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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.
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.
A new method combining isotope dilution mass spectrometry (IDMS) and standard addition has been developed to determine the mass fractions w of different elements in complex matrices: (a) silicon in aqueous tetramethylammonium hydroxide (TMAH), (b) sulfur in biodiesel fuel, and (c) iron bound to transferrin in human serum. All measurements were carried out using inductively coupled plasma mass spectrometry (ICP–MS). The method requires the gravimetric preparation of several blends (bi)—each consisting of roughly the same masses (mx,i) of the sample solution (x) and my,i of a spike solution (y) plus different masses (mz,i) of a reference solution (z).
Only these masses and the isotope ratios (Rb,i) in the blends and reference and spike solutions have to be measured. The derivation of the underlying equations based on linear regression is presented and compared to a related concept reported by Pagliano and Meija. The uncertainties achievable, e.g., in the case of the Si blank in extremely pure TMAH of urel (w(Si)) = 90% (linear regression method, this work) and urel (w(Si)) = 150% (the method reported by Pagliano and Meija) seem to suggest better applicability of the new method in practical use due to the higher robustness of regression analysis.
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.
Accurate and precise isotope ratio measurements of heavy elements are playing an increasinglyimportant role in modern analytical sciences and have numerous applications. Today, isotope ratio measurements are typically performed with two principal techniques: thermal ionization mass spectrometry (TIMS) and multiple collector-inductively coupled plasma mass spectrometry (MC-ICP-MS). To obtain accurate results by mass spectrometry, isotopic certified reference materials (iCRMs) are needed for mass bias correction and for the validation of the method used for analysis.Thus, it is of paramount importance to achieve measurement comparability of all data reported, and to assess measurement capability of each CRM producer/National Metrology Institute (NMI). Therefore, the international comparison (CCQM-P213) was performed to assess the analytical capabilities of NMIs for the accurate determination of copper isotope ratio delta values in high purity materials. The study was proposed by the coordinating laboratories, National Research Council Canada (NRC), National Institute of Standards and Technology (NIST), Bundesanstalt für Materialforschung und -prüfung (BAM) and Physikalisch-Technische Bundesanstalt (PTB), as an activity of the Isotope Ratio Working Group (IRWG) of the Consultative Committee for Amount of Substance - Metrology in Chemistry and Biology (CCQM). Participants included six NMIs and one designated institute (DI) from the six countries. Although no measurement method was prescribed by the coordinating laboratories, MC-ICP-MS with either standard-sample bracketing (SSB) or combined SSB with internal normalization (C-SSBIN) models for mass bias correction were recommended. Results obtained from the six NMIs and one DI were in good agreement.
This dataset represents the electronic supplementary material (ESM) of the publication entitled "Characterisation of conventional 87Sr/86Sr isotope ratios in cement, limestone and slate reference materials based on an interlaboratory comparison study", which is published in Geostandards and Geoanalytical Research under the DOI: 10.1111/GGR.12517. It consists of four files. 'ESM_Data.xlsx' contains all reported data of the participants, a description of the applied analytical procedures, basic calculations, the consensus values, and part of the uncertainty assessment. 'ESM_Figure-S1' displays a schematic on how measurements, sequences and replicates are treated for the uncertainty calculation carried out by PTB. 'ESM_Technical-protocol.pdf' is the technical protocol of the interlaboratory comparison, which has been provided to all participants together with the samples and which contains bedside others the definition of the measurand and guidelines for data assessment and calculations. 'ESM_Reporting-template.xlsx' is the Excel template which has been submitted to all participants for reporting their results within the interlaboratory comparison. Excel files with names of the the structure 'GeoReM_Material_Sr8786_Date.xlsx' represent the Rcon(87Sr/86Sr) data for a specific reference material downloaded from GeoReM at the specified date, e.g. 'GeoReM_IAPSO_Sr8786_20221115.xlsx' contains all Rcon(87Sr/86Sr) data for the IAPSO seawater standard listed in GeoReM until 15 November 2022.
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.
A new method combining isotope dilution mass spectrometry (IDMS) and standard addition has been developed to determine the mass fractions w of different elements in complex matrices: (a) silicon in aqueous tetramethylammonium hydroxide (TMAH), (b) sulfur in biodiesel fuel, and (c) iron bound to transferrin in human serum. All measurements were carried out using inductively coupled plasma mass spectrometry (ICP–MS). The method requires the gravimetric preparation of several blends (bi)—each consisting of roughly the same masses (mx,i) of the sample solution (x) and my,i of a spike solution (y) plus different masses (mz,i) of a reference solution (z).
Only these masses and the isotope ratios (Rb,i) in the blends and reference and spike solutions have to be measured. The derivation of the underlying equations based on linear regression is presented and compared to a related concept reported by Pagliano and Meija. The uncertainties achievable, e.g., in the case of the Si blank in extremely pure TMAH of urel (w(Si)) = 90% (linear regression method, this work) and urel (w(Si)) = 150% (the method reported by Pagliano and Meija) seem to suggest better applicability of the new method in practical use due to the higher robustness of regression analysis.
Determination of absolute (SI‐traceable) isotope ratios: The use of Gravimetric Isotope Mixtures
(2023)
The presentation is brief overview on how to use gravimetric isotope mixtures to determine SI traceable isotope ratios. There is no mass spectrometer on earth that directly measures isotope ratios. Mass spectrometers will always measure signal intensity ratios instead. The actual problem is that the measured intensity ratios differ more or less from the isotope ratios. The difference can be up to more than 10 % in case of lithium while it‘s below 1 % in case of the heavier elements like lead or uranium. Consequently, the signal intensity ratios are expressed for example in V/V depending on the type of mass spectrometer you are using, while the isotope ratios are expressed in mol/mol. This phenomenon is called Instrumental Isotopic Fractionation (or short IIF) but the more common name is still mass bias (even though this name is not entirely correct). To convert the measured into the isotope ratio usually a simple multiplication with a so-called correction (or short K) factor is done. Therefore, the problem is to determine the K factor. In absence of isotope reference materials the golden route is via gravimetric isotope mixtures, which will be explained within the presentation.