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 general characteristics and spectrometric features of a high resolution four-crystal reflection x-ray monochromator with wavelength analysis installed at the HASYLAB beam line L at DESY are presented. The monochromator is part of a spectrometer developed to calibrate x-ray absorption edge spectra in the energy range of 6–36 keV with a relative uncertainty ΔE/E from 10−5 to 10−6. This requires an extremely effective suppression of harmonics and also a negligible instrumental influence in order to obtain almost intrinsic spectra. As the results show, the monochromator fulfills the requirements, including very high stability. An example of the calibration procedure for the copper K edge is given as well as a comparison of the remeasured absorption edge energies with the previously tabulated data.

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.

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.

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.

The spacing of the {2 2 0} lattice planes of a 28Si crystal, used to determine the Avogadro constant by counting silicon atoms, was measured by combined x-ray and optical interferometry to a relative accuracy of 3.5 × 10−9. The result is d2 2 0 = (192 014 712.67 ± 0.67) am, at 20.0 °C and 0 Pa. This value is greater by (1.9464 ± 0.0067) × 10−6d2 2 0 than the spacing in natural Si, a difference which confirms quantum-mechanics calculations. This result is a key step towards a realization of the mass unit based on a conventional value of the Planck or the Avogadro constant.

We observe three effects in the Bragg diffraction of x rays in backscattering geometry from asymmetrically cut crystals. First, exact Bragg backscattering takes place not at normal incidence to the reflecting atomic planes. Second, a well-collimated (approximately 1 microrad) beam is transformed after the Bragg reflection into a strongly divergent beam (230 microrad) with reflection angle dependent on x-ray wavelength--an effect of angular dispersion. The asymmetrically cut crystal thus behaves like an optical prism, dispersing an incident collimated polychromatic beam. The dispersion rate is approximately 8.5 mrad/eV. Third, parasitic Bragg reflections accompanying Bragg backreflection are suppressed. These effects offer a radically new means for monochromatization of x rays not limited by the intrinsic width of the Bragg reflection.