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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.

Zusammenfassung Im November 2018 trat die Generalkonferenz für Maß und Gewicht (General Conference on Weights and Measures, CGPM), die höchste Instanz der Meterkonvention, zu ihrem 26. Treffen zusammen, um die Revision des Internationalen Einheitensystems (SI) zu beschließen. Die SI-Basiseinheit der Stoffmenge n, das Mol, wird nun über die Avogadro-Konstante N A = 6.022 140 76 × 10 23 mol {N_{\mathrm{A}}}=6.022\hspace{0.1667em}140\hspace{0.1667em}76\times {10^{23}}\hspace{0.1667em}\text{mol} definiert. Der Wert von N A {N_{\mathrm{A}}} wurde ohne Messunsicherheit festgelegt. Diese Revision trat am 20. Mai 2019 in Kraft. Bislang war das Mol über die Masse von 12 g des 12C-Isotops definiert und daher mit einer weiteren SI-Einheit, dem Kilogramm, verknüpft. Dieser Artikel beschreibt die Hintergründe, die Vorteile, die Motivation, die Realisierung (Mise en Pratique) und Weitergabe des Mol sowie die Änderungen nach der Revision. Die derzeit beste Methode der Realisierung und Weitergabe, die X-ray-crystal density (XRCD) Methode (Zählen der Si-Atome in einer Kugel aus hinsichtlich 28Si angereichertem Silicium) wird kurz beschrieben. Dabei wird besonderes Augenmerk auf die Bestimmung der molaren Masse dieses Materials gelegt, die wohl die Größe mit der kleinsten Messunsicherheit in der Chemie darstellt. Die durch die Revision verursachten Änderungen für den Alltag des Chemikers werden mit Beispielen verdeutlicht, um ein besseres Verständnis in Lehre und industrieller Praxis zu vermitteln.

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.

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 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 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).

A metrological challenge is currently underway to replace the present definition of the kilogram. One prerequisite for this is that the Avogadro constant, N A, which defines the number of atoms in a mole, needs to be determined with a relative uncertainty of better than 2 × 10−8. The method applied in this case is based on the x-ray crystal density experiment using silicon crystals. The first attempt, in which silicon of natural isotopic composition was used, failed. The solution chosen subsequently was the usage of silicon highly enriched in 28Si from Russia. First, this paper reviews previous efforts from the very first beginnings to an international collaboration with the goal of producing a 28Si single crystal with a mass of 5 kg, an enrichment greater than 0.9999 and of sufficient chemical purity. Then the paper describes the activities of a follow-up project, conducted by PTB, to produce a new generation of highly enriched silicon in order to demonstrate the quasi-industrial and reliable production of more than 12 kg of the 28Si material with enrichments of five nines. The intention of this project is also to show the availability of 28Si single crystals as a guarantee for the future realisation of the redefined kilogram.

The use of new silicon single crystals highly enriched in 28Si recently produced for the upcoming redetermination of the Avogadro constant requires knowledge of their molar masses. The isotopic composition data are collected independently in different laboratories but all using the virtual element technique with multicollector inductively coupled plasma mass spectrometers. In this framework, the comparison of the results with an independent measurement of the amount of at least one of the depleted isotopes is useful to limit hidden systematic errors. To this aim, the 30Si mole fraction of a sample of the new material was measured using a relative measurement protocol based on instrumental neutron activation analysis. The protocol is similar to that previously applied with the AVO28 silicon material used for the last determination of the Avogadro constant value with the exception that unknown and standard samples are not coirradiated. The x(30Si) = 5.701 × 10–7 mol mol–1 estimate is close to the expected o...

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.

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.

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.

The use of new silicon single crystals highly enriched in

At least four units of the International System of Units (SI) are on the way to a new definition. Especially for the unit of mass, the kilogram, a rigorous change is considered. Instead of the current definition, a 1kg-artifact in form of a Pt-Ir-cylinder, the intended formulation relates the unit of mass to a fundamental constant. In detail this requires in a first step a measurement of the chosen fundamental constant with contemporary lowest uncertainty and best reproducibility. The constant will then be fixed to that value. As an example the metre is related to the fixed constant speed of light.For the kg there are considered two ways: one is a watt balance, which determines the mass in units of the Planck constant, h. While at present the watt balances show a heterogeneous appearance, the second class of experiment the determination of the Avogadro constant, NA, which measures the mass in terms of the number of elementary entities has reached a considerable level of uncertainty and reproducibility. The fundament of the new determination of the Avogadro constant is a highly enriched 28Si crystal. The different working groups of the Avogadro team determine molar mass and lattice parameter of the crystal, and mass and volume of two precision spheres made from different positions, but of the same crystal. All measurements are carried out for both spheres and all measurement quantities are determined at least from two independent working groups, usually of different countries.

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.

ICP-MS has played a key role in inorganic chemical metrology for 25 years, from the 1993 CIPM feasibility study which led to establishment of the CCQM. Since that time, the Inorganic Analysis Working Group of the CCQM has organised 56 international comparisons involving measurements by ICP-MS and, in a recent comparison, 16 different national institutes submitted their results using the technique. Metrological applications of ICP-MS currently address an enormous range of measurements using a wide variety of instrumentation, calibration strategies and methodologies. This review provides an overview of the ICP-MS field with an emphasis on developments which are of particular relevance to chemical metrology. Examples from CCQM comparisons and the services available from the participants are used to illustrate how the capability and scope of ICP-MS methods have expanded far beyond the expectations of 1993. This is due in part to the research and development Programmes of the national institutes which participate in the CCQM. They have played a key role in advancing new instrumentation and applications for elemental analysis, isotope dilution mass spectrometry, determination of isotopic ratio or composition, and speciation of organometallic compounds. These developments are continuing today, as demonstrated by work in new fields such as heteroatom quantitation of proteins, characterisation and counting of nanoparticles using spICP-MS, and LA-ICP-MS analysis of solid materials.

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).

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.

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 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.

The latest determination of the Avogadro constant, carried out by counting the atoms in a pure silicon crystal highly enriched in (28)Si, reached the target 2 × 10(-8) relative uncertainty required for the redefinition of the kilogram based on the Planck constant. The knowledge of the isotopic composition of the enriched silicon material is central; it is measured by isotope dilution mass spectrometry. In this work, an independent estimate of the (30)Si mole fraction was obtained by applying a relative measurement protocol based on Instrumental Neutron Activation Analysis. The amount of (30)Si isotope was determined by counting the 1266.1 keV γ-photons emitted during the radioactive decay of the radioisotope (31)Si produced via the neutron capture reaction (30)Si(n,γ)(31)Si. The x((30)Si) = 1.043(19) × 10(-6) mol mol(-1) is consistent with the value currently adopted by the International Avogadro Coordination.

The photoelectron spectra of bimetallic, mass-selected NbnCo− clusters (n=3–15) measured at 4.66 eV photon energy are reported. The electronic structure changes of the binary clusters are discussed in comparison with the electronic structures of pure Nbn− clusters as a function of size evolution. Spectroscopic parameters like electron affinities (EAs) and vertical detachment energies (VDEs) are determined. The addition of one Co atom to the Nbn cluster core significantly perturbs the electronic structures of pure Nbn clusters at small cluster sizes. Electronic state merging can be explained by hybridization of Co 3d and 4s as well as Nbn 4d-derived valence orbitals. Tentative geometric structure postulations are carried out revealing the influence of the incoming Co atom toward the intact Nbn cluster core. In strong contrast to pure Nbn clusters, a highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gap closing of NbnCo at n=6 indicates a bulk-like evolution of electronic structures induced by charge transfer of Co 3d electrons.

Photoelectron spectroscopy of size-selected ConOm- clusters (n = 4−20; m = 0−2) is performed in a pulsed molecular beam experiment at photon energies of 3.49 and 4.66 eV. Cobalt oxide cluster anions are generated in a laser vaporization source and the photoelectron spectra are measured with a magnetic bottle photoelectron spectrometer. The size-dependent evolution of the electronic structure of the oxide clusters is discussed in terms of cluster composition. Threshold binding energy features are mainly contributed from Co d-derived orbitals throughout the complete series, indicating that the incoming oxygen atoms cause a minor influence on the electronic structures. Although for n ≥ 13 EAs and VDEs of Con and ConOm clusters overlap within the experimental resolution, at smaller cluster sizes, the values increase in the order of Con < ConO < ConO2. For Co4O3- and Co5O3-, the spectra indicate the presence of isomers with low EAs as peroxo and ozonide isomers. To compare the different channels of oxygen chem...

The anion photoelectron (PE) spectra of small mass-selected vanadium oxide clusters VnOm− (n=4–15; m=0–2) are measured at a fixed photon energy of 4.66 eV with the aid of a magnetic bottle photoelectron spectrometer. Cluster anions are generated in a pulsed laser vaporization cluster source. The electronic structure of VnOm− clusters is investigated as a function of size n and composition m with special regard to the increasing oxidation state. The addition of one or two oxygen atoms to the vanadium cluster core induces a change of the electronic structure in the near-threshold binding energy region below 2 eV. Main spectral features are contributed from the transition metal d-derived orbitals, whereas the oxygen 2p contribution induces a hybridization between vanadium and oxygen frontier orbitals in the entire series of the investigated clusters n=4–15. Generally, electron affinities and vertical detachment energies increase with increasing cluster size revealing size-dependent discontinuities. Furthermo...

Bimetallic cobalt (Co)−vanadium (V) clusters, ConVm- (n = 4−14, m = 0−2), are investigated using anion photoelectron spectroscopy at 4.66 eV photon energy. Electron affinities (EA) and vertical detachment energies (VDE) are determined, and the electronic structures of V- and V2-doped Con clusters are compared to those of pure Con clusters. Bonding and hybridization effects can be explained using a charge-transfer model. A peak shape analysis confirms the high stability of the Co12V cluster with a most plausible icosahedral structure with the V atom in the cage center. Together with ionization potentials (IP), the electronic structures of the clusters are compared to H2 chemisorption rate coefficients reported previously. Thus, this study completes the investigation of electronic properties and reactivity of the bimetallic ConVm clusters as a function of charge, size, and distribution. Although the reactivity of ConVm reveals a better correlation toward the EA rather than toward IP, no improved correlation...

Photodetachment photoelectron spectroscopy experiments on NbnAl− clusters have been carried out in a size range n=4 to 12 at 3.49 eV photon energy. The evolution of the electronic structure is discussed as a function of cluster size and composition. Electron affinities (EA) and vertical detachment energies are determined. One central point of this study is the direct comparison of the electronic structure of pure and Al-doped Nbn− clusters in the threshold binding energy region with regard to hybridization effects. Direct correlation between electronic structure and H2 chemisorption rate constants reported by Nonose et al. [Chem. Phys. Lett. 164 (1989) 427], is found for n=5 to 8 and n>9.

The size dependent evolution of the electronic structure of isolated gas-phase rhenium clusters Re n − ( n =2–40) is measured by photoelectron (PE) spectroscopy at 4.99 and 6.42 eV photon energies. For very small clusters the photodetachment threshold energies show a strong size dependence varying between 1.6 eV (Re 2 ) and 2.6 eV (Re 13 ). As for larger clusters, electron affinities (EA) increase smoothly toward bulk work function (WF). Bulk-like electronic features can already be observed around very small cluster sizes.

The photoelectron spectra of small mass-selected aluminum-rich AlnCo− (n=8–17) and cobalt-rich ConAlm− clusters (n=6,8,10; m=1,2) are measured at photon energies of 3.49 eV with the aid of a magnetic bottle photoelectron spectrometer. The electronic structures of the bimetallic clusters are compared with those of pure Aln− and Con− clusters, which are measured under the same conditions. The threshold behavior (electron affinities and vertical detachment energies) is analyzed, and the application of the electronic shell model reveals a similar shell structure of Co-doped Al clusters with a single heteroatom. Additional heteroatom doping induces shell perturbations. Compared to pure Aln clusters, single-atom doped clusters show a hybridization of Al s, p and Co d orbitals resulting in a merging of spectral features at low binding energies. The evolution of the electronic structure is compared with reported ionization potentials [Menezes and Knickelbein, Chem. Phys. Lett. 183, 357 (1991); Z. Phys. D 26, 322 (1993)]. The hydrogen chemisorption behavior of neutral aluminum cobalt clusters [Nonose et al., Chem. Phys. Lett. 164, 427 (1989)] shows a clear influence of Co d states at low binding energies in the case of AlnCo, whereas for ConAlm clusters (n>m) the geometric effect becomes more dominant.