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Home > Products & Services > Optical Fabrication > The Avogadro Project

The Avogadro Project


The kilogram is the only remaining fundamental unit within the International System of Units (or SI, from Système International d'Unités in French) which is defined in terms of an artifact. This mass standard comes in the form of a Pt-Ir cylinder kept in the International Bureau of Weights and Measures (or BIPM, from Bureau International des Poids et Mesures in French) situated in Paris. The proposition of the Avogadro Project is to redefine the kilogram in terms of the Avogadro constant.

Fabrication of a Silicon SphereBy definition, an Avogadro number of Carbon-12 atoms weigh exactly 12 grams. As such, the kilogram could bedefined as the mass of 1000/12 * Avogadro's number of Carbon-12 atoms. The Avogadro constant itself is obtained from the ratio of the molar mass to the mass of an atom. For a crystalline structure such as silicon, the atomic volume is obtained from the lattice parameter and the number of atoms per unit cell. The atomic mass is then the product of the volume and density.

The Avogadro Project involves an international collaboration between laboratories in Germany, Italy, Belgium, Japan, Australia and USA. Currently the Avogadro constant is known to an uncertainty of approximately 0.1 ppm. It is hoped that the uncertainty will be reduced to 0.01 ppm after a further five years.

In determining the Avogadro constant, the preferred method has been to use one of the high-precision spheres fabricated here at the ACPO. These come in the form of a highly polished 1 kg single crystal silicon sphere, fabricated with a roundness in range of 60 nm. Silicon is used because of its well known crystal structure, stability and its relative ease of use. The volume is determined from the measurement of the silicon sphere's diameter and roundness. Accurate measurement of the mass then allows the density to be derived.

Precision SpheresThe nominal diameter of a 1 kg Si sphere is 93.6 mm. In order to obtain an accuracy of 0.01 ppm in volume, the diameter must be known to a range of 0.6 nm. In other words, within one atom spacing. Such high accuracy requires specialised equipment and one such procedure is by optical interferometry using a precision etalon through a stabilised laser light. The measurements are sensitive to many parameters, particularly to those of temperature and pressure. An instability within the range of 2 mK would be sufficient to cause the silicon to expand by more than the allowable uncertainty. The refractive index of air (and hence the wavelength of the light) is sensitive to the surrounding air pressure. It is therefore necessary to carry out the measurements in a controlled environment.

High purity silicon boules have been produced especially for this project by Wacker in Germany. The silicon is produced by the float zone process and a very small quantity of nitrogen is introduced to minimise defects, but at a concentration sufficiently low as to not affect the molar mass. The determination of the molar mass is conducted though mass spectroscopy.

Corrections must be applied for surface impurities such as oxides and absorbed water. Typically, silicon has an oxide layer 3 to 4 nm thick, which is a mixture of SiO and SiO2. It is also possible for the surface to absorb some monolayers of water. Since much of the absorbed water is removed in a vacuum, a number of the key measurements are made in a vacuum environment. A further correction must then be applied for the difference in bulk modulus between the air and vacuum.

Before a permanent and absolute definition of the kilogram is introduced, the relative stability of the silicon sphere and the existing Pt/Ir aftifact will have to be monitored. The kilogram can then be defined in terms of a specific number of Carbon-12 atoms.


The limiting factors currently are:

  1. The variability from sample to sample of the isotopic abundances M(Si)
  2. The content of impurities and vacancies (n)
  3. Realisation of accurate density standards (m,V)

The list below first gives the current estimated uncertainty, followed by the ultimate uncertainties which can be expected if existing methods are pursued to their limits.

  • Molar Mass: 0.2 ppm to ultimately 0.05ppm.
  • Atoms per unit cell: 0.2 ppm to ultimately 0.01 ppm
  • Mass: 0.05 ppm to ultimately 0.01 ppm
  • Volume: 0.08 ppm to ultimately 0.02 ppm
  • Lattice parameter: 0.05 ppm to ultimately 0.01 ppm
  A finished sphere and another in fabrication

The roundness delta of the finished sphere (being held above) is about 50 nm on a 93.6 mm diameter. It is believed to be the roundest object in the world.

Ms Katie Green
Materials and Fabrication Manager
Phone: +61 2 9413 7620
fax: +61 2 9413 7200

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Last updated by Peter Saunders 16 August, 2007

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