Volume Measurement of a 28Si-Enriched Sphere for a Determination of the Avogadro Constant at NMIJ

For a determination of the Avogadro constant by the X-ray crystal density method, the volume of a Si sphere manufactured from a Si crystal isotopically enriched in ²⁸Si, named Si28-23Pr11, was measured at the National Metrology Institute of Japan (NMIJ). The volume was determined on the basis of diameter measurement in 2175 directions by an optical interferometer. The surface layers on the sphere were characterized by X-ray photoelectron spectroscopy and spectroscopic ellipsometry. Taking into account the effect of the surface layers on the diameter measurement, the volume of the Si core excluding the surface layers was determined with a relative uncertainty of 2.0×10^-8. The results were used to determine the Avogadro constant in 2017 by the International Avogadro Coordination project, which was used as an input datum to determine the CODATA 2017 adjusted value of the Planck constant h. This h value will be used in the new definition of the kilogram. This paper provides details of the measurement apparatus and the uncertainty analysis of the Si core volume measurement. In addition, an approach to reduce the uncertainty in the Si core volume determination is proposed for the accurate realization of the kilogram based on the new definition at NMIJ. Details of the approach are also provided.