Avogadro Project

Science > Mechanical Metrology > Mass and Density Standards > Avogadro Project

A new approach to defining and realising the SI unit of mass (kg) is being explored.

It is possible to define the kilogram as a fixed number of atoms of a particular substance, thus relating the kilogram to an atomic mass. Silicon is a good candidate for this approach because it can be grown as a large single crystal, in a very pure form. For such an artefact, whose molar mass M and volume V_o of the unit cell (with n atoms) are known, the mass m of the crystal can be derived from a determination of its volume V if N_A (the Avogadro constant) is known:

i.e. m = mass of a single atom multiplied by the number of atoms present

The molar mass, unit cell volume and volume of the artefact can all be measured directly. However, the above equation can be re-arranged in terms of N_A:

i.e. N_A = molar volume divided by the atomic volume

where is the density of the artefact and is calculated from its mass m (measured using the current definition) and volume V. This approach is therefore reduced to the problem of measuring N_A with a relative uncertainty of 1 part in 10⁸, which is equivalent to the uncertainty in the present definition of the kilogram.

Silicon Material

Very high purity boules (with a diameter of approximately 10 cm) are grown using the Float Zone process. They are nitrogen doped to reduce the content of swirl defects. The artefacts are manufactured as spheres by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Australia. An out of roundness of 50 nm is achievable, strongly correlated with crystal orientation.

A sphere has been chosen to provide mechanical robustness (no sharp edges or corners which can be easily damaged) and to aid in the measurement of its volume, which can be determined from the measurement of its mean diameter.

Measurement Techniques

Molar mass is determined using a precision Mass Spectrometer developed at the Institute for Reference Materials and Measurement (IRMM) in Belgium. The molar masses of each isotope (²⁸Si, ²⁹Si and ³⁰Si) are known with a relative uncertainty of less than 1 part in 10⁸. Thus, the measurement of the molar mass of naturally occurring silicon relies on determining the isotopic ratios.

The spacing between the (220) lattice planes is determined using Scanning X-ray Interferometers. This value can be converted to give the unit cell volume for the crystal. The separation between these planes is approximately 0.192 nm and has to be measured with a relative uncertainty of 3 parts in a billion!

A sphere is placed within an etalon and its diameter is measured using optical interferometry. Many diameters can be measured and an 'average' value determined, leading to a calculation of the volume. The diagram shows a novel interferometer being developed at the Physikalisch-Technische Bundesanstalt (PTB) in Germany.

Experiments at NPL and University of Surrey

NPL has a project to study the mass stability and surface condition of silicon artefacts used in the Avogadro project. Many of the surface measurements are being made with the expertise and facilities available at the University of Surrey.

An important question yet to be addressed is the best environment (ambient, reduced or vacuum pressure) in which the spheres should be kept and used? Due to the relatively large uncertainty associated with the need to apply buoyancy corrections when weighing in air, experiments to date have not had the necessary sensitivity to ascertain the impact of adsorption and de-sorption of contaminants. To increase the experimental sensitivity, the air density is being measured using a pair of 'air density artefacts'.

Measurements will also be made using NPL's existing facility for weighing in vacuum, thus overcoming the need to apply buoyancy corrections. In this manner, the mass loss due to de-sorption of contaminants from a sample's surface can be quantified. A new facility capable of accommodating up to six, 1 kg spherical artefacts in a vacuum is also being developed.

Corrections have to be applied to the measured bulk density of a sphere to take account for the presence of surface oxidation and possible contaminants (water, hydrocarbons etc). The density of an oxide is less than that of silicon. Furthermore, when determining the diameter interferometrically, the presence of an oxide leads to an apparent displacement of the surface. Ideally, the oxide should be of a uniform thickness, stable, with a well defined composition and thin. If these conditions are not met treatment will be required.

A range of complementary techniques (ellipsometry, XPS, RBS, TEM and AFM) are being used to fully characterise and monitor the stability of native oxides. Ultimately, the oxide thickness has to be determined with an uncertainty of less than 0.3 nm! The possibility of using a single preparation for both low and high index surfaces will be investigated. This will involve the use of a chemical etch to remove the native oxide and any amorphous silicon present, and the subsequent growth of an ultra thin thermal oxide.

For more information on this project contact Stephen Downes

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