On the interference of Kr during carbon isotope analysis of methane using continuous-flow combustion – isotope ratio mass spectrometry

Stable carbon isotope analysis of methane ( δ13C of CH4) on atmospheric samples is one key method to constrain the current and past atmospheric CH 4 budget. A frequently applied measurement technique is gas chromatography (GC) isotope ratio mass spectrometry (IRMS) coupled to a combustion-preconcentration unit. This report shows that the atmospheric trace gas krypton (Kr) can severely interfere during the mass spectrometric measurement, leading to significant biases inδ13C of CH4, if krypton is not sufficiently separated during the analysis. According to our experiments, the krypton interference is likely composed of two individual effects, with the lateral tailing of the doubly charged 86Kr peak affecting the neighbouring m/z 44 and partially them/z 45 Faraday cups. Additionally, a broad signal affecting m/z 45 and especiallym/z 46 is assumed to result from scattered ions of singly charged krypton. The introduced bias in the measured isotope ratios is dependent on the chromatographic separation, the krypton-to-CH 4 mixing ratio in the sample, the focusing of the mass spectrometer as well as the detector configuration and can amount to up to several per mil in δ13C. Apart from technical solutions to avoid this interference, we present correction routines to a posteriori remove the bias.


Introduction
Methane is the third most important greenhouse gas besides water vapour and CO 2 .The isotopic composition of atmospheric methane (CH 4 ) provides important constraints on globally integrated CH 4 sources and sinks (Kai et al., 2011;Levin et al., 2011).Both the concentration and the isotopic composition of atmospheric CH 4 in the past have been reconstructed from trapped bubbles in ice cores as well as from the interstitial air in snow pack (firn) on polar glaciers (Miller et al., 2002;Schaefer et al., 2006;Fischer et al., 2008;Sowers, 2011;Sapart et al., 2012).Originally, the dual-inlet technique coupled to an isotope ratio mass spectrometer (IRMS) was used (Stevens and Rust, 1982;Lowe et al., 1991).With the advent of the continuous-flow (CF) technique (Matthews and Hayes, 1978), a growing number of groups have developed systems that allow smaller quantities of CH 4 to be analysed, permitting routine analyses on ice core samples (Merritt et al., 1995;Rice et al., 2001;Miller et al., 2002;Ferretti et al., 2005;Sowers et al., 2005;Schaefer and Whiticar, 2007;Behrens et al., 2008;Umezawa et al., 2009;Melton et al., 2011;Sapart et al., 2011).An overview of these techniques is provided in Table 1.The general procedure for δ 13 C-CH 4 analysis on air samples using the CF-IRMS technique usually involves several steps to separate a large number of major and trace atmospheric components (see general scheme in Fig. 1).For ice core samples, an additional extraction step 32 1 Fig. 1.Simplified flow scheme used for  13 C analysis of CH 4 on air samples applying the 2 continuous flow-IRMS technique.The scheme provides an overview of basic components and 3 specific add-ons of the systems used in this study.The analysis comprises three main steps 4 (from left to right: extraction, purification and combustion of CH 4 to CO 2 , and finally the 5 detection in the isotope ratio mass spectrometer).The grey boxes represent the basic 6 components used by all laboratories and date back to the milestone publications in this field 7 (Merritt et al., 1995;Rice et al., 2001).An exception is the IMAU system described by Sapart 8 et al., 2011, where no pre-combustion GC is used and the separation of the gases is achieved 9 solely by a preconcentration step.Coloured symbols denote additional devices, which are 10 specific for the certain laboratory.Blue and green colours denote features of the Bern system, 11 while the yellow box is specific for the updated IMAU system.The injection loop (blue box) 12 allows injecting pure CH 4 and Kr into the GC flow to monitor the system and allow special 13 experiments.The pre-combustion trap and the post-combustion trap were included later on 14 into the updated Bern system to remove the Kr interference.The yellow box represents the 15 post-combustion GC which was included in the updated IMAU system to remove the Kr 16 interference.17 18 Fig. 1.Simplified flow scheme used for δ 13 C analysis of CH 4 on air samples applying the continuous-flow IRMS technique.The scheme provides an overview of basic components and specific add-ons of the systems used in this study.The analysis comprises three main steps (from left to right: extraction, purification and combustion of CH 4 to CO 2 , and finally the detection in the isotope ratio mass spectrometer).The grey boxes represent the basic components used by all laboratories and date back to the milestone publications in this field (Merritt et al., 1995;Rice et al., 2001).An exception is the IMAU system described by Sapart et al. (2011), where no pre-combustion GC is used and the separation of the gases is achieved solely by a preconcentration step.Coloured symbols denote additional devices, which are specific for the certain laboratory.Blue and green colours denote features of the Bern system, while the yellow box is specific for the updated IMAU system.The injection loop (blue box) allows injecting pure CH 4 and Kr into the GC flow to monitor the system and allow special experiments.The pre-combustion trap and the post-combustion trap were included later on into the updated Bern system to remove the Kr interference.The yellow box represents the post-combustion GC, which was included in the updated IMAU system to remove the Kr interference.
either by dry or melt extraction has to be performed first.The purified CH 4 is then admitted to a combustion interface where CH 4 is converted to CO 2 , which is subsequently measured in the IRMS.Here, the most abundant isotopologues of CO 2 are measured using Faraday cups for the mass-to-charge ratios (m/z) 44, 45 and 46.From these ion beam intensities, the δ 13 C of CH 4 is then calculated applying a correction for the isobaric contribution at m/z 45 due to the presence of 12 C 17 O 16 O (Craig, 1957).
The separation of CH 4 from the bulk air components (N 2 , O 2 and Ar) and also from minor components like CO is a delicate task.Usually, gas chromatography (GC) is used to separate CH 4 from CO, N 2 , and CO 2 , which would otherwise interfere with the mass spectrometric detection.In this respect, an interference with the atmospheric trace gas krypton (Kr) has not yet been considered during the method development.The noble gas krypton has a natural atmospheric abundance of 1099 ± 9 ppb (Aoki and Makide, 2005) and consists of many stable isotopes, with the most abundant being 84 Kr with 57 % and 86 Kr with 17 %.Although Kr is a trace gas, for several types of samples Kr levels are comparable or even higher than the corresponding CH 4 , e.g. for stratospheric samples (Rice et al., 2003;Röckmann et al., 2011) and air extracted from deep ice cores.
Since none of the Kr isotopes produces an ion that has exactly the same mass as the target ions with m/z 44, m/z 45 and m/z 46, Kr has not been regarded as an issue during δ 13 C analysis of CH 4 until now.The physico-chemical properties of CH 4 and Kr are very similar, making them hard to separate from one another.Similar boiling points (Kr = 119 K and CH 4 = 111 K) make cryo-separation impossible, and gas chromatographic separation has proven to be very difficult.To ensure a sufficient separation of CH 4 from Kr, the GC has to be operated at sub-ambient temperatures (Schüpbach et al., 2009) or at high flow rates (50 mL STP min −1 ) with a packed column at 25 • C (Burford and Bremner, 1972).
Here we show that Kr actually does interfere with the measurement of δ 13 C of CH 4 if Kr reaches the ion source together with the CO 2 peak derived from CH 4 combustion.The magnitude of the Kr interference depends on the preconcentration and GC separation of the Kr/CH 4 mixture, the mass spectrometer and its source settings.We will show that the bias introduced by this interference can be as large as 2 ‰ when dealing with atmospheric samples with low CH 4 concentrations (< 400 ppb).More generally, for other types of samples, like water samples, these CH 4 concentrations correspond to CH 4 / Kr ratios of < 0.5.For atmospheric samples, the Kr interference scales with the atmospheric CH 4 mixing ratio since Kr is a well-mixed, inert constituent with an atmospheric mixing ratio that is assumed to vary by only < 1 % between glacial and interglacial climate (Headly and Severinghaus, 2007;Ritz et al., 2011).
We demonstrate how this interference comes about and how this issue can be resolved.Initially, we discuss ways to identify Kr anomalies in chromatograms from δ 13 CH 4 analyses.In the second part of the manuscript we highlight techniques to correct for the Kr interference and compare these techniques.This paper focuses only on the aspect of Kr interference during δ 13 C analysis of CH 4 .However, based on the underlying mechanism of this interference we note that other IRMS applications might also be affected.This effect occurs in situations where a target species and a second species producing singly, doubly or triply charged ions with m/z close to the target masses are simultaneously present in the ion source due to co-elution or measurement of gas mixtures in dual inlet.For example Xe, which elutes in the vicinity of volatile Table 1.Collection of publications dealing with δ 13 C-CH 4 measurements in view of possible Kr interferences.The collection is not exhaustive and lists only some of the publications in the field of ice core and atmospheric measurements.To allow a faster orientation of which data set is produced by which method, we used the following scheme: technical paper (data paper).

Publication
Pre-combustion GC Technical details and remarks
Prior to the conversion of CH 4 to CO 2 , atmospheric CO 2 is removed from the air stream.After the combustion unit, the produced CO 2 is trapped at LN 2 , thus separating it from Kr.
Section 2 provides a brief overview on the setup of the four analytical systems where we identified the Kr interference.In Sect.3, δ 13 CH 4 chromatograms from the four analytical systems illustrate the common features and differences of the Kr interference.In Sect.4, we describe tests that can be performed to determine if and to what degree Kr interferes in the chromatogram.Experiments were performed to assess the Kr impact on δ 13 CH 4 analyses involving direct Kr injections into the CF-IRMS and dual-inlet systems.It will be shown that the Kr interference affect all three Faraday cups.We then discuss the experimental results to illustrate just how the Kr interference works.Finally, Sect. 5 presents a suite of possible solutions to either separate Kr from CH 4 or CH 4 -derived CO 2 , or correct for this effect in existing data sets.While the paper is structured in these consecutive steps, the reader might profit from a first quick look at Figs. 3 and 7. Note that for practical reasons we use the term CH 4 peak, which corresponds to the CO 2 peak from the original CH 4 peak.Additionally, δ 13 C denotes δ 13 C of a CH 4 sample without specifying it.
For the measurements and experiments described in this paper, we used four different analytical systems; they are named after the institutes or cities in which they were developed: AWI (Alfred Wegener Institute for Polar and Marine Research), Bern (University of Bern), IMAU (Institute for Marine and Atmospheric research Utrecht), and PSU (Penn State University).

AWI system
The AWI system is described in detail by Behrens et al. (2008) and was used to generate a δ 13 CH 4 data set covering the last deglaciation (Fischer et al., 2008) as well as a new data set covering the last glacial period (Möller et al., 2013).In short, the pre-purified CH 4 sample (together with Kr) is injected onto a 30 m CarbonPLOT column at 30 • C with a flow rate of ca.1.1 mL min −1 .The detector is an Isoprime IRMS equipped with five Faraday cups: a universal triple collector for m/z 44, 45 and 46 to calculate δ 13 C of CH 4 and two additional cups for m/z 28 and m/z 32 for monitoring the efficiency of the O 2 and N 2 separation of the trapping system.The five Faraday cups are connected to the following feedback resistors: 5 × 10 8 ("N 2 cup", m/z 28), 1 × 10 9 ("O 2 cup", m/z 32), 5 × 10 8 (major m/z 44), 5 × 10 10 (minor1, m/z 45), and 1 × 10 11 (minor2, m/z 46).

Bern system
The Bern system is an updated and more versatile followup device compared to the AWI system, and its description is currently in preparation.While the AWI system is constructed to measure only δ 13 C of CH 4 , the Bern system can analyse a larger suite of trace gases (CH 4 , N 2 O and its stable isotopologues, xenon, ethane, propane, methyl chloride, CF 4 ).For that reason the Bern system is equipped with additional technical features allowing special experiments to be performed, e.g. a bypass valve for the combustion oven, and additional valves to inject CH 4 and Kr mixtures in helium (He) onto the GC system (Fig. 1).Like the AWI system, the Bern system uses a 30 m CarbonPLOT column, at 30 • C with a flow rate of ca.1.0 mL min −1 .The Bern system uses an identical Isoprime IRMS to AWI, equipped with five Faraday cups: the raw data from the mass spectrometer measurements was processed using our in-house isotope software (Bock et al., 2010;Schmitt et al., 2011).After the identification of the Kr interference, two additional traps (pre-combustion trap and post-combustion trap) were installed to get rid of the Kr interference (Sect.5.3).This new system is referred to as the updated Bern system.

IMAU system
A detailed description of the IMAU system is provided elsewhere (Brass and Röckmann, 2010;Sapart et al., 2011).
A special feature of this system is that it lacks the precombustion GC common in other systems (Fig. 1).The IMAU system uses a Thermo Finnigan Delta plus XL as detector.After the Kr interference was identified, the system was modified to remove the interference (Sect.5.2).As shown in Fig. 1, a GC was added after the conversion of CH 4 to CO 2 (post-combustion GC), and this modified system is referred to as updated IMAU system.

PSU system
The measurements done at PSU use the system described earlier in Sowers et al. (2005).The mass spectrometer is a Finnigan MAT 252.Modifications to remove the Kr interference are in process.

Air samples
All four labs measured a set of three cylinders, which were part of an international round-robin study.These cylinders were filled at Niwot Ridge, Colorado, in 2007 to varying CH 4 concentrations with a balance of ultra-high-purity air (no CH 4 ) to mimic the pre-industrial period (PI, ∼ 900 ppb), the last glacial period (GLA, ∼ 380 ppb) and the present day (PD, 1870 ppb).The cylinders were then measured at NOAA to confirm the CH 4 values (GLA, cylinder no.CA01179 = 372 ppb; PI, cylinder no.CC71560 = 904 ppb; and PD, cylinder no.CA03560 = 1831 ppb).While the CH 4 concentration is different, the Kr concentrations of all cylinders should be at natural abundance (1099 ppb), as the GLA and PI cylinders were produced by diluting atmospheric air with CH 4free air.The three cylinders have the following CH 4 / Kr mixing ratios: 0.33 (GLA), 0.82 (PI) and 1.69 (PD), thus yielding CH 4 / Kr mixing ratios that vary by a factor of 5. Additionally, cylinder CA08289 (NOAA, Boulder) is used at Bern as a working standard containing 1508.2 ppb CH 4 , and IMAU used a natural whole-air working standard of Groningen ("GRO") air with 1981.2 ppb CH 4 for the experiments where pure Kr is added.

First hints and visual inspection of chromatograms
The possible existence of an interfering compound during the IRMS analysis of δ 13 C of CH 4 on air samples was first described in 2001 when Rice et al. (2001) described "an unknown contaminant peak".As the contaminant could not be identified, it remained unclear if this was only a problem of their specific setup or if it is a general feature of air samples.We believe that this unknown contaminant peak was Kr.In hindsight, it is unfortunate that this interference was not resolved as subsequent groups that developed new systems for δ 13 C analysis on CH 4 for air and ice core samples did not account for the Kr interference.This led to the current situation where many systems do not properly separate this "contaminant peak" from CH 4 , while others managed 33 1 Fig. 2. Comparison of the ion current ratios of the four systems (from top to bottom: Bern, 2 AWI, IMAU, PSU).The left column shows the minor1/major ratio ("45/44 ratio"); the middle 3 column shows minor2/major ("46/44 ratio"), the right column minor2/minor1 ("46/45 ratio").4 Natural air samples and air samples with added Kr are plotted as black lines and injections of 5 pure CH 4 are shown as red lines illustrating the anomalies seen in the Kr containing samples.6 Blue vertical lines mark the left and right integration limits.Green vertical lines mark the 7 maximum position of the Kr peak where we could determine its precise position.The Kr 8 interference in the AWI system is visually more pronounced compared to the Bern system due 9 to the differences in peak separation and focusing of the IRMS. 10 11 Fig. 2. Comparison of the ion current ratios of the four systems (from top to bottom: Bern, AWI, IMAU, PSU).The left column shows the minor1 / major ratio ("45 / 44 ratio"); the middle column shows minor2 / major ("46 / 44 ratio"), the right column minor2 / minor1 ("46 / 45 ratio").Natural-air samples and air samples with added Kr are plotted as black lines, and injections of pure CH 4 are shown as red lines, illustrating the anomalies seen in the Kr containing samples.Blue vertical lines mark the left and right integration limits.Green vertical lines mark the maximum position of the Kr peak where we could determine its precise position.The Kr interference in the AWI system is visually more pronounced compared to the Bern system due to the differences in peak separation and focusing of the IRMS.
The search for an interfering substance during δ 13 C analysis of air samples was started during the interlaboratory calibration exercise involving both air cylinders and glacial ice samples (see results in Table 2).The observed δ 13 C differences scaled with CH 4 mixing ratios and were as large as 2 ‰ for low CH 4 samples (e.g.CH 4 < 400 ppb).While the co-elution of CH 4 and Kr and the generation of a m/z 43 peak due to 86 Kr 2+ was recognised during the development phase of the Bern system, it was the addition of Kr to a natural-air sample (GRO) at IMAU that confirmed the Kr interference on δ 13 C.The effects on the measured δ 13 C and δ 18 O values were significant and scaled linearly with the Kr amount added.For each 1 ppm Kr addition, the δ 13 C values and δ 18 O values of the spiked air sample shifted by 0.79 ‰ and by Table 2. Collection of δ 13 C-CH 4 results from the interlaboratory calibration round robin.As described in Sect.2.5 these three cylinders with contrasting CH 4 mixing ratios are referred as GLA, PI, and PD.For some results Kr correction was applied using the following methods: a using the approach described in Sect.5.4, and b according to Sect.5.6.Besides the NIWA (National Institute of Water & Atmospheric Research) lab, which measured the cylinders with dual-inlet IRMS measurement and CF-IRMS, all results were obtained using CF-IRMS.The NIWA dual-inlet data were measured according to Lowe et al. (1999), and Kr would have been pumped away once CO 2 (from CH 4 ) was recovered from the combustion step.These values should be regarded as close to the true values.The NIWA CF-IRMS data were obtained using the method described in Miller et al. (2002) but used a CP-PoraBOND Q column (50 × 0.32 mm × 5 µm at 40 • C) instead of the Molecular Sieve 5A column at 80 • C used in the original publication.Ideally, the NIWA dual-inlet results and the values after Kr correction should be the same within their common error.Deviations among the results are the sum of differences due to referencing standards, amount effects, and imperfect Kr correction.7.2 ‰ towards heavier values, respectively.This experiment clearly showed that Kr did interfere and could explain a large part of the discrepancies between the labs.However, it was unclear whether the observed effect was specific for this system or if other systems were affected as well.Additionally, the nature of this interference had to be elucidated in order to come up with technical solutions and correction routines for older data sets.Since the ion current intensities of this interference are difficult to visualise in the chromatograms themselves, we chose to use the ratio of ion currents to identify the position of the Kr peak relative to the CH 4 peak.Commercial IRMS software packages usually provide graphs of the ion current ratios only for the measured total ion current ratios, i.e. the combined intensities for the sample peak and the background.When the interference in one of the ion current ratios is very pronounced, it is possible to identify it in the total ion current ratios (Rice et al., 2001;Schaefer and Whiticar, 2007).This is the case when the CH 4 and the interference peak are chromatographically well separated.However, when the two peaks strongly overlap, the influence is less visible.A more sensitive way to identify such interferences in chromatograms is to inspect ion current ratio plots where the background signal has been subtracted from the measured signal to yield the signal of the sample peak only.The plots of this paper show ion current ratios which were corrected for the background signal.Figure 2 shows the three ion current ratios for the time interval around the CH 4 peak.
The retention time of the CH 4 peak maximum is defined as 0 s.Throughout the paper we label the three ion current ratios according to the involved Faraday cups and the m/z of the ions which are commonly detected in this cup at CO 2 focusing: minor1 / major ("45 / 44"), minor2 / major ("46 / 44"), and minor2 / minor1 ("46 / 45").Note the m/z pairs are put in parenthesis (e.g."45 / 44") to indicate that only the target ions produced by CO 2 strictly adhere to this rule.It will be shown in this paper that a small fraction of the m/z 43 beam ( 86 Kr 2+ ) tails all the way into all three cups (major, minor1 and minor2).For the Bern, AWI and IMAU systems, air samples containing Kr (Fig. 2 black lines) are compared with pure-CH 4 samples (Fig. 2 red lines).For the systems where it was explicitly determined (see below and Figs. 3  and 4), the position of the Kr peak relative to the CH 4 peak is marked for orientation.As can be seen for all four systems, most ion current ratios of samples containing Kr deviate from the ratios of pure CH 4 .While these anomalies are well pronounced in all three ratios for the AWI system and resemble a Gaussian shape, the Bern system exhibits no visible anomaly for the "45 / 44 ratio", which will be discussed later.In the IMAU case, where Kr was added to natural air in increasing amounts, one sees that the anomalies become larger with more Kr added.Note that the large anomalies are only the result of large amounts of Kr to an air sample (3 times or 17 times the Kr amount of a natural sample (GRO)).The anomalies of the natural-air sample (GRO) are small and hard to detect without prior knowledge.In the case of the PSU system, an anomaly is only barely visible for the "45 / 44 ratio" and obscured by the internal fractionation within the peak (time shift due to mismatch of the resistorcapacitor pair).In conclusion, the visual inspection of the ion current ratios of all four systems points to an interfering substance present in natural-air samples.The appearance of this anomaly is specific for each of the four systems and depends on chromatographic separation and properties of the IRMS itself.These anomalies in the ion current ratios can be hidden especially when the background is not subtracted.It requires a careful comparison of the ratios from the natural-air sample with those from pure CH 4 to recognise this matrix effect.

Simple experiment to identify Kr in the chromatogram
The visual inspection of the chromatograms described above revealed that an interfering compound that we believe is Kr produces anomalies in the ion current ratios.Here we go one step further and provide a test to identify whether the retention time of Kr overlaps with the CH 4 peak.As mentioned above, the behaviour of Kr and CH 4 on GC columns is similar and can result in overlapping peaks with Kr eluting only a few seconds after CH 4 .The following experiment uses the fact that, for the electron energies used in the ion source of the IRMS (e.g.80 eV for the Bern system), ions with two (and sometimes three) electrons removed are also produced (Denifl et al., 2002;King and Price, 2008).Since the optical system of the IRMS separates ions according to their massto-charge ratio (m/z), heavy isotopes like 86 Kr can be readily transformed into m/z 43 86 Kr 2+ ions that strike the imaging plane close to the major ion Faraday cups.Therefore, 86 Kr 2+ ions can be easily monitored by shifting the accelerating voltage (AV) to higher values, e.g.4030 V instead of 3975 V for the CO 2 focusing for the Bern Isoprime, so that the m/z 43 86 Kr 2+ ions are detected in the m/z 44 cup.The m/z 43 beam ( 86 Kr 2+ ) falls into the major cup, while the m/z 45 beam (mostly 13 C 16 O 16 O) falls into minor2, monitoring the position of the CH 4 peak.This focusing test has the advantage that it can be run on any system with any natural-air sample without modifications to the CH 4 separation system.The results of these focusing experiments are shown in Fig. 3.
As can be seen in Fig. 3a, the chromatographic separation of CH 4 from Kr is about 6 s for the Bern system.Since the peak width (FWHM) for both CH 4 and Kr is also 5-6 s, both peaks do overlap considerably (Fig. 3a), but the overlap is system dependent.From this experiment we can derive the following conclusions.First, a considerable amount of doubly charged Kr ions are produced within the source of the IRMS.Second, 86 Kr 2+ ions allow identifying the retention time of Kr and illustrate that the GC conditions of the Bern and PSU systems are insufficient to separate Kr from CH 4 .Third, the position of the Kr peak and the observed anomalies seen in the ion current ratios (Fig. 2) are similar and suggest that Kr causes these anomalies.

Injections of pure Kr into GC flow
The visual peak inspection and the overlap of CH 4 and Kr from the focusing exercise point to Kr as the source of the interference.However, at this stage it remains unclear how Kr might interfere with the δ 13 C measurement since a direct isobaric effect seems unlikely as none of the Kr isotopes are expected to fall into the given Faraday cups at their nominal m/z as singly or doubly charged ions.Several studies report on non-isobaric interferences during stable isotope analysis of gas mixtures without a clear hint of the mechanisms behind them (Mariotti, 1984;Sarma et al., 2003).One possible mechanism generating our anomalies could be that the presence of Kr in the ion source changes the relative ionisation efficiency of the CO 2 isotopologues in the sense of "ionisation quench" coined by Meier-Augenstein et al. (2009).In dual-inlet applications such matrix interactions of gases in the ion source are commonly termed "chemical slope" (Severinghaus et al., 2003) and refer to differences in the composition of sample and standard gas mixture.While correcting for this effect is common practice, the underlying processes in the ion source are poorly understood.
Alternatively, Kr itself without any interaction with CO 2 produces the observed signals.A simple test to distinguish between these two possibilities is the injection of pure Kr.If the pure Kr does not produce a positive signal by itself, then the interference relies on the interaction of CO 2 and Kr in the ion source.In contrast, if Kr alone generates these signals, then some of the Kr ions are deflected from their expected flight path to fall into Faraday cups with m/z values up to 3 units higher.
To perform this experiment a mixture of pure Kr in He was injected via the injection loop into the GC flow of the Bern system (see Fig. 1).The amount of injected Kr roughly equals the amount of Kr of ca. 10 mL STP natural air; thus, a similar amount as is used in our routine ice core measurements.The injected Kr is cryofocused first and then sent to the pre-combustion GC (Fig. 1).After the Kr peak left the GC, the flow passes a dryer before admitting it to the ion source of the IRMS (operated at CO 2 configuration).Note that the combustion oven is bypassed in this experiment to prevent the generation of a small CO 2 peak from trace amounts of residual CH 4 present in the He flow.The results of this experiment are shown in Fig. 4, together with the measurement of a natural-air sample.Kr itself produces signals in all Faraday cups at a retention time of ca.6 s after the usual CH 4 peak maximum (Fig. 4c).This result supports the idea that Kr alone produces the signals detected in the three cups.A comparison with the signal intensities of the air sample (Fig. 4a) shows that the Kr intensities are clearly too small to be directly seen in the air sample itself; e.g. for the minor2 cup, the Kr signal is 4 mV at its maximum while for the air sample, the minor2 signal at the same time is ten times higher.Besides these two basic features, the experiment with pure Kr affords us the opportunity to investigate the general features observed in the ion current ratios of the air sample.A combusted CH 4 sample produces signal intensities (mV) in the three Faraday cups reflecting the natural abundance of the CO 2 isotopologues.For example, the signal of the major cup is a bit higher than the minor2 signal (Fig. 4a).In contrast, Kr produces a 4-times-higher minor2 signal compared to the signal on the major cup (Fig. 4c).In other words, the signals produced by Kr have a very different isotopic fingerprint compared to the CO 2 signals.In this example dealing with minor2 vs. major cup ("46 / 44 ratio"), Background-corrected ion current ratios ("46 / 44 ratio" in blue, "46 / 45 ratio" in green and "45 / 44 ratio" in black) of the atmospheric air sample (solid line) and pure CH 4 (dotted line), illustrating the anomalies seen in "46 / 44" and "46 / 45" but with no visible effect on "45 / 44".Panel (c) shows the beam intensities for a measurement where Kr was injected into the GC flow.Due to the chromatographic effect of the GC column, the retention time of the Kr peak is ca.6 s longer than the CH 4 peak, yet there is a considerable overlap.Note the signal measured at m/z 28 ("N 2 cup") can be directly related to 84 Kr 3+ , which has the exact value of m/z = 28.
the Kr signals translate into a very heavy apparent δ 18 O signature since the δ 18 O is mainly determined by the "46 / 44 ratio".When such an anomaly is added to the signals from combusted CH 4 , the observed "46 / 44 ratio" will increase as it is the case for the air sample (Fig. 4b, "46 / 44 ratio").In contrast, the minor1 / major ratio of both the air sample and Kr are comparable, with the signal on minor1 being slightly higher than on major (Fig. 4a and b).Consequently, the signals created by Kr do not produce a visible anomaly in the minor1 / major ratio as the "45 / 44 ratio" of the air sample closely follows the ratio of pure CH 4 (Fig. 4b "45 / 44 ratio").Note that this close match of the "45 / 44" signature of Kr and CO 2 is just a coincidence and only observed for the Bern system.The other three systems show anomalies in the "45 / 44 ratio" (Fig. 2), which translate into too-heavy δ 13 C values for natural-air samples as well.In addition to the more direct influence of the "45 / 44" anomaly on δ 13 C, the "46 / 44" anomaly also alters δ 13 C of CH 4 samples.This is due to the fact that the 17 O correction algorithm (Craig, 1957;Santrock et al., 1985) relies on assumptions regarding the natural proportions of the stable oxygen isotopes, i.e. the relative contribution of 17 O ( 12 C 17 O 16 O with m/z 45) and 18 O ( 12 C 18 O 16 O with m/z 46), which are violated by the Kr signals.

Injection of pure Kr at varied accelerating voltage
The previous experiments clearly showed that Kr is responsible for the observed effects; yet, the underlying mechanism cannot be unambiguously derived from these experiments.Because the m/z 43 beam produced by 86 Kr 2+ is only a few m/z units away from the target signals at m/z 44, m/z 45 and m/z 46, we propose two hypotheses.The first hypothesis assumes that the observed signals detected in the three Faraday cups are caused by ions with a mass-per-charge ratio corresponding to the nominal m/z of the cups, i.e. m/z 44, m/z 45 and m/z 46.Since ions with m/z 43 are available in the source, one might assume that light gases or their ions (e.g.He, H 2 or H) might react with 86 Kr 2+ ions to form molecules or adducts (Leckrone and Hayes, 1998;Sessions et al., 2001), which then could provide the necessary m/z 44, m/z 45 and m/z 46 signals.The other hypothesis assumes scattering processes lead to broader m/z distributions, e.g. that the lateral tail of the m/z 43 beam ( 86 Kr 2+ ) extends all the way to m/z 46, thus covering 3 m/z units.The fact that the major ion beam contributes some intensity to the neighbouring minor was already observed during the early days of dual-inlet IRMS and termed "pressure effect" or "pressure broadening" and has been treated with abundance sensitivity corrections (Deines, 1970;Mook and Grootes, 1973;Fallick and Baxter, 1977).Peak-tailing effects are also of concern during clumped-isotope analysis of CO 2 where far reaching tails of the major beam on the distant minor beams have been investigated (He et al., 2012).A peak-tailing effect was also observed during stable-sulphur analysis using SF 6 , giving rise to an abundance sensitivity correction to prevent scale compression and accuracy problems (Ono et al., 2006).However, in these cases it is the regular major beam which contributes intensity to the minor beam and not a contaminant species like Kr as assumed in our case.Figuring out the actual process leading to this interference is not only helpful in understanding the different phenomena seen in the four investigated systems, but also in making assumptions about the stability of this interference over time and its sensitivity to changes in focusing parameters, etc.These characteristics are important for developing robust correction routines on existing data sets.
To explore the nature of the interference in more detail we conducted two different experiments where the ion current intensities are monitored as a function of the AV.In the first experiment, Kr was repeatedly injected into the GC flow, while the AV was slightly changed after each injection.In a second experiment, Kr was continuously admitted to the ion source through a capillary, while the AV was changed over a wide range.

Kr injections onto GC flow at varied accelerating voltage
In the following experiment pure Kr was repeatedly (10 times) injected into the GC flow of the Bern system and cryofocused prior to GC separation.The amount of injected Kr roughly matches the Kr amount of a 10 mL air sample to provide realistic measurement conditions.Measurements were conducted using the CO 2 configuration, but after each Kr peak the AV of the ion source was slightly changed to cover a range from −5 V to +2 V relative to the peak centre (PC) value of the CO 2 focusing.Each Kr peak is preceded by a rectangular CO 2 peak from the reference port ("standard onoff type") and measured at the same AV to monitor the effect on the δ 13 C and δ 18 O values of CO 2 .Since the applied AV variations cover less than 0.1 m/z unit, the ion beams still fall into their respective Faraday cups.As a consequence, the δ 13 C and δ 18 O values of the rectangular CO 2 peaks are only slightly affected by these AV shifts (ca. 2 ‰ for both δ 13 C and δ 18 O, data not shown).In contrast, the maxima of the Kr peaks in the major cup (m/z 44 at PC) increase from ca. 0.5 mV to almost 6 mV, i.e. a factor of 12 as the AV is increased from −5 V to +2 V (Fig. 5a).Since the peak heights and areas for minor1 (m/z 45 at PC) and minor2 (m/z 46 at PC) remain fairly constant, the apparent isotopic ratios δ 13 C and δ 18 O of the Kr peaks show huge changes, reflecting these drastic changes in the beam ratios (Fig. 5b).We calculated these apparent δ 13 C and δ 18 O values by integrating the peak areas of the tiny Kr peaks for the three cups and applied the same algorithm as if they were CO 2 peaks.Our interpretation is that by increasing AV, the amount of 86 Kr 2+ falling into the major cup quickly increases since the steep tail of this m/z 43 beam is moved closer to the edge of the major cup.The observation of this strong intensity increase on the major cup thus rules out the notion of an ion with m/z 44 producing this interference.However, for the rather constant intensities measured on minor1 and minor2 this experiment cannot rule out the existence of an ion at m/z 45 or m/z 46 since the AV changes were too small to move the centred beam out of the Faraday cup, as can be inferred from the rather constant δ 13 C and δ 18 O values of the CO 2 rectangular peaks (data not shown) and illustrated in Figs. 6 and 7.
Apart from identifying the nature of this interference, this experiment provides valuable information regarding the effects of the Kr interference during sample measurements.From Fig. 5 it is obvious that the apparent δ 13 C or δ 18 O signatures of the Kr interference are not constant but depend on the peak centre setting.Consequently, the influence of Kr on the calculated δ 13 C values of CH 4 samples is not a constant property for any instrument, but both the sign and the magnitude of this effect are sensitive to the setting and stability of the source.As an example, at an AV offset of −1.5 V with respect to the peak centre, the apparent δ 13 C value of the Kr interference intersects with the range of δ 13 C values typical for natural CH 4 samples (around −40 to −70 ‰, red horizontal line in Fig. 5b).If samples are measured at this AV setting, then the Kr effect on δ 13 C of CH 4 will be relatively small and hard to detect.However, for AV offsets < −1.5 V the measured δ 13 C values will be heavier, and for AV offsets > −1.5 V δ 13 C will become progressively lighter.For δ 18 O, the Kr bias will always push towards higher values.Note that these values are specific for a certain focusing of a specific instrument.How subtle differences can produce very different effects can be seen in the results of the AWI and Bern instruments, which have identical IRMS.The AWI system shows a pronounced effect in "45 / 44" (i.e.δ 13 C), while the effect on "45 / 44" for the Bern instrument is small (compare Fig. 2a and d).Usually, the AV at peak centre is determined automatically during the peak centre procedure; thus the bias could be relatively constant for a certain focusing.However, after performing a peak centre its actual position can move by up to 1 V over the course of hours, thus generating a timedependent bias on the δ 13 C values during a measurement, which will add noise to the data set.On the other hand, the close relationship between apparent δ 13 C and δ 18 O values provides a means to correct biased δ 13 C measurements if the expected δ 18 O value of a sample can be predicted or assumed with good precision.This situation often holds for δ 13 C since the δ 18 O value of the CH 4 -derived CO 2 is not dependent on the CH 4 sample but set by the O 2 used during the combustion process.Therefore, the tight δ 18 O-δ 13 C correlation seen in Fig. 5b can be used to correct samples which are affected by the Kr interference (see Sect. 5.6).

Admission of Kr into the ion source at varied accelerating voltage
The aim of the following experiments is to better characterise the Kr interference using a wider m/z range.
To better understand an AV scan with pure Kr, we first present an AV scan for CO 2 (Fig. 6a).For practical reasons, the cups of the triple collector unit (universal collector) of most manufacturers have different widths (resolving slit width) to accommodate multipurpose usage, e.g.δ 15 N of N 2 , δ 18 O of O 2 .For the Bern IRMS, an AV change of 85 V is roughly equivalent to 1 m/z difference in this mass range.Figure 6b shows the ion current intensities for the three cups in fA for the same AV scan, but with Kr being admitted to the ion source.The 86 Kr 2+ ion beam with nominally m/z 43.0 starts to fall into the major cup at around +5 V and reaches plateau intensity at +20 V ("transition zone") with around 600 000 fA (Fig. 6b bottom panel).Zooming into the major signal reveals that after the initial steep drop to the left of the transition zone (towards higher m/z), the intensity only gradually decays when moving to −90 V, i.e. corresponding to ions with a nominal m/z of already 45 (see Fig. 6a with 85 V corresponding to about 1 m/z unit).The continuation to even-higher m/z is visible in the signal of minor1, where the intensity decreases from ca. 80 fA at +60 V (corresponding to ca. m/z 44.7) to ca. 30 fA at −90 V(corresponding to ca. m/z 46.0).Similarly, the continuation is visible in mi-nor2, where the Kr signal becomes almost flat at around 80 fA, covering a range of m/z 45.7 to m/z 47.0.The fact that Kr produces higher intensities for minor2 compared to mi-nor1 reflects the contrasting widths of the two cups: the wider minor2 cup collects Kr ions from a larger m/z range than the smaller minor1 cup (see also scheme of Fig. 7).Again, it is obvious that very small changes in the choice of the peak centre position can have a large effect on the apparent δ 13 C and δ 18 O signature of the Kr interference as already seen in Fig. 5b.Further, the flatness of the Kr signal in the region of m/z 45 and m/z 46 explains the strong linear correlation of δ 13 C and δ 18 O seen in the other experiments and measured air samples and is the basis for one of the correction methods explained below which rely on a linear relation of the m/z 45 and m/z 46 biases.7b and c) we used the measured data of Figs. 5 and 6 and the interpretation we derive from these experiments.It is clear from Fig. 6b that most ions are well focused into a sharp beam with steep flanks as intensity rapidly drops to < 1 / 1000 of the plateau level for a 15 V shift in the accelerating voltage, corresponding to about 0.2 m/z units.Only the close-by major cup is strongly affected by this broadening effect.This rapidly dropping signal close to the beam centre can be attributed to the abundance sensitivity effect (Deines, 1970).We refer this contribution of the total Kr signal as the 86 Kr 2+ tail since it corresponds to the lateral tail of the proper 86 Kr 2+ beam (light green curve Fig. 7b).However, the remarkable feature of the measured Kr signal is that this drop does not continue its rapid drop but decays only very slowly and finally becomes flat when its intensity reaches about 1 / 10,000 of the plateau signal at the 20 V distance from the plateau edge (Fig. 6b).This observation is not predicted by abundance sensitivity because in that case the signal far out of the beam centre (the region of minor1 and especially mi-nor2 cup) should drop more rapidly.One option to produce such an elevated background for higher masses far from the beam centre is that ions must have experienced a higher accelerating energy in the ion source.The other option would be interaction or scattering of 86 Kr 2+ ions with He, thus energy loss, after the ions passed the magnetic field.It is also conceivable that this flat contribution might be unrelated to the 86 Kr 2+ beam, but originate rather from unspecific, broad scattering of the more abundant singly charged Kr ions.For example, filament or ion source processes could produce a broad distribution of low-energy Kr + ions which then lead to a broad field of ions with apparent m/z in the range the CO 2 target masses.Likewise, Kr + ions could hit the flight tube and produce a field of secondary ions which reach the Faraday cups indirectly.We name this flat contribution Kr scatter (brown line in Fig. 7b).

Summary of experiments and concept of Kr interference
Figure 7c shows the sum of both contributions ( 86 Kr 2+ tail and Kr scatter ) resembling the general features of our experiments and illustrates the Kr interference.While the ion density of the total Kr signal gradually declines further away from the peak maximum at m/z 43, the transformation from the ion current (apparent fA unit) to the voltage unit (apparent mV unit) overcompensates this drop (Fig. 7c).As a consequence, the signals (on an apparent mV unit) gained from minor1 and minor2 are higher compared to the major signal.The signal intensities are spatially integrated according to the width of the Faraday cups: the wider the cup, the more ions from the tail are collected.Accordingly, the integrated signal from mi-nor2 is higher than the integrated minor1 signal.In summary, the Kr interference signal of a certain Faraday cup is not only a function of the ion flux at this position along the optical plane, but also depends on the width of the Faraday cup.We want to point out that these observations refer to IRMS measurements in continuous-flow mode where He is admitted continuously to the ion source, leading to a typical pressure of 2 × 10 −6 mbar.In dual-inlet mode the source pressure is about a factor of 10 lower.We have indications from additional tests with dual-inlet IRMS measurements (IMAU), where we admitted Kr without He background, that here the Kr interference is less pronounced.Based on these results we speculate that the m/z 43 ion beam is better focused at dualinlet conditions, but in continuous-flow mode it is broadened by collisions with He ions in the source or He atoms in the flight tube.A peak broadening during continuous-flow IRMS compared to dual inlet was also observed during stable sulphur isotope analysis using SF 6 (Ono et al., 2006).

Solutions for the Kr interference
The observations and experiments discussed above show that Kr can severely interfere with δ 13 C measurements of CH 4 samples if the Kr peak is within the integration boundaries of the CH 4 peak.Given the fact that the Kr interference can produce systematic offsets exceeding the analytical precision, we propose the following strategies to account for or eliminate this effect.
1. GC separation of Kr from CH 4 prior to conversion to CO 2 2. GC separation of Kr from CO 2 after the CH 4 -to-CO 2 conversion 3. Cryogenic separation of Kr from CO 2 after the CH 4 -to-CO 2 conversion 4. Raw beam time series correction using anomalies in the ion current ratios 5. Early peak cut-off at the right integration boundary 6.Correction using relations between δ45 and δ46 It is beyond the scope of this paper to discuss all strategies in great detail.Separate technical papers will deal with the individual solutions applied to a particular system.Instead, we want to provide an overview of possible solutions to let the reader make a first selection on the preferred strategy.
The six strategies fall into two classes.Strategies 1 to 3 are technical solutions, which prevent the peak overlap in the ion source and thus avoid the Kr interference for new measurements.Strategies 4 to 6 allow correcting existing data sets.These correction strategies were specifically developed for the existing data sets of our respective systems.As the four systems show different characteristics of the Kr interference, these correction strategies cannot be applied interchangeably.Consequently, we could not compare the performance of the three correction approaches, but discuss their strengths and limitations individually.

GC separation of Kr from CH 4
Of all the proposed solutions in this section, the chromatographic separation of CH 4 from Kr seems to be the most elegant and straightforward way since no additional device is needed besides the basic setup described by Merritt et al. (1995).The only requirement is that the chromatographic separation is good enough to allow a sufficient separation of CH 4 and Kr.Without knowing that Kr was the "unknown contaminant peak", Rice et al. (2001) were the first to master this problem with a cryo-GC at −50 • C. To maintain narrow peak width, they used high flow rates of 2.6 mL min −1 , thus a factor 2.5 higher than typically used for ice core analyses.This approach is also applied by others (Umezawa et al., 2009).Schaefer and Whiticar (2007) followed the same route and used a sub-ambient GC at 0°C to separate what they call N 2 O.However, they concluded that separation at 0 • C was insufficient, and a second GC column was introduced after the combustion oven.With the Bern system, we tested the option to better separate CH 4 from Kr using lower GC temperatures.For the experiments we used a 30 m PoraPLOT column at a flow rate of ca. 1 mL min −1 and measured the chromatographic separation between CH 4 and Kr for three temperatures: 5, 18, and 30 • C. A Kr-He mixture was injected onto the GC flow and cryofocused (Fig. 1).Measurements were made under CO 2 focusing conditions.We did not inject CH 4 but used the small amount of CH 4 cryofocused as blank contribution.This small CH 4 amount turned out to be ideal for these experiments as an amount of CH 4 comparable to samples would otherwise overwhelm the Kr peak.The results are shown in Fig. 8.For 30 • C (Fig. 8a) the separation is only 8 s -thus, insufficient -and results in comparable retention time differences to the CarbonPLOT column (ca.6 s).A reduction to 5 • C (Fig. 8c) shows that the separation of CH 4 from Kr is much better and amounts to 16 s, allowing Kr-free δ 13 C analysis of CH 4 .However, this low GC temperate had the disadvantage that N 2 O eluted very late and showed a very broad peak shape, which is not suitable for isotope analysis on N 2 O. Since in our ice core analysis we measure δ 13 CH 4 and N 2 O isotopes in the same run, we did not choose this route but decided to follow the route described in Sect.5.3.

Chromatographic separation after the CH 4 -CO 2 conversion
The following section describes the separation of Kr from the combusted CH 4 peak using a post-combustion GC column.
As shown above and from other studies (Rice et al., 2001), a sufficient separation of CH 4 from Kr requires low GC temperatures due to similar physico-chemical properties of CH 4 and Kr on the GC column.However, after the combustion oven the resulting CO 2 is relatively easy to separate from Kr since already at ambient temperatures (e.g. 30 • C) Kr elutes much earlier than CO 2 on regular GC columns.
The usage of a post-combustion GC column for δ 13 C of CH 4 was first described in Schaefer and Whiticar (2007), who included this device to separate what they interpreted as N 2 O.In the following, we show results from the updated IMAU δ 13 C system, where also a post-conversion GC column is used to avoid the Kr interference (Fig. 1).The additional component consists of a 12.5 m piece of PoraPlotQ column in a GC which is operated at 24 • C.This GC column was inserted between the Nafion dryer and the open split (see Fig. 1 in Sapart et al., 2011) and provides a separation of Kr from CO 2 (CH 4 ) of about 30 s (Fig. 9b).The figure also nicely shows the response of the IMAU mass spectrometer to pure Kr resulting in a very pronounced peak on the minor2 cup collecting the nominal m/z 46 ions.A much smaller peak can be seen on minor1 cup (nominal m/z 45).This observation fits with the experiments where pure Kr was added to an air sample and a strong enrichment for δ 18 O was observed while the enrichment for δ 13 C was smaller (7.2 ‰ for δ 18 O, and 0.79 ‰ for δ 13 C per 1 ppm Kr added).In contrast to the Bern system, here the Kr signal on the major cup < 0.1 mV is too small to be visible; thus, the intensities on minor1 and minor2 become fully expressed as anomalies, leading to the strong biases in δ 13 C and δ 18 O observed for the original IMAU system (compare with the Bern system, Figs. 4, 5 and 10).
To assess the overall performance of the updated IMAU system, the three intercomparison cylinders which were measured with the original IMAU system were remeasured with the updated system as well.A comparison between the original and updated IMAU systems shows that the Kr interference at IMAU amounted to ca. 2.38 ‰ for the GL cylinder, ca.0.88 ‰ for the PI cylinder and ca.0.05 ‰ for the PD cylinder (Table 2).The results from the updated IMAU method are also comparable with the measurements obtained at NIWA using dual inlet IRMS, which is free of Kr interference, and with the Kr-corrected results obtained from other labs.

Cryogenic separation of Kr from CO 2 after the CH 4 -CO 2 conversion
In this section we describe an alternative procedure to separate CO 2 and Kr after the combustion oven, based on the fact that CO 2 can be trapped on a capillary at liquid nitrogen (LN 2 ) temperature (−196 • C) while Kr passes this trap.
In the updated Bern system, such a trap is inserted after the combustion oven (post-combustion trap, Fig. 1).Such a trap not only separates CO 2 from Kr but also acts as a cryofocus yielding narrow, high-intensity CO 2 peaks after the capillary is lifted out of the LN 2 (Melton et al., 2011).A second movable trap is inserted before the combustion oven to trap any residual CO 2 from the GC flow (pre-combustion trap, Fig. 1).With the addition of these two traps, Kr now elutes sufficiently (we found 25 s to be a good value) before the sharp CH 4 -derived CO 2 peak, thus providing baseline separation between the two species (Fig. 10).The timing of the post-combustion trap is a critical parameter of this strategy to avoid trapping traces of combusted sample CO.While most of the CO is removed during the first purification step, a small fraction of CO remains and elutes before the CH 4 peak and becomes combusted to CO 2 as well (Fig. 10b).As can be seen in the example chromatogram, the post-combustion trap (trap down arrow in Fig. 10b) is lowered only after the COderived CO 2 peak has passed the trap.After a trapping time of 50 s, the capillary is lifted and produces the sharp CO 2 peak.Because Kr is not collected on this capillary, its retention time is basically the same as without the trap.Note that the length of the trapping time should not be unnecessary long since CO 2 bleeding from the combustion oven adds up to blank contribution, which has to be minimised.After the CO 2 peak is measured by the IRMS, a valve is switched to allow the N 2 O peak to bypass the combustion oven (Fig. 1, green circles).Note the different peak shape characteristics of the CH 4 -derived CO 2 peak and the N 2 O peak due to the cryofocusing step.

Subtracting the Kr interference peak from raw data
The above hardware solutions all eliminate the Kr interference.However, extant data sets require an algorithm for correcting for the Kr interference.One method for making the correction relies on the anomalies seen in the ion current ratios, which are particularly pronounced in the data set measured with the AWI system (Fig. 11a).This approach requires the time series of the IRMS acquisition file (raw beam data file) and software to read and process this data (Bock et al., 2010;Schmitt et al., 2011).With a set of equations the signal intensity of the Kr peak is calculated which produced these anomalies in the first place.The time series of these reconstructed Kr interferences are then subtracted from the measured time series to yield the corrected time series.The latter one is then used to calculate the δ 13 C values.
In detail, the correction is based on the following equations, with i representing the time series of an ion current and R the ratio of a pair of ion currents.In the case of the AWI measurements, the time series covers the interval beginning at the CH 4 peak start and extends to 10 s after the maximum of the CH 4 peak (see Fig. 11b).Note that the following equations and explanation only show the correction of the Kr interference on i 45 and R 45/44 ; the correction for i 46 is analogous to the i 45 example.We start by assuming that the CO 2 peak is pure CO 2 in the ion source, i.e. without Kr interference, and the major cup exclusively collects ions, with m/z 44 generating the time series of i 44 , minor1 only m/z (i 45 ), and minor2 only m/z 46 (i 46 ).In this case, the ion current ratio R In practice, R 45/44 is calculated by subtracting the "background ratio" defined as i 45 CO 2 / i 44 measured , from the ratio of the affected right peak side with the contaminated ratio, R 45/44 (CO 2 +Kr) .The peak section from which the "background ratio" is calculated is indicated by boxes in Fig. 11a.At this step we make the assumption that without any Kr interference the ratio in the background box would continue all the way to the right side, to the right integration boundary (8 to 10 s after CH 4 peak maximum).This assumption is reasonable at this step for defining the "background ratio" since pure-CH 4 peaks show an almost flat ratio over the whole CH 4 peak (see Figs. 2d-f and 11a).
The i 45 Kr−excess time series resembles a Gaussian peak shape with its maximum at the retention time of the Kr peak (Fig. 11b, blue dots), which indicates that the method allows extracting the Kr interference.Before continuing the calculation, we want to point out the counterintuitive temporal offset between the maximum of the Kr peak and the anomaly maximum of ion current ratio visible in Figs. 2, 4 and 11.Typically, the maximum of the Kr peak occurs a few seconds earlier than the maximum in the ion current ratio.Theoretically, if both the CH 4 -derived CO 2 peak and the Kr peak were ideally Gaussian, the background-corrected ion current ratio on the right side of the Kr peak should asymptotically approach the respective ion current ratio of the Kr peak itself.However, the ion current ratio usually shows a local maximum a few seconds after the maximum of the Kr peak and then declines towards the value of the CO 2 .Our interpretation is that both peaks are non-Gaussian and CO 2 has a longer residence time in the ion source and in the capillaries due to adsorption effects compared to the noble gas krypton.For that reason the measured ion current ratio in the region of the declining flank of the Kr peak becomes progressively dominated by CO 2 .The i 45 Kr−excess is not directly used for the correction but a fit to this time series.This fit is called i 45 Kr−excess fitted .The fit is more accurate and more robust to the selected "background ratio" used in Eq. (3) than the raw i 45 Kr−excess time series, and the entire Kr peak can be subtracted (see Fig. 11b).The fit is obtained by scaling the CH 4 -derived CO 2 peak with the height of the i 45 Kr−excess peak using the observation that a Kr peak and a CH 4 -derived CO 2 peak are of almost congruent peak shape.Accordingly, the fitting step aims to extract only the part of the R 45/44 anomaly that can be related to a Kr peak (Fig. 11b); for details see the corrected minor1 / major ratio (thin line, Fig. 11a) which is not a flat line as would be method, where the right integration boundary is shifted from 10 s to 3 s after the CH4 peak 10 maximum to cut-off a large fraction of the Kr peak.This method is more vulnerable to peak 11 shape variations leading to more noise in the results.12 13 Fig.12.Comparison of two methods to account for the Kr interference based on measurements with the AWI system using the three intercomparison cylinders with contrasting CH 4 / Kr mixing ratios.Plotted are the δ 13 C numbers, i.e. the differences between the original results and the results obtained after removing the Kr effect.Both methods reveal that with decreasing CH 4 concentrations (hence, CH 4 / Kr mixing ratios) δ 13 C becomes larger.(a) Results for the method of Sect.5.4, where the Kr interference is subtracted from the raw data time series.Coloured diamonds with error bars mark the cylinder measurements; grey circles show a data set of 152 ice core measurements.(b) Results for the relatively simple method, where the right integration boundary is shifted from 10 to 3 s after the CH 4 peak maximum to cut off a large fraction of the Kr peak.This method is more vulnerable to peak shape variations leading to more noise in the results.
the case if the full R 45/44 (raw anomaly) had been removed (Fig. 11a).Using i 45 Kr−excess fitted the measured time series can be corrected as follows: These equations provide a quantitative way to correct for the Kr interference measured on the minor1 cup.To correct the interference on the minor2 cup, equivalent equations for i 46 have to be solved.The corrected time series are then fed into our peak integration software to determine the peak areas within the integration limits of the CH 4 -derived CO 2 peak and finally the δ 13 C value.We have applied this correction to results from the intercalibration cylinders with contrasting CH 4 mixing ratios (CH 4 / Kr ratios) to demonstrate how the interference scales with CH 4 mixing ratio and to estimate the precision of this correction (Fig. 12a).We see a close linear relationship between the absolute correction, δ 13 C, and the inverse CH 4 mixing ratio (1/CH 4 ) with δ 13 C values of only 0.18 ‰ for the "present day" cylinder, 0.33 ‰ for the "preindustrial" cylinder and 0.81 ‰ for the "glacial" cylinder of the round-robin exercise.The standard deviation of the absolute correction, δ 13 C values, averaged over the three cylinders is 0.02 ‰; thus, the correction algorithm adds only little noise to the measurement noise of the results.In principle, this close linear relationship seen in Fig. 12a can be exploited to correct samples with known CH 4 mixing ratio in the sense of applying a calibration curve to samples.This approach could be valuable, if samples cannot be corrected individually with the above-described algorithm.To evaluate this route, Fig. 12a additionally shows the results from a large data set of ice core samples which were measured with the AWI system.Here we see that the individually corrected samples show a similar CH 4 dependency to the results from the cylinder measurements, yet the correlation is much weaker.The weaker correlation and the scatter around the regression line of the cylinder results do not reflect the correction method itself; the scatter is rather due to the temporal variability of the Kr effect.While the cylinder measurements were obtained within a few weeks, the ice core data set was measured over a period of two years with some changes in the source focusing parameters.From this we can conclude that if the relation of δ 13 C vs. 1 / CH 4 is used for correcting affected samples, this can be done very precisely when the calibration measurements are done in close proximity to the sample measurements.On the contrary, additional noise is added to the data when measurement and calibration are not performed at the same instrument conditions, as the relation of δ 13 C vs. 1 / CH 4 is subject to changes over time.

Early peak cut-off
Another method for correcting extant data for Kr may be employed when there is sufficient separation between the Kr and CH 4 peaks.The relative position of the Kr and CH 4 peaks must first be determined as discussed in Sect.4.1.Once the position of the Kr peak has been established, one can determine when to cut off the CH 4 peak in order to minimise the Kr interference.There is a trade-off involved in removing larger portions of the Kr interference as that requires larger portions of the sample peak to be removed as well.If we assume that the total Kr effect on δ 13 C for a sample amounts to 0.8 ‰, a 90 % cut-off of the Kr peak brings the remaining interference to 0.08 ‰, i.e. already below the usual measurement precision of ca.0.1 to 0.2 ‰.With this approach most of the Kr peak is removed, while only about 10 % of the CH 4 peak is lost.In the case of the AWI measurements this translates to a right integration boundary position of 3 s after CH 4 peak maximum.Clearly, this approach violates the rule that the entire peak must be used for isotope analysis, but this can be accommodated by the identical treatment principle (Werner and Brand, 2001).The consequences can be seen in Fig. 12b.The price for this cut is a higher noise level of ca.0.35 ‰ and a systematic bias of ca.0.2 ‰ which results from systematic differences of the isotopic ratio along the peak.The results of this simple cutting approach could be improved when a certain peak fraction, i.e. 10 %, is cut off instead of a fixed time as used here to accommodate for peak shape changes in different chromatograms.
The simplicity of this approach allows for a first check of whether and to what extent the δ 13 C data might be influenced by the Kr interference.It also provides confidence = 1.00) and this relation can be used to correct for the Kr interference without knowing the exact CH 4 -Kr mixing ratio of a sample.Note that here the δ46/δ45 slope is shown, i.e. the inverse value used in Eq. ( 9). in the more sophisticated correction algorithm presented in Sect.5.4 as it yields a correction of similar magnitude.We applied both the cut-off technique and the subtraction technique on the large ice core data set measured at AWI and conclude that both correction techniques provide similar δ 13 C-corrected values (data not shown).

Correction using relations between δ45 and δ46
The following section describes a correction routine applied by IMAU.The basis for this correction approach is the fact that the Kr interference affects both the minor1 and the mi-nor2 cup, thus δ45 (δ 45/44 ) and δ46 (δ 46/44 ) as shown in Fig. 13.This leads to biases for both δ 13 C and δ 18 O, which show a tight linear relation (e.g.Fig. 5).
A necessary prerequisite to using the δ45 / δ46 relation for correction is the fact that the δ 18 O of the combustion product CO 2 is very similar for sample and reference air peaks.This is usually the case because all oxygen atoms of CO 2 are derived from O 2 during the combustion process.Consequently, the δ 18 O deviation of a Kr-affected sample from a pure-CH 4 sample can be ascribed to the influence of the Kr interference on δ 13 C.Note that this assumption is only valid if sample and the pure CH 4 are measured closely together, at least on the same day; otherwise the δ 18 O values are subject to long-term drift caused by the redox state of the combustion furnace.To apply this correction, the relation of δ45 / δ46 for the Kr interference has to be acquired.For this, we used the results from the experiments where increasing amounts of Kr were added to a CH 4 sample (Sect.3).For the correction, the following equation is used: where δ 13 C corrected is the δ 13 C value after correction, δ 13 C measured is the raw measured value, δ 18 O sample and δ 18 O reference are the δ 18 O values of the sample and a bracketing reference measurement of pure CH 4 , and slope δ45/δ46 is the slope of the experiments from Sect. 3 (see Fig. 13).

J. Schmitt et al.: Kr interference during carbon isotope analysis
The value used for the slope is δ45 / δ46 = 0.1388 ± 0.0008 ‰, or approximately 0.14 ‰ in δ 13 C for 1 ‰ in δ 18 O.Note that for samples the introduced error stemming from the uncertainty of the slope is small and scales with the CH 4 / Kr mixing ratio.As an example, for a sample which is corrected by 1.39 ‰, a typical value for glacial ice samples, the error due to the slope amounts to only 0.008 ‰ and, thus, is small compared to the analytical uncertainty of ca.0.1 to 0.2 ‰.A second type of error results from the measurement uncertainty of δ 18 O for both the sample and the reference.Ideally, the measured δ 18 O values for samples and references should only deviate due to the Kr interference and should be equal for Kr-free CH 4 samples.However, the δ 18 O values might vary over time since the conditions of the combustion furnace can change with time.Depending on how and in which intervals the furnace is reoxidised with O 2 , the variability of δ 18 O is dependent on the system used and should be checked before this correction technique is used to correct a measured data set of δ 13 C.Moreover, changes in the IRMS source focusing may change the slope over time.The advantage of this method is that it does not involve special software to do the raw data correction as described in Sect.5.4.To calibrate this correction, it would suffice to have two gases with known and different CH 4 / Kr ratio.
Again, the results from the three intercomparison cylinders provide the means to assess the Kr correction.The comparison of Kr-corrected δ 13 C values measured with the original IMAU method and measurements with the updated IMAU system shows that the Kr-corrected values are very close to the results from the updated IMAU system and the dual-inlet measurement of NIWA (Table 2).

Summary and conclusions
This paper identified for the first time that Kr can severely interfere with the measurement of δ 13 C of CH 4 during CF-IRMS analysis.The interference for δ 13 C can be as large as 2 ‰ if samples are measured which have high Kr-to-CH 4 ratios, e.g.air extracted from ice core samples or stratospheric samples, relative to modern atmospheric air as reference gas.In the ion source of the mass spectrometer the krypton isotope 86 Kr produces doubly charged ions with a m/z of 43.We demonstrate that the lateral tail of this beam extends into the major and partly also into the minor1 cup, compromising the measured m/z 44 and m/z 45 signal.We speculate that the rather flat Kr interference observed in the minor2 cup (m/z 46) either results from a further extension of this 86 Kr 2+ tail or is due to reflections of the more abundant singly charged Kr ions.As a result, all three Faraday cups used for δ 13 C analysis are affected by the Kr interference.The sign and magnitude of this bias is specific for the used instrument and is dependent on the focusing; thus, the bias can change over time.In this sense, the Kr interference can lead to incorrect values, concentration effects (scale effects), and drifts over time and can simply increase the measurement noise.At constant instrument conditions, the δ 13 C bias of atmospheric CH 4 samples inversely scales with the CH 4 mixing ratio since the Kr mixing ratio can be regarded as constant.For example, air samples with lower CH 4 mixing ratios will yield higher (heavier) apparent δ 13 C values compared to samples with higher CH 4 mixing ratios.In the second part of the paper we presented several strategies to tackle the Kr problem.Existing methods can be adapted to separate Kr from CH 4 either before the combustion process or after conversion to CO 2 .For existing data sets we propose several correction methods to account for the Kr interference.
Regarding the implications of this effect, we identified the following fields of research using δ 13 C of CH 4 where the Kr interference could be relevant if it is not taken into account.The Kr interference is relevant if high accuracy in δ 13 C is needed and/or samples with low CH 4 / Kr ratio mixing ratios are analysed.Note that round-robin intercomparison studies aimed to identify offsets between laboratories cannot solve this issue if pure-CH 4 standards, synthetic-air mixtures (N 2 , O 2 ) or real samples with only one CH 4 / Kr ratio are distributed.Examples for such studies are as follows: -Palaeo-atmospheric studies on air with low CH 4 / Kr mixing ratios (atmospheric CH 4 mixing ratios as low as 360 ppb), e.g. during the glacial period.
-Current atmospheric studies in settings where the atmospheric CH 4 / Kr mixing ratio is considerably lowered due to a loss process (e.g.high-stratospheric air samples, microbial oxidation in aerobic soil layers).
-High-precision and -accuracy studies of recent atmospheric δ 13 CH 4 .Note that since the late 1990s when many δ 13 CH 4 long-term measurements started, by coincidence the atmospheric CH 4 mixing ratio has remained unusually stable.
-Studies analysing the interhemispheric gradient of δ 13 C which rely on measurements from different measurement systems.
-Fresh or sea water samples which had atmospheric contact having low CH 4 / Kr mixing ratios due to higher solubility of Kr compared to CH 4 .
The compilation shows that the Kr interference is most relevant for the atmospheric community since the demand on accuracy is often high.However, δ 13 C analyses on CH 4 in other sample matrices could be biased by this effect as well.
In the case of natural-water samples which equilibrated with the atmosphere, the higher solubility of Kr relative to CH 4 (about a factor of 1.8) leads to a lower CH 4 / Kr ratio for the dissolved gases in the water phase.In settings where CH 4 is consumed by methane oxidising bacteria (e.g.deep-water samples), CH 4 / Kr mixing ratios can approach values as low as 0.1 (nmol nmol −1 ) (Heeschen et al., 2004).Like for other types of studies where the fractionation factor of a sink process is analysed (e.g.stratospheric samples), any covariation between the CH 4 concentration and an erroneously measured δ 13 C finally translates into an erroneous assessment of the fractionation factor α.
The described effect in this paper could also be relevant for other precise measurements using IRMS, where the gas matrix of sample and standard are different and a variable component produces a large beam with a m/z close to a target mass of the analysed species.

Fig. 3 . 8 Fig. 3 .
Fig. 3. Chromatogram of an atmospheric air sample showing the separation 3 for the Bern-system (a) and the PSU system (b).The ion source of the IR 4 thus that the m/z 43 beam of 86 Kr 2+ falls into the major cup (black line 5 isotopologues of CO 2 with m/z 45 fall into the minor2 cup and mark the po 6 peak (blue line, left axis).7 8

Fig. 4 .
Fig. 4. Comparison of a CH4 peak of an air sample with the signals gained from an injection 3 of pure Kr measured with the Bern system at CO2 focussing.(a) Beam intensities in mV for 4 the CH4 sample peak (369 ppb CH4 with natural abundance of Kr) with the retention time 5 centred to the CH4 peak maximum.(b) Background corrected ion current ratios, "46/44 ratio" 6 in blue, "46/45 ratio" in green and "45/44 ratio" in black of the atmospheric air sample (solid 7 line) and pure CH4 (dotted line) illustrating the anomalies seen in "46/44" and "46/45" but no 8 visible effect on "45/44".Panel (c) shows the beam intensities for a measurement where Kr 9 was injected into the GC flow.Due to the chromatographic effect of the GC column, the 10 retention time of the Kr peak is ca.6 s longer than the CH4 peak, yet there is a considerable 11 overlap.Note the signal measured at m/z 28 ("N2 cup") can be directly related to 84 Kr 3+ which 12 has the exact m/z = 28 value.13 14 Fig. 4. Comparison of a CH 4 peak of an air sample with the signals gained from an injection of pure Kr measured with the Bern system at CO 2 focusing.(a) Beam intensities in mV for the CH 4 sample peak (369 ppb CH 4 with natural abundance of Kr) with the retention time centred to the CH 4 peak maximum.(b)Background-corrected ion current ratios ("46 / 44 ratio" in blue, "46 / 45 ratio" in green and "45 / 44 ratio" in black) of the atmospheric air sample (solid line) and pure CH 4 (dotted line), illustrating the anomalies seen in "46 / 44" and "46 / 45" but with no visible effect on "45 / 44".Panel (c) shows the beam intensities for a measurement where Kr was injected into the GC flow.Due to the chromatographic effect of the GC column, the retention time of the Kr peak is ca.6 s longer than the CH 4 peak, yet there is a considerable overlap.Note the signal measured at m/z 28 ("N 2 cup") can be directly related to 84 Kr 3+ , which has the exact value of m/z = 28.

Fig. 5 .Fig. 5 .
Fig. 5. Influence of slight changes in the accelerating voltage on the peak heights and 3 apparent isotopic signatures of Kr peaks.Results of Kr injection into GC flow carried out with 4 the Bern system with the source focused to CO2.(a) The upper panel shows the measured 5 peak heights for the three Faraday cups (major, minor1, minor2) of the Kr peak as a function 6 of the accelerating voltage; dots represent measurements and lines a linear fit for minor1 and 7 minor2, and a cubic fit for the major cup.(b) The lower panel shows the apparent isotopic 8 composition ( 13 C in red and  18 O in blue) of the Kr interference calculated from the peak 9 area of the Kr peaks; dots represent measurements and lines the linear fits.10 11 Fig. 5. Influence of slight changes in the accelerating voltage on the peak heights and apparent isotopic signatures of Kr peaks.Results of Kr injection into GC flow carried out with the Bern system with the source focused to CO 2 .(a) The upper panel shows the measured peak heights for the three Faraday cups (major, minor1, minor2) of the Kr peak as a function of the accelerating voltage; dots represent measurements and lines a linear fit for minor1 and minor2, and a cubic fit for the major cup.(b) The lower panel shows the apparent isotopic composition (δ 13 C in red and δ 18 O in blue) of the Kr interference calculated from the peak area of the Kr peaks; dots represent measurements and lines the linear fits.

Figure 7 Fig. 6 .Fig. 6 .
Figure7shows a schematic drawing which illustrates the involved Faraday cups and the positions of the respective ion beams for CO 2 and 86 Kr 2+ as well as the two effects which Schematic showing the Faraday cups and the involved ion beams of CO2 and the 2 contribution from Kr to help visualise the observed Kr interference during  13 C analysis as 3 observed with the Bern IRMS.(a) Estimated positioning and width of the Faraday cups and 4 the position of the respective ion beams (m/z) of the CO2 isotopologues and 86 Kr 2+ .(b) 5 Individual contributions from Kr.To illustrate the tailing of the m/z 43 86 Kr 2+ beam ( 86 Kr 2+ tail, 6 light green) into the major cup, an artificial density distribution is used to provide a reasonable 7 lateral distribution.The broad, unspecific part of the Kr interference, Krscatter, is illustrated by 8 a brown horizontal line.(c) The sum of the two Kr contributions is plotted in dark green, but 9 ion densities were converted to a mV unit using the respective values of the feedback resistors 10 of the Bern Isoprime machine; the thick line represents that part of the continuous beam 11 which becomes finally collected in the respective Faraday cups (vertical dashed lines mark the 12 geometric limits of the Faraday cups as a visualisation of the spatial integration of the Faraday 13 cup).14

Fig. 7 .
Fig. 7. Schematic showing the Faraday cups and the involved ion beams of CO 2 and the contribution from Kr to help visualise the observed Kr interference during δ 13 C analysis as observed with the Bern IRMS.(a) Estimated positioning and width of the Faraday cups and the position of the respective ion beams (m/z) of the CO 2 isotopologues and 86 Kr 2+ .(b) Individual contributions from Kr.To illustrate the tailing of the m/z 43 86 Kr 2+ beam ( 86 Kr 2+ tail , light green) into the major cup, an artificial density distribution is used to provide a reasonable lateral distribution.The broad, unspecific part of the Kr interference, Kr scatter , is illustrated by a brown horizontal line.(c) The sum of the two Kr contributions is plotted in dark green, but ion densities were converted to a mV unit using the respective values of the feedback resistors of the Bern Isoprime machine; the thick line represents that part of the continuous beam which becomes finally collected in the respective Faraday cups (vertical dashed lines mark the geometric limits of the Faraday cups as a visualisation of the spatial integration of the Faraday cup).

1Fig. 8 . 7 Fig. 8 .
Fig. 8. Chromatograms showing the separation between CH 4 (left peak) and Kr (right pe 2 on a PoraPLOT column for 30°C, 18°C and 5°C measured with the Bern system.The 3 interference is visible in all Faraday cups, either as a direct signal of 84 Kr 3+ in the m/z 28 4 (thin green line), or from the broad Kr interference for the minor1 and minor2 (thick red a 5 blue, respectively).6 7

Fig. 9 . 7 Fig. 9 .
Fig. 9. Chromatogram showing the separation of Kr from CH4-derived CO2 achieved with the 2 improved IMAU system, which includes a GC column after the combustion oven.Due to the 3 additional GC, Kr elutes before instead of after the CH4-derived CO2 peak as shown in the 4 chromatograms of Fig. 3. 5 6 7

Fig. 10 .Fig. 10 .
Fig. 10.Sample chromatogram showing the separation of Kr from CH4-derived CO2 for the 3 improved Bern system.(a) Full range plot of the narrow, cryofocused CH4-derived CO2 peak 4 and the broader N2O peak without cryofocusing step.(b) Zoomed plot to see the separation of 5 Kr from CH4-derived CO2.The arrow "trap down" marks the time when the capillary is 6 lowered into LN2 to trap the CO2 from the combustion oven.While CO2 becomes trapped at 7 LN2 temperature, Kr passes the capillary without delay and shows the typical Kr interference 8 signal.9 10 Fig. 10.Sample chromatogram showing the separation of Kr from CH 4 -derived CO 2 for the improved Bern system.(a) Full-range plot of the narrow, cryofocused, CH 4 -derived CO 2 peak and the broader N 2 O peak without the cryofocusing step.(b) Zoomed plot to see the separation of Kr from CH 4 -derived CO 2 .The arrow "trap down" marks the time when the capillary is lowered into LN 2 to trap the CO 2 from the combustion oven.While CO 2 becomes trapped at LN 2 temperature, Kr passes the capillary without delay and shows the typical Kr interference signal.

Fig. 11 .Fig. 11 .
Fig. 11.Compilation showing the principle of the Kr correction for an air sample measured 2 with the AWI-system.(a) Ion current ratios in bold lines are the uncorrected ratios, the 3 rectangle indicates the time interval that is used to determine the background to calculate the 4 Kr interference shown in the panel below.The thin line and the hatched area show the ratio 5 after the Kr correction, i.e. after the subtraction of the fitted Kr peak from the measured ion 6 current.The red dotted line is the ratio of pure CH 4 without Kr interference.The "46/45 ratio" 7 serves as an independent visual check whether the correction was successful since the 8 anomaly of this ratio is not used for the correction method.(b) Intensities for the three 9 Faraday cups of the CH 4 sample (left axis).The interference calculated from the anomalies 10 plotted in the ratios above (right axis) with the dots representing the calculated raw anomaly 11 for m/z 45 and m/z 46, the lines are a fit to the respective data used for correction.12 13

Fig. 12 .
Fig. 12.Comparison of two methods to account for the Kr interference based on 2 measurements with the AWI system using the three intercomparison cylinders with 3 contrasting CH4/Kr mixing ratios.Plotted are the  13 C numbers, i.e., the differences between 4 the original results and the results obtained after removing the Kr effect.Both methods reveal 5 that with decreasing CH4 concentrations (hence, CH4/Kr mixing ratios)  13 C becomes larger.6 (a) Results for the method of Sect.5.4, where the Kr interference is subtracted from the raw 7 data time series.Coloured diamonds with error bars mark the cylinder measurements, grey 8 circles show a data set of 152 ice core measurements (b) Results for the relatively simple 9

Fig. 13 . 7 Fig. 13 .
Fig. 13.Results of artificially adding pure Kr to a CH4 sample.(a) Both isotope ratios show a 2 linear relation of the  values with the amount of Kr added.(b) The isotope ratios are closely 3 correlated (r 2 =1.00) and this relation can be used to correct for the Kr interference without 4 knowing the exact CH4-Kr mixing ratio of a sample.Note that here the 46/45 slope is 5 shown, i.e. the inverse value used in Eq. (9).6 7 Fig. 13.Results of artificially adding pure Kr to a CH 4 sample.(a) Both isotope ratios show a linear relation of the δ values with the amount of Kr added.(b) The isotope ratios are closely correlated (r 2= 1.00) and this relation can be used to correct for the Kr interference without knowing the exact CH 4 -Kr mixing ratio of a sample.Note that here the δ46/δ45 slope is shown, i.e. the inverse value used in Eq. (9).