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.

New results are reported from an ongoing international research effort to accurately determine the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The surfaces of two 28 Si-enriched spheres were decontaminated and reworked in order to produce an outer surface without metal contamination and improved sphericity. New measurements were then made on these two reconditioned spheres using improved methods and apparatuses. When combined with other recently refined parameter measurements, the Avogadro constant derived from these new results has a value of N A = 6.022 140 76(12) × 10 23 mol -1 . The X-ray crystal density method has thus achieved the target relative standard uncertainty of 2.0 × 10 -8 necessary for the realization of the definition of the new kilogram.

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 28 Si from Russia. First, this paper reviews previous efforts from the very first beginnings to an international collaboration with the goal of producing a 28 Si 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 28 Si material with enrichments of five nines. The intention of this project is also to show the availability of 28 Si single crystals as a guarantee for the future realisation of the redefined kilogram.

Double isotope dilution surface-enhanced Raman scattering (double IDSERS) is qualified as a method for accurate and precise determination of biomarkers in human blood serum. Providing a full evaluation of the measurement uncertainty as well as traceability to a reference material sets the procedure in line with the requirements of a primary ratio method. Data evaluation is based on a partial least squares (PLS) model, whose prediction ability is validated from quantifying the uric acid concentration in both an artificial reference solution and a real human blood serum sample. With the proposed approach, the uric acid serum concentration can be determined with an uncertainty of 1.6% at a confidence level of 95%.

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.