OPTICAL MATERIALS: 'Quasiperfect' Si sphere is crucial to new measurement of Avogadro constant

The Avogadro project was started in 2003 by a consortium of measurement-standards laboratories.

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The Avogadro project was started in 2003 by a consortium of measurement-standards laboratories. Its goal is to count the number of atoms in a kilogram; from this, many benefits ensue, from a more accurate determination of the Avogadro constant (the number of atoms in a mole of material), to tests of the consistency of atomic physics.

The group has announced the most precise measurement ever of the Avogadro constant.1 At the heart of the experiment was a dislocation-free boule of pure silicon (Si) enriched to at least 99.99% 28Si, and polished into two "quasiperfect" spheres by the Australian Centre for Precision Optics (see figure). Their diameters of about 93.6 mm had to be known to an accuracy of 0.6 nm, and measured in a controlled environment held to a temperature accuracy of 2 mK or better.

The concentration of pointlike defects and vacancies in the Si was measured by IR and positron-lifetime spectroscopy, and then accounted for in the calculations. The lattice parameter of the Si at many locations was measured with x-ray interferometry, showing no intrinsic strain in the Si. The sphere volumes were measured using two differential optical interferometers, both with Fizeau cavities—one with planar and the other with spherical mirrors. The measurements were corrected for phase shifts and retardations from the surface oxide layer on the Si arising from interactions with the air (surface layer was characterized using x-ray fluorescence and other methods). The molar mass was measured via mass spectrometer.

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One of two spheres used for precisely determining the Avogadro constant is made of pure enriched 28Si from a dislocation-free boule; its diameter and variations in diameter are known to an accuracy of 0.6 pm. (Courtesy of Physikalisch-Technische Bundesanstalt)

The resulting measurement of the constant was 6.02214078(18) × 1023 mol-1, with a relative uncertainty of 3 × 10-8.

To "reinvent" the definition of the kilogram in terms of fundamental constants, the consortium must reduce measurement uncertainty to 2 × 10-8 or below.—John Wallace


1. B. Andreas et al., Physical Rev. Lett., 106, 030801 (2011).

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