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.

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.

The volumes of two 1 kg silicon spheres, AVO28-S5 and AVO28-S8, fabricated from a 28Si-enriched crystal were measured to determine the Avogadro constant by the x-ray crystal density method in the International Avogadro Coordination Project. The volumes were determined from diameter measurements of the two spheres using a laser interferometer with a flat etalon. In the diameter measurement, the sphere was placed between the two flat etalon plates. The gaps between the sphere and the etalon plates and the distance between the etalon plates were measured by phase-shifting interferometry with optical frequency tuning. The apparent volumes of the 28Si spheres were determined from the diameter measurement in many directions with relative combined standard uncertainties of 5.0 × 10−8 and 4.4 × 10−8 for AVO28-S5 and AVO28-S8, respectively. The effect of the surface layer on the diameter measurement was evaluated on the basis of the results of characterizing the sphere surface. By taking into account the effect of the surface layer, the silicon core volume excluding the surface layer and the actual volume including the surface layer were also determined. Details of the interferometer, data analysis and the uncertainty in the measurement are described.

For the accurate determination of the Avogadro constant, two 28Si spheres were produced, whose macroscopic density, in addition to other values, must be determined. To make a contribution to the new definition of the kilogram, a relative standard uncertainty of less than 2 × 10−8 has to be achieved. Each silicon surface is covered by a surface layer (SL). Consequently, correction parameters for the SL are determined to be applied to the mass and volume determination of the enriched spheres. With the use of a large set of surface analysing techniques, the structure of the SL is investigated. An unexpected metallic contamination existing on the sphere surface enlarges the uncertainty contribution of the correction parameters above the originally targeted value of 1 × 10−8. In the framework of this investigation this new obstacle is resolved in two ways. A new combination of analytical methods is applied to measure the SL mass mSL and the thickness dSL, including this new contamination, with an uncertainty of u(mSL) = 14.5 µg and 14.4 µg, respectively, and u(dSL) = 0.33 nm and 0.32 nm for the 28Si spheres AVO28-S5 and AVO28-S8, respectively.In the second part of the work, the chemical composition of these metallic contaminations is found to be Cu, Ni and Zn silicide compounds. For the removal of this contamination, a special procedure is developed, tested and applied to the spheres to produce the originally expected surface structure on the spheres. After the application of this new procedure the use of x-ray reflectometry directly at the spheres will be possible. It is expected to reduce the uncertainty contribution due to the SL down to 1 × 10−8.