The main motivation of the project was to remove – jointly with parallel works carried out by the NIST and NRC – the discrepancies observed between the 2010 results of the watt-balance and atom count experiments. The two experiments achieved now results that are both precise enough, and in sufficient agreement, to topple the present definition. Based also on the project results, in August 2015, was recommended a value of Planck’s constant having a 12 x 10-9 h uncertainty, over one-quarter of the 2010 uncertainty and within the requirements to make the kilogram redefini-tion possible.
The determinations of the Avogadro constant by atom counting contributed to the drafting of a set of instructions that allows the kilogram to be realized in practice at the highest level. The LNE and METAS, although did not yet deliver values of the Planck constant fulfilling the recommendations, progressed the European independence in the future mass metrology. Besides, to date, only the watt balance experiment run by the NRC (Canada) complies with the recommended performance, but many competing experiments have been put on the track worldwide.
The project demonstrated that, provided the source material is chemically and physically well char-acterized with respect to i) the mass fractions of the minor isotopes and impurities, ii) the value of the lattice parameter, and the iii) crystallographic perfection, material realizations of the kilogram and its submultiples in the form of crystal spheres require only volume measurements and surface characterizations. Once the invariant sphere-properties – that is, crystallographic perfection, chem-ical and isotopic purity, and lattice parameter – have been quantified, the count reduces to the measurement of the variable quantities – that is, geometrical, physical, and chemical characteriza-tion of the surface and volume. In practice, this corresponds to label a sphere by its density – instead of its mass – and to obtain its mass via volume measurements and surface characteriza-tion.
Long term impact is conditioned by the cost of enriched silicon. However, to realize a sphere that does not require recalibration by mass measurements, accepting that it is calibrated for the first time by a mass comparison against a 28Si standard, the use of enriched silicon is not strictly nec-essary. In fact, only the variable part of the atom-count procedure needs to be repeated and this recount does not depend on how the count was done the first time. Therefore, relatively cheap spheres – in principle, having the same crystallographic, chemical, and geometric perfections a of 28Si sphere – can be manufactured by using natural silicon. In principle, these standards will never require mass comparisons to be recalibrated and, if a breakthrough will make an accurate determi-nation of the isotopic composition possible, they open the door to a future spread of primary realizations.
Natural silicon spheres will be a tool to make kilogram realizations accessible to any laboratory capable to carry out surface characterizations and volume measurements. In addition, being mate-rial standards, silicon spheres will affect minimally the kilogram dissemination. Verifications will no longer be constrained by fears of irreversible mass changes, because mass changes can be identified, quantified, and explained by the parallel observation of volume and surface changes. Eventually, contrary to Pt-Ir standards, there are not (or significantly smaller) cost barriers to the usage of natural silicon mass-standards in secondary laboratories and industries.
