National Physical Laboratory

Avogadro Project

Silicon Unit Cell

The International Avogadro project relates the kilogram to the mass of a fixed number of atoms by measuring the number of atoms in a sphere of silicon.

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 V0 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 NA (the Avogadro constant) is known:

m = (M/NA)·(V·n/V0)

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 NA:

NA = (M/ρ)/(V0/n)

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

Silicon Avogadro Sphere

Silicon Avogadro sphere
where ρ 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 NA with a relative uncertainty of 1 part in 108, which is equivalent to the uncertainty in the present definition of the kilogram.

NPL, in collaboration with the University of Surrey, has developed an ellipsometer system capable of measuring the thickness of surface films on silicon spheres. We have also investigated a range of complementary techniques (ellipsometry, XPS, RBS, TEM and AFM) to fully characterise and monitor the stability of native oxides. NPL's weighing in vacuum facility has been used to measure the mass of an Avogadro sphere in air and vacuum as part of an International comparison.

For more information, contact Stephen Downes

Last Updated: 2 May 2013
Created: 19 Oct 2007