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Avogadro constant re-measured

Measurements on silicon composed of its natural isotopes have been completed as part of PTB’s “Avogadro-Project”. The project itself is to contribute to the redefinition of the unit of mass, the kilogram. In a follow-up project with enriched 28 Si, the measurement uncertainty is to be further reduced.

Stamp of the Italian Post, issued in 1956 on the 100th anniversary of the death of Amedeo Avogadro. The text on the stamp is a definition of the base unit mole for a gas.

The kilogram is the last quantity of the International System of Units, SI, still defined by a macroscopic body – the prototype kilogram. All other units are traced back to atomic processes, molecular properties or fundamental constants. By counting the atoms in a silicon crystal (mass: 1 kg) with highest precision, the definition of the unit of mass could be linked to the fundamental Avogadro constant.

The investigations were carried out on a high purity silicon single crystal produced by Wacker-Siltronic. The molar mass of the crystal was determined by mass spectrometry at the Institute for Reference Materials and Measurements of the European Union (IRMM) in Geel (relative measurement uncertainty: 4 µg/mol). At PTB, the following measurements were carried out: the lattice parameter of the material was linked to PTB’s crystal length standard (measurement uncertainty: 0,012 fm); the mass of the 1 kg silicon sphere – manufactured at the Australian metrology institute – was compared with the national mass standard (measurement uncertainty: 19 µg); the diameter of the sphere (92 mm) and thus the sphere volume were determined through several individual measurements (measurement uncertainty: 2,7 nm) with a spherical Fizeau interferometer especially developed for this application; and the thickness of the oxide layer was determined by ellipsometry (measurement uncertainty: 0,36 nm). Special attention was paid to determine the type and number of defects in the crystal material: several external research institutions supported the PTB investigations.

The measurement results have been filed in the Avogadro Database of the BIPM. Based on the determined values of density, molar mass, impurities and lattice parameter, the following value is obtained for the Avogadro constant: NA = 6,022 135 4 (16) · 1023 mol-1.

This value is in agreement with all previously published results obtained by this method. However, the new value is nearly 1 · 10-6 lower than the 1998 CODATA value based on the results of the watt balance experiment performed at the National Institute of Standards and Technology (NIST). This discrepancy still must be clarified before the unit of kilogram is finally defined.

A serious problem for the measurements on silicon of natural isotopic composition is the relative inaccuracy in the value for the molar mass. This is reflected in the overall measurement uncertainty of 2,7 · 10-7. In an international project with enriched 28Si, the measurement uncertainty is to be reduced by a factor 10.

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Phone: +49-531-592-0