Accurate determination of the density of a crystal silicon sphere

For an independent determination of the Avogadro constant, the density of a 1-kg crystal silicon sphere was determined by direct measurements of its mass and volume. A scanning-type interferometer was used to measure the diameters, and the volume was calculated from the mean of uniformly distributed diameters. The sphere was weighted using a balance for the prototype kilogram at the National Research Laboratory of Metrology (NRLM), and the mass was determined accurately by direct measurements of the buoyancy force acting on the sphere. The total uncertainty of the density is estimated to be 0.34 ppm. Effects of a thin oxide layer and impurities on the density of a pure crystal are evaluated