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.

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The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by counting the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.022,140,78(18) × 10(23) mol(-1), is the most accurate input datum for a new definition of the kilogram.

A value for the Avogadro constant, NA, was derived from new measurements of the lattice parameter, the density and the molar mass of a silicon single crystal. The result NA = 6.022 135 3 × 1023 mol−1 has a relative measurement uncertainty and is in excellent agreement with other published data based on the x-ray crystal density molar mass method, indicating the high repeatability of these experiments. The value differs significantly from the Committee on Data for Science and Technology's most recent recommended value of 6.022 141 99 × 1023 mol−1 by more than 1 × 10−6 NA.

We report on two sets of isothermal acoustic measurements made with argon close to the triple point of water using a 50 mm radius, thin-walled, diamondturned quasisphere. Our two isotherms yielded values for the Boltzmann constant, k B , which differ by 0.9 parts in 10 6 , and have an average value of k B = (1.380 649 6 ± 0.000 004 3) × 10 −23 J · K −1 . The relative uncertainty is 3.1 parts in 10 6 , and the average value is 0.58 parts in 10 6 below the 2006 CODATA value (Mohr et al. Rev Mod Phys 80:633, 2008), and so the values are consistent within their combined (k = 1) uncertainties.