Counting the atoms in a ²⁸Si crystal for a new kilogram definition

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 N_A, is larger by a factor 1.5 than that targeted. The measured value of the Avogadro constant, N_A = 6.022 140 82(18) × 10²³ mol⁻¹, is the most accurate input datum for the kilogram redefinition and differs by 16 × 10⁻⁸ N_A from the CODATA 2006 adjusted value. This value is midway between the NIST and NPL watt-balance values.