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.

Results are reported from a pilot study under the Consultative Committee for Amount of Substance (CCQM) to compare measurements of and resolve any relevant measurement issues in the amount of thermal oxide on (100) and (111) orientation silicon wafer substrates in the thickness range 1.5-8 nm. As a result of the invitation to participate in this activity, 45 sets of measurements have been made in different laboratories using 10 analytical methods: medium -energy ion scattering spectrometry (MEIS), nuclear reaction analysis (NRA), RBS, elastic backscattering spectrometry (EBS), XPS, SIMS, ellipsometry, grazing -incidence x-ray reflectometry (GIXRR), neutron reflectometry and transmission electron microscopy (TEM). The measurements are made on separate sets of 10 carefully prepared samples, all of which have been characterized by a combination of ellipsometry and XPS using carefully established reference conditions and reference parameters.The results have been assessed against the National Physical Laboratory (NPL) data and all show excellent linearity. The data sets correlate with the NPL data with average root-mean-square scatters of 0.15 nm, half being better than 0.1 nm and a few at or better than 0.05 nm. Each set of data allows a relative scaling constant and a zero thickness offset to be determined. Each method has an inherent zero thickness offset between 0 nm and 1 nm and it is these offsets, measured here for the first time, that have caused many problems in the past. There are three basic classes of offset: water and carbonaceous contamination equivalent to ∼1 nm as seen by ellipsometry; adsorbed oxygen mainly from water at an equivalent thickness of 0.5 nm as seen by MEIS, NRA, RBS and possibly GIXRR; and no offset as seen by XPS using the Si 2p peaks. Each technique has a different uncertainty for the scaling constant and consistent results have been achieved. X-ray photoelectron spectroscopy has large uncertainties for the scaling constant but a high precision and critically, if used correctly, has zero offset. Thus, a combination of XPS and the other methods allows the XPS scaling constant to be determined with low uncertainty, traceable via the other methods. The XPS laboratories returning results early were invited to test a new reference procedure. All showed very significant improvements. The reference attenuation lengths thus need scaling by 0.986 ± 0.009 (at an expansion factor of 2), deduced from the data for the other methods. Several other methods have small offsets and, to the extent that these can be shown to be constant or measurable, these methods will also show low uncertainty. Recommendations are provided for parameters for XPS, MEIS, RBS and NRA to improve their accuracy.  Crown

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.

The revision of the SI-the result of three decades of progress in metrology Michael Stock et al

No abstract

For the determination of the Avogadro constant by the x-ray crystal density method, an accurate volume measurement of 1 kg Si spheres is of primary importance. For this purpose, an optical interferometer was improved and used to measure the volumes of two 1 kg silicon spheres which were manufactured from a silicon crystal highly enriched in 28 Si. The apparent volumes of the spheres, which do not take into account the influence of the surface layers on the volume measurement by interferometry, were determined with a relative standard uncertainty of as small as 2.0 × 10 −8 . The surface of the spheres was characterized by using an improved spectroscopic ellipsometer. By considering the influence of the surface layers, the core volumes of the spheres, which exclude the surface layers, were determined. These results were used for the determination of the Avogadro constant in 2015 as a framework organized by the International Avogadro Coordination project. This paper provides details on the measurements, the improvements made to the apparatus, the data analysis and the uncertainty evaluation.