Precision determination of the density of a single crystal silicon sphere and evaluation of the Avogadro constant

Density measurements with relative uncertainty of 1×10^-7 have been made on a highly polished 1-kg single crystal silicon sphere with out-of-roundness <40 nm. Roundness was profiled using a 2-D Talyrond machine and 3-D profiles were produced. The diameter was obtained using optical interferometry for a series of breadth measurements at carefully selected points and by combining them with roundness data. The mass was obtained relative to a 1-kg stainless steel reference with appropriate corrections for air buoyancy and for convection currents due to small temperature differentials. Surface oxide thickness was measured using optical ellipsometry and the data were corrected for this oxide thickness. The molar mass, crystal quality and lattice parameter have been measured elsewhere, enabling a determination of the Avogadro constant to be made. The purpose is to obtain a definition of the kilogram in terms of a specific number of ¹²C atoms