest that gas flux through the orifice is enhanced by ∼20%, presumably due to increasing viscous flow, relative to the flux predicted for purely molecular flow at λ/D= 1.33. Thus, we are unable to distinguish between back-diffusion and partially viscous flow leading to a 20% reduction in (α − 1) values in this experiment. Decreasing the orifice size to achieve purely molecular flow (λ/D ≥ 10, i.e., D ≤ 10 μm at 1 mbar) would reduce the mass flow rate through the orifice more than 50-fold, increasing the experiment's duration to about a week. Such timescales are impractical for this experiment because atmospheric leaks would have become important. Cryo-trapping the diffused O2, however, would eliminate back-diffusion and isolate the viscous-flow contribution to the observed diffusive isotopic fractionation.
4.2. O2Electrolysis: Bond-Ordering Equilibration Independent of Bulk Isotopic Composition
where Q denotes an isotope of oxygen and M is a third body such as another O2 molecule. In a closed system, the bulk isotopic composition is determined by the O2/O3 mass balance and isotope effects in O3 formation [Hathorn and Marcus, 1999, 2000; Gao and Marcus, 2001], while oxygen atoms in their ground electronic state, O(3P), act as catalysts for bond reordering in molecular oxygen.
 When a ground-state oxygen atom forms a bond with an O2 molecule, it has three possible fates: ozone formation, inelastic scattering, and isotope exchange. A stable ozone molecule forms only when a third body, M, absorbs the excess energy released during O-O bond formation. Without that third body, the metastable O3 can redissociate to O(3P) + O2. If the O-O bond that breaks is the one that just formed, then inelastic scattering results. If the other bond breaks, then isotope exchange occurs. In either case, the liberated O(3P) atom perpetuates an autocatalytic cycle. Consequently, reaction (13a) occurs at rates at least several hundred times faster than that of (13b) at pressures of ∼50 mbar [Kaye and Strobel, 1983; Johnston and Thiemens, 1997; Wiegell et al., 1997]. This difference in rates will decouple Δ36 and Δ35 values from the bulk isotopic composition of O2: While 36Rmeasured and 35Rmeasuredchange with every applicable isotope-exchange event,36Rstochastic and 35Rstochastic vary only with δ18O and δ17O, which is governed by the O2/O3 mass balance.
 Excited atomic oxygen, O(1D), could also exchange isotopes with O2, but O(3P) chemistry should dominate the bond-ordering budget in most systems. Nearly all O(1D) atoms will be quenched to O(3P) eventually by N2 or O2, after which isotope exchange proceeds autocatalytically. Even in the presence of unconventional chemical physics on the O3 potential energy surface, the large number of O(3P) + O2 isotope exchange reactions occurring is predicted to yield an isotopic distribution in O2that is controlled by differences in zero-point energies in the O2 isotopologues [Hathorn and Marcus, 1999, 2000; Gao and Marcus, 2001]. Δ36 and Δ35 values, as measures of bond ordering and not bulk isotopic composition, are therefore expected to reflect mass-dependent isotopic equilibrium, while δ18O and δ17O, being measures of bulk isotopic composition only, will reflect the mass-independentisotope effects that dominate ozone-formation chemistry.
 To realize O(3P) + O2 isotope exchange in the laboratory, O2was electrolyzed with a radio-frequency discharge in a manner similar to the classic experiments ofHeidenreich and Thiemens . We fabricated a vessel out of a 100-mL round-bottom flask, a tungsten electrode (1.5 cm exposed to vacuum), and a 9-mm Louwers-Hapert vacuum valve outfitted with fluorinated-elastomer O-rings (Markez). The exterior wire lead was jacketed so the entire vessel could be immersed in a cold bath without wetting the wire. Electrolysis was initiated by setting a Tesla coil at its lowest audible level for one hour. Pressures inside the vessels were 50 to 60 mbar at 25°C, resulting in a mean free pathλ ≤ 30 μm versus the vessel's 2-cm radius; under these conditions, O(3P) + O2 reactions should primarily occur in the gas phase with only a minor contribution from surface chemistry. After the experiment, O3 was cryogenically separated from O2, which was passed through the GC system twice to remove residual O3 and any contaminants.
 Electrolysis experiments were performed at three bath temperatures: 25°C, −30°C, and −80°C. The vessel temperature was maintained by submerging the round-bottom flask into a water bath (25°C experiment) or ethanol bath (−30°C and −80°C experiments). Because the Tesla coil added heat to the vessel, the bath temperature was monitored and, if necessary, the bath was cooled, every 10 to 15 min. This procedure yielded stable bath temperatures to within ±3°C. Temperatures inside the reaction vessel were not measured, but we performed several additional blank experiments to estimate the effective internal temperatures: A thermocouple was inserted into the reaction vessel while it was open to atmosphere (P∼ 1 bar) and the temperature was monitored for 10 min with the Tesla coil on, simulating experimental conditions. Internal temperatures increased monotonically in all cases, by +10°C, +16°C, and +18°C for the 25°C, −30°C, and −80°C baths, respectively. Therefore, we estimate that effective, time-integrated temperatures inside the reaction vessel were +5°C, +8°C, and +9°C warmer than the 25°C, −30°C, and −80°C baths, respectively.
 The results of the electrolysis experiments are presented in Figure 7 and Table 3. Δ36 and Δ35are consistent with bond-ordering equilibrium at the temperature of the experiments (1 to 3‰).δ18O and δ17O were depleted <1‰ along a slope = 1.0 line in triple-isotope space (δ17O versus δ18O), indicating that <5% of the O2 was converted into stable O3 [Heidenreich and Thiemens, 1983]. The depletions increased as temperature decreased (faster O3 formation rate), as expected for a changing O2/O3 mass balance. These results are consistent with our prediction that isotopic ordering (Δ36 and Δ35values) and bulk-isotope abundances are controlled by two different mechanisms in this system, one of which [O(3P) + O2 isotope exchange] equilibrates Δ36 and Δ35 despite persistent disequilibrium in the O2/O3 system.
 Autocatalytic O(3P) + O2 isotope exchange is the most likely mechanism to equilibrate Δ36 and Δ35 because of (i) its high bimolecular reaction rate, (ii) the paucity of permanent O(3P) sinks in the experiment, (i.e., surfaces, O3, or another O(3P)), and (ii) its minimal effects on δ18O and δ17O of O2. Furthermore, we observe nearly quantitative agreement between our measured Δ36 and Δ35 values and those expected from theory [Hathorn and Marcus, 2000; Wang et al., 2004]. Wall/surface effects cannot be ruled out, but the results from a previous study of O3 chemistry by Morton et al. suggest wall effects are insignificant in our apparatus. For example, the surface of the tungsten electrode during electrolysis likely resembles a high-temperature plasma, so significant oxygen-isotope exchange on that surface would probably reflect high temperatures rather than the low temperatures consistent with our results. Experimental deviations from theory were 0.1–0.3‰ in Δ36, similar to our stated measurement uncertainty; therefore, at most, high-temperature isotope exchange occurred at 10% the rate of gas-phase oxygen-isotope exchange. Isotope effects in other reactions involving excited-state species (e.g., O(1D) and O2(1Δg)) could also lead to deviations from isotopic equilibrium, but this system appears to be dominated by of O(3P) + O2 isotope exchange reactions. Future experiments with UV photolysis of O2 and O3 may yield further insight.
5. 18O18O and 17O18O in Tropospheric Air
 We measured Δ36 and Δ35 in ∼20 cm3 samples of tropospheric air collected at the UCLA Court of Sciences in October 2011. Our measurements yield Δ36 = 2.05 ± 0.24‰ and Δ35 = 1.4 ± 0.5‰ (2σ; see Table 4), where quoted uncertainties reflect propagation of both random and systematic errors in the analysis. Reproducibility between sample preparations is ±0.08‰ and ±0.2‰ for Δ36 and Δ35 (2 s.e., n = 5), respectively. This external precision includes the corrections for residual 36Ar and relatively small composition-dependent nonlinearity (seeAppendix B).
Table 4. Measured Isotopic Composition of O2 in Tropospheric Air
The δ18O and δ17O are reported against VSMOW using a laboratory standard gas calibrated with San Carlos Olivine (δ18O = 5.2‰, δ17O = 2.7‰). Our results are consistent a previous direct determination of the O2 bulk isotopic composition (δ18O = 23.51‰ and δ17O = 12.18‰) [Thiemens and Meagher, 1984]. A more recent measurement has reported δ18O = 23.88‰ and δ17O = 12.08‰ [Barkan and Luz, 2005].
External standard error of replicate gas preparations; systematic uncertainties increase 2σ limits to ±0.24‰ and ±0.5‰ in Δ36 and Δ35, respectively.
 Atmospheric O2is in a non-equilibrium steady state between oxygen photosynthesis and respiration. Its bulk oxygen-isotope composition (δ18O = 23–24‰) reflects biosphere processes on millennial timescales [Bender et al., 1994], plus a small contribution (∼0.3‰ in δ18O) from stratospheric photochemistry and subsequent oxygen-isotope transfer to CO2 [Yung et al., 1991; Luz et al., 1999; Luz and Barkan, 2011]. Most of the δ18O enrichment in atmospheric O2 arises from respiration, but its effects on Δ36 and Δ35 are not known because β36/34 and β35/34 values for respiration have not yet been measured.
 The effects of photosynthesis and respiration on Δ36 and Δ35 could be rendered insignificant, however, even when the biosphere dominates the bulk isotopic budget, if isotopic reordering of the atmospheric O2 reservoir occurs on timescales shorter than O2 cycling through the biosphere. Therefore, one must consider the role of O(3P) + O2isotope exchange reactions in the bond-ordering budget of atmospheric O2. As we showed in Sections 2 and 4.2, O(3P) + O2 isotope exchange reactions can drive Δ36 and Δ35 toward equilibrium values in a closed system with a negligible effect on the bulk isotopic composition of O2 in that system. The atmosphere, too, can be considered a closed system with respect to the oxygen isotopes in O2on sub-millenial timescales, with a O2/O3 mass balance yielding δ18O, Δ17O ≤ 0.3‰ [Luz et al., 1999; Young et al., 2002; Luz and Barkan, 2011]. Our reported tropospheric Δ36 and Δ35 values are consistent with isotopic equilibrium near 255 K, which is similar to the globally averaged tropospheric temperature of 251 K [Vinnikov and Grody, 2003], but O(3P) + O2 isotope exchange in the stratosphere probably has an influence on the tropospheric budget. Ultimately, a full consideration of the atmospheric Δ36 and Δ35budgets will require an accounting of the biosphere's effects as well. We will evaluate not only the relative rates of isotope-exchange and biological processes, but also the range of expected biological fractionations, inSection 5.2, with the aim of presenting testable hypotheses for future study.
5.2. Model for 18O18O and 17O18O in the Atmosphere
 We constructed a model of the atmosphere to investigate the balance of photosynthesis, respiration, and O(3P) + O2isotope exchange on the bond-ordering budget for O2 in the troposphere. The mole fraction of 18O18O in the troposphere, χT36, at steady state, can be described by the mass balance equation:
In equation (14), χP36 is the oxygen fraction of 18O18O for the photosynthetic end-member,α36,R is the respiratory fractionation factor, and χTeq36 and χS36 are the oxygen fractions of 18O18O for the tropospheric-equilibrium and stratospheric mixing end-members, respectively. The downward (FST) and upward (FTS) stratosphere-troposphere fluxes are in balance, i.e.,FST = FTS = 4.9 × 1018 mol O2 yr−1 [Appenzeller et al., 1996; Hoag et al., 2005], as are the photosynthetic (FP) and respiratory (FR) fluxes, i.e., FP = FR = 3.0 × 1016 mol O2 yr−1 [Luz et al., 1999; Blunier et al., 2002]. We have also included E, the rate of O2 equilibration in the troposphere (in mol O2 yr−1), in the mass balance equation. Inclusion of this term is supported by predictions of an O(3P) concentration of order 103 cm−3, constrained by tropospheric NOx and O3 concentrations [Brasseur et al., 1990; Liang et al., 2006]. A summary of model parameters can be found in Figure 8 and Table 5. Similar mass balance equations can be written for all the other O2 isotopologues and are not shown here.
Fraction of 18O18O in O2at isotope-exchange equilibrium in the troposphere
See section 4.4.2 (Δ36 = 1.7–2.1‰)
18O18O/16O16O fractionation for respiration
See section 4.4.3
 In the following sections, we will discuss the likely consequences of the transport of stratospheric air (5.2.1), tropospheric isotope exchange reactions (5.2.2), and biological processes (5.2.3) on the tropospheric budget of Δ36. We then conduct a sensitivity test (5.2.4) to determine the primary influences on tropospheric Δ36. The arguments that follow will also be valid for Δ35, but we will confine our discussion to Δ36 because of better analytical precision in our measurements. For simplicity, we have omitted the loss of 18O and 17O atoms from the O2 reservoir via O(1D) + CO2 isotope exchange in the stratosphere, which should decrease δ18O and δ17O by ∼0.3‰ [Luz et al., 1999; Luz and Barkan, 2011]; while the primary source of stratospheric O(1D), O3 photolysis, affects the O2 mass balance, the O(1D) + CO2reaction does not generate additional bond-ordering fractionation because it does not involve O2.
5.2.1. Flux of High-Δ36 O2 From the Stratosphere
 First, we estimate the stratospheric end-member,χS36, which is expected to be an equilibrium-like value facilitated by O(3P) + O2 isotope exchange reactions. High O(3P) and O2 concentrations in the stratosphere suggest that O(3P) + O2 isotope exchange occurs there readily (see Figure 9): Average expected chemical lifetimes of O2 with respect to oxygen isotope exchange, τO2, range from 160 days at 15 km to several minutes at 50 km (see Figure 2) [Brasseur et al., 1990; Wiegell et al., 1997; Brasseur and Solomon, 2005]. These short τO2 times suggest that a typical air parcel, which upwells into the O(3P)-rich stratosphere at tropical latitudes, will have its O-O bonds re-ordered before it re-enters the O(3P)-poor troposphere in the middle and high latitudes >1 year later [Holton et al., 1995; Plumb, 2007; Engel et al., 2009; Holzer et al., 2012]. O2chemistry involving other short-lived species (e.g., HOx, NOx, and ClOx) may have a minor influence. Because rates of transport across the tropopause are generally much slower than rates of O(3P) + O2 isotope exchange, we expect that Δ36 and Δ35will be temperature-stratified until a “horizon” is reached where the timescale of stratosphere-troposphere exchange (STE) is much shorter than that of isotopic equilibration at the in situ temperature. This isotope-exchange horizon probably lies in the climatological tropopause layer (∼15 km;T = 190–200 K), where τO2 is comparable to the dynamical STE lifetime of days to months. A descent velocity of 0.2–0.4 mm s−1 from stratospheric residual circulation at the midlatitude tropopause [Rosenlof, 1995] implies that the average sinking air parcel descends 1 km altitude in 30–60 days (ΔT ∼ 5 K, or 0.1‰ in Δ36). This transit time, τ1km, is comparable to τO2 between 15–20 km (T ∼ 200 K).
 We therefore estimate that O2 entering the troposphere from the stratosphere has χS36 and χS35 corresponding to Δ36,S = 3.0‰ and Δ35,S = 1.6‰, the equilibrium values at T ∼ 200 K. While our predicted value is uncertain due to a simplified STE scheme ignoring seasonal variations and isentropic STE [Holton et al., 1995], isotope-exchange lifetimes of less than a day above 25 km suggest that air entering the troposphere from the stratosphere is unlikely to have Δ36 values lower than 2.7‰. Furthermore, the effects of a changing 18O and 17O inventory in the O2/O3 system are limited because sequestration of oxygen isotopes in CO2 via O(1D) + CO2isotope-exchange reactions occurs much more slowly in the stratosphere than O(3P) + O2 isotope exchange (due to low O(1D) and CO2 concentrations [Yung et al., 1991; Boering et al., 2004; Liang et al., 2007]). Future measurements of stratospheric air, combined with 2-D modeling of intrastratospheric transport, should provide a more accurate stratospheric end-member. Note that the STE flux of 4.9 × 1018 mol O2 yr−1 [Appenzeller et al., 1996; Hoag et al., 2005] would cycle through a mass of O2 equivalent to the atmospheric inventory (3.7 × 1019 mol O2) in 7.6 years; autocatalytic oxygen-isotope exchange in the stratosphere would therefore alter the tropospheric O2bond-ordering signature on decadal timescales.
5.2.2. Gas-Phase Isotope-Exchange Reactions in the Troposphere
 In the troposphere, O(3P) chemistry could drive Δ36 and Δ35 toward equilibrium values at tropospheric temperatures. The troposphere's equilibrium 18O18O and 17O18O fractions in O2, χTeq36 and χTeq35, might reflect the global average tropospheric temperature of 251 K (Δ36 = 2.1‰ and Δ35 = 1.1‰ [Vinnikov and Grody, 2003]) because the troposphere is well-mixed on timescales of about a year. The main tropospheric O(3P) source, NO2, however, is emitted primarily at the surface by combustion processes and biological denitrification. NO2 is also produced by lightning above the planetary boundary layer (1–3 km). At the surface, the photochemical NO2 lifetime is several hours, significantly less than the timescale of mixing across the planetary boundary layer (∼1 week). The presence of that vertical transport barrier suggests that Δ36 and Δ35 may be sensitive to the vertical distribution of NO2. Weighting the tropospheric temperature profile by a vertical profile of NO2 would yield an effective temperature of 281 K (Δ36 = 1.7‰ and Δ35 = 0.9‰). In any case, tropospheric O(3P) concentrations are related to Eusing known isotope-exchange rate coefficients (kO+O2 ∼ 3 × 10−12 cm3 s−1 [Wiegell et al., 1997]), O2 concentrations, and an estimate of the volume of the troposphere (Vtroposphere ≈ 7.7 × 109 km3):
Using this equation, [O(3P)]avg = 1 × 103 cm−3, [O2]avg = 4.0 × 1018 cm−3, and 12 h of photochemistry each day, tropospheric O(3P) + O2 isotope exchange cycles through 2.4 × 1018 mol O2 per year, or a mass equivalent to the atmospheric O2 inventory in 15 years.
5.2.3. O2 Flux to and From the Biosphere
 The annual flux of O2 to and from the biosphere, at ∼1/160 the size of the STE flux [Luz et al., 1999; Hoag et al., 2005], may only be a minor contribution to the tropospheric Δ36 and Δ35 budgets. Still, the potential fractionations associated with the biosphere are important. Water oxidation during photosynthesis may yield O2 with χP36 and χP35 near the stochastic distribution because photosynthesis does not discriminate between oxygen isotopes [Guy et al., 1993; Helman et al., 2005]. Moreover, O2cannot inherit a bond-ordering signature from water because H2O contains no O-O bonds. Respiration leaves the O2 residue between 10 and 30‰ enriched in δ18O with a mass dependence β34/33 ≈ 0.516 [Lane and Dole, 1956; Guy et al., 1989; Kiddon et al., 1993; Angert et al., 2003; Helman et al., 2005]. These fractionations resemble those of closed-system Knudsen diffusion (β34/33 = 0.512), which would lead to χT36α36,R and χT35α35,R that are depleted relative to the stochastic distribution in the residue (i.e., Δ36 ≈ −2‰ and Δ35 ≈ −1‰ using β36/34 = 0.52 and β35/34 = 0.68; see Section 2.3). Oxygen consumption during photosynthesis, and possible associated oxygen-atom recycling in certain autotrophs [Eisenstadt et al., 2010], could therefore alter the effective photosynthetic abundances, χP36 and χP35, coming from aquatic environments. Nonetheless, the overall biosphere signature likely yields Δ36, Δ35< 0. Laboratory experiments identifying the bond-ordering signatures of photosynthesis and respiration will allow one to constrain further their contributions to the atmospheric Δ36 and Δ35 budgets.
5.2.4. Interpretation of 18O18O Measurements
 We tested the sensitivity of the tropospheric Δ36 budget to various fractionations using our box model (equation (14) and Figure 8) and the fluxes and mixing end-members justified in the preceding sections. The simplified biosphere in the model, with photosynthetic O2 having a bulk isotopic composition δ18O = 4‰ and α34,R = 0.98 (ε = −20‰), yielded a steady state δ18O = 24.4‰. Subtracting 0.3‰ due to O-atom transfer to CO2 in the stratosphere yields δ18O = 24.1‰, similar to previous measured and modeled values [Barkan and Luz, 2005; Luz and Barkan, 2011]. While our measured δ18O of O2 is less than this value (see Table 1), the difference is attributable to the assumed bulk isotopic composition in our primary standard (San Carlos Olivine, δ18O = 5.2‰). The interpretation of Δ36 is not affected by this subtle difference in bulk isotopic composition between model and the data.
 First, we will consider the biosphere alone in the absence of gas-phase bond-ordering equilibration due to O(3P) + O2 isotope exchange reactions. Using χP36 corresponding to the stochastic distribution, the measured tropospheric Δ36 value (+2.05‰) can only be obtained with β36/34= 0.476 for respiration, which is a value lower than the theoretical limit for gas-phase kinetic processes involving O2 [Young et al., 2002] and much lower than the value suggested in Section 5.2.3. Moreover, after including the effects of O(3P) + O2 isotope exchange in the stratosphere, respiration alone was unable to balance the flux of χS36 from the stratosphere for any value of β36/34; the STE flux is too large. Increasing the biosphere-atmosphere flux of O2 only yields modest decreases in tropospheric Δ36 (e.g., 2.7‰ for tenfold increases in FR and FP versus 3.0‰ for the base estimate). Alternately, χP36 would need to yield photosynthetic O2 with Δ36 ∼ −160‰ (when β36/34= 0.515 for respiration) to balance the high-Δ36 air entering the troposphere from the stratosphere. Given that primary O2 evolution does not discriminate between 16O16O, 16O17O, and 16O18O [Guy et al., 1993; Helman et al., 2005], a 160‰ disparity between 18O18O and 16O18O is implausible.
 Including tropospheric O(3P) + O2isotope exchange, however, can balance the STE flux of high-χS36 air. To explain Δ36 ≤ 2.29‰, the 2σ upper limit to our measured tropospheric Δ36, E must be ≥2 × 1019 mol O2 yr−1, corresponding to [O(3P)]avg ≥ 4 × 103 cm−3. A vertical gradient in tropospheric O(3P) would alter these estimates: Weighting the tropospheric temperature profile by a vertical profile of NO2 (see Section 5.2.2), yields E = 0.6 − 5 × 1019 mol O2 yr−1, and [O(3P)]avg = 1 − 10 × 103 cm−3 can explain the entire 2σ range in measured Δ36. A similar tropospheric O(3P) concentration range is obtained even if we use our lower estimate of χS36 corresponding to Δ36 = 2.7‰ coming from the stratosphere. These O(3P) concentrations, derived using our two-box model, are thus consistent with global models [Brasseur et al., 1990; Brasseur and Solomon, 2005; Liang et al., 2006].
 Based on our analysis of Δ36 and Δ35, O(3P) + O2 isotope exchange appears to exert the primary influence on isotopic bond ordering in tropospheric O2. While the effects of O2production and consumption by the biosphere are yet to be determined, gas-phase chemistry in the stratosphere and troposphere is sufficient to explain our measured value of Δ36 in tropospheric air. Future detailed studies on Δ36 and Δ35 in stratospheric O2, photochemistry, and isotopic fractionations associated with the biosphere will lay the groundwork for applications relevant to the atmospheric chemistry and biogeochemical cycling of O2.
6. Conclusions and Outlook
 We have measured proportional enrichments in 18O18O and 17O18O of 2.05 ± 0.24‰ and 1.4 ± 0.5‰ (2σ), respectively, in tropospheric air. Based on our laboratory experiments and a box model for atmospheric O2, we hypothesize that these enrichments are primarily driven by O(3P) + O2isotope-exchange reactions occurring in the stratosphere and troposphere. Due to the sensitivity of tropospheric Δ36 on the STE flux, atmospheric temperature profile, and O(3P) concentration, we hypothesize that measurements of bond ordering in tropospheric O2may be able to constrain atmospheric dynamics and free-radical chemistry in the present, and perhaps also in the past.
 Temporal variations in Δ36 and Δ35in the ice core record, specifically, may trace anthropogenic and climate-driven changes in atmospheric chemistry and circulation on decadal timescales. For instance, the main sources of tropospheric O(3P) were greatly reduced, relative to today, during preindustrial times: NOxemissions have been estimated to be as little as one-fifth those of the present-day, while tropospheric O3 concentrations may also have been reduced by half [Thompson, 1992; Martinerie et al., 1995]. Lower tropospheric O(3P) concentrations would decrease the tropospheric bond-ordering equilibration rate (E in equation (14) and Figure 8), shifting the steady state tropospheric Δ36value up toward the stratospheric mixing end-member value. A fivefold reduction in tropospheric O(3P) could result in as much as a 0.5‰ increase in tropospheric Δ36relative to the present-day value, depending on the effective tropospheric temperature used forχTeq36 and assuming no change in the STE flux. A recent prediction of only modest changes to tropopause temperature (∼+1°C) and STE flux during the Last Glacial Maximum could potentially also be tested [Rind et al., 2009].
 The triple-isotopologue mass dependences,β36/34 and β35/34, may also be used to constrain the oxygen budget in closed systems such as soils [Aggarwal and Dillon, 1998; Lee et al., 2003] and the ocean's interior [Kroopnick and Craig, 1976; Bender, 1990]. Bulk isotopic fractionations of up to +15‰ have been observed, which would result in a change of −1.3‰ in Δ36 of the residue (using β36/34 = 0.522). Over this range in bulk isotopic composition, a β36/34 difference of 0.002 would result in a 0.1‰ difference in Δ36. These triple-isotopologueβvalues provide additional information that augments the “triple-isotope”β34/33 values (i.e., relating δ18O and δ17O) used to partition oxygen consumption fluxes into their component mechanisms [Angert and Luz, 2001; Young et al., 2002; Angert et al., 2003], and may prove valuable where oxygen cycling mechanisms are poorly understood. Interpreting measured Δnvalues using mass-dependent fractionation laws represents a general approach to multi-isotopologue systematics that can be applied to any environment where single-phase isotope-exchange equilibration is not the dominant process. The sensitivity of Δ36 and Δ35 to diffusion, and not gravitational fractionation, for example, may comprise a test of physical fractionation mechanisms in glacial firn and ice layers, including countercurrent flux [Severinghaus et al., 1996] and bubble close-off [Severinghaus and Battle, 2006].
 Finally, this study highlights the potential value of high-resolution gas-source IRMS instruments for understanding atmospheric systems. Our analyses of18O18O and 17O18O in O2were possible on a low-resolution IRMS only after significant sample preparation and mass spectrometry of large gas samples. High-resolution instruments may be able to resolve18O18O from 36Ar well enough to reduce the sample handling artifacts and instrumental ion corrections that ultimately limit the precision in the present study. Detailed analyses of these species in O2trapped in ice cores, or in low-O2 zones in the oceans, will likely require sensitivity and precision higher than what is currently available.
Appendix A:: β-Values That Preserve Δ36 and Δ35
 Here, we derive the triple-isotopologue mass dependencesβ36/34 and β35/34 that preserve Δ36 and Δ35 values. We will omit the contribution of 17O17O to mass-34 O2 for simplicity, as the errors it imposes on Δ36 and Δ35 in the case of gravitational fractionation are <10−6‰. References to mass-34 O2 herein describe 16O18O species exclusively.
 During an arbitrary fractionation process, isotopologue abundances change from Ri to Rf according to α values for each isotopologue relative to 16O16O:
In most cases, O2 is near natural abundance and the 18O and 16O18O α values are comparable, yielding
The stochastic distributions for 18O18O and 17O18O in gases with composition Rf are therefore
for a gas with Rf/Rf,stochastic = Ri/Ri,stochastic (i.e., Δ36 and Δ35 values unchanged upon fractionation from Ri to Rf). Equation (A5) then resembles equation (3) with β36/34 = 0.500; therefore, β36/34 = 0.500 preserves Δ36 as it is defined in equation (2b). Finally, we recognize that the β35/34 preserving Δ35depends on the “triple-isotope” mass dependenceβ34/33: Values of β35/34 between 0.667 and 0.654 preserve Δ35 for specific values of β34/33 between 0.500 and 0.530, respectively, a range in β34/33 spanning equilibrium, kinetic, and gravitational fractionation [Young et al., 2002].
 For a gas in a gravitational potential (equation (5)), α values depend on the mass differences between isotopologues:
 Purified O2samples were analyzed on a dual-inlet Thermo-Finnigan MAT 253 IRMS equipped with 9 Faraday cups. The gas was equilibrated with the IRMS's sample bellows at ∼240°C for 35 min. Passive equilibration yielded analyses that consistently fractionated light (0.3–1‰ inδ18O) relative to their known bulk isotopic composition. Therefore, we “mixed” the gas by alternating the bellows volume between 25% and 100% three times every 200 s during the equilibration. An operating system script was written to automate this task, which eliminated the bulk isotopic fractionation (<0.02‰ in δ18O).
 Two of the Faraday cups had wide geometries to accommodate multicollection of O2 and CO2 on the same detector array. Amplifier resistor values of 5 × 107, 1 × 1011, 1 × 1010, 3 × 1011, and 1 × 1012 Ω yielded nominal detection voltages of 4000, 5500, 3500, 45, and 400 mV at m/z= 32 (wide cup), 33, 34 (wide cup), 35, and 36, respectively, with an ion-source pressure of ∼2.5 × 10−7 mBar. A 3 × 1011-Ω resistor was used form/z= 35 detection because we identified an electronic noise source coming from a switch on its amplifier board, particular to this Faraday cup-amplifier configuration, which degraded the signal-to-noise ratio (SNR) at higher resistor values; the 3 × 1011-Ω resistor on them/z = 35 amplifier board yielded a SNR similar to that of a 1 × 1012-Ω resistor on a switchless board. The resulting lower voltage onm/z= 35 was therefore the most sensitive to inaccuracies arising from long-term electronic drifts of order 1 mV (e.g., electronic offsets).
 Our working standard gas had a bulk isotopic composition of δ18O = −12.404‰ and δ17O = −6.457‰ against Vienna Standard Mean Ocean water, calibrated by assuming that San Carlos Olivine has a composition δ18O = 5.200‰ and δ17O = 2.742‰.
 Sample peak shapes are shown in Figure B1. Under typical ion-source pressures, we observed that all the minor ion beams had negative, pressure-sensitive baselines, or “pressure baselines,” that reduced the observed voltage relative to its true value. The magnitudes of these baselines varied with source pressure, conductance (modulated by the position of the “sulfur window”), extraction, and various tuning parameters, and they are qualitatively different from the zero-analyte backgrounds that were routinely subtracted as part of typical measurements. In general, these pressure baselines were negligible form/z = 33 and 34 (−6 and −2 mV, respectively, resulting in errors of order 0.001‰ in δ17O and δ18O), but significant for m/z= 35 and 36 (about −18 and −75 mV, respectively). They were affected by the presence of a strong magnetic field (i.e., a rare earth magnet) near the inlet to the Faraday cups. Secondary electrons inadequately quenched by the Faraday-cup electron suppressors and/or produced by collisions of ions with the sides of the IRMS flight tube are thought to be the source of these baselines.
 Pressure baselines were not of equal magnitude on either side of the molecular ion peaks. The high-voltage (low-mass) side was typically more negative (seeFigure B1). Placing a rare earth magnet on the flight tube near the detector array corrected this disparity, indicating that stray electron splatter may be its root cause. Measurements made with the magnet in place were consistent with those made without the magnet, albeit slightly noisier. Furthermore, the low-voltage (high-mass) side yielded the best reproducibility, so it was used, without the magnet, for pressure-baseline corrections.
 To measure these pressure baselines, we employed an acceleration-voltage-switching protocol similar to one being developed for measurements of mass-47 CO2 [He et al., 2012]. First, the sample and standard sides of the IRMS were pressure-balanced onm/z= 32 to within 15 mV at an acceleration voltage corresponding to the pressure baselines, i.e., 9.450 kV. Next, sample and standard pressure-baseline voltages form/z= 33–36 were measured in three IRMS sample-standard measurement cycles. The acceleration voltage was then increased to a value corresponding to peaks in the analyte signal, i.e., 9.485 kV, for 10 IRMS measurement cycles. Last, the acceleration voltage was switched back to the previous pressure-baseline setting, and another three measurement cycles were taken. During each measurement cycle, sample and standard signals were each integrated for 10s after an idle time of 20s. Each acquisition block was composed of 6 pressure-baseline and 10 on-peak measurement cycles, yielding a total analysis time of ∼25 min. Reported values are external averages and standard errors from 4–6 acquisition blocks.
 An example of the m/z = 36 signal during an acquisition block is shown in Figure B2. The pressure-baseline voltage increases (gets less negative), while the on-peak voltage decreases (gets less positive) with time; calculating the magnitude of the molecular signal requires that one account for both trends simultaneously. The pressure baseline was interpolated from a linear regression of the background voltage from the measurement cycles before and after the 10 on-peak measurement cycles. Separate linear regressions were generated for the sample and standard sides to mitigate errors due to sample-standard pressure imbalance. The molecular signal on each side for a measurement cycle was then calculated as the difference between the on-peak voltages and the interpolated pressure-baseline voltages. Signals atm/z= 35 were derived in the same way using its observed and pressure-baseline voltages.
 Signal hysteresis during the acceleration-voltage switching protocol is a potential concern; stray electronic capacitances of the order pF can increase theRC signal relaxation time, τRC,significantly from its nominal 2-s value on them/z = 36 cup (R = 1 × 1012 Ω and C= 2 pF). If the electronic relaxation time exceeded the time in between switching, the contrast between the observed and pressure-baseline measurements would have been smaller than the true values, leading to a scale compression in the resulting Δ36 and Δ35 values. Using τRC= 2 s and a 20-s idle time, we calculate that the signal contrast (i.e.,V36 × exp(20s/−τRC)) will decrease by 0.045‰ at most in Δ36, which is less than our reported precision. To evaluate if hysteresis was significant for our measurements, we tested a different method for calculating V36that was sensitive to longer-term (minutes to hours) instrumental drifts rather than the shorter-term (seconds to minutes) drifts of concern for the procedure depicted inFigure B2. The alternate method used pressure-baseline trends that were measured as separate 10-cycle acquisition blocks before and after every 2–3 blocks of on-peak measurements; the average linear regression values used to calculateV36 values. Results from both methods were consistent with one another within 0.1‰ in Δ36.
B2. Ion Corrections for 36Ar and Instrumental Nonlinearities
 A final ion correction for 36Ar was applied during analyses of O2 because it was still present at ppb levels in both the reference gas and in gas samples. This ion correction, dependent on both bulk isotopic composition (δ34) and the m/z = 40 voltage ratio (sample/standard; V40,SA/V40,STD), was calculated by measuring the dependence of Δ36 versus V40,SA/V40,STDfor high-temperature gases of two differentδ34 values (see Figure B3). To generate these ion-correction lines, standard gases were passed through the GC system with varied collection times. Longer collection times led to higherV40,SA/V40,STD because more argon from the helium stream was collected (see Section 3.1) These lines constituted the high-temperature (Δ36 ∼ Δ35∼ 0) reference against which experimental samples were compared. Argon-corrected Δ36 values were obtained by taking the difference between the uncorrected Δ36value and a high-temperature reference line at a givenV40,SA/V40,STD.
 The argon correction lines for δ34 = 34.9 ± 0.9‰ and 21.0 ± 1.0‰ were offset, but parallel within the fit uncertainties of their respective linear regressions. Plotting the ordinate as an ion current instead of a Δ36 value yields similar results (not shown). These observations indicate the presence of a subtle nonlinearity between measured and actual Δ36 values over that range in δ34that may be a general feature of ‘clumped-isotope’ analyses at high source pressures [Huntington et al., 2009]. The small molecular signals in our analyses in particular, i.e., V36< 500 mV may also be subject to amplifier nonlinearities. To account for these nonlinearities, we assumed that the slopes of the argon-correction lines (i.e., of Δ36 versus V40,SA/V40,STD) were invariant, and that their intercepts varied linearly with δ34. We used the best fit δ34 = 34.9‰ slope (1 s.e., n = 13, r2 = 0.9989, MSWD = 1.8) in the expression,
to find the intercepts, b, for the δ34 = 34.9‰ and 21.0‰ data (n = 4; r2 = 0.9991, MSWD = 0.02; see Figure B3). The resulting relationship between b and δ34, based on these two tie points, was
after accounting for nonzero Δ36of the two high-temperature standards, i.e., Δ36 = 0.03‰ and 0.02‰ at 800°C and 1000°C, respectively. Reported uncertainties are 1σ estimated using a Monte Carlo simulation (see section B3). The dependence of b on bulk isotopic composition is of an opposite sign from that which has been reported for Δ47 measurements [Huntington et al., 2009; Dennis et al., 2011], but it is of the same sign as that reported in another study in which pressure baselines were measured [He et al., 2012].
 For an O2 sample of a given δ34, our reported Δ36 value was calculated using the equation:
This equation can be used only when both terms in the difference correspond to the same bulk composition δ34. Therefore, b was first calculated for the sample's δ34 (i.e., that for Δ36vs.working std) using equation (B2), after which Δ36,stochastic was calculated for the sample's V40,SA/V40,STD. Atmospheric O2 had δ34 = 36.275 ± 0.080‰ (2 s.e.), close to one of our standard gases (δ34 = 34.9‰), where the nonlinearity correction was comparable to the 1σ total uncertainty in Δ36 (0.1‰).
 For our Knudsen diffusion experiment (Section 4.1), some uncertainty in Δ36arises from the composition-dependent nonlinearity relationship derived in the previous section, because the bulk isotopic composition of both the diffused and residue populations were significantly (>10‰ inδ34) outside the range for which high-temperature gases were available. Because of the relative difficulty in generating low-argon O2 standards over a wider range of bulk isotopic composition, we are unable to include a larger range of bulk isotopic composition at this time. Still, we see excellent agreement, within our reported uncertainty, between our data and the model of the experiment using equation (12).
B3. Uncertainty Estimates
 To estimate the uncertainty in final Δ36values associated with these ion-correction and nonlinearity relationships, which dominated the total uncertainty, we built a Monte Carlo simulation ofequation (9). We sampled 100,000 points on each of 4 different Gaussian distributions corresponding to the δ34 (abscissa) and b (ordinate) values. Uncertainties in the slope and intercept of equation (B1) were calculated this way, as were Δ36,stochastic uncertainties at specific V40,SA/V40,STD values. These uncertainties were added in quadrature with the analytical standard error in Δ36vs.working std to obtain 1σ uncertainty limits for the final Δ36 values.
 For Δ35 measurements, an argon correction was not necessary because m/z= 35 is not isobaric with an argon isotope. In addition, a composition-dependent nonlinearity was not identified, perhaps because the analytical precision of individual measurements was ±0.2‰ (1σs.e.); that uncertainty may exceed the magnitude of composition-dependent nonlinearity over our range inδ35∼ 30–57‰. External (multisample) averages for high-temperature gases withδ35 = 51 ± 1‰ and 32 ± 2‰ (1 s.d.) yielded Δ35values that were not significantly different from each other. Therefore, because we could not rule out a composition-dependent nonlinearity for Δ35, we used 2 external standard errors as the uncertainty bounds for the high-temperature standard when propagating uncertainty in Δ35. Higher-precision measurements of Δ35 should be possible with higher amplification on the m/z = 35 Faraday cup with a new detector array that does not have the SNR problems we experienced (see section B1).
 All DFT calculations were made with the Quantum Espresso code [Giannozzi et al., 2009] using a 50 Rydberg energy cutoff for the plane wave basis set. Electronic wave vectors in the Brillouin zone were sampled on a shifted 4 × 4 × 4 Monkhorst-Pack grid, and the phonon density of states was sampled using a shifted Monkhorst–Pack-like grid [Gonze et al., 2002] with three distinct wave vectors. Calculated vibrational frequencies were scaled downward by 3.5% so that the peroxide O-O stretching mode frequency matched Raman measurements in BaO2 (843 cm−1 [Efthimiopoulos et al., 2010]). This scale factor ignores anharmonicity in both the model and the Raman measurement, which is expected to have small effects on isotopic ordering [Wang et al., 2004; Schauble et al., 2006; Cao and Liu, 2012]. Anharmonicity-corrected frequencies don't appear to be known for BaO2.
 Trial calculations with higher plane wave cutoff energies and denser electronic wave vector grids yielded very similar energies and optimized crystal structures. The room temperature 18O-18O bond-ordering equilibrium calculated with a 1-wave vector phonon sample and different barium pseudopotential (Ba.pbe-nsp-van.UPF fromhttp://www.quantum-espresso.org) are within ∼0.01‰ of the present result, suggesting that the choice of barium pseudopotential is not critical. This is also consistent with the very low frequencies observed for all modes other than the O-O stretch; low-frequency modes are not expected to strongly affect isotopic ordering. The optimized crystal structure and frequencies of Raman-active vibrational modes are very close to those determined by a recent DFT study using projector-augmented waves [Efthimiopoulos et al., 2010] Assuming anharmonicity of no more than a few percent in the O-O stretching mode, and that lattice modes do not contribute significantly to isotopic ordering in BaO2, the calculated 18O2 equilibrium might reasonably be expected to be accurate to ∼0.02‰ to 0.03‰ at room temperature and above. Uncertainty in these calculations ought to scale with isotopologue mass, and therefore be correspondingly smaller for 17O18O and 17O17O: ∼0.01–0.02‰ and ∼0.01‰, respectively.
 Below (see also Figure C1) are the polynomials fit to estimated isotopologue and isotopic equilibria using temperatures in Kelvin. BaO2 equilibria were fit for T ≥ 250 K, and show a maximum misfit of 0.003‰. For clumped O2 isotopic equilibria, the fits are for T ≥ 170 K with a maximum misfit of 0.004‰ in Δn values and 0.09‰ in α. BaO2 (this study)
 We thank K. Ziegler and V. Brillo for experimental assistance, H. P. Affek, Q. Li, and C. Deutsch for helpful discussions, Y. L. Yung for providing a sample output from his atmospheric model, and the reviewers (J. Severinghaus and two anonymous others) for their comments on the manuscript. This research was supported by the National Science Foundation Earth Sciences Postdoctoral program (EAR-1049655 to L.Y.Y.), grant EAR-0961221 to E.D.Y., and grant EAR-1047668 to E.A.S.