State-of-the-art mass determination of ²⁸Si spheres for the Avogadro project

For a new determination of the Avogadro constant to play a role in the future redefinition and realization of the mass unit, the mass measurements involved need to be carried out at a very high level of accuracy. From a mass comparison among two 1 kg ²⁸Si spheres and the 1 kg platinum–iridium (Pt/Ir) mass standards, the mass of the spheres must be determined with a combined standard uncertainty of less than 5 µg. The BIPM, the PTB and the NMIJ have carried out such a state-of-the-art mass comparison in air and under vacuum in order to reach this target set by the International Avogadro Coordination (IAC). The results obtained for the spheres AVO28-S5 and AVO28-S8 involved in the comparison have demonstrated that by using air buoyancy artefacts and sorption artefacts it is possible to achieve a relative uncertainty of 4.1 × 10⁻⁹. The reference value for each sphere has been determined, taking into account the traceability of the masses to the International Prototype of the kilogram, , in due consideration of the correlations among 17 standards used directly or indirectly in this comparison.