Simple spreadsheet templates for the determination of the measurement uncertainty of stable isotope ratio delta values

Measurement Uncertainty and Risk of False Compliance Assessment Applied to Carbon Isotopic Analyses in Natural Gas Exploratory Evaluation

The concept of uncertainty in an isotopic analysis is not uniform in the scientific community worldwide and can compromise the risk of false compliance assessment applied to carbon isotopic analyses in natural gas exploratory evaluation. In this work, we demonstrated a way to calculate one of the main sources of this uncertainty, which is underestimated in most studies focusing on gas analysis: the δ13C calculation itself is primarily based on the raw analytical data. The carbon isotopic composition of methane, ethane, propane, and CO2 was measured. After a detailed mathematical treatment, the corresponding expanded uncertainties for each analyte were calculated. Next, for the systematic isotopic characterization of the two gas standards, we calculated the standard uncertainty, intermediary precision, combined standard uncertainty, and finally, the expanded uncertainty for methane, ethane, propane, and CO2. We have found an expanded uncertainty value of 1.8‰ for all compounds, except for propane, where a value of 1.6‰ was obtained. The expanded uncertainty values calculated with the approach shown in this study reveal that the error arising from the application of delta calculation algorithms cannot be neglected, and the obtained values are higher than 0.5‰, usually considered as the accepted uncertainty associated with the GC-IRMS analyses. Finally, based on the use of uncertainty information to evaluate the risk of false compliance, the lower and upper acceptance limits for the carbon isotopic analysis of methane in natural gas are calculated, considering the exploratory limits between -55‰ and -50‰: (i) for the underestimated current uncertainty of 0.5‰, the lower and upper acceptance limits, respectively, are -54.6‰ and -50.4‰; and (ii) for the proposed realistic uncertainty of 1.8‰, the lower and upper acceptance limits would be more restrictive; i.e., -53.5‰ and -51.5‰, respectively.

Re-determination of R(13C/12C) for Vienna Peedee belemnite (VPDB)

RATIONALE

The isotope ratio for the internationally agreed but virtual zero-point of the carbon isotope-delta scale, Vienna Peedee belemnite (VPDB), plays a critical role in linking carbon isotope delta values to the SI. It is also a quantity used for various data processing procedures including '17O correction', clumped isotope analysis and conversion of carbon isotope delta values into other expressions of isotopic composition. A value for RVPDB(13C/12C) with small uncertainty is therefore desirable to facilitate these procedures.

METHODS

The value of RVPDB(13C/12C) was determined by errors-in-variables regression of isotope delta values traceable to VPDB measured by isotope ratio mass spectrometry against isotope ratios traceable to the SI by use of gravimetric mixtures of 12C- and 13C-enriched d-glucose measured by multicollector inductively coupled plasma mass spectrometry.

RESULTS

A value of RVPDB(13C/12C) = 0.0111105 ± 0.0000042 (expanded uncertainty, k = 2) was obtained.

CONCLUSIONS

The new value for RVPDB(13C/12C) agrees very well with the consensus values calculated from previous measurement results proposed by Kaiser and by ourselves, as well as recent determinations independent of mass spectrometry. The expanded uncertainty of 0.4‰ when expressed as an isotope delta value is a tenfold improvement over the previous best measurement of the isotopic composition of carbon.

Forensic application of isotope ratio mass spectrometry (IRMS) for human identification

Application of isotope ratio mass spectrometry (IRMS) to skeletal remains has become an important tool to investigate human behavior and history. Isotopic variations in collagen, enamel, and keratin reflect variations in an individual's diet and drinking water. Since food and water sources typically are geographically linked, isotope testing can assist in forensic identification by classifying remains to a likely geographic or population origin. If remains are commingled, differences in diet or geographic origin also can support their separation. The usefulness of IRMS in forensic science is dependent on the underlying quality and surety of the isotope test results; in other words, we need to understand their reliability in interpretations. To take ownership of isotopic data quality, we recommend asking a series of questions:Here, we use data collected during the buildout and accreditation of an isotope testing program at the Defense POW/MIA Accounting Agency (DPAA) to answer the above questions for the forensic application of IRMS for human identification. While our primary focus is on the preparation and analysis of bone collagen, the questions above should be considered whenever isotope testing is used in forensic casework. Whether the populations of interest are drugs or humans, olives or explosives, users need to evaluate their isotopic data and interpretations to ensure they are scientifically sound and legally defensible.

Characterisation of new reference materials IAEA-610, IAEA-611 and IAEA-612 aimed at the VPDB δ13 C scale realisation with small uncertainty

RATIONALE

LSVEC, the second anchor Reference Material (RM) for the VPDB δ¹³ C scale realisation, was introduced in 2006. In 2015, its δ¹³ C value was found to be drifting and, in 2017, its use as an RM for δ¹³ C was officially discontinued by IUPAC. New RMs of low uncertainty are needed. This paper describes the preparation and characterisation of IAEA-610, IAEA-611 and IAEA-612 (calcium carbonate, of chemical origin) which shall serve as a set of RMs aimed at anchoring the VPDB scale at negative δ¹³ C values.

METHODS

The preparation and characterisation of IAEA-610, IAEA-611 and IAEA-612 were performed by addressing the contemporary technical requirements for RM production and characterisation (ISO Guide 35:2017). The three RMs were produced in large quantities, and the first batch was sealed into ampoules (0.5 g) to ensure the integrity of the RM during storage; additional batches were sealed for long-term storage. The most accurate method of CO₂ preparation and stable isotope measurements was used, namely carbonate-H₃ PO₄ reaction under well-controlled conditions combined with well-tested stable isotope ratio mass spectrometry.

RESULTS

The assigned values of δ¹³ C and associated uncertainties are based on a large number of analyses (~10 mg aliquots) performed at IAEA and address all the known uncertainty components. For aliquots down to ~100 μg, the δ¹³ C uncertainty is increased. The uncertainty components considered are as follows: (i) material homogeneity, (ii) value assignment against IAEA-603, (iii) potential storage effects, (iv) effect of the ¹⁷ O correction, and (v) mass spectrometer linearity and cross-contamination memory in the ion source.

CONCLUSIONS

The new RMs IAEA-610, IAEA-611 and IAEA-612 have been characterised on the VPDB δ¹³ C scale in a mutually consistent way. The use of three RMs will allow a consistent realisation of the VPDB δ¹³ C scale with small uncertainty to be established, and to reach metrological compatibility of measurement results over several decades.

Systematic comparison of post-column isotope dilution using LC-CO-IRMS with qNMR for amino acid purity determination

Determination of the purity of a substance traceable to the International System of Units (SI) is important for the production of reference materials affording traceability in quantitative measurements. Post-column isotope dilution using liquid chromatography-chemical oxidation-isotope ratio mass spectrometry (ID-LC-CO-IRMS) has previously been suggested as a means to determine the purity of organic compounds; however, the lack of an uncertainty budget has prevented assessment of the utility this approach until now. In this work, the previously published ID-LC-CO-IRMS methods have not only been improved by direct gravimetric determination of the mass flow of ¹³C-labelled spike but also a comprehensive uncertainty budget has been established. This enabled direct comparison of the well-characterised ID-LC-CO-IRMS method to quantitative nuclear magnetic resonance spectroscopy (qNMR) for purity determination using valine as the model compound. The ID-LC-CO-IRMS and qNMR methods provided results that were in agreement within the associated measurement uncertainty for the purity of a sample of valine of (97.1 ± 4.7)% and (99.64 ± 0.20)%, respectively (expanded uncertainties, k = 2). The magnitude of the measurement uncertainty for ID-LC-CO-IRMS determination of valine purity precludes the use of this method for determination of purity by direct analysis of the main component in the majority of situations; however, a mass balance approach is expected to result in significantly improved measurement uncertainty.

Practical and theoretical considerations for the determination of δ13 CVPDB values of methylmercury in the environment

RATIONALE

Analytical methods that can identify the source and fate of mercury and organomercury compounds are likely to be useful tools to investigate mercury in the environment. Carbon isotope ratio analysis of methylmercury (MeHg) together with mercury isotope ratios may offer a robust tool to study environmental cycling of organomercury compounds within fish tissues and other matrices.

METHODS

MeHg carbon isotope ratios were determined by gas chromatography/combustion-isotope ratio mass spectrometry (GC/C-IRMS) either directly or following derivatization using sodium tetraethylborate. The effects of a normalization protocol and of derivatization on the measurement uncertainty of the methylmercury δ¹³ C_VPDB values were investigated.

RESULTS

GC/C-IRMS analysis resulted in a δ¹³ C_VPDB value for an in-house MeHg reference material of δ¹³ C_VPDB  = -68.3 ± 7.7‰ (combined standard uncertainty, k = 1). This agreed very well with the value obtained by offline flow-injection analysis/chemical oxidation/isotope ratio mass spectrometry of δ¹³ C_VPDB  = -68.85 ± 0.17‰ (combined standard uncertainty, k = 1) although the uncertainty was substantially larger. The minimum amount of MeHg required for analysis was determined to be 20 μg.

CONCLUSIONS

While the δ¹³ C_VPDB values of MeHg can be obtained by GC/C-IRMS methods with or without derivatization, the low abundance of MeHg precludes such analyses in fish tissues unless there is substantial MeHg contamination. Environmental samples with sufficient MeHg pollution can be studied using these methods provided that the MeHg can be quantitatively extracted. The more general findings from this study regarding derivatization protocol implementation within an autosampler vial as well as measurement uncertainty associated with derivatization, normalization to reporting scales and integration are applicable to other GC/C-IRMS-based measurements.

Assessing Aerobic Biotransformation of Hexachlorocyclohexane Isomers by Compound-Specific Isotope Analysis

Contamination of soils and sediments with the highly persistent hexachlorocyclohexanes (HCHs) continues to be a threat for humans and the environment. Despite the existence of bacteria capable of biodegradation and cometabolic transformation of HCH isomers, such processes occur over time scales of decades and are thus challenging to assess. Here, we explored the use of compound-specific isotope analysis (CSIA) to track the aerobic biodegradation and biotransformation pathways of the most prominent isomers, namely, (-)-α-, (+)-α-, β-, γ-, and δ-HCH, through changes of their C and H isotope composition in assays of LinA2 and LinB enzymes. Dehydrochlorination of (+)-α-, γ-, and δ-HCH catalyzed by LinA2 was subject to substantial C and H isotope fraction with apparent ¹³C- and ²H-kinetic isotope effects (AKIEs) of up to 1.029 ± 0.001 and 6.7 ± 2.9, respectively, which are indicative of bimolecular eliminations. Hydrolytic dechlorination of δ-HCH by LinB exhibited even larger C but substantially smaller H isotope fractionation with ¹³C- and ²H-AKIEs of 1.073 ± 0.006 and 1.41 ± 0.04, respectively, which are typical for nucleophilic substitutions. The systematic evaluation of isomer-specific phenomena showed that, in addition to contaminant uptake limitations, diffusion-limited turnover ((-)-α-HCH), substrate dissolution (β-HCH), and potentially competing reactions catalyzed by constitutively expressed enzymes might bias the assessment of HCH biodegradation by CSIA at contaminated sites.

Kinetic Isotope Effects of the Enzymatic Transformation of γ-Hexachlorocyclohexane by the Lindane Dehydrochlorinase Variants LinA1 and LinA2

Compound-specific isotope analysis (CSIA) can provide insights into the natural attenuation processes of hexachlorocyclohexanes (HCHs), an important class of persistent organic pollutants. However, the interpretation of HCH stable isotope fractionation is conceptually challenging. HCHs exist as different conformers that can be converted into each other, and the enzymes responsible for their transformation discriminate among those HCH conformers. Here, we investigated the enzyme specificity of apparent ¹³C- and ²H-kinetic isotope effects (AKIEs) associated with the dehydrochlorination of γ-HCH (lindane) by two variants of the lindane dehydrochlorinases LinA1 and LinA2. While LinA1 and LinA2 attack γ-HCH at different trans-1,2-diaxial H-C-C-Cl moieties, the observed C and H isotope fractionation was large, typical for bimolecular eliminations, and was not affected by conformational mobility. ¹³C-AKIEs for transformation by LinA1 and LinA2 were the same (1.024 ± 0.001 and 1.025 ± 0.001, respectively), whereas ²H-AKIEs showed minor differences (2.4 ± 0.1 and 2.6 ± 0.1). Variations of isotope effects between LinA1 and LinA2 are small and in the range reported for different degrees of C-H bond cleavage in transition states of dehydrochlorination reactions. The large C and H isotope fractionation reported here for experiments with pure enzymes contrasts with previous observations from whole cell experiments and suggests that specific uptake processes by HCH-degrading microorganisms might modulate the observable HCH isotope fractionation at contaminated sites.

Calling all archaeologists: guidelines for terminology, methodology, data handling, and reporting when undertaking and reviewing stable isotope applications in archaeology

Stable isotope analysis has been utilized in archaeology since the 1970s, yet standardized protocols for terminology, sampling, pretreatment evaluation, calibration, quality assurance and control, data presentation, and graphical or statistical treatment still remain lacking in archaeological applications. Here, we present recommendations and requirements for each of these in the archaeological context of: bulk stable carbon and nitrogen isotope analysis of organics; bulk stable carbon and oxygen isotope analysis of carbonates; single compound stable carbon and nitrogen isotope analysis on amino acids in collagen and keratin; and single compound stable carbon and hydrogen isotope analysis on fatty acids. The protocols are based on recommendations from the Commission on Isotopic Abundances and Atomic Weights of the International Union of Pure and Applied Chemistry (IUPAC) as well as an expanding geochemical and archaeological science experimental literature. We hope that this will provide a useful future reference for authors and reviewers engaging with the growing number of stable isotope applications and datasets in archaeology.

Characterization of Substrate, Cosubstrate, and Product Isotope Effects Associated With Enzymatic Oxygenations of Organic Compounds Based on Compound-Specific Isotope Analysis

Enzymatic oxygenations are among the most important biodegradation and detoxification reactions of organic pollutants. In the environment, however, such natural attenuation processes are extremely difficult to monitor. Changes of stable isotope ratios of aromatic pollutants at natural isotopic abundances serve as proxies for isotope effects associated with oxygenation reactions. Such isotope fractionations offer new avenues for revealing the pathway and extent of pollutant transformation and provide new insights into the mechanisms of catalysis by Rieske non-heme ferrous iron oxygenases. Based on compound-specific C, H, N, and O isotope analysis, we present a comprehensive methodology with which isotope effects can be derived from the isotope fractionation measured in substrates, the cosubstrate O₂, and organic oxygenation products. We use dioxygenation of nitrobenzene and 2-nitrotoluene by nitrobenzene dioxygenase as illustrative examples to introduce different mathematical procedures for deriving apparent substrate and product isotope effects. We present two experimental approaches to control reactant and product turnover for isotope fractionation analysis in experimental systems containing purified enzymes, E. coli clones, and pure strains of environmental microorganisms. Finally, we present instrumental procedures and sample treatment instructions for analysis of C, H, and N isotope analysis in organic compounds and O isotope analysis in aqueous O₂ by gas and liquid chromatography coupled to isotope ratio mass spectrometry.