To measure the seven-dimensional isotopic composition of N2O, we used an updated version of the QCLAS platform described by Kantnerová et al. (2020a). This instrument consists of a dual-laser spectrometer (QC-TILDAS-DUAL, Aerodyne Research Inc., USA) with quantum cascade laser sources emitting at 2142 and 2182 cm-1 to quantify the eight most abundant isotopologues of N2O, as shown in Fig. 1. We implemented an astigmatic Herriott multipass cell (AMAC-36LW, Aerodyne Research Inc.) with 36 m optical path length in 350 mL volume to replace the cell (210 m, 2500 mL) originally installed in this instrument (Kantnerová et al., 2020a). This smaller cell improves signal-to-noise, normalized to the sample amount, by substantially reducing the light loss upon reflection and by lowering the interference fringe level. It also enables faster sample gas extraction and sample-reference exchange time. To compensate for the shorter path length, we measure samples as mixtures of ∼8 % N2O in N2, instead of the ∼1.65 % mixtures used previously. At a typical working pressure of 4.8 hPa, ∼4 µmol of N2O are introduced into the multipass cell for each measurement cycle. To reduce the effects of temperature, the QCLAS was housed in a temperature-controlled plexiglass box (IndTec 400, Elinter, Switzerland), supplementing the temperature regulation of the spectrometer (ThermoRack 401, Solid State Cooling, USA). As a net result, variations in the laboratory temperature of ±0.5 K are dampened to ±20 mK in the outer box and ±5 mK or better at the spectrometer cell. This level of temperature stability is necessary to achieve the required measurement precision (Bajnai and Hare, 2025).

To enable fast cycling between samples and reference materials, a customized gas inlet system was constructed (Fig. 1), similar to those described previously (Hare et al., 2022; Wang et al., 2020b; Zhang et al., 2025). This system consists of pneumatic valves (Swagelok, USA) connected by stainless-steel tubing, and is evacuated stepwise by a screw (PDV500, Ebara, Japan) and a turbomolecular pump (HiCube Eco 80, Pfeiffer Vacuum, Germany). It allows defined amounts of N2, 8 % N2O-in-N2 working gas, and samples to be delivered to the intermediate gas volume (Fig. 1), from which they can then be expanded into the multipass cell. Gas flows into the inlet system are controlled by critical orifices, as shown on Fig. 1, including two options for sample introduction (30, 50 µm). The operation of the spectrometer and inlet system are coordinated by custom scripts within the spectrometer control software (TDLWintel, Aerodyne). Samples are typically delivered to the spectrometer in 10 mL stainless steel cylinders (Arbor Fluidtec-Swagelok, Switzerland) containing between 30 µmol and 2 mmol of pure N2O.

A sample-measurement cycle consists of three sample injections, each bracketed by injections of 8 % N2O-in-N2 working reference gas (PanGas, Switzerland). For each working reference gas aliquot, the intermediate volume is filled to the target pressure of 27 hPa with 8 % N2O-in-N2, while for each sample gas aliquot, pure N2O is introduced into the intermediate volume first (2.2 hPa) and then topped up to a total pressure of 27.0 hPa with N2 (6.0 grade). On expansion into the multipass cell, sample and reference gas aliquots yield a pressure of 4.8 hPa. Spectral data are collected for two minutes for each injection, during which time the next sample or working reference gas aliquot is prepared in the inlet system. At the end of each measurement phase the cell is evacuated to <0.02 hPa and the next gas aliquot is introduced within one minute.

Absorption spectra are recorded at 1 s temporal resolution and concentrations of individual isotopologues are quantified in real time by TDLWintel (Aerodyne Research Inc.). Ratios Rrawi of individual isotopologues i to the main isotopic species 14N14N16O are calculated for both sample and working reference gases. Then, delta values (δi) are calculated for each sample gas aliquot, normalized against the preceding and following working reference gas measurements, according to Eq. (1): 1δi=(Rraw, samplei/Rraw work refi)-1+δwork refi

Finally, δi are corrected for concentration dependency effects by normalizing to the ratio of 14N14N16O between sample and working reference. For the singly substituted isotopologues 14N15N16O, 15N14N16O, 14N14N18O, and 14N14N17O, delta values δ15N^α, δ15N^β, δ18O, and δ17O are reported on the international isotope ratio scales, Air-N2 and VSMOW, respectively. The values for the working reference gas were assigned by measurement against the reference material RM1A (Mohn et al., 2022). For the clumped isotopologues 14N15N18O, 15N14N18O, and 15N15N16O, the parameter Δi describes the abundance of isotopologue i relative to a stochastic reference frame (Eiler, 2007; Magyar et al., 2016). As an intermediate parameter, we also define Δ∗i, the clumped isotopic abundance calculated as if the working gas has a composition Δi of 0 ‰ for all isotopologues, and so then the measured δi of these isotopologues against the working reference gas can be converted to values of Δ∗14N15N18O, Δ∗15N14N18O, and Δ∗15N15N16O by accounting for the Δi of the working gas.

By mixing highly isotopically-enriched 14N15N18O, 15N14N18O, 15N15N16O, and 14N14N18O, prepared previously by thermal decomposition of labelled ammonium nitrate (Kantnerová et al., 2020a; Mohn et al., 2022), with natural-abundance N2O, we created reservoirs of N2O “isotopically-spiked” to ∼500 ‰ in each of these isotopologues. Briefly, a defined volume of the isotopologue of interest was injected into an evacuated 2 L high-pressure cylinder using a Vici multi-position valve (Vici Valco, USA) equipped with a sample loop. After flushing the loop with natural abundance N2O the cylinder was topped off to ∼32 bar. The total amount of added N2O was determined gravimetrically (PBK987-B60, Mettler-Toledo, Switzerland). The prepared gases were used for the experiments described in the following sections.

For equilibration of N2O over γ-Al2O3, we used a vertical tube furnace (Vevor, China) with a custom glass reaction vessel, which was attached to a vacuum line for sample introduction and collection and evacuated by an oil-free rotary (NeoDry 7E, Kashiyama, Japan) and a turbomolecular pump (HiCube Eco 80, Pfeiffer). This system, depicted in Fig. S1 in the Supplement was developed from the equilibrium furnace described in Zhang et al. (2025). The pressure in the vacuum line was monitored with a pair of gauges for pressures below 1 mbar (PKR361, Pfeiffer) and between 0 and 4 bar (Leo 1, Keller Pressure, Switzerland). The bottom of the glass reaction vessel was loaded with 1.0 g of γ-Al2O3, provided as cylindrical pellets 1.8” (3.16 mm) in diameter and ∼2–7 mm long (Aluminum oxide, γ-phase, catalyst support, high surface area; ThermoFisher, Germany). The pellets extended to a height of ∼1 cm in the vessel. The same γ-Al2O3was used for all experiments without replacement. The temperature of the reactor was monitored with a K-type thermocouple placed at its very bottom, alongside the catalyst pellets, and logged (Hobo, Onset Computer, USA). The uncertainty in equilibration temperature was estimated as ±2 K, dominated by a temperature gradient in the reaction vessel (1.3 Kcm-1) and the temporal variation of the furnace temperature (±1.0 K).

In a first series of experiments, we explored the role of temperature in γ-Al2O3 activation by sequentially pre-heating the catalyst at increasing temperatures between 338 and 551 °C. In each experiment, the catalyst was heated for ∼1 h while the reaction vessel was evacuated with the turbomolecular pump. The pressure over the catalyst typically rose to between 0.01 and 0.1 mbar during this pre-heating phase, before returning to <0.01 mbar. Then, the equilibration vessel was restored to 200 °C, and once the temperature stabilized, 1.2 mmol of 14N15N18O- or 15N14N18O-spiked N2O (“458-spike”, “548-spike”) was introduced. After a duration of at least 20 h, N2O was cryogenically trapped out of the reaction vessel, expanded in a known volume to estimate the N2O recovery, stored in a 10 mL stainless steel cylinder for storage until analysis, and then analyzed by QCLAS as described in Sect. 2.1.

After the temperature threshold for catalyst activation was established, further experiments, with incubation periods between 6 and 162 h, were conducted to establish the equilibrium nature and evaluate the kinetics of the reactions of N2O isotopologues over γ-Al2O3. For these experiments, the catalyst was periodically re-activated by heating at 550 °C for >1 h. Once activated, the catalyst was kept under vacuum (∼10-6 mbar) and reactivation was not required for ≥1 month. For each equilibration experiment, the temperature of the reaction vessel was set between 153 and 220 °C, and either 0.3 or 1.2 mmol of N2O of various isotopic compositions was introduced. At the end of each experiment, N2O was cryogenically collected and analyzed as described in the Sect. 2.1.

To determine the isotopic fractionation effects during thermal decomposition of N2O over γ-Al2O3, a series of experiments was conducted in which 500 µmol of isotopically-labelled or natural-abundance N2O was exposed to the catalyst at 498 °C. After reaction durations of 15–64 min, residual N2O was extracted cryogenically and decomposition products, likely N2, O2, and NO (Lewis and Hinshelwood, 1938), were removed under vacuum. The collected N2O was stored in a 10 mL stainless steel cylinder for subsequent isotope analysis. The kinetic isotope effects of thermal decomposition (15ε, 18ε, and εSP) were quantified using a closed-system Rayleigh model and the expression δ=δ0-εln⁡[N2O]/[N2O]0, where δ0 is the starting isotopic composition.

Optimal averaging times and calibration intervals for the spectrometer were evaluated by analyzing 8 % N2O-in-N2 working reference gas at the typical cell operating pressure of 4.8 hPa and using the Allan–Werle variance technique (Werle et al., 1993) (Fig. 2). We achieved Allan deviation minima of <0.2 ‰ for all isotopologue ratios in less than 100 s, but observed impaired performance for integration times of more than 500 s, due to drift effects. This precision is adequate to resolve differences observed to date among natural or experimental materials (Kantnerová et al., 2020b, 2022; Magyar, 2017; Magyar et al., 2016) or predicted in literature (Schmidt and Johnson, 2015; Wang et al., 2004; Yeung, 2016), and matches or exceeds previous approaches (Kantnerová et al., 2020a; Magyar et al., 2016). To achieve the same precision for samples, rapid sample – reference switching is essential, so we established and optimized a measurement scheme to analyze one “reference–sample–reference” set in 480 s and triplicate sample analyses in less than 20 min. Since all samples are measured against the same internal working reference gas, results can be compared for samples measured in different analytical sessions. In addition, we find that the magnitude and even sign of concentration dependence correction associated with each isotopologue can vary over time. Such variation has been observed in another recent study measuring 17O in CO2 by laser spectroscopy (Ellis et al., 2025) and supports our approach of determining a specific concentration correction factor for each sample. To test its performance, we introduced repeated injections of working reference gas into the spectrometer over the course of ∼15 min and processed the data as if half of the pulses were a sample; the standard error for three “sample” pulses, each bracketed by two “reference” pulses, ranged from 0.09 ‰ to 0.18 ‰ for all isotopologue ratios (Fig. S2).

We tested the effect of different pre-treatment conditions, including temperatures, heating sources and duration, and evacuation on the activity of γ-Al2O3 for catalyzing isotope exchange reactions in N2O. Preliminary experiments showed that heating γ-Al2O3 with a natural gas torch under vacuum, as described by Magyar et al. (2016) and Kantnerová et al. (2020a), resulted in inconsistent results. Therefore, using the on-line furnace described in Sect. 2.3 we systematically tested the influence of activation temperature on isotope exchange. We evaluated activation by heating 14N15N18O-spiked N2O, with a Δ∗14N15N18O of 512 ‰, under consistent conditions and found a sharp activation threshold between 467 and 515 °C (Fig. 3). Using a logistic fit to these data we estimate the midpoint temperature of the activation path as 490 ± 4 °C (1 SE). Catalyst activation at temperatures below this threshold led to only subtle changes in Δ∗14N15N18O, while catalyst activated at 515 °C and higher uniformly showed a drop of >400 ‰ towards expected equilibrium values. These results are consistent with the choice of temperatures between 550 and 567 °C to activate γ-Al2O3 for catalysis of exchange among methane clumped isotopologues and between CH4, H2, and other hydrocarbons, which in turn followed from the temperature required to convert boehmite, γ-AlO(OH), to γ-Al2O3 (Eldridge et al., 2019; Robertson et al., 1975; Wang et al., 2020a). Although it has been shown that γ-Al2O3 does not serve as a catalyst for methane isotope equilibration in the absence of thermal activation (Turner et al., 2021), the lower threshold of activation has not been explored thoroughly. In a subset of experiments, we also activated γ-Al2O3 at 550 °C in the presence of O2, but did not observe quantifiable effects on catalytic activity; these experiments were again motivated by work with methane and hydrocarbons in which such an oxygen activation step is included to enhance catalytic activity (Eldridge et al., 2019, 2023; Robertson et al., 1975; Turner et al., 2021). Based on the outcome of these experiments, we chose 550 °C and a minimum of 1 h as standard catalyst activation conditions for subsequent experiments.

To establish that the reactions undergone by N2O isotopologues in the presence of γ-Al2O3 are of an equilibrium nature, we relied on three lines of evidence: (1) convergence on a common isotopic composition from distinctly different starting materials; (2) time-invariance of isotopic composition for extended time intervals after convergence; and (3) matching theoretical temperature dependence predictions. The first two criteria, the principles of convergence and time-invariance, have a strong basis in isotope geochemistry to identify equilibrium reactions in geochemical or petrological settings (O'Neil, 1986). The materials described in Sect. 2.2, with elevated values of Δ∗14N15N18O and Δ∗15N14N18O, were exposed to the activated catalyst at 200 °C for durations between 6 and 117 h. We found that after one day these materials had converged on narrow ranges in Δ∗14N15N18O and Δ∗15N14N18O (Fig. 4), and that rapid progress towards that range was already achieved after 6 h (Fig. 5). For Δ∗14N15N18O, starting materials at 512 ‰, 3.0 ‰, and -0.3 ‰ converged to 10.32 ± 0.60 ‰, apart from one experiment, which displayed a residual Δ∗14N15N18O of 79.7 ‰ after 24 h. This outlier, for the first sample measured after γ-Al2O3 activation at the lower temperature threshold (515 °C), suggests as-yet uncharacterized complexity to the activation of γ-Al2O3, and the need to verify results by repetitive equilibration experiments. Likewise, for Δ∗15N14N18O, a value of -11.07 ± 0.55 ‰ was converged upon from starting materials at 458.6 ‰, 9.1 ‰, and 0.0 ‰. At the same time, for all equilibration experiments on N2O with enhanced Δ∗14N15N18O and Δ∗15N14N18O, SP values increased from ∼ -2 ‰ to 0 ‰ in the starting materials to 20.9 ± 0.4 ‰ after 24 h (Fig. 5). This robust convergence on a putative equilibrium isotopic composition is our first indication of equilibrium reactions at work, for the three parameters SP, Δ∗14N15N18O, and Δ∗15N14N18O.

Complementary to convergence is time-invariance of isotopic composition after equilibrium has been reached, as long as thermodynamic conditions remain constant. This was confirmed by consistency of SP values at 20.9 ± 0.4 ‰, even when heating for durations of up to one week (162 h) (Fig. 5). Likewise, in all cases where the catalyst was activated at 550 °C, and in all but one case for an activation between 515 and 550 °C, the values of Δ∗14N15N18O and Δ∗15N14N18O achieved at 24 h were the same as those seen out to one week (162 h) (Fig. 5). In contrast, any kinetic effect associated with N2O decomposition or rearrangement is expected to lead to continuous evolution in isotopic composition for as long as concentration continues to change. A more specific comparison of isotopic evolution under kinetic and equilibrium conditions is discussed in Sect. 3.4.

The third confirmation that equilibration has been reached is the agreement with theoretical predictions of differences in Δ∗14N15N18O, Δ∗15N14N18O, and SP for different equilibration temperatures. Based on the Urey–Bigeleisen–Mayer quantum statistical mechanical framework using anharmonic potential energy surfaces (Bigeleisen and Friedman, 1950; Bigeleisen and Mayer, 1947; Cao and Liu, 2012; Urey, 1947; Wang et al., 2004), and validated by a Feynman path-integral approach (Webb and Miller, 2014), we have robust estimates for Δ14N15N18O, Δ15N14N18O, and SP at equilibrium (Fig. 6). We introduced N2O over γ-Al2O3 and held it at temperatures of 154, 178, 191 and 218 °C. We compare the results to the experiments conducted for >24 h at 200 °C, discussed in the preceding sections. This temperature range was chosen based on the slow kinetics seen between 25 and 100 °C and enhanced decomposition at temperatures above 200 °C observed previously (Kantnerová et al., 2020a; Magyar et al., 2016). For SP, theoretical predictions indicate differences of 5.23 ± 0.24 ‰ for N2O equilibrated at 154 °C relative to 218 °C, which agrees within analytical uncertainties with the observed span of 4.92 ± 0.17 ‰ (Fig. 6). Changes seen for the clumped parameters Δ∗14N15N18O and Δ∗15N14N18O for N2O equilibrated between 154 and 218 °C also match theoretical predictions, but with more scatter around the expected values (Fig. 6). For instance, for Δ∗15N14N18O, experimental results for the maximum (218 °C) and minimum (154 °C) temperatures show an offset of -2.5 ± 0.3 ‰, matching the expected value of -2.7 ± 0.12 ‰, but deviations from theoretical predictions are seen for measurements at 178 and 191 °C. It is not clear whether these deviations arise from the larger analytical uncertainty of clumped isotope measurements relative to a smaller predicted range in the parameters Δ∗14N15N18O and Δ∗15N14N18O, or incomplete equilibration of these doubly substituted isotopologues in the time allotted, especially at lower temperatures. Finally, while the variation in SP, Δ∗14N15N18O, and Δ∗15N14N18O between 154 and 218 °C matches equilibrium temperature dependencies well, a systematic offset is observed between the theoretical predictions and observed values for all three parameters. The interpretation and application of this offset is discussed further for the clumped isotopologues in Sect. 3.6, and for SP in Sect. 3.7.

The behavior of N2O heated at 218 °C requires further discussion. When the amount of N2O typical for other experiments, ∼1.2 mmol, was introduced over γ-Al2O3 at this temperature, we did not see convergence in SP, Δ∗14N15N18O, or Δ∗15N14N18O (Fig. S3). We posit that above 200 °C, reactions associated with thermal decomposition may start to outpace isotope exchange reactions and impart a kinetic isotope effect. However, when only 0.3 mmol of N2O was introduced to the catalyst, we found that it converged on values of SP, Δ∗14N15N18O, and Δ∗15N14N18O consistent with outcomes at other temperatures, even with relatively poor yields of 50 %–70 %. Whether this empirical result depends on variations in the relative kinetics of exchange to decomposition at different catalyst-to-N2O ratios, or differences of the pressure dependencies of these two reactions, remains to be explored further. Subsequently, a 300 µmol N2O sample was reacted over γ-Al2O3 at 200 °C, where its composition was found to be indistinguishable from 1200 µmol samples; its results are reported among those already discussed.

We posited in the preceding section that through the expression of a kinetic isotope effect, thermal decomposition would be expected to lead to continuous evolution in the isotopic composition of all isotopologue ratios in the residual fraction as N2O is destroyed, and that thereby it can readily be distinguishable from equilibrium isotope effects. To provide an explicit comparison, we evaluated the isotopic evolution of Δ∗14N15N18O-spiked and natural-abundance N2O subjected to heating at 498 °C in the presence of γ-Al2O3 (Fig. 7). In both experiments, nearly half of the supplied N2O was destroyed within 15 min, reaching about 80 % after one hour. Nitrogen isotope effects 15ε of 3 ‰–5 ‰ and oxygen isotope effects 18ε of 5 ‰–9 ‰ were observed, reflecting an increased durability of heavy isotopologues relative to 14N14N16O (Bigeleisen, 1949), with higher values for Δ∗14N15N18O-spiked N2O. Both 15ε and 18ε are of smaller magnitude than the isotope effects reported for homogeneous decomposition of N2O in quartz-glass tubes at 1000 °C (Ogawa and Yoshida, 2004). Surprisingly, 14N15N16O and 15N14N16O are decomposed at similar rates with a slight preference for destruction of 14N15N16O (Fig. 8), resulting in an εSP of ∼-1 ‰ (Fig. S4). In contrast, previous observations of thermal decomposition and of the destruction of N2O by photolysis or by bacterial reduction all found distinct enrichment in SP, rationalized by a 15N–16O bond stronger than the 14N–16O alternative (Kantnerová et al., 2020b; Ogawa and Yoshida, 2004; Ostrom et al., 2007). The final element of differentiation between kinetic and equilibrium effects comes from the behavior of Δ∗14N15N18O and Δ∗15N14N18O. With increasing decomposition, Δ∗14N15N18O decreased in both natural-abundance and spiked N2O, while Δ∗15N14N18O increased for spiked N2O and remained constant for natural abundance N2O. For neither starting N2O do Δ∗14N15N18O and Δ∗15N14N18O approach the values of 5.7 ‰ and -5.6 ‰ predicted for equilibrium at 498 °C (Fig. 7). Together these pieces of evidence lead us to conclude that some amount of rearrangement among isotopologues accompanies decomposition.

With these results in mind, we revisit the equilibration experiments described in the preceding section. In the ideal situation where only an equilibrium isotope effect is acting on these N2O samples over γ-Al2O3, the amount of N2O would not change. This was clearly observed for lower equilibration temperatures (154, 178, 191 °C) with yields of 90 %–95 %, while experiments at intermediate (200 °C) and higher temperatures (218 °C) for comparable experimental periods showed reduced yields of 70 %–90 % and 50 %–70 %, respectively. To further evaluate any imprint of kinetic isotope effects associated with this extent of decomposition, we consider the evolution of the bulk isotope composition over the course of equilibration experiments. We find that indeed the subtle variation seen in δ18O and δ15N across all equilibrium experiments matches the expression of the kinetic isotope effects determined here, but that SP and the clumped parameters Δ∗14N15N18O and Δ∗15N14N18O do not appear to be controlled by these kinetic isotope effects (Fig. 9). Nevertheless, we cannot exclude the possibility that some of the variation seen in repeated measurements at 200 °C comes from variable expression of kinetic isotope effects. Indeed, a decomposition fraction of 30 % could drive changes in SP, Δ∗14N15N18O, and Δ∗15N14N18O of -0.36 ‰, -1.59 ‰, and 1.42 ‰, respectively, and so could contribute to the variability seen in repeated equilibrium experiments (Sect. 3.6 and 3.7, Table S1 in the Supplement). Therefore, an important element of any subsequent application of this work will be to choose experimental conditions that minimize decomposition and maximize yield, while still achieving complete exchange.

In a preliminary series of experiments, N2O spiked in Δ∗15N15N16O was also heated over γ-Al2O3. Here we found that even after 94 h at 200 °C the value of Δ∗15N15N16O remained elevated at 558 ‰. Therefore, we conclude that the catalyst γ-Al2O3 only activates the N–O bond in N2O, and not the N–N bond, and accordingly facilitates equilibrium isotope reactions among position-specific and 18O-bearing isotopologues, but not those involving 15N15N16O. To find alternative catalysts or conditions that activate 15N15N16O remains a challenge for future work. In the meantime, it is impossible to establish an absolute reference frame for Δ15N15N16O and so we will continue to report results on a relative basis as Δ∗15N15N16O; such an approach has also been proposed and applied for ethane and other compounds recalcitrant to equilibration (Clog et al., 2018; Gilbert, 2021).

Having found that the abundances of the isotopologues 14N15N18O and 15N14N18O can be brought to equilibrium isotopic distributions between 153 and 218 °C, we use this outcome to establish an absolute reference frame for future measurements of Δ14N15N18O and Δ15N14N18O. Since 200 °C is the temperature where we evaluated the conditions of convergence and time-invariance and have the most robust replicated dataset, we use these measurements to determine the values of Δ14N15N18O and Δ15N14N18O of our working gas against a true stochastic distribution of rare isotopes among isotopologues. These values, reported in Table 1, can then be used to convert values of Δ∗14N15N18O and Δ∗15N14N18O, as reported here or in future studies, to Δ14N15N18O and Δ15N14N18O. Previous N2O clumped isotope studies also sought to achieve such an absolute reference frame. Early mass spectrometric work was limited by the need to use measurements of Δ14N15N18O in equilibrated samples to account for ion source scrambling in the generation of the 15N18O+ ion used to measure this isotopologue (Magyar et al., 2016), while first QCLAS studies lacked the full suite of convergence, time-invariance, and temperature dependency results used here to confirm the equilibrium nature of the reactions of N2O isotopologues over γ-Al2O3 (Kantnerová et al., 2020a). By establishing this absolute reference scale and reporting future results on it, we enable their interpretation in the context of theoretical predictions or natural phenomena where the true distribution of isotopes among isotopologues is relevant, and we also facilitate comparisons among different labs and analytical approaches for measuring these parameters.

For N2O equilibrated at 200 °C, we observed an offset of -3.43 ± 0.36 ‰ between predicted SP values and our repeated equilibration experiments (Table 1). This was not expected since SP is defined as the difference of two parameters, δ15N^α and δ15N^β, both connected through a chain of reference materials to the international Air-N2 scale. Therefore, SP should reflect an absolute determination of the relationship of 14N15N16O and 15N14N16O. The key point of connection is through the thermal decomposition of ammonium nitrate to N2O, whereby δ15N^α and δ15N^β values are assigned to N2O by comparison to the precursor δ15N-NO3- and δ15N-NH4+,determined using established means and reference materials. This procedure has been repeated in a number of laboratories (Harris et al., 2014; Mohn et al., 2016, 2022; Toyoda and Yoshida, 1999; Westley et al., 2007). Currently, to maximize comparability among labs, the ammonium nitrate decomposition conducted at Tokyo Tech (Toyoda and Yoshida, 1999), now Science Tokyo, is commonly used as the basis for setting the δ15N^α and δ15N^β for other laboratories and reference materials (Mohn et al., 2022; Ostrom et al., 2018). However, the decomposition of ammonium nitrate has been found to exhibit significant variation in assigned δ15N^α and δ15N^β values, controlled by yield and isotopic fractionation (Mohn et al., 2016). Mohn et al. (2022) found an offset of -1.51 ‰ in SP between the outcome of ammonium nitrate decomposition according to current best practices and the reference frame based on Toyoda and Yoshida (1999). This deviation is in the same direction, although of smaller magnitude, as that estimated here from thermodynamic equilibrium; together these provide two lines of evidence to suggest an offset between the current international reference frame for δ15N^α and δ15N^β and the true ratio of 14N15N16O versus 15N14N16O. To follow up from this conclusion will require further equilibration experiments – best would be to subject international reference materials with well-characterized δ15N and δ18O to equilibration over γ-Al2O3 at optimal conditions for maximum yield. Thereby we can determine if the uncertainty in the results reported here is tied to the equilibration experiments themselves, including possible imprints of a kinetic isotope effect from thermal decomposition. This work can be coupled to further repeat measurements of equilibrated reference materials to evaluate any room for improvement in measurement or gas handling procedures. The outcome of such equilibrium experiments can also be compared to other approaches that provide an estimate of the absolute relationship between 14N15N16O and 15N14N16O, whether novel spectroscopic methods (Griffith et al., 2009; Łapiński et al., 2001; Schlagin et al., 2025) or alternative experimental frameworks (Sadiek et al., 2025). If such experiments and measurements confirm the conclusions drawn here, the international N2O isotopomer community will need to determine how to harmonize these latest results with the existing reference frame for δ15N^α and δ15N^β.

Finally, it is necessary to note that SP, defined as the difference in δ15N between α and β nitrogen atoms, is only an approximation of the equilibrium constant for Reaction (R1), which is the ratio 15Rα/15Rβ; for an equilibrated sample. As discussed in Magyar et al. (2016) and Sadiek et al. (2025), for some combinations of δ15N^α and δ15N^β this difference becomes significant, but for the set of samples described in this study, and for many natural samples, SP is remarkably close as an approximation to the ratio 15Rα/15Rβ. Here, the difference between this ratio and SP was between 0.001 ‰ and 0.3 ‰ across all samples. Therefore, we can quantitatively compare SP to predicted equilibrium constants.