Milestone for the kilo

Scientists have succeeded in counting the number of atoms in a crystal of silicon with unprecedented accuracy, marking a major step forwards in efforts to define the kilogram (kg) on the basis of physical constants.

The work, published in the journal Physical Review Letters, was partly supported by the EU through the IMERA Plus (‘Implementing metrology in the European research area – plus’) project. IMERA Plus, which received EUR 21 million under the ‘Coordination of research activities’ budget line of the Seventh Framework Programme (FP7), brings together national metrology research institutes from across Europe to tackle fundamental questions such as the definition of the kilogram.

Today, most measurements are based on fixed physical constants. For example, the International Bureau of Weights and Measures (BIPM) defines a metre as ‘the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second’, while a second is ‘the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom’.

Just one measure has defied definition in this way: the kilogram, which is still defined by the BIPM as ‘equal to the mass of the international prototype of the kilogram’. That international prototype is a block of platinum-iridium (Pt-Ir) kept at the BIPM’s offices in Paris, France. Yet despite the fact that it is kept in carefully controlled conditions, the official kilogram’s weight is not constant; scientists estimate that it has changed by around 50 micrograms over the last century. The hunt is therefore on to come up with a clear, fixed definition of the kilogram.

Since 2003, the international Avogadro project, which is coordinated by the Physikalisch-Technische Bundesanstalt (PTB) in Germany, has been working to arrive at a definition of the kilogram based on the Avogadro constant. In the case of an element, the Avogadro constant refers to the number of atoms in an amount of material whose mass in grams is equivalent to the element’s atomic weight. As such, the Avogadro constant ‘links the atomic and the macroscopic properties of matter’, the researchers write.

In this study, an international team of researchers sought to measure the number of atoms in a single, 1 kg crystal of silicon. According to the team, silicon was chosen because it can be grown into extremely pure, large, and almost perfect crystals. The ultimate goal of the Avogadro project is to measure the Avogadro constant in such a crystal with a measurement uncertainty of just 2 x 10 to the power of -8. The process drew on the expertise of metrology institutes around the world.

The researchers used two spheres, both of which were polished in Australia. The perfection of the crystals was then assessed, as was the influence of crystal lattice defects. The Italian metrology institute (INRIM) employed X-ray interferometry to determine the lattice parameter; its findings were confirmed by comparison measurements on a natural silicon crystal at the US National Institute of Standards and Technology (NIST).

The masses of the two silicon spheres were compared to the mass of kilogram standards held at the BIPM, the PTB and the National Metrology Institute of Japan (NMIJ). The spheres’ silicon dioxide surface layer was subjected to a battery of tests, including X-ray radiation and synchrotron radiation. The contamination of the surface with copper and nickel silicides was also measured and its influence on spheres’ volume and mass assessed. Finally, the team at the PTB used a new mass-spectrometric method to determine the molar mass of the spheres.

Their efforts allowed them to count the number of atoms in the samples with a measurement uncertainty of just 3 x 10 to the power of -8. ‘The value obtained … is the most accurate input datum for a new definition of the kilogram,’ the researchers write.

In a statement, the PTB notes: ‘The result is a milestone on the way towards a successful realisation of the new kilogram definition on the basis of fundamental constants whose values have been fixed.’

The researchers stress that their definition is still not accurate enough to replace the prototype kilogram in Paris; to do that, they would need to achieve an uncertainly level of 2 x 10 to the power of -8, as required by the BIPM’s Consultative Committee for Mass (CCM). However, it does look like that Parisian chunk of metal’s days as the definitive kilogram are numbered.

The researchers conclude: ‘The agreement between the different realisations is not yet as good as it is required to retire the Pt-Ir kilogram prototype, but considering the capabilities already developed and the envisaged improvements it seems to be realistic that the targeted uncertainty may be achieved in the foreseeable future.’

For more information, please visit:

Physikalisch-Technische Bundesanstalt (PTB):

Physical Review Letters:

European Association of National Metrology Institutes (EURAMET):

International Bureau of Weights and Measures (BIPM):

Source: European Commission CORDIS

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