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An interlaboratory comparison (ILC)was organised to characterise 87Sr/86Sr isotope ratios in geological and industrial reference materials by applying the so-called conventional method for determining 87Sr/86Sr isotope ratios. Four cements (VDZ 100a,VDZ 200a, VDZ 300a, IAG OPC-1), one limestone (IAG CGL ML-3) and one slate (IAG OU-6) reference materials were selected, covering a wide range of naturally occurring Sr isotopic signatures. Thirteen laboratories received aliquots of these six reference materials together with a detailed technical protocol. The consensus values for the six reference materials and their associated measurement uncertainties were obtained by applying a Gaussian, linear mixed effects model fitted to all the measurement results. By combining the consensus values and their uncertainties with an uncertainty contribution for potential heterogeneity, reference values ranging from 0.708134 mol mol-1 to 0.729778 mol mol-1 were obtained with relative expanded uncertainties of ≤ 0.007 %. This study represents an ILC on conventional 87Sr/86Sr isotope ratios, within which metrological principles were considered and the compatibility of measurement results obtained by MC-ICP-MS and by MC-TIMS is demonstrated. The materials characterised in this study can be used as reference materials for validation and quality control purposes and to estimate measurement uncertainties in conventional 87Sr/86Sr isotope ratio measurement.
Isotope ratio applications are on the increase and a major part of which are delta measurements, because they are easier to perform than the determination of absolute isotope ratios while offering lower measurement uncertainties. Delta measurements use artefact-based scales and therefore scale conversions are required due to the lack of the scale defining standards. Such scale conversions often form the basis for comparing data being generated in numerous projects andtherefore need to be as accurate as possible. In practice, users are tempted to apply linear approximations, which are not sufficiently exact, because delta values are defined by nonlinear relationships. The bias of such approximations often is beyond typical measurement uncertainties and its extent can hardly be predicted. Therefore, exact calculations are advised. Here, the exact equations and the bias of the approximations are presented, and calculations are illustrated by real-world examples. Measurement uncertainty is indispensable in this context and therefore, its calculation is described as well for determining delta values but also for scale conversions. Approaches for obtaining a single delta measurement and for repeated measurements are presented. For the latter case, a new approach for calculating the measurement uncertainty is presented, which considers covariances between the isotope ratios.
The Uncertainty Paradox: Molar Mass of Enriched Versus Natural Silicon Used in the XRCD Method
(2020)
The X-ray crystal density method uses silicon spheres highly enriched in 28Si as a primary method for the dissemination of the SI base unit kilogram yielding smallest possible uncertainties associated with the mass m within a few parts in 10-8. This study compares different available and newly developed analytical methods and their results for the determination of the molar mass M of silicon highly enriched in 28Si (Me) and of silicon (Mx) with an almost natural isotopic distribution. While for Me relative uncertainties urel(Me) in the lower 10-9 range are obtained routinely, it was not possible to fall below a value of urel(Mx) < 4 x 10-6 in the case of natural silicon, which is approximately three orders of magnitude larger. The application of the state-of the-art isotope ratio mass spectrometry accompanied with sophisticated thoroughly investigated methods suggests an intrinsic cause for the large uncertainty associated with the molar mass of natural silicon compared to the enriched material.