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Multi-collector inductively coupled plasma-mass spectrometry (MC-ICP-MS) has evolved significantly since its introduction in 1992. The second and third generation instruments now allow isotope ratio measurements at unprecedented precisions, 0.001 % or better. However, precision alone is not enough for producing accurate and reliable isotope ratio measurements. Metrological considerations such as the selection of suitable calibration strategies, proper assessment of instrumental biases, and the estimation of overall measurement uncertainty remain critical to the measurement process. Properly assessed, measurement uncertainty then provides the interval within which a result can be considered both accurate and precise.
All mass spectrometric measurements are affected by instrumental mass discrimination and produce isotope ratios that are biased relative to their “true” ratio. To produce accurate and traceable isotope ratio measurements, it is imperative that certified isotope reference materials (iCRMs) be used for calibration and validation purposes. iCRMs reporting absolute isotope ratios are an analyst’s first choice, particularly when its uncertainty is sufficient for the intended use. However, when smaller uncertainties are required to resolve subtle differences between samples, delta-scale measurements become important. Here, the difference between an isotope ratio measured in a sample and in an internationally accepted isotope reference material (iRM) is determined. This deviation can be positive or negative relative to the iRM, is called a delta value, and is often expressed in per mil units.
This presentation will highlight the potential for MC-ICP-MS to produce isotope ratio measurements with minimal uncertainties by examining three applications involving Mg isotopes: 1) the certification of a set of iCRMs for their absolute isotope ratio using a gravimetric isotope mixture approach; 2) the comparison of these iCRMs with currently accepted Mg delta-scale reference materials through intercalibration, and 3) the determination of isotope fractionation exponents for geochemical applications.
In the past, δ26/24Mg measurements were referenced to NIST SRM 980, the initial zero of the δ26/24Mg scale. With the development of MC-ICPMS, the detection of small but measurable isotopic differences in different chips of SRM 980 became apparent. To solve this problem a suite of magnesium isotope reference materials, ERM-AE143, -AE144 and -AE145, has been certified in a first study by applying an ab initio calibration for absolute Mg isotope ratios without any a priori assumptions, a procedure which fulfils all requirements of a primary method of measurement. We could achieve for the first time measurement uncertainties for isotope amount ratios close to the typical precision of magnesium delta values, δ26/24Mg, which are at the 0.1 ‰ level (2SD). In addition, it was demonstrated that commonly used fractionation laws are invalid for correcting Mg isotope ratios in multi-collector ICPMS as they result in a bias which is not covered by its associated uncertainty. Depending on their type, fractionation laws create a bias up to several per mil, with the exponential law showing the smallest bias between 0.1 ‰ to 0.7 ‰.
With these isotope reference materials, it is possible to establish SI-traceability for magnesium delta measurements. To realize this, we organized a second study within which five expert laboratories participated to cross-calibrate all available magnesium isotope standards, which are NIST SRM 980, IRMM-009, ERM-AE143, ERM-AE144, ERM-AE145 and the standards DSM3 and Cambridge-1. The mean δ26/24Mg values for the individual iRMs, calculated from the laboratory means show 2 SD reproducibilities varying between 0.025 and 0.093 ‰. Propagated measurement uncertainties suggest a standard uncertainty of about 0.1‰ for δ26/24Mg determinations (2SD). Thus, SI traceability for magnesium isotope amount ratios and delta values is demonstrated to be established.
The continuous improvement of analytical procedures using multi-collector technologies in ICP-mass spectrometry has led to an increased demand for isotope standards with improved homogeneity and reduced measurement uncertainty. For magnesium, this has led to a variety of available standards with different quality levels ranging from artefact standards to isotope reference materials certified for absolute isotope ratios. This required an intercalibration of all standards and reference materials, which we present in this interlaboratory comparison study. The materials Cambridge1, DSM3, ERMAE143, ERM-AE144, ERM-AE145, IRMM-009 and NIST SRM 980 were cross-calibrated with expanded measurement uncertainties (95% confidence level) of less than 0.030‰ for the δ25/24Mg values and less than 0.037‰ for the δ26/24Mg values. Thus, comparability of all magnesium isotope delta (δ) measurements based on these standards and reference materials is established. Further, ERM-AE143 anchors all magnesium δ-scales to absolute isotope ratios and therefore establishes SI traceability, here traceability to the SI base unit mole. This applies especially to the DSM3 scale, which is proposed to be maintained. With ERM-AE144 and ERM-AE145, which are product and educt of a sublimation-condensation process, for the first time a set of isotope reference materials is available with a published value for the apparent triple isotope fractionation exponent θapp, the fractionation relationship ln α(25/24Mg)/ln α(26/24Mg).
The determination of the mass fractions of bromide, sulfate, and lead as well as the isotopic composition of the lead (expressed as the molar mass and the amount fractions of all four stable lead isotopes) in an aqueous solution of sodium chloride with a mass fraction of 0.15 g/g was the subject of this comparison. Even though the mass fractions ranged from 3 μg/g (bromide) to 50 ng/g (lead), almost all results reported agreed with the according KCRVs.
An introduction into absolute isotope ratios is given, with application fields ranging from fundamental science to geochronology and forensics. This is followed by a proposal for developing new calibration approaches for obtaining absolute isotope ratios at unrivaled uncertainty levels. This new developments will set the basis for improvements in all scientific fields.
An international comparison study on the accurate determination of the molar mass M(Si) of silicon artificially enriched in 28Si (x(28Si) > 0.9999 mol mol−1) has been completed. The measurements were part of the high level CCQM-P160 pilot study assessing the ability of National Metrology Institutes (NMIs) and Designated Institutes (DIs) to make such measurements at the lowest possible levels of measurement uncertainty and to identify possible difficulties when measuring this kind of sample. This study supports the molar mass measurements critical to disseminating the silicon route to realizing the new definitions for the kilogram and the mole. Measurements were also made by one external research institute and an external company. The different institutes were free to choose their experimental (mass spectrometric) set-ups and equipment, thereby enabling also the comparison of different techniques. The investigated material was a chemically pure, polycrystalline silicon material. The subsequent modified single crystalline secondary product of this material was intended for the production of silicon which was used for two additional spheres in the context of the redetermination of the Avogadro constant NA, required for the revision of the International System of Units (SI) via fundamental constants which came into force from May 2019. The CCQM pilot study was organized by Physikalisch-Technische Bundesanstalt (PTB). Aqueous silicon solutions were shipped to all participating institutions. The data analysis as well as the uncertainty modelling and calculation of the results was predefined. The participants were provided with an uncertainty budget as a GUM Workbench® file as well as a free software license for the duration of the comparison. The agreement of the values of the molar mass (M(Si) = 27.976 942 577 g mol−1) was excellent with ten out of 11 results reported within the range of relative uncertainty of 1 × 10−8 required
for the revision of the SI.
The theory of a new calibration approach for obtaining absolute isotope ratios of multi-isotopic elements without the use of any standard has been developed. The calibration approach basically uses the difference in the instrumental isotope fractionation of two different types of mass spectrometers, leading to two different fractionation lines in a three-isotope diagram. When measuring the same sample with both mass spectrometers, the different fractionation lines have one point in common: this is the ‘true’ logarithmized isotope ratio pair of the sample. Thus, the intersection of both fractionation lines provides us with the absolute isotope ratios of the sample. This theory has been tested in practice by measuring Cd and of Pb isotope ratios in the certified reference materials BAM-I012 and NIST SRM981 by thermal ionization mass spectrometry and by inductively coupled plasma mass spectrometry while varying the ionization conditions for both mass spectrometers. With this experiment, the theory could be verified, and absolute isotope ratios were obtained, which were metrologically compatible with the certified isotope ratios. The so-obtained absolute isotope ratios are biased by − 0.5% in average, which should be improved with further developments of the method. This calibration approach is universal, as it can be applied to all elements with three or more isotopes and it is not limited to the type of mass spectrometers applied; it can be applied as well to secondary ion mass spectrometry or others. Additionally, this approach provides information on the fractionation process itself via the triple-isotope fractionation exponent θ.
The calibration of isotope ratio measurements is an ongoing challenge since instrumental isotope fractionation (IIF) has been detected in mass spectrometry (MS). There is a variety of approaches which either bypass IIF such as delta measurements or refer to reference materials (RMs) and thus shifting the problem of calibration to somebody else: the RM producer. For certifying isotope RMs with absolute isotope ratios only a few approaches are available, namely the isotope mixture approach, the double spike approach, the mass bias regression model and total evaporation in TIMS. All of them require either enriched isotopes, isotope RMs of another element or an RM for correcting residual error. As the enriched isotopes required for the isotope mixture and the double spike approach need to be fully characterized beforehand, all mentioned calibration approaches require a standard.
Here, a new and standard-free calibration approach for obtaining absolute isotope ratios of multi-isotopic elements has been developed. The underlying principle is that each MS suffers from IIF and thus yields a specific isotope fractionation line in a three-isotope diagram. When applying a second MS featuring a different ionization mechanism, we obtain a second isotope fractionation line with a different slope in the same three-isotope diagram. In both cases the absolute isotope ratios range somewhere on the isotope fractionation line. Consequentially, the intersect of both lines yield the absolute isotope ratios of the measured sample. This theory has been tested by measuring Cd and Pb isotope ratios of suitable isotope RMs with a TIMS and an ICP-MS, both equipped with multi-collector array. During the measurements the ionization conditions were changed such that different extent of the isotope fractionation has been achieved. With the resulting data set the theory described above could be verified. The obtained absolute isotope ratios were metrologically compatible with the certified isotope ratios. The remaining average bias of -5 ‰ can be reduced with further improvements. The calibration approach is universal and can be applied to any multi-isotopic element and it is not limited by the type of the mass spectrometer.