While in earlier times, the unit of length may have been set by the foot of the king, the French Revolution originated the metric system, with units of length, time, and mass rooted in the natural world, independent of the contingencies of human history. Nowadays, the second is defined by counting 9192631770 beats of the valence electron of an isolated cesium-133 atom flipping its spin in the magnetic field of the cesium nucleus, and the metre is the distance travelled by light in a vacuum in 1/299792458 of a second.
It's just the unit of mass, the kilogram, which is still defined in an old-fashioned, 19th century style, by a prototype meticulously kept in a vault of the Pavillon de Breteuil near Paris, France.
|The International Prototype of the Kilogram (IPK) inside three nested bell jars at the Bureau International des Poids et Mesures (BIPM, International Bureau of Weights and Measures), Paris, France.|
Using a material artefact such as the Prototype as the standard of mass has a few obvious disadvantages: It is not easy to reproduce exactly, and it is even subject to tiny changes over time, for example by accumulation of contaminants on the surface, which are not completely understood.
Thus, as Peter Becker and Arnold Nicolaus write in their feature article "The marathon race to an new atomic kilogram" (Europhysics News 40(1), 2009, pp 23-26), the Comité International des Poids et Mesures (CIMP, the International Committee for Weights and Measures) hopes to reach a redefinition of the kilogram by 2011, linking the unit of mass to fundamental constants of nature, in a way that is reproducible with a measurement uncertainty of the order 10−8.
There are now two main roads which are being explored to reach these goals, the Watt balance and the Avogadro Project. While the Watt balance tries to link the kilogram to the Planck constant h by electro-mechanical experiments and exploiting the Josephson and quantum hall effects, the Avogadro Project aims at counting as accurate as possible the atoms in sphere of pure silicon, thus linking the unit of mass to the mass of a single silicon atom.
I find the approach of the Avogadro Project very intriguing, because it is so elementary.
In the current definition of the Système International, the base unit mole is linked to the kilogram: It's the amount of a substance which contains as many particles as there are carbon atoms in 12 gram of monoisotopic carbon-12. This number is the famous Avogadro constant, NA = 6.02214179(30)×1023, a huge number which is currently known with an uncertainty of 5×10−8.
Now, if there was a way to reliably count the number of a atoms in a piece of matter to a higher accuracy, on could revert the relation of the mole and the kilogram: The kilogram then could be defined as the mass of a certain amount of atoms. This is the idea behind the Avogadro Project.
To put this idea in practice, one fabricates spheres out of silicon single crystals, whose diameters are measured to within parts of a nanometre. From the accurately known size of the silicon crystal unit cell, one can then calculate the number of atoms in the sphere to a very high precision. If one knows the isotopic composition of the silicon, or uses highly enriched, nearly monoisotopic silicon-28, one can calculate the mass of the sphere.
|One of the "Silicon Avogadro Spheres" at the National Physical Laboratory (NPL), Teddington, UK.|
Peter Becker and Arnold Nicolaus, who are working on the Avogadro Project at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig, the German national metrology institute, describe in their report the many complicated steps and technically challenges to be met to realise the elementary idea of the "counting of atoms".
And it is a truly international project: The highly enriched silicon-28 is produced in Russia, it is grown in defect-free single crystals in Berlin, and processed to the perfect spheres by the Australian Centre for Precision Optics (ACPO). The Australian laboratory also has the means to precisely measure the size of the sphere. Finally, the surface of the sphere, which is covered by a thin film of oxide, is characterized by the British National Physical Laboratory (NPL).
|A "Silicon Avogadro Sphere" as seen by the Australian Centre for Precision Optics: Colour encodes the diameter of the sphere along different directions, running from 93.634370 mm (blue) to 93.634415 mm (red). From Peter Becker and Arnold Nicolaus: The marathon race to an new atomic kilogram.|
It is not clear yet whether the Avogadro Project can reach the accuracy requested by the International Committee for Weights and Measures, and if it can outdo the Watt balance project as the method of choice to define the kilogram. Anyway, it is a wonderfully elegant idea to define a unit of mass: Just link it to the mass of a silicon atom and count atoms.
- Peter Becker and Arnold Nicolaus: The marathon race to an new atomic kilogram, Europhysics News 40 (1) 2009, 23-26.
- Wanted: A new kilogram (Physikalisch-Technische Bundesanstalt Braunschweig)
- The Avogadro Project at the Australian Centre for Precision Optics of the Commonwealth Scientific and Industrial Research Organisation
- The Avogadro Project at the National Physical Laboratory