Towards a redefinition of the kilogram
The kilogram is the last remaining base unit of the International System of Units (SI) which is still defined by a material artefact. In the present SI "the kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram" which since 1889 has been kept at the BIPM. The main disadvantage of this definition is that it relies on the long term stability of the mass of a material artefact.
When the international prototype of the kilogram (IPK) was manufactured, another six official copies with exactly the same characteristics were also produced. The mass of each official copy has been compared to the mass of the IPK on three separate occasions since 1889 (see the graph below). The average mass of the official copies seems to increase over time with respect to the mass of the IPK, with a drift of approximately 50 µg in 100 years.
Relative mass differences between each of the six official copies and the IPK. These mass comparisons have taken place on three occasions since 1889. The mass of the IPK defines the zero value of the vertical axis of this graph.
To ensure the long-term stability of the mass unit, it is advisable to link the unit of mass to a fundamental constant. Therefore, the General Conference for Weights and Measures (CGPM) recommended at its 21st meeting (1999) that “national laboratories continue their efforts to refine experiments that link the unit of mass to fundamental or atomic constants with a view to a future redefinition of the kilogram” (Resolution 7). The redefinition of the kilogram would also benefit three other base units: the ampere, the mole and the candela, the definitions of which depend on the kilogram.
At the present time, two experiments have succeeded in linking a fundamental constant to the mass of the IPK with a relative uncertainty below 5 parts in 108: these are the Avogadro project and the watt balance.
- The Avogadro project is an international collaboration whose aim is to measure the ratio between the mass of the silicon-28 atom and the mass of the IPK:
in order to determine the Avogadro constant NA. The experiment establishes a direct link between the kilogram and an atomic mass. The principle consists of counting the number of silicon atoms in a 1 kg nearly perfect single-crystal silicon-28 sphere. The lattice parameter of the crystal is accessible to macroscopic measurements, thus avoiding the need to count single atoms. Silicon is used because it is one of the best known materials and can be grown as high purity, large, and almost perfect single crystals.
- The watt balance links the Planck constant h to the mass of the IPK, i.e. it measures the ratio:
The value of h/m28Si, the units of which are independent of mIPK, is already well-known (relative uncertainty = 1.4 × 10-9) and so serves to check the consistency of the two previous methods.
Once these fundamental constants (h, NA) are accurately measured in the present SI, it will be possible to fix the numerical value of the chosen fundamental constant instead of fixing mIPK and so redefine the kilogram. There is a general agreement that h will be chosen.
After the redefinition has taken place, a number of watt balances will be needed to realize the new definition of the kilogram in practice. As the present custodian of the international prototype of the kilogram, the BIPM's future role will be to permanently operate a watt balance to provide a realization of the new definition of the kilogram for national metrology institutes.
After the redefinition and to guarantee robustness, it would be advisable to frequently compare a common measurement obtained from all the available watt balances. For this purpose, it would be beneficial to have a macroscopic mass standard as stable as possible over time. For this reason, the BIPM is currently working to maintain and study an ensemble of macroscopic mass standards (“the BIPM ensemble of mass standards”). In addition, by weighing one (or more) of the artefacts using all the available watt balances (and transfer mass standards), the whole “ensemble” will be traceable to the world-wide ensemble of watt balances.