Absolute measurement of the density of silicon crystals in vacuo for a determination of the Avogadro constant

An absolute measurement of the density of silicon crystals used for a determination of Avogadro constant is described. Two 1-kg spheres of nearly perfect geometries were fabricated from a single-crystal silicon ingot both for measuring their densities and for determining the density distribution in the ingot. A scanning type optical interferometer was used to measure their diameters in vacuo. Their volumes were obtained by fitting the diameters to a series of spherical harmonics. Thickness of oxide layers on their surfaces was measured by using an ellipsometer to evaluate its effect on their volumes. The masses of the spheres were measured by using a precision balance for the prototype kilogram. The relative total uncertainty of the densities, determined by direct measurements of their masses and volumes in vacuo, is estimated to 1.1×10^-7