Volume Measurement of a ²⁸Si-Enriched Sphere to Realize the Kilogram Based on the Planck Constant at NMIJ

The kilogram based on the Plank constant will be realized at the National Metrology Institute of Japan (NMIJ) by using the X-ray crystal density method. In this study, for the realization, the volume of a ²⁸ Si-enriched sphere, named AVO28-S5c, was measured. The volume was determined from diameter measurements taken in many directions using an optical interferometer. The apparent volume of the sphere, which does not consider the influence of the surface layers on the volume measurement, was determined with a relative standard uncertainty of $1.8\times 10^{-8}$ . The reproducibility of the kilogram realization is important for the reliable dissemination of the kilogram at the NMIJ. Therefore, the volume determined in this study was compared with that determined in 2016. These volumes were shown to agree with the uncertainty. This article provides details on the measurements, improvements of the interferometer, data analysis, and uncertainty evaluation.