An accurate 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, 6.02214084(18) x 10^23 mol^-1, is the most accurate input datum for a new definition of the kilogram.Comment: 4 pages, 5 figures, 3 table

A new generation of 99.999% enriched 28Si single crystals for the determination of Avogadro's constant

A metrological challenge is currently underway to replace the present definition of the kilogram. One prerequisite for this is that the Avogadro constant, NA, which defines the number of atoms in a mole, needs to be determined with a relative uncertainty of better than 2  ×  10−8. The method applied in this case is based on the x-ray crystal density experiment using silicon crystals. The first attempt, in which silicon of natural isotopic composition was used, failed. The solution chosen subsequently was the usage of silicon highly enriched in 28Si from Russia. First, this paper reviews previous efforts from the very first beginnings to an international collaboration with the goal of producing a 28Si single crystal with a mass of 5 kg, an enrichment greater than 0.9999 and of sufficient chemical purity. Then the paper describes the activities of a follow-up project, conducted by PTB, to produce a new generation of highly enriched silicon in order to demonstrate the quasi-industrial and reliable production of more than 12 kg of the 28Si material with enrichments of five nines. The intention of this project is also to show the availability of 28Si single crystals as a guarantee for the future realisation of the redefined kilogram

Lattice strain at c-Si surfaces: a density functional theory calculation

The measurement of the Avogadro constant by counting Si atoms is based on the assumption that Si balls of about 94 mm diameter have a perfect crystal structure up to the outermost atom layers. This not the case because of the surface relaxation and reconstruction, the possible presence of an amorphous layer, and the oxidation process due to the interaction with the ambient. This paper gives the results of density functional calculations of the strain components orthogonal to crystal surface in a number of configurations likely found in real samples

Avogadro constant measurements using enriched 28Si monocrystals

Since 2011, the International Avogadro Coordination has been measuring the Avogadro constant by counting the atoms in enriched Si-28 monocrystals. This communication provides guidance on how the recently published results should be used to update the values of the Avogadro constant measured so far

Contributions of precision engineering to the revision of the SI

All measurements performed in science and industry are based on the International System of Units, the SI. It has been proposed to revise the SI following an approach which was implemented for the redefinition of the unit of length, the metre, namely to define the SI units by fixing the numerical values of so-called defining constants, including c, h, e, k and NA. We will discuss the reasoning behind the revision, which will likely be put into force in 2018. Precision engineering was crucial to achieve the required small measurement uncertainties and agreement of measurement results for the defining constants