Volume measurements of 28Si-enriched spheres using an improved optical interferometer for the determination of the Avogadro constant

For the determination of the Avogadro constant by the x-ray crystal density method, an accurate volume measurement of 1 kg Si spheres is of primary importance. For this purpose, an optical interferometer was improved and used to measure the volumes of two 1 kg silicon spheres which were manufactured from a silicon crystal highly enriched in Si-28. The apparent volumes of the spheres, which do not take into account the influence of the surface layers on the volume measurement by interferometry, were determined with a relative standard uncertainty of as small as 2.0 x 10(-8). The surface of the spheres was characterized by using an improved spectroscopic ellipsometer. By considering the influence of the surface layers, the core volumes of the spheres, which exclude the surface layers, were determined. These results were used for the determination of the Avogadro constant in 2015 as a framework organized by the International Avogadro Coordination project. This paper provides details on the measurements, the improvements made to the apparatus, the data analysis and the uncertainty evaluation.