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International Avogadro Project
Summary
Mass measurements at the BIPM
Published results
Special issue on
International determination of the Avogadro constant

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The International Avogadro Coordination (IAC) project formally began as an international effort whose scope is to determine the Avogadro constant NA with a relative uncertainty equal to or less than 2 × 10−8. It continues as the International Avogadro Project.

The IAC is a collaboration between the BIPM, the INRIM (Italy), the IRMM (Belgium), the NIST (United States), the NMIA (Australia), the NMIJ/AIST (Japan), the NPL (United Kingdom), and the PTB (Germany) which started in 2004.

Within the framework of the IAC, the most recent determination of the Avogadro constant (2011) is NA = 6.022 140 82(18) × 1023 mol−1 with a relative uncertainty of 3.0 × 10−8 (Metrologia, 2011, 48(2), S1-S13 and Phys. Rev. Lett., 2011, 106, 030801).

The IAC project started in 2004 and was completed in April 2011. A new Memorandum of Understanding (MoU) for cooperation to determine the Avogadro constant using an isotopically enriched silicon crystal will take over from the IAC for a further six years.


The Avogadro constant and the New SI | Principle of the measurement of NA | Results
Mass measurements at the BIPM: Method | Results
Publications


0The Avogadro constant and the New SI

The Avogadro constant expresses the number of elementary entities per mole of substance. In the present SI, by definition, {NA} atoms of Carbon-12 weigh exactly 12 grams.1

At present, a new approach to define and realize the SI unit of mass (the kilogram) is being investigated. Essentially, the kilogram could be defined as the mass of {NA}*1000/12 carbon-12 atoms by fixing the numerical value of NA. For this redefinition to take place, NA would need to be accurately known in the present SI system. This is the purpose of the IAC project. In this context, a relative uncertainty of 2 × 10−8 on NA has been recommended, Recommendation G1 (2010), by the Consultive Committee for Mass and Related Quantities (CCM).

The redefinition of the kilogram could also be based on a fixed numerical value of the Planck constant, h. If that was the case, an accurate determination of NA would still be crucial because it would provide an alternative method to determine h via the molar Planck constant, NAh which is very well known:

u(NAh)

NAh
< 10−9
0Principle of the measurement of NA

In order to relate the kilogram to an atomic mass, the number of silicon atoms in two 1 kg single-crystal silicon spheres is counted by exploiting their ordered arrangement in the crystal. The spheres are highly enriched (99.995 %) with the 28Si isotope. The expression of the Avogadro constant is therefore based on:

NA = n M

ρ a3

where n, ρ, M and a are respectively the number of atoms per unit cell (n = 8), the density, the molar mass and the lattice parameter of the crystal.

Silicon unit cell

Fig. 1. Silicon unit cell. The unit cell of silicon has a cubic packing arrangement of 8 atoms. The unit cell volume is measured by determining the lattice parameter a, which is the length of one of the sides of the cube.

This new approach by using an isotopically enriched silicon crystal overcomes the previously limiting problem of accurately determining the isotopic composition of a natural silicon crystal. The experiment uses isotope dilution mass spectrometry (IDMS) combined with multicollector inductively coupled plasma mass spectrometry to determine the molar mass of silicon-28 with unprecedented accuracy. The isotopic composition, molar mass, mass, volume, density and lattice parameter of the two 28SI kilogram spheres were accurately determined and their surfaces were chemically and physically characterized at the atomic scale (see details in Metrologia, 2011, 48(2), S1-S13). Impurity concentration and gradients in the enriched crystal were measured by infrared spectroscopy and taken into account.

Production of the spheres (Fig. 2) began in 2004 with the isotopic enrichment of SiF4 gas by centrifugation at the Central Design Bureau of Machine Building in St Petersburg (Russian Federation). The enriched gas was subsequently converted into SiH4 and chemical vapour deposition was used to grow a polycrystal at the Institute of Chemistry of High-Purity Substances of the Russian Academy of Sciences. In 2007, a 5 kg 28Si boule was grown by the Leibniz-Institut für Kristallzüchtung (Germany). Two 28Si spheres, AVO28#5 and AVO28#8, were manufactured from the boule and were shaped into nearly perfect spheres by the Australian Centre for Precision Optics. Silicon was chosen because it can be grown into large, high-purity and almost perfect single crystals

A highly polished silicon sphere

Fig 2. A silicon sphere (PTB image).

0Results

The most recent determination of the Avogadro constant, NA = 6.022 140 82(18) × 1023 mol−1 (relative uncertainty of 3.0 × 10−8) (Phys. Rev. Lett., 2011, 106, 030801) is at present the most accurate determination of a fundamental constant which can be used for a new definition of the kilogram.

At present several measurements are still being refined. The final scope is to achieve a relative uncertainty of 2.0 × 10−8 on the determination of NA.


1. The Avogadro constant NA = {NA} [mol−1].
     
Summary


Mass measurements at the BIPM
Published results