Enrico Massa

Determination of the Avogadro constant by counting the atoms in a 28Si crystal.

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.

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 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.

Improved measurement results for the Avogadro constant using a 28Si-enriched crystal

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 28Si-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

Present Status of the a Vogadro Constant Determination from Silicon Crystals with Natural Isotopic Composition

N_A = 6.022 140 76(12) \times 10^{23}

Measurement of the lattice parameter of a silicon crystal

mol

Measurement of the {2 2 0} lattice-plane spacing of a 28Si x-ray interferometer

^{-1}

Accurate measurements of the Avogadro and Planck constants by counting silicon atoms

. The X-ray crystal density method has thus achieved the target relative standard uncertainty of

Si lattice parameter measurement by centimeter X-ray interferometry

2.0 \times 10^{-8}

The lattice parameter of the 28Si spheres in the determination of the Avogadro constant

necessary for the realization of the definition of the new kilogram.

Model selection in the average of inconsistent data: an analysis of the measured Planck-constant values

The determination of the Avogadro constant from two selected silicon crystals is described. The density, molar mass, and lattice spacing of the two crystals were measured at NMU, PTB, IRMM, IMGC, and NIST. When all the data are combined, it leads to the Avogadro constant of 6.022 1353 (21) times 1023 mol-1 with a relative combined standard uncertainty of 3.4 times 10-7