Determination of the Avogadro constant by accurate measurement of the molar volume of a silicon crystal

In order to determine the Avogadro constant by the x-ray crystal density method, the molar volume of silicon in a single crystal grown by the float-zone method was determined by absolute measurements of the density and the molar mass of the crystal. The density was directly determined by mass and volume measurements of 1 kg spheres fabricated from the crystal. For the volume determination, a scanning-type optical interferometer was developed to measure the diameters of the spheres. The molar mass measurements were calibrated using synthetic isotope mixtures prepared from enriched silicon isotopes. Two spheres for density measurements, and fourteen samples for molar mass measurements, were systematically prepared from the crystal to evaluate distributions of the density and the isotopic composition of the crystal. The results give a molar volume of 12.0588646 cm 3 /mol with a standard uncertainty of 0.0000026 cm 3 /mol, at 22.500 °C and 0 Pa after correction for impurities. When this value is combined with the lattice constant of the crystal determined using a combined x-ray/optical interferometer, a value of 6.0221550 × 10 23 mol -1 with a standard uncertainty of 0.0000016 × 10 23 mol -1 is obtained for the Avogadro constant.