Improvements to the Volume Measurement of 28Si Spheres to Determine the Avogadro Constant

In the determination of the Avogadro constant using the X-ray crystal density method with a ²⁸Si-enriched crystal prepared by the International Avogadro Coordination (IAC) project, the volume measurement and surface analysis of ²⁸Si spheres play a crucial role. For accurate volume determination, an optical interferometer has been improved taking account of the geometrical shape of the optical components. Furthermore, a new spectroscopic ellipsometer with a sphere rotation system has been developed for accurate surface analysis. The optical interferometer and the ellipsometer have been used for the volume determination and surface analysis of the ²⁸Si spheres repolished by the IAC, respectively. On the basis of the preliminary uncertainty estimation, the relative standard uncertainty of the apparent volume measurement has been reduced from 4.4 $times 10^{-8}$ to 2.7 $times 10^{-8}$ by the improvement of the interferometer. The number of ellipsometric measurement points on the sphere surface has been increased from 20 to 7782 by the installation of the new ellipsometer, yielding more reliable information on the sphere surface. Details of the improvements and the preliminary results of the measurements of the ²⁸Si spheres are given.