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 me thod, the molar volume of silicon in a single crystal grown by the float-zo ne method was determined by absolute measurements of the density and the mo lar mass of the crystal. The density was directly determined by mass and vo lume measurements of 1 kg spheres fabricated from the crystal. For the volu me determination, a scanning-type optical interferometer was developed to m easure the diameters of the spheres. The molar mass measurements were calib rated using synthetic isotope mixtures prepared from enriched silicon isoto pes. Two spheres for density measurements, and fourteen samples for molar m ass 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 12.058 8646 cm(3)/mol with a standard un certainty of 0.000 0026 cm(3)/mol, at 22.500 degrees C and 0 Pa after corre ction 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 6.022 1550 x 10(23) mol(-1) with a standard uncertainty of 0.0000 016 x 10(23) mol(-1) is obtained for the Avogadro constant.