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2016/32/1 Sphere with stand and case, silicon / glass / timber / metal / plastic, made by Achim Leistner, for CSIRO / Avogadro Project, Sydney, New South Wales, Australia, 1994-2000. Click to enlarge.

One kilogram silicon sphere made at CSIRO for the Avogadro Project

This sphere was produced as part of an international project known as the Avogadro project. The goal of the Avogadro Project is to measure the value of the Avogadro constant to extreme precision, thereby allowing the mass of the kilogram to be defined in terms of the Avogadro constant. This would do away with the current physical artefact (a cylinder made of an alloy of platinum and iridium) and allow the kilogram to be reproduced in any laboratory by following a prescribed procedure.

Since …


Object No.


Object Statement

Sphere with stand and case, silicon / glass / timber / metal / plastic, made by Achim Leistner, for CSIRO / Avogadro Project, Sydney, New South Wales, Australia, 1994-2000

Physical Description

A polished silicon sphere measuring 93.6 mm in diameter, and having a mass of 1 kilogram. The sphere is mounted on three clear support legs, which are attached to a rectangular black base. The sphere and its supports are surrounded by a silver coloured metal ring. There is a silver plaque at one end of the base with an inscription.


No marks on the sphere. There is a plaque is inscribed with the words 'Achim Leistner / Fifty years a Master Optician and Atom Masseur / "You can't do better than that" / 19 September 2000'.



This sphere was made for the Avogadro project, an international effort to redefine the kilogram in terms of the Avogadro constant (a fundamental physical constant). Perfect spheres of single-crystal silicon (such as this) are produced and the exact volume and number of atoms in the sphere measured, allowing the value of the Avogadro constant to be very precisely measured. The sphere was chosen as the ideal shape because it has no corners or edges (to minimise chipping and wear), and because - provided a sufficiently perfect sphere can be manufactured - the volume can be calculated from a single measured parameter (the diameter). Silicon was chosen over other elements (such as carbon) as the material for the sphere, as there already exist mature processes for the production and manipulation of ultra-high purity silicon from the electronics industry.

The fabrication of the spheres is a multi-step process. To begin with an ingot or boule of single-crystal silicon is produced. This is 'grown' through a procedure known as the Float zone (FZ) process. From there, the production of the sphere is carried out in three main steps: (1) rough shaping using diamond tools and course loose abrasives, (2) fine grinding using loose abrasives down to a precision of 1 micrometre, and (3) polishing and finishing. The boules are manufactured in Germany and Japan, while the spheres are produced (through the grinding and polishing procedure described above) at CSIRO in Australia.

There are several parameters and factors which need to be carefully measured or controlled during the production. This includes: roundness characterisation, surface impurities, diameter measurement, mass measurement, molar mass, lattice parameter, and crystal structure. Achieving sufficient roundness, and characterising any imperfections are critical if the volume is to be derived directly from the diameter. The diameter of the sphere is measured using a technique called optical interferometry and the mass was measured against a 1 kg stainless steel working standard, using a high precision balance. The molar mass of the silicon sphere is determined using a technique called mass spectrometry, and the lattice parameters were measured using X-ray crystal diffraction.

There are 7 main laboratories around the world involved in the Avogadro project and in the measurement of the various parameters listed above. This includes IRMM (Belgium), PTB (Germany), IMGC (Italy), NRLM (Japan) NIST (USA), NPL (UK), and CSIRO/NML (Australia). Some parameters are measured and verified by all 7 laboratories, while others (e.g. the molar mass and lattice parameters) are measured by just one or two (depending on their capabilities) and shared with the other organisations in the project. Australia and the CSIRO, however, have played a critical role, as CSIRO is currently the only organisation which manufactures the spheres used in the project.

This sphere was made by Achim Leistner at CSIRO. Leistner has made his career in crafting precision optics, and was the Master Optician for the Avogadro project. Leistner's fabrication method involves precision handcrafting, to ensure minimisation of any irregularities. In addition to scientific instruments he uses his hands to feel for any imperfections in the surface of the spheres, and his fabrication method has been found to be superior to any purely machine-based method.

This sphere is one of the prototypes produced in the development and testing of the methodology. It was considered the very first meaningful sphere produced for the project, in terms of its precision in roundness and surface quality. While the final spheres are made of a single isotope of silicon, this one is made of naturally-occurring silicon, which comprises a mixture of isotopes. However, as far as the roundness is concerned, the quality of the sphere is as good as any of the final spheres made for the Avogadro Project.



Over the last 200 years, the definition of a kilogram has changed several times, as technology has advanced and as the required accuracy has increased. In 1895 a gram was defined by the mass of one cubic centimetre of water at 0 degrees (the freezing point of water, with a kilogram being one thousand times this mass. This definition was refined a few years later, in 1799, with the mass being measured at a temperature of 4 degrees instead (which represents the point of maximum density of water). The same year, the Kilogram de Achives was produced, a platinum cylinder which remained the mass-standard for the kilogram from the next 90 years.

In 1875 a new mass kilogram was produced - a cylinder made of an alloy of 90% platinum and 10% iridium, known as the International Prototype Kilogram (IKP). The cylinder measures 39.17 mm in both dimeter and height (a right-cylinder), with the shape chosen to minimise the surface area. The addition of Iridium improved on the previous standard by increasing the hardness while retaining the desirable properties of platinum, such as high density and extreme resistance to oxidation. In 1883 the IKP was weighed and the mass found to be indistinguishable from the Kilogram de Archives. In 1889 is was formally ratified as the kilogram and has remained the standard ever since.

As of 2014 the kilogram remains the only SI unit still defined by a physical artefact. The metre and second have both recently been redefined in terms of fundamental physical constants, allowing them to be reproduced in any laboratory by following a prescribed procedure. In 2005, at the 94th meeting of the International Committee for Weights and Measures (CIPM), it was recommended that the same be done for the kilogram.

Several methods have been suggested for redefining the kilogram (some of which have since been abandoned). One of these is the Watt balance, which measures the electric power necessary to oppose the weight of a kilogram test mass as it is pulled by the Earth's gravity. Another approach is the 'atom counting' method, which involves determining the exact volume and exact number of atoms in a perfect sphere of silicon. This allows the value of the Avogadro constant (a fundamental constant) to be determined with great accuracy, and for the kilogram to be defined in terms of the Avogadro constant.

As of 2016, spheres are capable of being manufactured with sufficient quality to allow the measurement of the Avogadro constant to an uncertainty of 1 part in 10^7, which is comparable to the current accuracy achieved with the IKP. However, in order to replace the IKP, the uncertainty still needs to be improved by an order of magnitude (i.e. down to 1 part in 10^8). In order to do so, however, significant technological advancements will be required beyond what is currently available. It is expected that a new definition for the kilogram will replace the existing physical artefact in 2018.

This sphere is one of the prototypes used in the Avogadro project, and was given to Leistner in 2000, to acknowledge his 50 years of service in the field of precision optics, and his contribution to the Avogadro project in particular.


Credit Line

Gift of Achim Leistner, 2016

Acquisition Date

8 September 2016

Cite this Object


One kilogram silicon sphere made at CSIRO for the Avogadro Project 2023, Museum of Applied Arts & Sciences, accessed 1 June 2023, <>


{{cite web |url= |title=One kilogram silicon sphere made at CSIRO for the Avogadro Project |author=Museum of Applied Arts & Sciences |access-date=1 June 2023 |publisher=Museum of Applied Arts & Sciences, Australia}}