Novel calibration with correction for drift and non-linearresponse for continuous flow isotope ratio mass spectrometryapplied to the determination of d15N, total nitrogen, d13C andtotal carbon in biological material†

K. E. Anders Ohlsson* and P. Håkan Wallmark

Department of Forest Ecology, Swedish University of Agricultural Sciences, S-901 83 Umeå,Sweden. E-mail: Anders.Ohlsson@sek.slu.se; Fax: +46 90 7867750

Received 1st February 1999, Accepted 3rd March 1999

With automated analysis of a batch of samples using an elemental analyser isotope ratio mass spectrometer, theinstrumental response is often non-linear (e.g., the isotope ratio varies with sample size) and is affected bychanges over time (drift). Traditionally, drift and non-linearity effects are compensated for by including severalreference samples in the batch with elemental masses, which closely match those of the samples. The novelcalibration method presented here corrects for both drift and non-linearity, and thus allows for a wider range ofsample masses in the batch, while accuracy and precision is maintained at the level attained by the traditionallyaccepted calibration procedure without increasing the number of reference samples.

Automated elemental analyser isotope ratio mass spectrometry(EA-IRMS) is commonly performed by analysing sequenctiallya group of samples including reference samples.1,2 Thisprocedure allows high-precision relative measurements ofisotope ratios with compensation for instrumental drift, whichmay occur during the processing of a batch of typically onehundred samples and a throughput of ca. 4 samples per hour. Inorder to favour measurement accuracy and precision, thesample and reference should have similar chemical and isotopiccomposition.3

A non-linear effect of the element mass in the sample on theresults from an EA-IRMS measurement is often observed,4–6

although, for example, the isotope ratio should ideally beindependent of element mass. This non-linearity effect isusually reduced by matching samples and references withregards to element mass, i.e. the sample mass is adjusted suchthat its element content is approximatively equal (e.g. within ±20%) to that of the reference samples.

The element mass effect may stem from a non-linearresponse of the mass spectrometer part, but may also arise in theelemental analyser or the interface between the two systemcomponents. For example, the effect of element mass (orsample mass) on the analytical result has been recognized in thedetermination of total carbon, nitrogen and hydrogen using anautomated elemental analyser with a thermal conductivitydetector (TCD).7,8 The parameters of the calibration models,which were used to compensate for the mass effect, werechanged by factors external to the detector, e.g. gas flow rate,7choice of reagents7 and sample mass.8

Close sample matching with regards to mass is impracticalfor three reasons: (i) it might necessitate an initial extra sampleanalysis in order to determine a coarse estimate of the elementalcontent, which will allow a more suitable sample amount to beselected,3 (ii) in some cases the material available is limited anddoes not allow for two analyses, and (iii) it often increases thetime necessary for weighing out the samples if their elementmasses have to fall within narrow preset limits. Furthermore, inthe case where the element content of the individual samples in

a group varies widely, matching of reference and sample isdifficult to achieve. Finally, dual mode (two elements, e.g. Cand N) isotopic analysis is facilitated when the referencematerial need not be matched to within the linear ranges of boththese elements.

In this study, we present a novel calibration model forEA-IRMS on plant material in particular, and continuous flow(CF)-IRMS in general, where the effects on the analyticalresults of drift and elemental mass are corrected. Thiscalibration model allows the element mass of the samples in abatch to vary within a larger interval compared to thatrecommended conventionally, but does not require an increasednumber of references.

Experimental

Instrumentation

The instrument system consisted of a continuous flow IRMS(20-20 Stable Isotope Analyser, Europa Scientific Ltd, Crewe,UK)9 interfaced with an elemental analyser unit (ANCA-NTsystem, solid/liquid preparation module, Europa Scientific).1The operating conditions are shown in Table 1. The instrumentwas sited in a thermostatted room at 20 °C in order to increasethe temporal stability of the analytical results, while changes inthe temperature is the principal cause of drift in the measuredratio.9 For analysis, the samples were placed in cylindrical tinfoil containers (6 3 4 mm id) and sample masses weremeasured. A batch of about one hundred samples are introducedsequentially into the EA unit by an autosampler. Eachindividual sample is combusted completely in an oxidizingcolumn (chromium oxide, copper oxide and silver wool) andinto which a pulse of oxygen is added concurrent with sampleintroduction. The carbon and nitrogen content of the sample isquantitatively converted into CO2 and N2, respectively (anyNOx gas is reduced to N2 in a copper column where also excessoxygen is removed). The carbon dioxide and nitrogen formedare separated using a GC column and transfered with the Hecarrier gas through a thermal conductivity detector and then tothe IRMS inlet, where a small part of the sample gas enters the

† Presented as a poster at the 1998 Stable Isotope Mass Spectrometry UsersGroup (SIMSUG 98) meeting 7–8th January, 1998, Nottingham, UK.

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mass spectrometer. The time interval needed for running onesample for dual mode (C and N) analysis is 900 s, which meansthat a batch of 100 samples is measured in 25 h.

The three ion collectors of the magnetic sector IRMS willfirstly record the transient signals at mass to charge ratio m/z =28 (14N14N), 29 (15N14N) and 30 (15N15N), respectively, andthen, after automatic adjustment of the ion source, m/z = 44(12C16O16O), 45 (mainly 13C16O16O) and 46 (mainly12C18O16O). Each of these transient collector ion currents wasintegrated and background corrected yielding I1

N, I2N and I3

N,respectively, for N2 and I1

C, I2C and I3

C for CO2. The instrumentsoftware uses measurement results of these quantities forreferences (at least one reference in the beginning of the batch)and samples to calculate the total amounts of carbon andnitrogen as well as d13C and d15N of the samples. Thisunpublished derivation is similar to the quadratic method givenby Santrock et al.10 where account is taken of the presence ofless abundant molecular CO2 ions, e.g. 12C17O16O. Withrepeated measurement of references, e.g. one reference forevery ten samples, the effect of drift in the instrumentalresponse on the analytical result can be reduced mathematicallyafter a completed run of a batch of samples.

For later use, we here mention that the instrument softwarecalculates the total integrated peak area A (A is proportional tothe total carbon or nitrogen content) which is defined as:

A Ii= Â1 2 3, ,

(where A is measured in coulombs)

Batch design

In this study, the design (sequence of samples and references)used for each sample batch was modified after instrumentalanalysis to suit three different calibration schemes:

1. ‘Accepted(n)’ calibration (n = number of references). Inaccordance with the instrument manufacturer’s recommenda-tion, the references are placed equidistantly throughout thebatch with about ten samples in between. (These ten samplesconsist of reference samples for the novel calibration method,matched and unmatched test samples for nitrogen and carbon,and sometimes other samples not involved in this calibrationcomparison.) The references are marked as such in the

instrument software when results are calculated. A narrowsample mass distribution is used where the total variation is ±ca. 10% of the mean value.

2. ‘Novel(n)’ calibration. The novel calibration methodpresented in this work requires that the distribution of thereference sample masses covers the corresponding distributionof the samples. Here a set containing approximatively the samenumber (n) of reference samples as for the accepted calibrationis selected. This set has a broader distribution where the samplemass varies with a factor of up to the approximate value 7(except in batch 3 where it is 19 and 5, for C and N respectively)times the minimum mass.

3. ‘Novel(2n)’ calibration. In this case the novel calibrationmethod was applied using the n references selected for the‘accepted’ calibration and another n reference samples (2n intotal). The latter n references were paired with and placedimmediately prior to the ‘accepted’ references.

Fig. 1 shows the distribution of reference samples withregards to mass and analysis time (position in the batch) for oneof the batches (no. 3) analysed in this study; the other batcheshad a similar reference sample distribution. The sequence ofsamples in a batch starts with three empty tin containersfollowed by two dummy samples (reference sample material)and the first reference sample. The results from measurement ofthe initial empty samples are used for blank correction of allresults in the batch, in order to compensate for the contributionsof any carbon or nitrogen present in the tin container or in theadded oxygen gas. Empty sample containers are also includedsparsely throughout the batch for monitoring of possiblememory effects which may reduce measurement accuracy.

For comparison of the performance of the three calibrationprocedures, two groups of test samples were measured: (i)‘Matched’ test samples, for which the sample mass distributionmean and width are similar to the corresponding parameters ofthe distribution of the references for the accepted calibrationmethod, and (ii) ‘unmatched’ test samples whose distribution isdissimilar to the corresponding reference distribution, e.g. withregard to width only (batch 1 and 3, see Fig. 2A for carbon inbatch 3) or mean value (see Fig. 2B for carbon in batch 2).

Because the test samples have about the same carbon contentas the reference samples but only half of their nitrogen content,different test sample groups must be selected in order to obtainsample matching with regards to carbon or nitrogen, re-spectively. This circumstance makes it difficult to design abatch which is well suited for the present comparison ofcalibration models with matched and unmatched test samples.This difficulty is the reason why only results for carbon is givenfor some of the batches in this study, although all batches wererun in dual isotope mode.

Table 1 Typical operating conditions

Elemental analyser

Column Temperature/°C

Oxidation 1000Reduction 600GC 30

He carrier flow 60 ml min21

Oxygen and helium inlet linepressure set equal

Oxygen pulse length 25 s

Sample drop 30 s after start of O2 pulse

Mass spectrometer

Ion source CO2 N2

High tension (HT)/V 2490 3890Beam focus (%) 90 90Ion repeller/V 0 0Electron energy/eV 290 290Trap current /mA 100 600Source pressure = 5 3 1026 mbar

Peak height ion current (nA) (for 4.2 mg 2.7 4.1reference sample)

Analyser pressure = 1.6 3 1027 mbar

Fig. 1 Mass and time (position) distribution of reference samples in batch3: 5 = accepted calibration (21 references) and 2 = novel calibration (22references).

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Calibration model

The calibration model is described here for carbon but is validfor nitrogen as well with only appropriate changes in nota-tion.

The data calculated by the instrument software (EuropaScientific Ltd.), using only a single reference in the first positionof the batch of samples, are used as ‘raw’ instrumentalresponses (Cr and dr for total carbon and d13C, respectively).

These raw data are corrected:

C = CrkCAkCt (1)

d = dr + kdA + kdt (2)

where the ks are correction factors/terms, which depend on thetotal integrated peak area (subscript A; A ª element mass;compensation for the mass effect) and the analysis time(subscript t; compensation for drift in the instrumental re-sponse); the latter corresponds to the position in the sequence ofsamples in a batch.

The correction factors are expressed as polynomials:

k a AA ii

i

==Â

0

3

(3)

k b tt ii

i

==Â

0

3

(4)

The polynomial coefficients (ai and bi) are obtained using theoptimization algorithm included in the solver tool of thespreadsheet program Microsoft® Excel 97 SR-1 (version 7.0a;Microsoft Corp., USA). The standard deviation (s) of theanalytical results (C or d) for the references is minimized with

the constraint that the mean value of the results should equal theaccepted reference value. The number of terms to be included inthe polynomial expansion is judged by visual inspection of theraw and corrected data and the extent to which the s value isdecreased when terms are added in eqns. (3) and (4). Thecorrected C and d values should not depend on A or t, and,therefore, these values plotted either against A or t should fit astraight horizontal regression line (see Fig. 3).

Sample materials

The composition (C and N) and isotopic ratios (d13C and d15N)of wheat flour (used here as reference material) and maize flour(test sample material), have been calibrated previously againststandard reference materials (SRM) (NBS 18, NBS 19, USGS24 and LSVEC for d13C; IAEA-N-2, IAEA-NO-3 and USGS 25for d15N; acetanilide, EDTA and urea for total-C and total-N).The isotopic SRMs were obtained from IAEA, Vienna, Austria,and the element standards (pure compounds) from MikrokemiAB, Uppsala, Sweden. The thereby accepted values (see Table2) have been confirmed in an interlaboratory comparison withone exception, the value of d15N for maize flour was determinedby another laboratory to be 2.30 (s = 0.26, n = 3).

Results and discussion

Calibration method comparison

The performance of the novel calibration model presentedabove was compared with the accepted method of calibrationusing the results obtained by measuring three batches ofsamples (see Experimental). Batch 1 and 3 were designed andanalysed under conditions typically prevailing when simultane-ous 13C- and 15N-analysis is performed in our laboratory usingthis instrument, i.e. typical with regard to drift, sample types,sample sizes and instrumental settings. The results from themeasurement of batch 1 and 3 are, therefore, representative ofresults routinely obtained for this type of analysis. On thecontrary, batch 2 was measured under atypical conditions,where a large instrumental drift (Fig. 3C and D: 20.2‰ h21 ford13C) was intentionally introduced into the results by allowingthe temperature of the room, where the instrument was located,to increase gradually from 20 to ca. 25 °C during the batch run.The results of the comparison of the novel and acceptedcalibration methods are given in Tables 3–5.

The accuracy of the results presented in Tables 3–5 wasevaluated by comparing each mean value with the correspond-ing accepted value of that quantity (see Table 2) and testingstatistically for significant differences between the mean valuesunder the assumption that the t-distribution is applicable.11 Thiscomparison showed that, in terms of accuracy, both the noveland accepted calibration methods perform adequately, but a fewdiscrepancies should be commented upon. The maximumrelative errors were 0.8 and 3.5% for total-C and total-N,respectively, while 60% of these results showed no significantdifference at all. For d13C, 75% of the results were accurate, i.e.no significant difference existed, while for the remaining resultsthe maximum significant deviation was 0.09‰. For d15Ndetermined under normal operating conditions (batch 3), theresults were fully accurate, but with severe drift present (batch2), a maximum difference of the value 0.5‰ was noted. Usinginstead 2.30 as the accepted value of d15N, which wasdetermined independently by another laboratory (see Experi-mental), all results equal this accepted value.

The precision of the test results (number = m) is heremeasured by their standard deviation (s) given in parentheses inTables 3–5. The standard deviations, s1 and s2, obtained with theaccepted(n) and novel(n) calibration methods, respectively,

Fig. 2 Carbon mass against time (position in batch) for (5) matched and(2) unmatched test samples. A: batch 3, B: batch 2. Arrows indicate theaverage carbon mass of reference samples used in the accepted calibra-tion.

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were compared using a statistical F-test on the ratio of their twocorresponding variances, s1

2/s22 (see Table 6).11 This ratio is

assumed to be distributed according to the Fk1,k2distribution,

where the degree of freedom is k1 = k2 = m 2 1. For thedetermination of d13C and total-C, the outcome of thecomparison is clearly in favour of the novel calibration method,which shows a significant improvement in precision in one thirdof the cases. For d15N and total-N, the novel calibration methodperformed at least equally well as the accepted method, exceptin the single case for d15N with severe drift and matchedsamples (batch 2), where the accepted method yielded the bestprecision. This exception is produced in a situation which theaccepted calibration is designed to handle effectively and,therefore, it is instead noteworthy that the novel calibrationperforms rather well even in this case.

Characteristics of the novel calibration

Fig. 3 illustrates how the novel calibration model works for thedetermination of d13C and how the application of correctionfactors reduces significantly the variation in the d13C results andtheir dependence on element mass. Note that the additivecorrection factor was determined using the reference wheatsamples at d13C = 224.5 ‰ and could still be successfullyapplied for correction of the test maize sample results at d13C =2 11.1‰. The selection of a purely additive correction factor

for the d-results (for 13C and 15N) is, therefore, justifiedempirically. For the total-C and total-N results, we followed thetradition in the research area of elemental analysis to use amultiplicative correction to reduce the effect of element mass(or sample mass) on the analytical results7,8 and also obtainedsupportive results from the total-N and -C determinations ofbatch 3. We have thus found forms for mathematical correctionof instrumental responses that produce valid results, at leastwith the plant material samples used here. Therefore, we havenot systematically explored various alternative additive ormultiplicative (or combinations thereof) correction schemes.

Automated mass spectrometric analyses of sample seriesover time periods of days almost inevitably involve correctionof the results for changes over time in the instrumental response(drift). The present mass spectrometer software uses theresponses of two reference samples for interpolative calculationof drift correction factors for a small number of intermediate(ca. 10) test samples. The novel calibration instead utilizes aprocedure similar to a least-square minimization, where theresponses for all reference samples in a batch contributes to thedetermination of the drift correction factor for a particularsample. Thereby the effect of random variations in the referenceresponses on the correction term is reduced. In addition, thenovel calibration model is multivariate and yields simultaneouscorrection for drift and elemental mass effect in the single step,where the standard deviation of the reference responses isminimized. This novel calibration approach is economic in the

Fig. 3 Correction of d13C values using the novel calibration model for (A and B) batch 3 (normal operating conditions) and (C and D) batch 2 (severe drift):3 = uncorrected results and corrected results are shown by 5 for wheat references and < for maize test samples; * (on the right side of the figures) =accepted values.

Table 2 Accepted values for sample materialsa

Sample Material C (% m/m) d13CPDB (‰) N (% m/m) d15Nair (‰) n(N) n(C)

Reference Wheat flour 44.27 (0.27) 224.50 (0.087) 1.98 (0.025) 4.35 (0.18) 42 32Test Maize flour 43.85 (0.11) 211.09 (0.074) 1.01 (0.022) 2.61 (0.20) 10 21

a Standard deviations are given in parentheses. Number of replicates = n

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sense that, with unchanged or even improved performance, thenumber of references in a batch need not be increased comparedto the number used conventionally [cf. results for novel(n)versus accepted calibration in Tables 3–5]. Also note that withthe novel calibration no further improvement in terms ofprecision is obtained with a doubled number of references [cf.Tables 3 and 4: novel(n) versus novel(2n)]. It should bementioned that for batches 1 and 3 the drift is small and the masseffect gives the largest contribution to the variation in theresults. On the contrary, for batch 2 Fig. 3C and D shows thatdrift is the dominating source of variation in the results, asituation which the accepted calibration model is designed for,but still the accepted and novel procedures perform at the samelevel of accuracy and precision. The results in Fig. 3C and Dalso justifies the use of an additive drift correction factor for thed13C values.

Table 3 Comparison of novel and accepted calibration methods: Batch1a

Calibration method C (% m/m) d13CPDB (‰)

Matched maize samples (16)Accepted (22) 43.834 (0.086) 211.176 (0.078)Novel (24) 43.867 (0.065) 211.040 (0.063)Novel (47) 43.853 (0.064) 211.042 (0.062)

Unmatched maize samples (22)Accepted (22) 43.824 (0.085) 211.164 (0.147)Novel (24) 43.825 (0.066) 211.050 (0.097)Novel (47) 43.823 (0.063) 211.063 (0.095)

a Total carbon (C) and d13C results determined under normal operatingconditions. In parentheses are given: (i) the number of samples andreferences used (first column) and (ii) standard deviations of the analyticalresults.

Table 4 Comparison of novel and accepted calibration methods: Batch 2a

Calibration method C (% m/m) d13CPDB (‰) N (% m/m) d15Nair (‰)

Matched maize samples (19/C, 18/N)Accepted (23) 43.777 (0.088) 211.071 (0.127) 1.021 (0.013) 2.330 (0.080)Novel (20) 43.770 (0.054) 211.154 (0.172) 1.024 (0.010) 2.320 (0.120)Novel (41) 43.796 (0.054) 211.143 (0.169) 1.021 (0.010) 2.316 (0.129)

Unmatched maize samples (18/C, 19/N)Accepted (23) 43.775 (0.105) 211.002 (0.301) 1.023 (0.014) 2.133 (0.151)Novel (20) 43.841 (0.104) 211.073 (0.282) 1.041 (0.016) 2.443 (0.216)Novel (41) 43.866 (0.104) 211.043 (0.243) 1.036 (0.017) 2.452 (0.219)

a Total element content and d results determined while drift was provoked by use of a non-thermostatted room. In parentheses are given: (i) the number ofsamples and references used (first column) and (ii) standard deviations of the analytical results.

Table 5 Comparison of novel and accepted calibration methods: Batch 3a

Calibration method C (% m/m) d13CPDB (‰) N (% m/m) d15Nair (‰)

Matched maize samples (11)Accepted (21) 44.117 (0.566) 211.054 (0.269)Novel (22) 44.197 (0.707) 211.074 (0.155)

Unmatched maize samples (11/C, 8/N)Accepted (21) 43.847 (1.584) 211.165 (0.426) 1.047 (0.025) 2.583 (0.292)Novel (22) 44.355 (1.671) 211.078 (0.144) 1.040 (0.019) 2.448 (0.151)

a Total element content and d results determined under normal operating conditions. In parentheses are given: (i) the number of samples and references used(first column) and (ii) standard deviations of the analytical results.

Table 6 F-test on the ratio of variances (R = s12/s2

2) of results from accepted(n) (s12) and novel(n) (s2

2) calibrationa

C (% m/m) d13CPDB (‰) N (% m/m) d15Nair (‰)

Batch 1Matched samples

R (1/R)Confidence level (%) NS NS

Unmatched samplesR (1/R) 2.30Confidence level (%) NS ca. 96

Batch 2Matched samples

R (1/R) 2.66 0.44 (2.25)Confidence level (%) ca. 96 NS NS 95

Unmatched samplesR (1/R)Confidence level (%) NS NS NS NS

Batch 3Matched samples

R (1/R) 3.01Confidence level (%) NS 95

Unmatched samplesR (1/R) 8.75 3.74Confidence level (%) NS 99.9 NS 95

a The Fk2 1,k2 1 distribution is used where k is the number of test samples. Levels of confidence below 95% are considered non-significant (NS).

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For measurement of the isotopic ratio using our CF-IRMSsystem, the instrument manufacturer specifies a linear range ford13C and d15N, which typically spans an element mass range ofbetween x and 4x, where x is the lower linear range limit. Thevalue of x is also specified for each analyte. With the presentnovel calibration procedure, the mass range useful for measure-ment can be expanded. Thereby batch measurement of sampleswith large variation in elemental mass is facilitated. Moreover,simultaneous analysis of e.g. d13C and d15N for each samplerequires that the C- and N-element masses are within theirrespective linear ranges. With narrow linear ranges for both Cand N, and for a given sample mass, the combined measurementrange where simultaneous C- and N-isotopic analysis ispossible, is often small or sometimes non-existent. In thissituation, the expansion of the measurement range, allowed bythe novel calibration, will increase the range overlap andthereby alleviate the requirement to weigh in the samples withina narrow mass interval or even make simultaneous analysisfeasible.

The present novel calibration method involves a linearregression where the sum of the squares of ej = yj 2 yj

model isminimized [y = drj (individual raw d results), yj

model = dacc

2kdAj 2 kdtj and dacc is the constant accepted value], althoughhere the formulation is slightly different: the standard deviationof dj = drj + kdAj + kdtj is minimized under the condition that themean value of all dj is equal to dacc. With regression methodsthere is always the problem to decide upon the presence ofinteraction terms and the maximum order of terms which shouldbe included in the model. For this selection of terms, elaborateprocedures have been described,12 truncation criteria have beensuggested13 and, where replicate measurements are available,the F-test has been applied to judge the significance of theinclusion of further terms in the model.13 In the present case,with no replicates (each batch run is unique), we recommend asimple but still adequate term selection procedure where thestandard deviation of the corrected response dj is minimized,with as few terms as possible, while monitoring the outcome intwo plots with dj against A and t, respectively. Visualization ofthe results is thus a useful aid for truncation of the process ofterm selection as well as making initial suppositions on thenumber of terms necessary to include. Furthermore, we excludeinteraction terms between the two variables A and t because theyshould be independent and the correction procedure hasoperated successfully so far without their inclusion. We alsowant to mention that the variation in the results typicallyincreases with decreasing sample mass and that application ofweighed linear regression would perhaps further improve thecorrection.

Non-linear instrumental response

The measured isotope ratio should ideally be independent ofsample size, which requires the instrumental responses of thedetector channels to be linearly related to sample mass over thedesired mass range. In practice, however, the response is oftennon-linear and thus the isotope ratio depends on the amount ofsample (or the element mass or partial pressure of the measuredgas; the common generic term is ‘pressure effect’). No singlegeneral cause for the non-linearity has been identified, andtherefore, each individual intrumental system has to beconsidered separately when deciding upon the type of correc-tion to be applied. With skilled but time-consuming adjustmentsof instrumental parameters, it is often possible to improve thelinearity, as was shown by Prosser9 who obtained a linear rangeof between 0.4 and 2.8 mg carbon using the same type of EA-IRMS system as in this study.

In the past, several authors have found causes for non-linearity in the mass spectrometer part of the instrument.14,15

For example, Craig14 suggested that coulombic forces between

ions lead to beam broadening and overlap at neighbouring m/zdetectors (abundance sensitivity), which give rise to a ‘pressureeffect’ provided that the overlap is non-linear. Later, the majorcause for the observed abundance sensitivity has been identifiedas the total pressure inside the analyser, but the overlap obtainedwas linear and could thus not explain the pressure effect.9,15

Other workers thought that the pressure effect was mainly dueto mass discrimination either at the capillary mass spectrometerinlet, where flow conditions change from viscous to molecularflow, or in the ion source itself.5

More recently, with continuous flow GC-combustion-IRMS,a major cause for the observed pressure effect was locatedexternally to the MS part, possibly being a kinetic isotopiceffect at the open split at the exit of the combustion column.16

With an elemental analyser system (very similar to the EAinstrument used here) equipped with a thermal conductivitydetector, and thus without mass spectrometric detection, non-linear responses existed and were corrected for by use ofcalibration equations.7

With the present instrument, the non-linearity of the responsecan be minimized by manipulation of ion source and ion opticsparameters, and the remaining non-linearity is possibly due tocauses located inside, as well as outside, the MS part of the totalinstrument system. Because the reasons for the non-linearinstrumental response are incompletely known and may varybetween instrument configurations and with operating condi-tions, the type of correction applied (the combination of additiveand multiplicative factors) must be selected in each particularcase. Here, with a CF-EA-IRMS from Europa Scientific,empirical support was obtained for the use of an additivecorrection for d13C- and d15N-determination in plant samplematerial. With a similar CF-system from the same manu-facturer, but adapted for isotopic analysis of sulfur, Eriksen17

used additive correction of the results after having confirmedthat this was appropriate by inspection of the results ofmeasurements of both sample and standard gas at varioussample gas pressures.

Conclusions

Non-linearities and drift in the instrumental response in thedetermination of isotopic ratios can be corrected convenientlyusing the presented novel calibration model and a commonspreadsheet computer program. This allows for work with alarger range of sample sizes, which in turn facilitates dual modeanalysis. Further work is however envisaged, in order to, forexample, (i) reach a more fundamental understanding of thecauses of the non-linear response and thereby find routes toreduce it by altering hardware design, (ii) facilitate thevalidation of the correction procedure in each particular case,(iii) optimize the calibration of batch analysis, e.g. with regardsto selection of the number of reference samples needed, and (iv)fully utilize chemometric principles for multivariate calibra-tion.

Acknowledgements

We gratefully acknowledge Peter Högberg for comments andfinancial support of this work. The IRMS instrumentation wasfunded by The Swedish Council for Planning and Coordinationof Research (FRN).

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