Gravity and anisotropy effects in the volume determination of Si spheres for the kilogram realisation

The counting of 28Si atoms plays a fundamental role in the realisation of the unit of mass in terms of stipulated values of fundamental physical constants. In this realisation, the measurement of the volume of a 28Si sphere is a fundamental step. This paper reports a finite element analysis of the self-weight effect on the volume determination, taking the crystal anisotropy into account. The sphere volume might be overestimated from 0.3 × 10−9 to 5.1 × 10−9 (relative terms), depending on the crystal orientation and measurement procedure.