Determination of the Avogadro Constant

Measurements are reported on the densities and isotopic-abundance ratios of nearly perfect Si single crystals. These, when combined with optical interferometry of the crystal repeat distance, yield a new value for the Avogadro constant. This result, $N_A=6.022\mathrm{}0943\times {10}^{23}$ ${\mathrm{mol}}^{-1\mathrm{}}$ (1.05 ppm), represents a more than thirty-fold reduction in the uncertainty of previous direct measurements.