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Several highly-enriched 28Si crystals were produced to enable a better determination of the Avogadro constant through removing the uncertainty associated with the abundance determination of the minor isotopes 29Si and 30Si.

Like in the previously published LA-ICP-MS method, the sample itself acts as the perfectly matrix matched reference material, but the combination with isotope dilution improves the uncertainty and accuracy of the novel LA-ID-ICP-MS method.

This Feature highlights the role of metrology, the science of measurement, in maintaining the infrastructure we all rely on for accurate chemical measurements. In particular, the recent change to the definition of the mole, the unit of chemistry, is explained.

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) −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.

The present work introduces a novel approach for the quantitative and SI-traceable analysis of element contents in solid materials with laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). The laser ablation and the nebulizer system were connected to the torch using a y-piece. Several standard solutions having well-known element contents were introduced one after the other into the plasma simultaneously with the ablated material. In contrast to all other quantification methods the solid sample itself serves as the reference and the content of an analyte element was calculated based on the well-known content of the matrix element (like Si in a glass sample). Equations to describe the novel method were derived inspired by the standard addition method. To investigate the feasibility of the novel method, the contents of Pb and Rb were analysed in two commercially available standard reference materials (NIST SRM 610 and 612 glass samples). These solid samples were analysed together with solutions of different mass fractions of silicon as the reference element (R) and lead or rubidium as the analyte elements (A). The mass fractions of Pb and Rb measured in the two certified reference materials (CRMs) were equal to the certified values within the limits of their expanded uncertainties (U(wx(A)) with k = 2). Compared to other quantification methods, this new method enables SI-traceability for the measurement results without the need to employ preferably matrix-matched solid reference materials, which will be a great benefit for the application of laser ablation in general, especially considering the extreme lack of matrix-matched CRMs. The new method is best-suited to determine impurities in highly pure samples with a mass fraction of the matrix element close to 1 g g−1.

One way of obtaining isotope ratios, traceable to the International System of Units, is the gravimetric isotope mixtures method. Adapting this method to carbon dioxide is challenging since measuring all twelve isotopologues at once with a gas mass spectrometer is currently not possible. The calculation of the mass bias correction factors is no straightforward task due to the fact that the isotopic equilibrium has to be considered. This publication demonstrates a potential way of adapting this method to carbon dioxide while considering isotope equilibrium. We also show how we prepared binary blends from enriched/depleted carbon dioxide parent gases and how equilibrating the different gases by heating affects the measurements. Furthermore, we reveal mathematical limitations of our approach when the gases are not in isotope equilibrium and which issues occur due to measurement limitations. In a simulation, using authentic data, we asses our approach in terms of achievable uncertainties and discuss further improvements, like using atomic spectroscopy methods.

Absolute isotope ratios cannot be determined directly by mass spectrometry. The measured ion intensities are biased by many effects like mass fractionation or discrimination and amplifier gain. To correct the ion intensities, calibration factors are needed. These calibration factors can be derived by comparing the known isotope ratios of a reference material and its measured intensity ratios, provided that these materials have been characterized traceable to the International System of Units (SI). As mentioned above, absolute isotope ratios are not directly available but are necessary for calibration. Thus, if there is no well-characterized reference material or it is out of stock, another solution for this problem must be found. Nier [Nier, 1950] already presented a solution for this problem through gravimetrically prepared mixtures back in 1950. Mana and Rienitz [Mana and Rienitz, 2010] derived an analytical solution for the needed calibration factors for a system of three isotopes from this idea. Until then, calibration factors could only be determined iteratively. This paper shows how calibration factors can be derived from gravimetrically prepared mixtures for a system of any number of isotopes. In contrast to iterative methods, the method presented here is not affected by possible poor convergence or local minima. The subsequent uncertainty propagation is much more straightforward being another big advantage. Two examples are given to demonstrate the overall validity of this approach. In the first example, this approach is applied to the seven-isotope system of mercury. In the second, using carbon dioxide, it is shown that this method can also be applied to a system of twelve isotopologues. Additionally, we present an EXCEL® application GIMiCK, which allows every user to calculate calibration factors for any number of isotopes and isotopologues.

Lead isotope amount ratios are commonly used in diverse fields such as archaeometry, geochemistry and forensic science. Currently, five reference materials with certified lead isotope amount ratios are available, namely NIST SRM 981, 982 and 983, GBW-04442 and NMIJ 3681-a. Only NIST SRM 981 and NMIJ 3681-a have approximately natural isotopic compositions, and NIST SRM 981 is predominantly used for correcting mass discrimination/mass fractionation in the applied mass spectrometric procedures. Consequently, there is no other certified reference material available to be used for validation and/or quality control of the analytical procedures applied to lead isotope amount ratio measurements. To fill this gap, two new reference materials have been produced and certified for their lead isotope amount ratios. For both certified reference materials, complete uncertainty budgets have been calculated and SI traceability has been established. This provides the users with independent means for validating and verifying their analytical procedures and for conducting quality control measures. ERM-EB400 is a bronze material with a nominal lead mass fraction of 45 mg kg-1 and certified lead isotope amount ratios of n(206Pb)/n(204Pb) = 18.072(17) mol mol-1, n(207Pb)/n(204Pb) = 15.578(18) mol mol-1 and n(208Pb)/n(204Pb) = 38.075(46) mol mol-1 with the associated expanded uncertainties (k = 2) given in brackets. ERM-AE142 is a high-purity solution of lead in 2% nitric acid with a nominal mass fraction of 100 mg kg-1 and certified Pb isotope amount ratios of n(206Pb)/n(204Pb) = 21.114(17) mol mol-1, n(207Pb)/n(204Pb) = 15.944(17) mol mol-1 and n(208Pb)/n(204Pb) = 39.850(44) mol mol-1 with the associated expanded uncertainties (k = 2) given in brackets. Both materials are specifically designed to fall within the natural lead isotopic variation and to assist users with the validation and verification of their analytical procedures. Note that while one of these reference materials requires the chemical separation of Pb from its matrix (ERM-EB400), the other does not (ERM-AE142). As additional information, δ208/206PbNIST SRM981 values are provided for both materials. For ERM-AE142, a delta value of δ208/206PbNIST SRM981 = -28.21(30) ‰ was obtained, and for ERM-EB400, a delta value of δ208/206PbNIST SRM981 = -129.47(38) ‰ was obtained, with the associated expanded uncertainties (k = 2) given in brackets.

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.

Main text CCQM-K143 is a key comparison that assesses participants' ability to prepare single element calibration solutions. Preparing calibration solutions properly is the cornerstone of establishing a traceability link to the International System of Units (SI), and therefore should be tested in order to confirm the validity of CCQM comparisons of more complex materials. CCQM-K143 consisted of participants each preparing a single copper calibration solution at 10 g/kg copper mass fraction and shipping 10 bottled aliquots of that solution to the coordinating laboratory, the National Institute of Standards and Technology (NIST). The masses and mass fraction for the prepared solutions were documented with the submitted samples. The solutions prepared by all participants were measured at NIST by high performance inductively coupled plasma optical emission spectroscopy (HP-ICP-OES). The intensity measurements for copper were not mapped onto values of mass fraction via calibration. Instead, ratios were computed between the measurements for copper and simultaneous measurements for manganese, the internal standard, and all subsequent data reductions, including the computation of the KCRV and the degrees of equivalence, were based on these ratios. Other than for two participants whose measurement results appeared to suffer from calculation or preparation errors, all unilateral degrees of equivalence showed that the measured values did not differ significantly from the KCRV. These results were confirmed by a second set of ICP-OES measurements performed by the Physikalisch-Technische Bundesanstalt (PTB). CCQM-K143 showed that participants are capable of preparing calibration solutions starting from high purity, assayed copper metal. Similar steps are involved when preparing solutions for other elements, so it seems safe to infer that similar capabilities should prevail when preparing many different, single-element solutions. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/. The final report has been peer-reviewed and approved for publication by the CCQM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

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 isotopic composition and molar mass M of silicon in a new crystal (code: Si28-33Pr11) measured by isotope ratio mass spectrometry using a high-resolution multicollector-inductively coupled plasma mass spectrometer (MC-ICP-MS) is presented using the virtual-element isotope dilution mass spectrometry (VE-IDMS) method. For this new crystal, M = 27.976 950 48 (16) g/mol was determined with urel(M) = 5.7 &times, 10&minus, 9. The &ldquo, X-ray-crystal-density (XRCD) method&rdquo, one of the primary methods for realizing and disseminating the SI units kilogram and mole in the recently revised SI, is based on &ldquo, counting&rdquo, silicon atoms in silicon single crystal spheres. One of the key quantities is the isotopic composition&mdash, expressed by the molar mass M&mdash, of the three stable isotopes 28Si, 29Si, and 30Si in the material highly enriched in 28Si. M was determined with lowest possible uncertainty using latest improvements of the experimental techniques. All uncertainties were estimated according to the &ldquo, Guide to the expression of uncertainty in measurement, GUM&rdquo, The results of the new crystal are discussed and compared with the four previously available crystals, establishing a worldwide limited pool of primary reference spheres of highest metrological quality.

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, ERM-AE143, 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 molar mass M and isotopic composition (expressed in amount-of-substance fractions x( i Si) of the silicon isotopes 28Si, 29Si, and 30Si) of a new silicon crystal (notation: Si28-23Pr11) highly enriched in the 28Si isotope have been determined independently at PTB and NMIJ by measuring exactly the same sample solutions using both a high resolution multicollector-inductively coupled plasma mass spectrometer (MC-ICP-MS). This crystal will be used for the complementary determination of the Avogadro constant N A and thus providing one of many key parameters in the planned redefinition of the SI units kilogram and mole, using fundamental constants. Samples from three different axial positions in the crystal ingot, each divided into several radial positions were measured in order to probe possible variations of the molar mass and isotopic composition. Results obtained at PTB and NMIJ agreed within the limits of uncertainty. The application of the latest improved measurement techniques as well as an improved determination of the calibration factors (K) required to correct for mass bias effects resulted in an averaged M = 27.976 942 666(40) g mol−1 with a relative combined uncertainty u c,rel(M) = 1.4 × 10−9. The course of M as a function of the origin of the measured samples suggests no significant inhomogeneity within the limits of the claimed uncertainty throughout the crystal supporting its applicability for the determination of a new N A. This extends to x(28Si) and x(29Si). Variations in x(30Si) as a function of the sample location were observed, but a systematic relation to physical origins cannot be claimed. Compared to the previous silicon crystal ('AVO28', notation: Si28-10Pr11) used for the latest determination of N A, the enrichment increases from x(28Si) = 0.999 957 52(12) mol mol−1 ('AVO28') to x(28Si) = 0.999 984 470(39) mol mol−1 (Si28-23Pr11, discussed in this paper) which is at least in part responsible for a reduction of the associated measurement uncertainty u(M).

Following the revision of the International System of Units (SI), that takes effect on 20 May 2019, the unit mole is defined by using a fixed number of elementary entities. This number is the fixed numerical value of the Avogadro constant, which is the defining constant of the unit mole. This definition was made possible because the determination of the Avogadro constant had reached a level of relative uncertainty that allowed its value to be fixed and, at the same time, safeguard continuity of measurement results before and after the definition. The motivation for the revision of the SI and the mole in particular will be explained and the experimental work that allowed it is summarized.

For the first time, an international comparison was conducted on the determination of the purity of a high purity element. Participants were free to choose any analytical approach appropriate for their institute's applications and services. The material tested was a high purity zinc, which had earlier been assessed for homogeneity and previously used in CCQM-K72 for the determination of six defined metallic impurities. Either a direct metal assay of the Zn mass fraction was undertaken by EDTA titrimetry, or an indirect approach was used wherein all impurities, or at least the major ones, were determined and their sum subtracted from ideal purity of 100%, or 1 kg kg−1. Impurity assessment techniques included glow discharge mass spectrometry, inductively coupled plasma mass spectrometry and carrier gas hot extraction/combustion analysis. Up to 91 elemental impurities covering metals, non-metals and semi-metals/metalloids were quantified. Due to the lack of internal experience or experimental capabilities, some participants contracted external laboratories for specific analytical tasks, mainly for the analysis of non-metals. The reported purity, expressed as zinc mass fraction in the high purity zinc material, showed excellent agreement for all participants, with a relative standard deviation of 0.011%. The calculated reference value, w(Zn) = 0.999 873 kg kg−1, was assigned an asymmetric combined uncertainty of +0.000 025 kg kg−1 and −0.000 028 kg kg−1. Comparability amongst participating metrology institutes is thus demonstrated for the purity determination of high purity metals which have no particular difficulties with their decomposition/dissolution process when solution-based analytical methods are used, or which do not have specific difficulties when direct analysis approaches are used. Nevertheless, further development is required in terms of uncertainty assessment, quantification of non-metals and the determination of purity of less pure elements and/or for those elements suffering difficulties with the decomposition process.

A new generation of silicon crystals even further enriched in (28)Si (x((28)Si)0.999 98 mol/mol), recently produced by companies and institutes in Russia within the framework of a project initiated by PTB, were investigated with respect to their isotopic composition and molar mass M(Si). A modified isotope dilution mass spectrometric (IDMS) method treating the silicon as the matrix containing a so-called virtual element (VE) existing of the isotopes (29)Si and (30)Si solely and high resolution multicollector inductively coupled plasma mass spectrometry (MC-ICP-MS) were applied in combination. This method succeeds also when examining the new materials holding merely trace amounts of (29)Si (x((29)Si) ≈ 5 × 10(-6) mol/mol) and (30)Si (x((30)Si) ≈ 7 × 10(-7) mol/mol) extremely difficult to detect with lowest uncertainty. However, there is a need for validating the enrichment in (28)Si already in the precursor material of the final crystals, silicon tetrafluoride (SiF4) gas prior to crystal production. For that purpose, the isotopic composition of selected SiF4 samples was determined using a multicollector magnetic sector field gas-phase isotope ratio mass spectrometer. Contaminations of SiF4 by natural silicon due to storing and during the isotope ratio mass spectrometry (IRMS) measurements were observed and quantified. The respective MC-ICP-MS measurements of the corresponding crystal samples show-in contrast-several advantages compared to gas phase IRMS. M(Si) of the new crystals were determined to some extent with uncertainties urel(M)1 × 10(-9). This study presents a clear dependence of the uncertainty urel(M(Si)) on the degree of enrichment in (28)Si. This leads to a reduction of urel(M(Si)) during the past decade by almost 3 orders of magnitude and thus further reduces the uncertainty of the Avogadro constant NA which is one of the preconditions for the redefinition of the SI unit kilogram.

We report an appropriate preparation of binary isotope calibration mixtures of the three stable isotopes of magnesium to be used in the ab initio calibration of multicollector mass spectrometers (ICPMS and TIMS). For each of the three possible combinations of binary mixtures (“24Mg” + “25Mg”, “24Mg” + “26Mg”, and “25Mg” + “26Mg”), three individual setups have been prepared under gravimetric control, each of them with an isotope ratio close to unity, and a total magnesium mass fraction close to 20 mg kg−1. The preparation was designed to occur via an intermediate dilution of a parent solution of a highly purified specimen of the isotopically enriched magnesium materials. For the application as calibration mixtures, a complete uncertainty budget was set up, and is presented and discussed in detail, including the aspects that went into the design of the dilution and mixing approach to minimize uncertainty. The principle parameters for the purpose of the later calibration of the mass spectrometers are the absolute masses of isotopically enriched magnesium materials in the primary calibration mixtures. For the first time relative expanded uncertainties U (k = 2) for these masses of ≤0.005% could be achieved for all mixtures.

For the first time, an ab initio calibration for absolute Mg isotope ratios was carried out, without making any a priori assumptions. All quantities influencing the calibration such as the purity of the enriched isotopes or liquid and solid densities were carefully analysed and their associated uncertainties were considered. A second unique aspect was the preparation of three sets of calibration solutions, which were applied to calibrate three multicollector ICPMS instruments by quantifying the correction factors for instrumental mass discrimination. Those fully calibrated mass spectrometers were then used to determine the absolute Mg isotope ratios in three candidate European Reference Materials (ERM)-AE143, -AE144 and -AE145, with ERM-AE143 becoming the new primary isotopic reference material for absolute isotope ratio and delta measurements. The isotope amount ratios of ERM-AE143 are n(25Mg)/n(24Mg) = 0.126590(20) mol mol−1 and n(26Mg)/n(24Mg) = 0.139362(43) mol mol−1, with the resulting isotope amount fractions of x(24Mg) = 0.789920(46) mol mol−1, x(25Mg) = 0.099996(14) mol mol−1 and x(26Mg) = 0.110085(28) mol mol−1 and an atomic weight of Ar(Mg) = 24.305017(73); all uncertainties were stated for k = 2. This isotopic composition is identical within uncertainties to those stated on the NIST SRM 980 certificate. The candidate materials ERM-AE144 and -AE145 are isotopically lighter than ERM-AE143 by −1.6‰ and −1.3‰, respectively, concerning their n(26Mg)/n(24Mg) ratio. The relative combined standard uncertainties are ≤0.1‰ for the isotope ratio n(25Mg)/n(24Mg) and ≤0.15‰ for the isotope ratio n(26Mg)/n(24Mg). In addition to characterizing the new isotopic reference materials, it was demonstrated that commonly used fractionation laws are invalid for correcting Mg isotope ratios in multicollector 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‰ and 0.7‰.

A complete uncertainty budget including all relevant uncertainty contributions is one of the requirements for an unbroken traceability chain to the International System of Units (SI). Measured ion intensity ratios need to be corrected for any mass bias effects. Correcting the measured ratios is usually done with mass bias correction factors (K-factors). These can be derived from gravimetric isotope mixtures. The resulting absolute isotope ratios are traceable to the SI, provided the uncertainty contribution stemming from the calibration is also considered. Since the computation of K-factors for even small systems containing only a small number of isotopes is challenging, the uncertainty evaluation is also not a straightforward task. This paper presents a way of calculating the uncertainty associated with calibration factors by applying the Monte Carlo method. An EXCEL-based tool is presented that is capable of performing such uncertainty calculations for systems with up to 12 isotopes. Additionally, two examples are given to demonstrate the application of this tool and to validate it.

The isotopic compositions (molar mass, M) of the first and new silicon crystals highly enriched in $^{28}\text{Si}(> 99.99\ \%)$ used for the determination of the Avogadro constant were measured using a high resolution multicollector ICP mass spectrometer and applying a modified isotope dilution mass spectrometry technique. Relative uncertainties $u_{\text{rel}}(M) were obtained: a reduction by almost three orders of magnitude in ten years. This study compares the homogeneities in M(Si) of the first “AVO28” crystal and the first crystal (Si28-23Pr11) of the “Kilogram-2” project.

Improved measurements on silicon crystal samples highly enriched in the 28Si isotope (known as 'Si28' or AVO28 crystal material) have been carried out at PTB to investigate local isotopic variations in the original crystal. This material was used for the determination of the Avogadro constant NA and therefore plays an important role in the upcoming redefinition of the SI units kilogram and mole, using fundamental constants. Subsamples of the original crystal have been extensively studied over the past few years at the National Research Council (NRC, Canada), the National Metrology Institute of Japan (NMIJ, Japan), the National Institute of Standards and Technology (NIST, USA), the National Institute of Metrology (NIM, People's Republic of China), and multiple times at PTB. In this study, four to five discrete, but adjacent samples were taken from three distinct axial positions of the crystal to obtain a more systematic and comprehensive understanding of the distribution of the isotopic composition and molar mass throughout the crystal. Moreover, improved state-of-the-art techniques in the experimental measurements as well as the evaluation approach and the determination of the calibration factors were utilized. The average molar mass of the measured samples is M??=??27.976 970 12(12) g mol?1 with a relative combined uncertainty uc,rel(M)??=??4.4 ×10?9. This value is in astounding agreement with the values of single samples measured and published by NIST, NMIJ, and PTB. With respect to the associated uncertainties, no significant variations in the molar mass and the isotopic composition as a function of the sample position in the boule were observed and thus could not be traced back to an inherent property of the crystal. This means that the crystal is not only 'homogeneous' with respect to molar mass but also has predominantly homogeneous distribution of the three stable Si isotopes.

A two-step separation procedure for the quantification of Pd and Pt in automotive exhaust emissions using isotope dilution mass spectrometry was established using a combination of cation and anion exchange chemistry. AG 50W-X12 was used as cation exchange resin and DGA as weakly basic anion exchange resin. This procedure enabled the effective separation of Pd and Pt from the matrix and from interfering elements. Additionally Pd and Pt were collected in separate chromatographic fractions, which increased the precision of the isotope ratio determination by separate measurements using single collector sector field ICPMS. The analytical procedure was validated by analysing the synthetically prepared samples and the certified reference materials BCR-723 (road dust) and IAEA-450 (algae). For the SI-traceable results complete uncertainty budgets were calculated yielding relatively expanded uncertainties (k = 2) of ≈1% for analyte masses in the ng range. Procedure blanks of 55 pg Pd and 3 pg Pt were obtained. The detection limits were calculated as 12 pg for Pd and 7 pg for Pt. Additionally, Pd and Pt blank levels of different filter materials are presented as well as the first results for automotive exhaust particles collected on cellulose filters.

Gravimetrically prepared mono-elemental reference solutions having a well-known mass fraction of approximately 1 g/kg (or a mass concentration of 1 g/L) define the very basis of virtually all measurements in inorganic analysis. Serving as the starting materials of all standard/calibration solutions, they link virtually all measurements of inorganic analytes (regardless of the method applied) to the purity of the solid materials (high-purity metals or salts) they were prepared from. In case these solid materials are characterized comprehensively with respect to their purity, this link also establishes direct metrological traceability to The International System of Units (SI). This, in turn, ensures the comparability of all results on the highest level achievable. Several national metrology institutes (NMIs) and designated institutes (DIs) have been working for nearly two decades in close cooperation with commercial producers on making an increasing number of traceable reference solutions available. Besides the comprehensive characterization of the solid starting materials, dissolving them both loss-free and completely under strict gravimetric control is a challenging problem in the case of several elements like molybdenum and rhodium. Within the framework of the European Metrology Research Programme (EMRP), in the Joint Research Project (JRP) called SIB09 Primary standards for challenging elements, reference solutions of molybdenum and rhodium were prepared directly from the respective metals with a relative expanded uncertainty associated with the mass fraction of U rel(w) < 0.05 %. To achieve this, a microwave-assisted digestion procedure for Rh and a hotplate digestion procedure for Mo were developed along with highly accurate and precise inductively coupled plasma optical emission spectrometry (ICP OES) and multicollector inductively coupled plasma mass spectrometry (MC-ICP-MS) methods required to assist with the preparation and as dissemination tools.

High resolution multicollector inductively coupled plasma mass spectrometry (HR-MC-ICP-MS) was applied for the determination of the isotopic composition and molar mass of a silicon crystal material (“Si28”) highly enriched in the 28Si isotope (x(28Si) > 0.9999 mol/mol). Due to experimental improvements and a straightforward advancement of an analytical closed-form approach for correction of mass bias in isotope ratio measurement, the uncertainty associated with the molar mass u rel(M) was further reduced to 6.1E-9. The current molar mass of the “Si28” material used for the redetermination of the Avogadro constant was M(Si) = 27.976 970 22(17) g/mol which differs by − 4.9 · 10 –8 g/mol (− 1.8E − 9 relative) from the value published by the International Avogadro Coordination (IAC) in 2011. The uncertainty budget as well as the main features of the new extended theory for calibration factor determination are presented additionally.

The local distribution of the isotopic composition and molar mass M of a new silicon crystal (Si28-24Pr11) highly enriched in the 28Si isotope is reported, with focus on the experimental methods as well as on the associated uncertainties. The crystal was used in 2018 for the production of two additional silicon spheres for the realization and verification of the Avogadro constant NA using the “X-ray-crystal-density (XRCD) method” which is a primary method for the dissemination of the revised SI units mole and kilogram. 17 subsamples have been investigated (from five different axial and in several radial positions) by isotope ratio mass spectrometry using a multicollector-inductively coupled plasma mass spectrometer (MC-ICP-MS). The average molar mass of the crystal is M = 27.976 933 787(77) g/mol with a relative combined uncertainty uc,rel(M) = 2.7 × 10−9. The mean amount-of-substance fraction of 28Si is x(28Si) = 0.999 993 104 (66) mol/mol indicating that this crystal has the highest enrichment in this isotope which has ever been used for the determination of NA. No local variations in M and x(iSi) (i = 28, 29, and 30) could be identified due to material properties. The results are compared with those from two previous enriched crystals.

Correction for ‘Preparation and characterization of primary magnesium mixtures for the ab initio calibration of absolute magnesium isotope ratio measurements’ by Björn Brandt et al., J. Anal. At. Spectrom., 2016, 31, 179–196.

Triple isotope dilution mass spectrometry (triple IDMS) has been applied for the first time on protein quantification, especially on transferrin. Transferrin as an acute phase protein is a marker for several inflammation processes in the human body. Therefore, in Germany, the accurate and precise measurement of this important analyte is required. In this work, a new approach to triple IDMS is described and compared to double IDMS. Also, complete uncertainty budgets for both methods were set up to demonstrate the ability of this method to be used as a reference procedure. The relative expanded uncertainty (k = 2) for triple IDMS (3.6 %) is smaller than the one for double IDMS (4.0 %). The content of transferrin found in the human serum reference material ERM-DA470k/IFCC ((2.41 ± 0.08) g/kg) with both methods was in good agreement with each other and with the certificate. For triple IDMS ((2.426 ± 0.086) g/kg) and for double IDMS ((2.317 ± 0.092) g/kg), transferrin was determined. Although triple IDMS is a little more time consuming compared to double IDMS, there is the advantage that the isotopic composition of the spike material does not have to be determined. This is very useful especially in case of a marginal isotopic enrichment in the spike or problems with the accurate measurement of the spike isotope ratio.

A novel method of isotope amount ratio measurements using state-of-the-art techniques of a double focusing sector field mass spectrometer combined with isotope dilution mass spectrometry (IDMS) has been applied connecting analytical chemistry with metrology in chemistry aiming at the determination of the Avogadro constant (NA). The molar mass M(“Si28”) and the corresponding isotopic composition of an artificial silicon crystal material highly enriched in the 28Si isotope has been measured for the first time using a combination of a modified IDMS- and a multicollector-ICP-mass spectrometer (MC-ICP-MS) technique. A value M(“Si28”) = 27.97697027(23) g/mol has been determined. This corresponds to a relative uncertainty urel = 8.2 × 10−9 (k = 1). From this silicon crystal material two 1 kg spheres were manufactured which are used by the International Avogadro Coordination (IAC) in order to reassess (NA) with an associated relative measurement uncertainty urel(NA) ≤1 × 10−8. The experiment presented here is the advancement and completion of parts 1 and 2 of this series of papers, describing the theoretical and general experimental applicability of the novel method. The current work summarizes the experimental findings aiming at the determination of the molar mass of the “Si28” material with the lowest uncertainty possible so far. The experimental prerequisites and bottlenecks for examining this highly enriched silicon material as well as experimental proofs for the verification of the presented results are described in detail. The experimental results are supplemented by an uncertainty budget according to the Guide to the Expression of Uncertainty in Measurement (GUM).

Within the scope of re-determining the Avogadro constant, the content of impurities in ultra-pure, mono-isotopically enriched silicon 'Si28' was measured by infrared spectrometry. The calibration factors required for the calculation of the concentrations from the maximum absorption coefficients had to be determined in this context for the isotopically enriched material. For this purpose a model was prepared, which enables conversion of the factors for Si with natural isotopic abundance. On the basis of these results, the concentrations of the three most decisive impurities in the enriched material were determined. These are oxygen atoms on interstitial sites and substituting carbon and boron atoms which occupy silicon sites. Whereas carbon and oxygen were measured in accordance with standardized procedures modified for the particular metrological use, the absorption measurement of the boron was carried out differently to the conventional standard. The concentrations determined for the three types of crystal impurities are high enough to make a correction of the lattice parameter for the 'Si28' material necessary.

This paper concerns an international research project aimed at determining the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The counting procedure was based on the measurement of the molar volume and the volume of an atom in two 1 kg crystal spheres. The novelty was the use of isotope dilution mass spectrometry as a new and very accurate method for the determination of the molar mass of enriched silicon. Because of an unexpected metallic contamination of the sphere surfaces, the relative measurement uncertainty, 3 × 10−8 NA, is larger by a factor 1.5 than that targeted. The measured value of the Avogadro constant, NA = 6.022 140 82(18) × 1023 mol−1, is the most accurate input datum for the kilogram redefinition and differs by 16 × 10−8 NA from the CODATA 2006 adjusted value. This value is midway between the NIST and NPL watt-balance values.

The molar mass of a new silicon crystal material highly enriched in 28Si ('Si28', x(28Si) >99.99%) has been measured for the first time using a combination of a modified isotope dilution mass spectrometry (IDMS) technique and a high resolution multicollector-ICP-mass spectrometer. This work is related to the redetermination of the Avogadro constant NA with an intended relative measurement uncertainty urel(NA) ≤ 2 × 10−8. The corresponding experimental investigations of the International Avogadro Coordination (IAC) were performed using this novel 'Si28' material. One prerequisite of the redetermination of NA is the determination of the isotopic composition and thus molar mass of 'Si28' with urel(M('Si28')) ≤ 1 × 10−8. At PTB, a molar mass M('Si28') = 27.976 970 27(23) g mol−1 has been determined with an associated relative uncertainty urel(M('Si28')) = 8.2 × 10−9, opening the opportunity to reach the target uncertainty of NA.

To determine the Avogadro constant by counting the atoms in quasi-perfect spheres made of a silicon crystal highly enriched with 28Si, the isotopic composition of the crystal was measured in different laboratories by different measurement methods. This paper examines the consistency of the measurement results.

An alternative post column online double isotope dilution inductively coupled plasma mass spectrometry (ID-ICP-MS) method was developed. The resulting equation allows a straightforward calculation of the mass concentration of the analyte in the sample from the measured isotope ratio chromatogram. The use of a balance to determine and monitor the mass flow of the spike and a solution of the species under investigation as the reference are the two core components of this new method. Changes in the viscosity of the system eluent-analyte-spike will not affect the results due to the direct determination of the mass flow rate. The use of the species under investigation as the reference makes the method independent of the injected volume. To simplify matters, the integration of the isotope ratio chromatogram was done with Excel using Simpson's rule instead of sophisticated programs for transformation and integration. The advantages of the new approach were demonstrated with the help of the determination of selenomethionine in the selenized yeast reference material SELM-1 with liquid chromatography coupled to ICP-MS (HPLC ID-ICP-MS) applying the new online double IDMS method.

The isotopic abundances and thus molar mass M(Si) of a silicon crystal material with natural isotopic abundances have been measured for the first time using multicollector-ICP-mass spectrometry (MC-ICP-MS) in combination with a novel concept of a modified isotope dilution mass spectrometry (IDMS)-method. This experimental work is the further development of part 1 of this series of papers. While part 1 describes the theoretical background and the mathematical derivation of the novel concept in detail, the measurements presented here serve to validate the novel concept and give experimental proof of its capability. Moreover, the also new method for the analytical calculation of calibration factors needed in the determination of absolute isotope amount ratios has been tested successfully. Silicon isotopic abundances have been measured directly from an aqueous alkaline matrix following a new sample preparation protocol developed within the framework of this study. A molar mass of M(Si) = 28.08548(13) g/mol with an associated relative uncertainty of urel = 4.6 × 10−6 (k = 1) has been measured. This is in excellent agreement with the current IUPAC value for the molar mass of natural silicon M(Sinat) = 28.08550(15) g/mol with urel = 5.3 × 10−6 (k = 1). An uncertainty budget according to the Guide to the Expression of Uncertainty in Measurement (GUM) was calculated to assess the presented results and to validate the novel concept with the help of experimental data. The development of a new experimental procedure is presented in detail and the contributions to the uncertainty are discussed in comparison to part 1 of this work.

A new method applying isotope dilution mass spectrometry to determine the molar mass of a silicon sample, highly enriched with respect to 28Si, has been proposed recently. This paper describes a different way of calculating the molar mass by solving an equation linking the measurement results to the ratio between the amount-of-substance fractions of 28Si and 30Si in the sample. The mathematical model and the final measurement equation are much more straightforward than those previously reported, though fully equivalent.

The determination of absolute isotope amount ratios requires the calibration of mass spectrometric measurements. In this paper, for the first time, the relevant calibration factors are given via exact analytical equations. It extends the results of a previous investigation, based on a simple two-isotope model, to a three-isotope system. Particular emphasis is given to silicon, because of its role in the determination of the Avogadro constant. The conditions ensuring the existence and uniqueness of the calibration-equation solutions are related as well.

The development of a new method for the experimental determination of absolute isotopic abundances using a modified isotope dilution mass spectrometry (IDMS) technique is described. The intention and thus main application will be the quantification of molar masses M of highly enriched materials with improved measurement uncertainty ( U rel ( M ) ≈ 10 −8 with k = 2). In part 1 of the current work, the theoretical foundation of the new method and its mathematical derivation is shown in detail, while part 2 will cover the experiments based on the new method described. Its core idea is the introduction of a virtual element (VE) consisting of all isotopes but the one having the largest or smallest abundance. IDMS is used to determine the mass fraction of this VE in its matrix, namely the element itself. A new set of equations serve to calculate all isotopic abundances (even the large one omitted with the introduction of the VE) merely from the mass fraction of the VE. A comprehensive uncertainty budget according to the Guide to the Expression of Uncertainty in Measurement (GUM) was set up in order to discuss and validate the novel concept. The hypothetical input data of the uncertainty budget were estimated to resemble a silicon material highly enriched with respect to 28 Si used in the context of the international Avogadro Project . Considering the calculated results, the experimental determination of the molar mass of the above mentioned silicon seems very promising. As far as the authors know, this will be the first time IDMS was applied to determine a molar mass.

Metrologically traceable reference values add an essential benefit to interlaboratory comparisons: unlike consensus values, they can be used to establish national and international comparability. Furthermore, the participating laboratories obtain a reliable and unbiased benchmark to check their results for accuracy. Usually, metrologically traceable reference values are obtained by so-called primary methods which demand excessive efforts at great expense. Within the framework of two national drinking-water interlaboratory comparisons (proficiency testing rounds), a new approach to provide metrologically traceable reference values was applied. It is solely based on existing data which were collected during the comparison itself. Lead (Pb) measurements serve as an example to show how metrologically traceable reference values were derived from the lead amount added during sample preparation and the amount of lead already present in the drinking-water matrix used to prepare these samples. Within this approach, the matrix content is calculated in a way similar to a standard addition experiment. An uncertainty budget for the reference value was set up which describes the link to the corresponding SI units. Isotope dilution mass spectrometry (IDMS) as a primary method was used to validate this approach in the case of cadmium, chromium, copper, lead, and nickel.

Ion chromatography was used to determine anionic impurities in sodium chloride. All measurements were carried out as standard addition experiments.

A complete metrological traceability system for measurement results of chemical analysis was set up. Core components are pure substances (national standards) characterised at the highest metrological level, primary solutions prepared from these pure substances and secondary solutions deduced from the primary solutions and intended for sale. The relative uncertainty of the element mass fraction of the primary substances and solutions is < 0.01 and < 0.05%, respectively. For the certification of transfer solutions and for stability testing, a precision measurement method for element contents has been developed by means of optical emission spectrometry (ICP OES) by which uncertainties between 0.1 and 0.05% can be achieved. The dissemination to field laboratories is effected with the aid of a calibration laboratory of the German Calibration Service (DKD) which certifies the element content of the secondary solutions with an uncertainty ≤ 0.3%. Calibration with these solutions enables the user to establish traceability of his measurement results to the International System of Units (SI). Currently, the system comprises Cu, Fe, Bi, Ga, Si, Na, K, Sn, W, and Pb.

In order to make analytical measurement results traceable to the SI units in the field of clinical chemistry, an ion chromatographic (IC) measurement procedure has been developed which allows the amount of substance of the four so-called electrolytes Na, K, Mg and Ca as well as that of Li to be determined efficiently in human serum and with high accuracy. The IC measurement procedure was validated using primary measurement procedures confirmed by international comparison measurements and is proposed for use as a transfer standard when comparing measurements with clinical reference laboratories. The solutions used for calibration were gravimetrically prepared from pure substances (salts). Their chemical compositions had been iteratively fitted to those of the samples. The serum samples were mineralized by microwave-assisted digestion. The following relative expanded uncertainties for the average elemental contents were obtained: Li 0.4%, Na 0.14%, K 0.6%, Mg 0.8% and Ca 0.4%.

The possibility of using neutron activation analysis to link up a secondary to a primary mono-elemental solution was investigated. A procedure was developed for the determination of the ratio between the mass fractions of two solutions. The use of a monitor element was essential to limit the effect of the non-uniformity of the neutron flux during irradiation. The proposed procedure was tested in the case of two molybdenum solutions having the same mass fraction. Although the experiment did not reach the goal, possible ways are suggested to reach the target expanded uncertainty of 0.1 %.

An overview of the present results and status of the molar mass of a silicon crystal highly enriched in ²⁸Si used for a new determination of the Avogadro constant is given with special emphasis on the cooperation between NIST, NRC, and PTB currently working on this topic. Using an experimental combination of multicollector ICP and isotope dilution mass spectrometry, a new approach developed by PTB for the measurement of the isotopic composition has been applied. It focuses on the isotope ratio treatment of ³°Si/²⁹Si mainly, avoiding the more uncertain measurement of ratios related to the main isotope ²⁸Si., 2012 Conference on Precision Electromagnetic Measurements (CPEM 2012), July 1-6, 2012, Washington, DC, USA, Series: CPEM Digest