Analytical and Bioanalytical Chemistry

, Volume 405, Issue 9, pp 2799–2814 | Cite as

Ensuring the reliability of stable isotope ratio data—beyond the principle of identical treatment

Review

Abstract

The need for inter-laboratory comparability is crucial to facilitate the globalisation of scientific networks and the development of international databases to support scientific and criminal investigations. This article considers what lessons can be learned from a series of inter-laboratory comparison exercises organised by the Forensic Isotope Ratio Mass Spectrometry (FIRMS) network in terms of reference materials (RMs), the management of data quality, and technical limitations. The results showed that within-laboratory precision (repeatability) was generally good but between-laboratory accuracy (reproducibility) called for improvements. This review considers how stable isotope laboratories can establish a system of quality control (QC) and quality assurance (QA), emphasising issues of repeatability and reproducibility. For results to be comparable between laboratories, measurements must be traceable to the international δ-scales and, because isotope ratio measurements are reported relative to standards, a key aspect is the correct selection, calibration, and use of international and in-house RMs. The authors identify four principles which promote good laboratory practice. The principle of identical treatment by which samples and RMs are processed in an identical manner and which incorporates three further principles; the principle of identical correction (by which necessary corrections are identified and evenly applied), the principle of identical scaling (by which data are shifted and stretched to the international δ-scales), and the principle of error detection by which QC and QA results are monitored and acted upon. To achieve both good repeatability and good reproducibility it is essential to obtain RMs with internationally agreed δ-values. These RMs will act as the basis for QC and can be used to calibrate further in-house QC RMs tailored to the activities of specific laboratories. In-house QA standards must also be developed to ensure that QC-based calibrations and corrections lead to accurate results for samples. The δ-values assigned to RMs must be recorded and reported with all data. Reference materials must be used to determine what corrections are necessary for measured data. Each analytical sequence of samples must include both QC and QA materials which are subject to identical treatment during measurement and data processing. Results for these materials must be plotted, monitored, and acted upon. Periodically international RMs should be analysed as an in-house proficiency test to demonstrate results are accurate.

Keywords

Stable isotope ratio measurements Isotope-ratio mass spectrometry Reference materials Principle of identical treatment Quality assurance Quality control 

Introduction

Instrumentation to measure the ratios of light stable isotopes (hydrogen, carbon, nitrogen, oxygen, and sulfur) at natural abundance has become increasingly common across a range of disciplines for many diverse purposes. Irrespective of the purpose for which data are acquired they should have two attributes:
  • within-laboratory results must be consistent and repeatable over long time periods

  • laboratory results must be reproducible by other laboratories.

The first point equates broadly with in-house precision or repeatability1 and has long been the modus operandi of stable isotope laboratories, often operating within a single research group with their own reference materials (RM) and sometimes their own reporting scales. The second point equates largely with accuracy or between-laboratory reproducibility, and was traditionally only important within small groups, for example isotope hydrology laboratories. The need for inter-laboratory comparability is now crucial to facilitate globalisation of scientific networks and the development of international databases to support scientific and criminal investigations. Comparability can only be achieved when data are traceable to the international δ-scales: Vienna standard mean ocean water (VSMOW), Vienna PeeDee belemnite (VPDB), air-N2, and Vienna Canyon Diablo troilite (VCDT).

It is important to remember that isotope-ratio measurements are not absolute but are reported relative to international measurement standards, for example2 [3]:
$$ {\delta^{13 }}{{\mathrm{C}}_{\mathrm{unknown}}}=\frac{{R{{{\left( {^{13}\mathrm{C}{/^{12 }}\mathrm{C}} \right)}}_{\mathrm{unknown}}}-R{{{\left( {^{13}\mathrm{C}{/^{12 }}\mathrm{C}} \right)}}_{\mathrm{standard}}}}}{{R{{{\left( {^{13}\mathrm{C}{/^{12 }}\mathrm{C}} \right)}}_{\mathrm{standard}}}}} $$
(1)

For this reason, stable isotope measurements stand or fall on the correct selection, calibration, and use of RMs and, for the same reason, any discussion of quality will invite a discussion of RMs.

Several publications have already addressed issues of quality within the stable isotope laboratory and can be seen to approach the subject from three converging directions; some publications describe the development of RMs for calibration and quality control (QC) and quality assurance (QA) [4, 5], some publications address technical shortcomings and seek to improve the precision or reliability of measurements [6, 7] and some publications address the practice of QC within the stable isotope laboratory [8]. In this article, we consider what lessons can been learned from a series of inter-laboratory comparison (ILC) exercises organised by the Forensic Isotope Ratio Mass Spectrometry (FIRMS) network [9] in terms of RMs, technical limitations, and the management of data quality. These exercises involved distributing materials to laboratories for flash-combustion elemental analysis (EA) and thermal conversion elemental analysis (TC/EA) 3 and subsequent isotopic determination. Results are reviewed against a background of QA/QC concerns and current practices of EA and TC/EA isotope determinations.

Some of the principles that follow are drawn from the Good Practice Guide for Isotope Ratio Mass Spectrometry [10] compiled by members of the FIRMS network, together with the UK National Measurement System (available as a free download from the FIRMS and NMS websites). Both the Guide and this article are intended for all isotope scientists interested in long-term compatibility of data for use in, e.g., meta-analysis.

Lessons learned from six inter-laboratory comparisons exercises

Since 2002 the FIRMS network has organised a series of ILCs with the objective of improving the global compatibility of stable isotope data [9]. The purpose was to examine differences between the distributed materials and differences versus international RMs. The materials distributed during six ILCs are listed in Table 1 and were intended to represent materials of forensic interest, for example cutting agents, human remains, and explosives. Each distribution was also intended to contain one material deemed “easy” to analyse and one material considered more “challenging” e.g. cellulose and ammonium nitrate.
Table 1

Summary of the FIRMS network ILCs materials [9]

ILC

Year

Materials

Isotopes determined

#1

2002

(a) Cane sugar

δ13C δ15N

(b) Flour

#2

2004

(a) Polyethylene film

δ13C δ15N δ2H

(b) Phenacetina

#3

2006

(a) Paper

δ13C δ15N δ2H δ18O

(b) Paper

(c) Horse haira

#4

2008

(a) Benzocainea

δ13C δ15N δ2H δ18O

(b) Poly(ethylene glycol)

#5

2009

(a) Cellulose

δ13C δ15N δ2H δ18O

(b) Bone

(c) Ammonium nitratea

#6

2011

(a) Glycine

δ13C δ15N δ2H δ18O

(b) 4-Nitroacetanilide

(c) Sodium nitratea

aMaterials regarded as “challenging” for the analyst

Laboratories were requested to perform 10 measurements for each element of each analyte and only data from laboratories returning nine or more results were included in subsequent analysis. One-way analysis of variance (ANOVA) was used to estimate the underlying within-laboratory standard deviation (sd) (repeatability) and between-laboratory sd (reproducibility) shown in Fig 1. Repeatability derived in this way is the average across participating laboratories and individual laboratories should aim to achieve, or improve on, this value [1].

Is exercise good for you?

Repeatability (precision) was good within laboratories, but reproducibility (accuracy) was poorer between laboratories (Table 2). When the pairs of the distributed materials were referenced against each other, in an attempt to minimize any local variations, between-laboratory reproducibility was still poor (Δ1/2 results, Table 2). The best Δ1/2 sd (0.18 ‰) was achieved for two samples of paper (distributed during ILC#3) confirming a common sense view that similar sample types give the best results.
Table 2

Median summary statistics for ILC# 1-6

 

Repeatability (‰)

Reproducibility (‰)

Δ1/2 Reproducibility (‰)a

δ13C

0.07

0.20

0.23

δ15N

0.12

0.28

0.69b

δ2H

1.6

7.6

5.48b

δ18O

0.4

1.8

10.85b

a\( {\varDelta_{1/2 }}=\frac{{{\delta_{{sampl{e_1}}}}+1}}{{{\delta_{{sampl{e_2}}}}+1}}-1 \)

bData from ILC#6 only, glycine vs. 4-acetanilide

Results for δ13C measurements were generally good and consistent across the range of ILCs. Poor δ13C repeatability and reproducibility for a sample of horse hair (Fig. 1 3c) partly resulted from two morphological forms and consequential lack of isotopic homogeneity. This emphasised the need for fine grinding before analysis, because homogeneity will ultimately limit the precision of IRMS.

The summary statistics for δ15N measurements revealed a general pattern of improvement over time with the exception of ammonium nitrate (Fig. 1 5c) and sodium nitrate (Fig. 1 6c), which were intended to be challenging and may suggest problems in the underlying chemistry when analysing compounds in high oxidation states (+5) by oxygen-combustion.4 4-Nitroacetanilide (Fig. 1 6b), which contains nitrogen in its two extreme oxidation states (−3 and +5) proved less challenging and may point to a lack of homogeneity in the other nitrate samples, because small and large crystals may differ in isotopic composition [12].

Differences between repeatability and reproducibility were far more pronounced for δ2H and δ18O measurements which may be attributed to the limited availability of suitable, solid RMs (discussed below). Worryingly, δ2H and δ18O reproducibility seems to become worse over the course of the ILCs and this may reflect the growth in the availability and application of TC/EA outpacing a growth in QC/QA. Although the exchange of hydrogen (and to a lesser extent oxygen) between samples and atmospheric moisture has been reported as a potential problem [13], there was little correlation between exchangeable hydrogen and poor reproducibility, e.g. cellulose (Fig. 1 5a), which contains a very large number of exchangeable hydrogen atoms, yielded very satisfactory results (possibly because cellulose is a familiar analyte). In contrast, poor results obtained for poly(ethylene glycol) (Fig. 1 4b) may suggest a problem with absorbed and/or adsorbed moisture rather than hydrogen exchange. The poorest results were obtained for ammonium nitrate (Fig. 1 5c), for which exchange of hydrogen seemed very rapid, and which may also reflect the difficulty in generating CO from nitrates and/or the interference of N2 with isobaric CO used for δ18O measurements [7].

Problems and solutions for ILC

Reporting the wrong results

For a number of samples, some δ18O results deviated from the consensus mean by approximately 30 ‰ suggesting that these were reported vs. VPDB rather than VSMOW, as requested.5 More worryingly, some laboratories presented data which deviated from the consensus mean by approximately 60 ‰, suggesting they had incorrectly applied a conversion from VPDB to VSMOW δ-scales. Such basic errors emphasised the need for peer review of final reports and also the need for identical scaling (see PIS below). It may, also, be suspected that if data were reported vs. VPDB (a scale normally reserved for carbonates) that the Craig correction for 17O has been applied (see PIC), introducing more subtle errors, compounded by incorrect scaling.

δ-values of RMs

As part of the ILC reporting procedure, laboratories were asked to record the RMs used and the δ-value assigned. The δ-values assigned to two commonly used RMs (IAEA-CH-6 and IAEA-N-1) during ILC#2 and 3 are summarised in Fig. 2. For both RMs, the spread of values is greater than the median repeatability.6 Poor reproducibility may arise from poor calibration by assigning wrong values to international RMs but this can be corrected if the δ-values assigned to the RMs are quoted alongside any data.
Fig. 1

Trends in results from ILCs 1–6. Blue (light) bars represent repeatability (within-laboratory sd) and red (dark) bars reproducibility (between-laboratory sd)

Shift and stretch

In line with recent recommendation [15], ILCs requested participating laboratories to report δ13C data in the form “… on the VPDB scale normalised by assigning a value of −46.6 ‰ to LSVEC”. In discussions with participating laboratories, it was apparent some laboratories simply did not understand this instruction and reported data generated by the instrument, using a single point anchor to the working gas. Failure to normalise data to the international δ-scales is a fundamental obstacle to inter-laboratory comparability. This point is treated further below as PIS, principle of identical scaling, where two-point anchoring is recommended for routine work.

Summary, lessons from ILC

The FIRMS ILC exercises indicated that within-laboratory precision (repeatability) is relatively easy to achieve, but that the isotope community must still attend to issues relating to different analytes, calibration, and between-laboratory standardization. Participation in ILC exercises is valuable for all concerned, and truly necessary to move towards generating data that can be readily shared between laboratories and deemed “trustworthy” in data bases.

Standards

The subject of standards is steeped in semantics and it is useful to begin with a few definitions.

Calibration or primary reference materials [2] describe the physical materials which currently define the international δ-scales (Table 3) also described as international measurement standards.
Table 3

The physical materials which define the international δ-scales

VSMOW2

Water

δ2H = 0 ± 0.3 ‰

vs. VSMOW

δ18O = 0 ± 0.02 ‰

vs. VSMOW

NBS 19

Calcium carbonate

δ13C = +1.95 ‰

vs. VPDB

δ18O = −2.2 ‰

vs. VPDB

Air N2

Atmospheric nitrogen

δ15N = 0.0 ‰

 

IAEA-S-1

Silver sulfide

δ34S = −0.3 ‰

vs. VCDT

The subject of stable isotope RMs can be complex, for example, the life story of VSMOW2 is summarised as:
 

NBS 1

Water sample prepared by the National Bureau of Standards, USA

 

 

1961

SMOW

Virtual material defined by Craig with reference to NBS 1

 

 

1968

SMOW

Water defined as zero for δ2H and δ18O scales with no associated uncertainty

 

 

1978

VSMOW

SMOW is renamed to avoid confusion with the virtual material

 

 

2009

VSMOW2

Water replacement for VSMOW with associated uncertainty

RM δ-values are not based on absolute measurements but are consensus values (typically derived from ILC exercises) specifically intended to facilitate inter-laboratory comparability.7 This short history illustrates that RMs are replaced over time but that continuity is maintained by inter-calibrations.

Equation (1) gives an unrealistically simple view of isotope-ratio measurements. The raw data produced by an instrument will, most likely, be calibrated by single point anchoring against a laboratory working gas.8 For traceability to the international δ-scales, data must be calibrated using two point normalisation (or scaling) which is typically performed by use of software external to the analytical instrument software (see PIS). This requirement comes about, in part, because the international scales for δ2H, δ18O, and δ13C are currently defined by the difference thebetween the primary RM and a secondary RM (Table 4) and it is recommended that data are reported on this basis e.g. “ data are expressed on the VSMOW scale normalised by assigning a value of −427.5 ‰ to SLAP2” [16].
Table 4

The RMs which provide a second anchor point for the international δ-scales

SLAP2

Water

δ2H = −427.5 ± 0.3 ‰

vs. VSMOW

δ18O = −55.50 ± 0.02 ‰

vs. VSMOW

LSVEC

Lithium carbonate

δ13C = −46.6 ‰

vs. VPDB

Standards for quality control

Many of the international RMs are available in limited quantities only and their use for routine, internal QC or QA would be impractical and expensive. Several international RMs are, however, currently available without restriction9 e.g. water, glutamic acid, and hair. A laboratory must determine whether the matrix and/or δ-value range of these materials are appropriate for their specific applications but, for many routine measurements, the daily use of these international RMs is strongly encouraged. As a general rule, for δ13C/δ15N analysis USGS40 and USGS41 should be analysed and for δ2H and δ18O USGS42 and USGS43 should be analysed (with every batch of samples). A laboratory must develop its own RMs when close matrix matching or specific δ-values are deemed necessary.

Before any international RM is released to the scientific community a number of criteria must be rigorously demonstrated [17], and selection of in-house QC materials should follow the same guidelines:
  1. 1.

    isotopic homogeneity to the smallest amount used;

     
  2. 2.

    stable and constant isotopic content over a long time period;

     
  3. 3.

    easy to handle during weighing or other preparatory step; and

     
  4. 4.

    a single, pure chemical compound (preferably).

     
It is important to remember that, many international RMs have associated uncertainty (usually expressed as one standard deviation based on ILC). This uncertainty will propagate into the uncertainty of any in-house RM and contribute to the overall uncertainty budget for measurements. The statistically optimised strategy for minimising normalisation errors [18, 19] is very much in accord with common sense thinking:
  • select RMs bracketing the range of possible δ-values expected;

  • select RMs characterised by low uncertainty; and

  • analyse RMs several times.

If pure chemical RMs are purchased from commercial suppliers, the isotopic composition will be “a pig in a poke” and a laboratory may need to purchase and test many samples to obtain materials with sufficient range to act as scaling RMs.10 An alternative is to blend RMs from isotopically enriched and depleted materials to match closely the δ-values of international RMs. Whether purchased or prepared, RMs must be ground to fine, homogeneous powders because variations in crystal size and morphology may affect isotopic composition [12] (especially when blending materials with different δ-values). Although much effort is involved, a few tens of grams of in-house RM will suffice for many years.

Calibration of in-house δ15N and δ13C RMs is depicted in Fig. 3, which illustrates a number of important issues. δ15N RMs were calibrated against three ammonium sulfate standards which span the range of likely measurements. An organic international RM (IAEA-600 caffeine) was then analysed to act as a QA material: the calibrated δ-value (+1.0 ± 0.0) did not differ significantly from the recommended value (+1.0 ± 0.2 ‰). In-house QC materials spanning a range similar to that of the international RMs and QA materials lying in the typical measurement range were then calibrated. Figure 3 shows the instrument is “well behaved” for δ15N measurements (slope = 0.99) but that significant scale compression occurs for δ13C measurements (slope = 0.91) when the same tuning conditions are used. This effect must be addressed by stretching the measured δ-values (see PIS, below)11 by using calibrated RMs.
Fig. 2

The values which participating laboratories assigned to international RMs IAEA-CH-6 and IAEA-N1 during the 2004 and 2006 ILC exercises

There should be no need to re-calibrate in-house RMs but it is sensible periodically to check accuracy by analysing the international RMs, effectively acting as a single-laboratory proficiency test (PT) [1].

Standards for quality assurance

Quality assurance materials act as “check standards”, “controls”, or “known unknowns” in a run of samples, ensuring that QC-based corrections produce acceptable results when applied across an analytical sequence. Accurate and precise QA results indicate a well-functioning analytical system.

QA standards should be analysed and the results monitored on a daily basis to ensure that the whole process of preparation, measurement, and reporting is operating correctly. Standards intended for use in QA should have additional characteristics [17];
  1. 5.

    chemically similar to the samples to be measured

     
  2. 6.

    the isotopic composition should be in the range of the samples to be measured

     

Practical implementation of point 5 warrants further consideration (see PIT, below) but, for example, a suitable QA material for tree ring dating would comprise homogeneous whole wood particles of approximately the same consistency as a sample, prepared by milling a piece of wood into small particles [20]. The QA standard, consistent in mass with a typical sample, can then be processed with each batch of samples so that the QA standard is exposed to the same potential errors as a sample.

The continuous-flow, flash-combustion EA-IRMS interface for δ13C/δ15N/δ34S measurements, can be regarded as a “one size fits all” means of sample introduction, converting a sample quantitatively to H2O, CO2, N2, and SO2.12 This can be demonstrated by comparing the gases evolved from weighed samples of known elemental composition, illustrated in Fig. 4 for the combustion of five potential in-house QA materials. When utilising an EA-IRMS system, in-house RMs must still comply with points 1–6 but every sample does not require a suite of matrix-matched RMs.
Fig. 3

Typical calibration of in-house QC (triangles) and QA (squares) materials against international reference materials (diamonds). For δ15N (a) calibration the international RMs used were IAEA-N1, IAEA-N2, and USGS25. For δ13C (b) calibration the international RMs used were NBS18, IAEA-CH-6, IAEA-CH-3, IAEA-CH-7, and LSVEC

In contrast, TC/EA is beleaguered with technical issues and much effort has been expended in developing appropriate RMs for organic δ18O measurements [21, 22] (discussed below). International water RMs have been used to calibrate organic standards (IAEA-601 and IAEA-602) which are now available to calibrate solid, in-house RMs [23]. Because most organic oxygen is substantially enriched in 18O relative to ocean water, these RMs usefully extend the (VSMOW-SLAP) scale to positive δ18O values.

Calibration of organic δ2H RMs against the VSMOW-SLAP scale is a non-trivial undertaking, because hydrogen is subject to many of the same instrumental issues as δ18O measurement and analytical procedures must also eliminate or, more likely, account for the ready exchange of hydrogen from a large number of functional groups [13, 24, 25].

Principles to guide laboratory practice

The principle of identical treatment (PIT)

More than a decade ago, a seminal publication by Werner and Brand [17] introduced the principle of identical treatment (PIT or IT principle) as a means of obtaining consistent results from analysis of stable isotopic composition. Brand revisited this topic in 2009 [26] and showed how an analytical scheme, founded on in-house RMs and control charts, had underpinned consistent δ-value assignments over many years.

The IT principle requires that:
  • samples and RMs are subject to the same chemical and physical processing;

  • samples and RMs are introduced through the same instrument preparation/inlet system; and

  • samples and RMs are as similar in chemical nature as appropriate for the technique.

The desirable characteristics of RMs are listed above and, as noted, some pragmatism must be applied when considering the meaning of “identical”. The crucial factor is that the instrument preparation/inlet behaves in an identical manner toward both samples and RMs, e.g. flash-combustion EA must convert both samples and RMs quantitatively to CO2. If samples undergo any treatment before IRMS analysis, QA standards (similar in weight to a typical sample) should be processed with each batch of samples to reflect the uncertainties associated with sample processing. For EA-IRMS, laboratories might develop QA standards for different types of sample, e.g. plant, animal, and soil, and run these routinely with samples. For TC/EA, closer matching of QA materials to the samples seems necessary, e.g., QA paper standards are needed for TC/EA analysis of paper, whereas a general plant standard may suffice for EA-IRMS analysis of paper samples.

Another facet of the IT principle is to formulate an analytical sequence which defines the number of samples, QC/QA materials, and blanks to be analysed in each batch and the order in which these are analysed. If these materials are run at regular intervals it is possible to correct for any drift in the internal instrumental δ-scale and, as a “rule of thumb”, between 10–35 % of instrument time will be occupied processing QA/QC materials and replicate samples.

Table 5 shows a typical run sequence template from a stable isotope ecology laboratory (a template from a forensic laboratory is given in the Guide [10]). Such templates are highly desirable because they provide a mechanism to track samples from the preparation area to the autosampler carousel and to the raw data. Information can be cut/paste into the instrument run table and raw data cut/paste back into the external package to assign the final values on the respective international δ-scale. A laboratory handling a small number of samples may perform these processes by use of spreadsheets, however, as sample throughput increases, the use of relational databases or laboratory information management systems (LIMS) is to be recommended.13 Such systems can also generate performance charts for the δ-values derived from QA materials, providing a means of monitoring the analytical process and the status of the RMs.
Table 5

A typical run sequence template used in a stable isotope laboratory for simultaneous determination of δ13C, δ15N, and δ34S. The QC material (bovine muscle) is interspersed throughout the run at small, medium, and large sizes. Samples are weighed close to the medium size so that the size range of the standards brackets the sizes of the samples. Any corrections are, therefore, made by interpolation rather than by extrapolation. QA are run to check that any corrections developed with the principle standard give the right answer when applied to samples and to this “known unknown”

Table 6

Results from sequential analysis of bovine liver RM

103 × δ15NAir

103 × δ13CVPDB

103 × δ34SVCDT

7.46

−21.43

7.68

7.46

−21.58

7.72

7.48

−21.57

7.43

7.75

−21.59

7.38

7.47

−21.50

7.74

7.38

−21.51

7.30

7.27

−21.60

6.94

7.47

−21.52

7.34

7.49

−21.59

6.91

7.69

−21.52

7.33

7.19

−21.54

7.10

7.46

−21.55

7.80

7.63

−21.62

7.66

7.45

−21.52

7.84

7.45

−21.54

7.80

7.70

−21.44

7.63

7.36

−21.71

7.82

The bovine muscle RM (Table 5) was developed as the principal in-house RM by calibration against international RMs. Two related RMs were developed by grinding antipyrine with sulfate to make mixtures with high and low mole factions of sulfur (1.5 % and 0.5 % respectively). These two “S-mix” standards served to check for oxygen isotope contributions in δ34S isotope determinations, with no isotopic difference expected for high vs. low S-mix isotope values when oxygen isotope buffering is working correctly [27]. Routine work showed little variation in the difference between bovine muscle and S-mix isotope values, indicating a stable two-point anchoring scheme with QC standards. The precision for bovine muscle and S-mix isotope analyses serves as a QA check for typical work with animal, plant, and soil samples.

Samples analysed for δ34S are, typically, large and do not need blank or memory corrections, but require size-based corrections (estimated from plots of area vs. δ-value for the bovine muscle RM) applied to all data. The difference (Δ34S) between the bovine muscle and the mix determines any stretch corrections needed. The overall quality of the data is judged by the precision of the corrected data for the QC standard, the accuracy of the QA materials and the agreement between replicates. Replicates are splits of the same well-ground samples and a difference of zero is expected for each replicate pair, or for the average of these pairs.

The principle of identical correction (PIC)

The “raw” data generated by instrument software will almost certainly have undergone some form of correction which is usually invisible to the operator.14 Further corrections can be applied in external software packages, the degree of correction applied being partly dictated by the precision demanded from the final data. The principle of identical correction simply requires that equivalent algorithms are applied to all data. Corrections should always be kept to the minimum necessary, because over-correction can introduce unwanted artefacts into data.

Ion beam corrections for δ13C

Carbon isotopic abundance is typically determined from the mass spectrum of CO2 (m/z 44, 45, and 46) with the main 13C information contained in the m/z 45 ion current. Approximately 7 % of this signal is contributed by 17O and corrections are made to account for this interference. Measurements of 18O at m/z 46 are used to estimate the contribution of 17O by use of proportionality rules and a fraction of this value is subtracted from the ion current at m/z 45. Instrument software will usually provide the operator with an option to select the correction algorithm (or disable it) and a laboratory should be consistent in which algorithm is used.

The Craig algorithm [28] assumes that 17O/16O variations are half 18O/16O variations (λ = 0.5) and, although subsequent studies have reported λ values between 0.5 and 0.53 [29], the “Craig” algorithm is retained to maintain comparability with published data, especially δ13C determination of carbonates. The SSH algorithm (developed by Santrock, Studley, and Hayes) [30] uses a fractionation factor of λ = 0.516 and an iterative correction. This correction is often regarded as more mathematically rigorous and is widely applied to organic materials. Applying the Craig and SSH algorithms to the same raw data will produce δ13C values with differences that exceed the precision of modern IRMS instruments, but usually within 0.1 ‰.

Similar corrections exist for measurements based on CO and other gases [31] and a laboratory must be aware of these and apply them even-handedly.

Linearity, sample size, and δ2H corrections

Sample preparation and instrument dilution systems can cause isotopic changes (fractionation) that vary with sample size, and these size-related variations are best corrected via regression of measured δ-value vs. peak area for RMs. For example, if RM data fall on a line with slope m the correction would be:
$$ {\delta_{\mathrm{corrected}}}={\delta_{\mathrm{measured}}} - \left( {m \times \mathrm{area} + b} \right) + {\delta_{\mathrm{RM}}} $$
(2)

Good linearity generally requires adjusting the ion source conditions to achieve the same δ-value, irrespective of sample size or peak intensity, often at the expense of sensitivity, The linearity of an instrument can be measured by varying the intensity of the working gas or by analysing different amounts of the RM. A laboratory must measure the linearity of an instrument and determine whether this correction is necessary. If an sd of, say, 0.2 ‰ is acceptable, it may be easier to ignore this correction and limit the range of sample peak sizes, relative to the working gas, to those which produce this variation of δ-values.

Hydrogen isotope measurements require a special case of size-related corrections, with ion interactions in the source producing H3+ ions in the source and creating an excess 1H2H signal [32]. This is routinely addressed by means of an H3+ correction factor that is typically measured each day.

Blank corrections

During EA work, gases evolved from tin or silver capsules and atmospheric gases introduced by the autosampler will inevitably cause a signal from a blank analysis. It is often easy to ignore this correction as a 50 mV blank will have a minimum effect on a 5,000 mV sample peak unless the difference in δ-values is vast. This correction, however, becomes increasingly important as sample peak size decreases. To determine the true δ-value of the blank, two RMs, with widely spaced δ-values, can be analysed at decreasing sample size [33].15 The δ-values of the two RMs will tend towards that of the blank and provide two simultaneous equations which can be solved to give the δ-value of the blank, as illustrated in Fig. 6. In making these blank corrections, it is important that the blanks have constant size and that the mass spectrometer is tuned to be linear, so that the only size-dependent variations in mass and δ-value arise from mixing of samples and blanks. Direct measurements of blanks are also possible with high sensitivity systems [34, 35, 36].
Fig. 4

Plot of the peak area of evolved CO2 vs. weight of carbon for five in-house QA materials with known carbon content (benzocaine, caffeine, phenacetin, sucrose, and urea). Five trend lines are shown but are barely distinguishable, indicating that identical treatment has been achieved

Memory and drift corrections

Determination of δ18O by TC/EA can be subject to memory effects as CO exchanges oxygen with residues of previous samples. These effects are also apparent for δ2H determinations and occur during the introduction of solid or liquid samples. The simple approach to counter this effect is to disregard the first or first few replicate analyses of a sample. This approach, however, wastes sample and instrument time and increases the frequency with which the silver residue must be removed. An alternative is to subtract a specified fraction of up to four preceding samples from the result [37]. This is not the easiest of operations because the various algebraic terms must be obtained by trial and error and, if variable amounts of sample are analysed, this factor must be included in the memory-correction algorithm.

It is good practice to analyse RMs at regular intervals during an analytical sequence, because any change in the measured δ-value may reveal a problem with the instrument and may also be used to correct for any drift of the internal δ-scale of the instrument. The problem of δ-scale drift is rarely encountered except for δ2H determinations. Because hydrogen is difficult to remove from the vacuum system the background H2 composition may change over time. To correct for this, data are normalised by use of a fractional combination of the measured δ-values of the bracketing RMs [34]. Figure 5 shows an example of δ2H analysis based on the sequence given in Table 5 assuming that the drift in δ-value is linear and that the position of a sample in the autosampler carousel is a suitable proxy for the passage of time.
$$ {\delta_{\mathrm{drift}\ \mathrm{corrected}}}={\delta_{\mathrm{measured}}}-m\times \mathrm{Position} $$
(3)
where m is the slope of the linear drift curve (Fig. 6) and Position is autosampler position.
Fig. 5

Illustration of the method used to determine the true δ15N value of an instrument blank; two simultaneous equations can be solved to provide the δ-value of the blank (in this example −3.50 ‰ vs. air)

The principle of identical scaling (PIS)

Having taken “raw”, 17O-corrected data from the instrument and applied all necessary corrections, it is essential to shift and stretch data to fit the international δ-scale. The international scales for δ2H, δ18O and δ13C (VSMOW and VPDB) are now defined by two RMs and it is best practice to apply two-point normalisation using in-house RMs which have been calibrated against two or more international RMs.16

Stable isotope results are frequently scaled or normalised [38] by:
  • “shifting” the data to correct for bias; and

  • “stretching” the data to correct for scale-compression.

If the range of isotopic abundances being measured spans only a small range (for example 5 ‰) for any given element, the effect of normalisation will be small and only a shift correction may be necessary (in effect single-point anchoring) but for larger ranges, and greater precision, the data must also be stretched to the international δ-scales. To explain why this is important, Fig. 3 shows significant scale compression for δ13C measurements (slope = 0.91 compared with an ideal 1.00), which must be corrected by stretching the measured data, and an offset (−2.17) which must be corrected by shifting the measured data. In this example:
Fig. 6

An example of QC (diamonds) samples used for drift correction of δ2H data . Corrected data are shown (squares and dotted line)

$$ {\delta_{\mathrm{scaled}}}=\frac{{\left( {{\delta_{\mathrm{measured}}}+2.17} \right)}}{0.91 } $$
(4)

The principle of error detection (PED)

The most basic principle of error detection is an independent check of results before a report leaves the laboratory, the core question being: “do these data correspond to these samples?” During the FIRMS ILCs it was apparent that some laboratories transcribed data into the wrong fields e.g. δ15N data were presented as δ13C data. When reviewing 30 plus sets of data, this is an easy mistake to spot but if a single set of data were given to a customer there would be no way of knowing that these data were erroneous.

Whilst it is straightforward to instigate a system of running QA samples, this is a futile exercise if these data are never reviewed or acted upon: consider the following warning example. Over the course of study a PhD student submitted samples to a centralised IRMS service and included his own QA material alone with every batch. Results for this material showed that δ15N measurements changed by 2 ‰ over the course of three years. Although the laboratory routinely ran their own QA materials, staff were too busy to compile and review the results and, thus failed to identify a problem with the EA oxygen introduction which had resulted in poor combustion. Acceptable performance criteria for QA must be determined, documented, and, above all reviewed [39], ideally on a daily basis.

To detect errors in individual measurements it is necessary to repeat a specific number of analyses. A typical stable isotope ecology laboratory may analyse every 4th to 12th sample in duplicate and examine the sd of the difference between replicates. A forensic laboratory may analyse each sample six times (or more) and consider the repeatability for a single sample. Which approach is “correct” depends on how well we need to know our result.

Table 6 presents δ15N, δ13C, and δ34S data recorded for a bovine liver RM during the course of a single analytical run similar to the template above (Table 5). This sequence of data was randomised 100 times and the cumulative summary statistics (average and sd) calculated to demonstrate how replicate analyses help us to know our δ-value.

Figure 7a shows the difference between the cumulative average δ15N value for a given number of replicate analyses and the overall average for each of the 100 randomised sequences. Clearly, as more data are acquired the average tends towards an asymptote which will be the mean. On the basis of this plot, it is easy to see that most of the randomised sequences produce a result within 0.1 ‰ of the mean after two or three replicate analyses. However, to be certain that the average value lies within 0.1 ‰ of the mean eight or nine replicate analyses would be necessary. Very similar patterns are observed for δ13C and δ34S data.
Fig. 7

Summary statistics based on 100 randomised sequences of data from Table 6 versus the number of replicate analyses (a) average δ15N (b) cumulative standard deviation for δ13C (squares), δ15N (diamonds), and δ34S (triangles)

Figure 7b shows the cumulative sd averaged across 100 randomised sequences. This value does not change significantly following 2–5 analyses but, again, eight or more analyses may be needed to maximise stability. Overall, therefore, the numerical result (which will be reported) does not change substantially whether running duplicate or multiple analyses, what changes is the level of confidence with which that result can be reported. Researchers should perform this type of power analysis with their own data to determine how best to use instrument measurement capacity for the confidence levels required.

In summary, a laboratory should examine its data to develop an approach that generates results that are fit-for-purpose. Isotopic measurements in a database will typically record mean, sd, and number of replicates, most of the fields containing background information and other chemical and physical data. Replicating every 4th–12th sample or analysing each sample 4–9 times are contrasting strategies that are both fit for the purpose of populating this type of database and both approaches are defensible.

Notes on current practices with EA and TC/EA - IRMS

The principles above must always be supported by good analytical practice, because no amount of QC or QA will compensate for poor practical work. The following sections are intended to alert users to potential problems with less common isotopic analyses using TC/EA and EA-IRMS examples. It will always be impossible to record all the tips and tricks that are learned over many years and newcomers are strongly advised to visit an established laboratory and observe their working practices.

Considerations for δ18O measurements by TC/EA

The underlying principle of TC/EA is the Schuetze/Unterzaucher reaction, which exploits a large excess of carbon, at high temperature, to produce hydrogen and carbon monoxide from oxygen-bearing materials [40].
$$ {{\mathrm{H}}_2}\mathrm{O}+n\mathrm{C}\to \mathrm{CO}+{{\mathrm{H}}_2}+\left( {n\text{--} 1} \right)\mathrm{C} $$
(5)
or
$$ {{\mathrm{C}}_x}{{\mathrm{H}}_{2y }}{{\mathrm{O}}_{\mathrm{z}}}+n\mathrm{C}\to z\mathrm{CO}+y{{\mathrm{H}}_2}+\left( {n+x\text{--} z} \right)\mathrm{C} $$
(6)

Whether or not this process is more complex and/or less predictable than flash-combustion EA is a matter for discussion, but the reaction is complicated by the fact that carbon is present in a solid form which varies from pure glassy carbon to graphite with possible further reactions with accumulated silver.

Continuous-flow δ18O analysis is best suited to compounds which contain only C, H, and O and even carbonates do not release oxygen quantitatively under standard reaction conditions.17 Nitrates are believed to be reduced quantitatively to N2 which can be used for δ15N measurements [11] but reduced forms of nitrogen undergo complex reactions with carbon to liberate N2 which is reported to be useless for isotopic analysis [11] and causes problems with δ18O measurements.

Problems with nitrogen

Nitrogen reacts with residual oxygen at the MS filament to form [14N16O]+ which is detected as m/z 30 together with [12C18O]+. Although N2 and CO are separated by the conventional TC/EA gas chromatography (GC) column, NO+ is observed long after gaseous N2 has left the ion source. Various modifications have been suggested to eliminate N2 from the ion source, including diversion using an additional four-way valve and/or dilution with helium [6, 7, 41]. Also recommended is increasing the length of the GC column to increase the separation of N2 and CO to provide a wider time window in which to divert and/or dilute the nitrogen peak [7].

Problems with other gases

Other problematic gases can be generated by the TC/EA, for example CCl4 and CF4 from halide anions and CS2 from sulfur compounds. The use of chemical traps containing different combinations of charcoal, magnesium perchlorate, and Carbosorb between the reactor and the GC column is recommended to trap acidic chemicals and guard against fine dust particles. Even with chemical traps in place, it is important to check chromatographic performance routinely, and to reactivate the GC column periodically.

Exchangeable oxygen

Having successfully eliminated interfering gases, the CO (quantitatively generated from a sample) can exchange oxygen with oxygen-bearing surfaces at high temperature. A number of modifications have been conceived to prevent CO contacting oxygen-bearing surfaces, for example an outer tube manufactured from silicon carbide and an inner molybdenum foil liner. The most widely adopted modification, however, is the so-called “bottom feed” reactor which borrows heavily from the design of GC injectors. The helium carrier gas is applied from the bottom connector, passes outside the internal glassy carbon tube, entering the tube at the top and passing directly through the core of the reactor [42]. Despite these precautions, exchange with oxygen from residues of previous samples can still lead to substantial memory effects (see PIC) and regular replacement of the reactor filling and careful monitoring of results with RMs are necessary to produce reliable analytical results.

Exchangeable hydrogen

Many of the problems which affect δ18O measurements by TC/EA will also affect δ2H measurements, with the added complication that a great many organic materials will readily exchange hydrogen with atmospheric moisture. For δ2H/δ18O measurements it is advantageous (if not essential) to dry samples to eliminate any contribution from adsorbed and/or absorbed moisture18 and to monitor this process by identical treatment of QA materials. To maintain sample integrity the use of a closed or “zero-blank” autosampler is also recommended.

Considerations for δ34S measurements by EA

Most laboratories measure δ34S from the mass spectrum of SO2 produced by an elemental analyser similar to those used for C and N isotopic analysis.19 The analysis differs in that one reaction tube is used for both oxidation and reduction of samples and, usually, 10–20 times larger samples (2–10 mg) are used, because sulfur is present at low abundance (0.3–1.3 %) in most organic materials. Smaller samples (0.2–1.0 mg S) can be analysed by use of cryofocus systems [43, 44].

Combustion

Combustion of sulfur-containing samples takes 10–30 s and produces several gases, including SO3, as well as SO2. Typically, a few milligrams (2–10 mg) of vanadium pentoxide are mixed intimately with the weighed sample in a tin capsule to promote oxidation and SO2 formation. Any SO3 formed will be reduced to SO2 over hot copper in the bottom part of the reactor. The important points for the reaction conditions are:
  • The linear flow rate in the reactor must be sufficient to force combustion gases down through the hot tube, rather than back into the cooler upper part of the combustion tube where SO3 will stick and ultimately give a poor peak shape at the mass spectrometer.

  • Occasionally, yellow deposits are seen coating the white magnesium perchlorate in drying tubes and are usually a sign that flow rates are too high.

  • The copper in the lower part of the reactor should be maintained between 830 °C and 910 °C. Hotter temperatures will melt the copper and lower temperatures will result in copper sulfate formation, trapping sulfur and causing poor peak shapes [45].

  • There must be an excess of oxygen to accommodate large samples and promote strong oxidation. Because sulfur isotopes are much more sensitive to poor combustion than either N or C [45], this may require more oxygen.

Equilibration

SO2 can vary in isotope composition because of oxygen or sulfur isotopes and it is important to minimize any oxygen isotope variation when measuring S isotopes. There is no routine way of measure directly the oxygen isotope values of SO220 and most laboratories apply identical treatment to produce SO2 with the same oxygen composition from both standards and samples. This was traditionally achieved via a multi-step process involving oxidation to sulfate, reduction to sulfide, and combustion with addition of isotopically identical oxygen to all samples and standards. More recently, these steps have been replaced by installing post-combustion reactors in the EA system to equilibrate and buffer the oxygen isotope values. A second reactor tube filled with quartz chips is maintained at a high temperature (890 °C), with a 1–12 cm layer of copper oxide sometimes inserted mid-column to improve equilibration.21 Problems with oxygen isotopes are most easily seen when large quantities of water are present from combustion of organics and when this is not rapidly removed to a constant background [46]. Water of combustion seems responsible for most equilibration reactions involving oxygen isotopes [46], and magnesium perchlorate traps are used after the combustion reactor to remove most water, allowing a small amount of water to travel with the SO2 in the second reactor and promote final equilibration.

Common problems and solutions for δ34S analysis

Most problems result from poor combustion and are solved by simplifying the combustion tube to quartz wool, quartz chips, and copper wire only [27], such that combustion tubes are relatively inexpensive. This makes it easy to check and replace misperforming combustion tubes. Problems with combustion tubes are usually because of:
  • carbon soot deposits because of poor combustion and insufficient oxygen;

  • copper melting because of placement too near the centre of the furnace; and

  • peak tailing when copper is placed near the cool bottom of the reactor.

Some samples (especially sediments) are sometimes difficult to combust. Adding a solution of ammonium nitrate to the sample and drying in a tin capsule will usually solve this problem by promoting flash-type combustion. Unfortunately, N isotope measurements are contaminated by the ammonium nitrate and must be made on separate aliquots of the sample.

Stainless steel fittings and stainless steel tubing leading from the hot reactors can be used for SO2 work, but should be regularly rinsed with water and, occasionally, with hot nitric acid to remove material volatilized from the hot reactors and depositing on cooler surfaces downstream.

Conclusions

A series of ILC exercises organised by the FIRMS network has shown that although laboratories could generate stable isotope data with acceptable in-house repeatability (precision) for a given sample type, the reproducibility (accuracy) of these results between laboratories left much scope for improvement. Different isotopic composition for different sample types analysed in the same laboratory (Δ) were also unimpressive. To achieve better results in future we suggest the following steps in laboratory practice:
  1. 1.

    Obtain RMs, with internationally agreed δ-values, spanning a range of approximately 50 ‰. Check the δ-values assigned and document these with all reported data.

     
  2. 2.

    Assess the suitability of international RMs to act as routine QC materials and, if necessary, prepare matrix matched, in-house RMs spanning a range of approximately 50 ‰ (RM rules 1–4).

     
  3. 3.

    Use RMs to determine whether corrections for sample size, blank, and memory effects are necessary or desirable.

     
  4. 4.

    Demonstrate that the instrument preparation and/or inlet system behaves in the same way for international and in-house RMs over a range of sample size and conditions. Focus on the Δ difference between the RMs.

     
  5. 5.

    Prepare in-house standards to be used for routine QA, chemically similar to “real” samples and with typical δ-values (follow RM rules 1–6).

     
  6. 6.

    Demonstrate that all preparation steps and the instrument preparation and/or inlet system behave the same for QC/QA materials and typical samples.

     
  7. 7.

    Develop an analytical sequence to include both QC and QA materials with every batch of samples.

     
  8. 8.

    Ensure that QC, QA, and sample data are processed and corrected in an identical manner—in both instrument and by external software.

     
  9. 9.

    Monitor the δ-values for QA materials and act on any significant deviations or trends.

     
  10. 10.

    Periodically analyse international RMs as an in-house proficiency test and act on any significant deviations.

     

The rules for reference materials

  1. 1.

    isotopic homogeneity to the smallest amount used;

     
  2. 2.

    stable and constant isotopic content over a long time period;

     
  3. 3.

    easy to handle during weighing and other preparatory steps;

     
  4. 4.

    a single, pure chemical compound (preferably);

     
  5. 5.

    chemically similar to the samples to be measured; and

     
  6. 6.

    the isotopic composition should be in the range of the samples to be measured.

     

Footnotes

  1. 1.

    A critical review of the use of these terms is presented by Thompson [1]

  2. 2.

    The form of this equation follows SI guidelines [2]. Historically, the value was multiplied by 1000 to give values in permil or by 106 to give values in per meg (ppm)

  3. 3.

    Also known as high temperature conversion, high temperature pyrolysis, and carbon reduction

  4. 4.

    Analogous problems have been reported when analysing reduced forms of nitrogen by TC/EA [11]

  5. 5.

    The difference between the VSMOW and VPDB scales is not additive. The conversion determined by Coplen [14] is widely accepted but authors should always state when this formula has been applied (δ18OVSMOW = 1.03091 × δ18OVPDB + 30.9)

  6. 6.

    At the time of ILC#3, the IAEA assigned the values δ13C = −10.43 ‰ and δ15N = +0.4 ‰

  7. 7.

    The δ-value and uncertainty assigned to many of the international RMs has been re-assessed and reassigned over time and it is important to check these periodically. The most reliable source of information is the CIAAW website: http://www.ciaaw.org

  8. 8.

    Because isotopic differences can be measured most precisely when these differences are small, the δ-value of the working gas should be within the range of isotopic compositions to be measured

  9. 9.
  10. 10.

    With the exception of hydrogen, RMs spanning a range of approximately 50 ‰ will encompass most of the natural variation observed

  11. 11.

    This is not the same as linearity correction, which compensates for changes in δ-value in response to variations in sample size

  12. 12.

    This may not be true for elements in extreme oxidation states, specifically nitrates

  13. 13.

    LIMS for isotopic measurements can be obtained from http://isotopes.usgs.gov/research/topics/lims.html

  14. 14.

    Peak integration settings will have a profound effect on the data and must be applied uniformly

  15. 15.

    The δ-values measured for very small peaks can vary unpredictably, because of integration issues, but acceptable measurements of peak area are still possible

  16. 16.

    The introduction of a second anchor point for the VPDB scale in 2006 [15] resulted in the reassignment of many of the δ13C values for international RMs so it is important to report the values assigned together with any analytical data

  17. 17.

    Higher temperatures and/or chemical additives, for example AgCl, have been proposed as remedies

  18. 18.

    Drying over phosphorus pentoxide, at elevated temperature and under vacuum for several days, is usually recommended [13]

  19. 19.

    Although it is possible to perform measurements on SO+ this is generally considered less sensitive and less reliable because of problems with blanks and interference

  20. 20.
    Oxygen isotope corrections for δ34S are theoretically possible when both SO+ and SO2+ are measured from the same sample [46, 47]. These general formulae apply [36]:
    $$ {\delta^{18}}\mathrm{O}=24.02\times {\delta^{66}}-23.024\times {\delta^{50 }}\,\mathrm{and}\,{\delta^{34}}\mathrm{S}=1.0908\times {\delta^{66}}-0.0908 \times {\delta^{18}}\mathrm{O} $$

    The latter formula also gives the conventional way of calculating δ34S from δ66 values under the assumption that samples and standards are prepared with the same oxygen isotope composition, so that δ18Ο is zero and can be ignored

  21. 21.

    If the copper is omitted higher temperatures can be used to speed equilibration

References

  1. 1.
    Thompson M (2012) Precision in chemical analysis: a critical survey of uses and abuses. Anal Meth 4:1598–1611. doi:10.1039/c2ay25083g CrossRefGoogle Scholar
  2. 2.
    Coplen TB (2011) Guidelines and recommended terms for expression of stable-isotope-ratio and gas-ratio measurement results. Rapid Commun Mass Spectrom 25(17):2538–2560. doi:10.1002/rcm.5129 Google Scholar
  3. 3.
    Brand WA (2011) New reporting guidelines for stable isotopes – an announcement to isotope users. Isotopes Environ Health Stud 47(4):535–536. doi:10.1080/10256016.2011.645702 CrossRefGoogle Scholar
  4. 4.
    Coplen TB, Qi H (2012) USGS42 and USGS43: Human-hair stable hydrogen and oxygen isotopic reference materials and analytical methods for forensic science and implications for published measurement results. Forensic Sci Int 214(1–3):135–141. doi:10.1016/j.forsciint.2011.07.035 CrossRefGoogle Scholar
  5. 5.
    Schimmelmann A, Albertino A, Sauer PE, Qi H, Molinie R, Mesnard F (2009) Nicotine, acetanilide and urea multi-level 2H, 13C and 15N abundance reference materials for continuous-flow isotope ratio mass spectrometry. Rapid Commun Mass Spectrom 23(22):3513–3521. doi:10.1002/rcm.4277 CrossRefGoogle Scholar
  6. 6.
    Hagopian WM, Jahren AH (2012) Elimination of nitrogen interference during online oxygen isotope analysis of nitrogen-doped organics using the “NiCat” nickel reduction system. Rapid Commun Mass Spectrom 26(16):1776–1782. doi:10.1002/rcm.6285 CrossRefGoogle Scholar
  7. 7.
    Qi H, Coplen TB, Wassenaar LI (2011) Improved online δ18O measurements of nitrogen- and sulfur-bearing organic materials and a proposed analytical protocol. Rapid Commun Mass Spectrom 25(14):2049–2058. doi:10.1002/rcm.5088 CrossRefGoogle Scholar
  8. 8.
    Coplen TA, Qi H (2009) Quality assurance and quality control in light stable isotope laboratories: A case study of Rio Grande, Texas, water samples. Isotopes Environ Health Stud 45(2):126–134. doi:10.1080/10256010902871952 CrossRefGoogle Scholar
  9. 9.
    Carter JF, Hill JC, Doyle S, Lock C (2009) Results of four inter-laboratory comparisons provided by the Forensic Isotope Ratio Mass Spectrometry (FIRMS) network. Sci Justice 49(2):127–137. doi:10.1016/j.scijus.2008.12.002 CrossRefGoogle Scholar
  10. 10.
    Carter JF, Barwick VJ (eds) (2012) Good practice guide for isotope ratio mass spectrometry. LGC/FIRMS, ISBN 978-0-948926-31-0Google Scholar
  11. 11.
    Kornexl BE, Gehre M, Höfling R, Werner RA (1999) On-line δ 18O measurement of organic and inorganic substances. Rapid Commun Mass Spectrom 13:1685–1693. doi:10.1002/(SICI)1097-0231(19990830)13:16<1685::AID-RCM6991>3.0.CO;2-9CrossRefGoogle Scholar
  12. 12.
    David GE, Coxon A, Frewa RD, Hayman AR (2010) Isotope fractionation during precipitation of methamphetamine HCl and discrimination of seized forensic samples. Forensic Sci Int 200(1–3):123–129. doi:j.forsciint.2010.03.043 CrossRefGoogle Scholar
  13. 13.
    Qi H, Coplen TB (2011) Investigation of preparation techniques for δ2H analysis of keratin materials and a proposed analytical protocol. Rapid Commun Mass Spectrom 25(15):2209–2222. doi:10.1002/rcm.5095 CrossRefGoogle Scholar
  14. 14.
    Coplen TB, Kendall C, Hopple JA (1983) Comparison of stable isotope reference samples. Nature 302(5905):236–238. doi:10.1038/302236a0 CrossRefGoogle Scholar
  15. 15.
    Coplen TB, Brand WA, Gehre M, Gröning M, Meijer HAJ, Toman B, Verkouteren RM (2006) New guidelines for δ13 C measurements. Anal Chem 78(7):2439–2441. doi:10.1021/ac052027c CrossRefGoogle Scholar
  16. 16.
    Coplen TA (1994) Reporting of stable hydrogen, carbon and oxygen isotopic abundances (Technical Report). Pure Appl Chem 66(2):273–275CrossRefGoogle Scholar
  17. 17.
    Werner RA, Brand WA (2001) Referencing strategies and techniques in stable isotope ratio analysis. Rapid Commun Mass Spectrom 15:501–519. doi:10.1002/rcm.258 CrossRefGoogle Scholar
  18. 18.
    Skrzypek G, Sadler R (2011) A strategy for selection of reference materials in stable oxygen isotope analyses of solid materials. Rapid Commun Mass Spectrom 25(11):1625–1630. doi:10.1002/rcm.5032 CrossRefGoogle Scholar
  19. 19.
    Skrzypek G, Sadler R, Paul D (2011) Error propagation in normalization of stable isotope data: a Monte Carlo analysis. Rapid Commun Mass Spectrom 24(18):2697–2705. doi:10.1002/rcm.4684 CrossRefGoogle Scholar
  20. 20.
    Porter TJ, Middlestead P (2012) On estimating the precision of stable isotope ratios in processed tree-rings. Dendrochronologia 30(3):239–242. doi:10.1016/j.dendro.2012.02.001 CrossRefGoogle Scholar
  21. 21.
    Coplen TB, Qi H (2010) Applying the silver-tube introduction method for thermal conversion elemental analyses and a new δ 2H value for NBS 22 oil. Rapid Commun Mass Spectrom 24(15):2269–2276. doi:10.1002/rcm.4638 CrossRefGoogle Scholar
  22. 22.
    Qi H, Gröning M, Coplen TB, Buck B, Mroczkowski SJ, Brand WA, Geilmann H, Gehre M (2010) Novel silver-tubing method for quantitative introduction of water into high-temperature conversion systems for stable hydrogen and oxygen isotopic measurements. Rapid Commun Mass Spectrom 24(13):1821–1827. doi:10.1002/rcm.4559 CrossRefGoogle Scholar
  23. 23.
    Brand WA, Coplen TB, Aerts-Bijma AT, Böhlke JK, Gehre M, Geilmann H, Gröning M, Jansen HG, Meijer HAJ, Mroczkowski J, Qi H, Soerge K, Stuart-Williams H, Weise SM, Werner RA (2009) Comprehensive inter-laboratory calibration of reference materials for δ18O versus VSMOW using various on-line high-temperature conversion techniques. Rapid Commun Mass Spectrom 2009(7):999–1019. doi:10.1002/rcm.3958 CrossRefGoogle Scholar
  24. 24.
    Wassenaar LI, Hobson KA (2003) Comparative equilibration and online technique for determination of non-exchangable hydrogen of keratins for use in animal migration studies. Isotopes Environ Health Stud 39(3):211–217. doi:10.1080=1025601031000096781 CrossRefGoogle Scholar
  25. 25.
    Landwehr JM, Meier-Augenstein W, Kemp HF (2011) A counter-intuitive approach to calculating non-exchangeable 2H isotopic composition of hair: treating the molar exchange fraction fE as a process-related rather than compound-specific variable. Rapid Commun Mass Spectrom 25(2):301–306. doi:10.1002/rcm.4854 CrossRefGoogle Scholar
  26. 26.
    Brand WA (2009) Maintaining high precision of isotope ratio analysis over extended periods of time. Isotopes Environ Health Stud 45(2):135–149. doi:10.1080/10256010902869097 CrossRefGoogle Scholar
  27. 27.
    Fry B (2007) Coupled N, C and S stable isotope measurements using a dual-column gas chromatography system. Rapid Commun Mass Spectrom 21(5):750–756. doi:10.1002/rcm.2892 CrossRefGoogle Scholar
  28. 28.
    Craig H (1957) Isotopic standards for carbon and oxygen and correction factors for mass-spectrometric analysis of carbon dioxide. Geochim Cosmochim Acta 12:133–149. doi:doi.org/10.1016/0016-7037(57)90024-8 CrossRefGoogle Scholar
  29. 29.
    Brand WA, Assonov SS, Coplen TA (2010) Correction for the 17O interference in δ13C measurements when analyzing CO2 with stable isotope mass spectrometry (IUPAC Technical Report). Pure Appl Chem 82(8):1719–1733CrossRefGoogle Scholar
  30. 30.
    Santrock J, Studley SA, Hayes JM (1985) Isotopic analyses based on the mass spectrum of carbon dioxide. Anal Chem 57:1444–1448. doi:10.1021/ac00284a060 CrossRefGoogle Scholar
  31. 31.
    Kaiser J, Röckmann T (2008) Correction of mass spectrometric isotope ratio measurements for isobaric isotopologues of O2, CO, CO2, N2O and SO2. Rapid Commun Mass Spectrom 22(24):3997–4008. doi:10.1002/rcm.3821 CrossRefGoogle Scholar
  32. 32.
    Sessions AL, Burgoyne TW, Hayes JM (2001) Correction of H3 + contributions in hydrogen isotope ratio monitoring mass spectrometry. Anal Chem 73:192–199. doi:10.1021/ac000488m CrossRefGoogle Scholar
  33. 33.
    Fry B, Brand W, Mersch FJ, Tholke K, Garritt R (1992) Automated analysis system for coupled d13C and d15N measurements. Anal Chem 64(3):288–291. doi:10.1021/ac00027a009 Google Scholar
  34. 34.
    Polissar PJ, Fulton JM, Junium CK, Turich CC, Freeman KH (2009) Measurements of δ 13C and δ 15N isotopic composition of nanomolar quantities of C and N. Anal Chem 81(2):755–763. doi:10.1021/ac801370c CrossRefGoogle Scholar
  35. 35.
    Ogawa NO, Nagata T, Kitazato H, Ohkouchi N (2010) Ultra-sensitive elemental analyzer/isotope ratio mass spectrometer for stable nitrogen and carbon isotope analyses. In: Ohkouchi N, Tayasu I (eds) Earth, life and isotopes. Kyoto University press, Kyoto, pp 339–354Google Scholar
  36. 36.
    Fry B (2006) Stable isotope ecology. Springer, New York. doi:10.1007/0-387-33745-8 CrossRefGoogle Scholar
  37. 37.
    Gröning M (2011) Improved water δ2H and δ18O calibration and calculation of measurement uncertainty using a simple software tool. Rapid Commun Mass Spectrom 25(19):2711–2720. doi:10.1002/rcm.5074 CrossRefGoogle Scholar
  38. 38.
    Paul D, Skrzypek G, Fórizs I (2007) Normalization of measured stable isotopic compositions to isotope reference scales – a review. Rapid Commun Mass Spectrom 21(18):3006–3014. doi:10.1002/rcm.3185 CrossRefGoogle Scholar
  39. 39.
    Thompson M, Wood R (1993) The international harmonized protocol for the proficiency testing of (chemical) analytical laboratories (Technical Report). Pure Appl Chem 65(9):2123–2144CrossRefGoogle Scholar
  40. 40.
    Santrock J, Hayes JM (1987) Adaptation of the Unterzaucher procedure for determination of oxygen-18 in organic substances. Anal Chem 59(1):119–127. doi:10.1021/ac00128a025 CrossRefGoogle Scholar
  41. 41.
    Hunsinger GB, Stern LA (2012) Improved accuracy in high-temperature conversion elemental analyzer δ18O measurements of nitrogen-rich organics. Rapid Commun Mass Spectrom 26(5):554–562. doi:10.1002/rcm.6132 CrossRefGoogle Scholar
  42. 42.
    Gehre M, Geilmann H, Richter J, Werner RA, Brand WA (2004) Continuous flow 2H/1H and 18O/16O analysis of water samples with dual inlet precision. Rapid Commun Mass Spectrom 18(22):2650–2660. doi:10.1002/rcm.1672 CrossRefGoogle Scholar
  43. 43.
    Stricker CA, Rye RO, Johnson R, Rye RO, Johnson CA, Bern C (2006) An automated cryo-focusing approach for sulfur isotope analysis of organic and other low-level sulfur materials. In: The 5th International Conference on Applications of Stable Isotope Techniques to Ecological Studies, Belfast, IrelandGoogle Scholar
  44. 44.
    Hansen T, Burmeister A, Sommer U (2009) Simultaneous δ 15N, δ 13C and δ 34S measurements of low biomass samples using a technically advanced high sensitivity elemental analyzer connected to an isotope ratio mass spectrometer. Rapid Commun Mass Spectrom 23:3387–3393. doi:10.1002/rcm.4267 CrossRefGoogle Scholar
  45. 45.
    Dugan G (1977) Automatic carbon, hydrogen, nitrogen, sulfur analyser chemistry of sulfur reactions. Anal Lett 10:639–657. doi:10.1080/00032717708059229 CrossRefGoogle Scholar
  46. 46.
    Fry B, Silva SR, Kendall C, Anderson RK (2002) Oxygen isotope corrections for online d34 S analysis. Rapid Commun Mass Spectrom 16:854–858. doi:10.1002/rcm.651 CrossRefGoogle Scholar
  47. 47.
    Holt BD, Engelkemeir AG (1970) Thermal decomposition of barium sulfate to sulfur dioxide for mass spectrometric analysis. Anal Chem 42(12):1451–1453. doi:10.1021/ac60294a032 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Queensland Health Forensic and Scientific ServiceArcherfieldAustralia
  2. 2.Griffith University–Australian Rivers InstituteQueenslandAustralia

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