  New results are reported from an ongoing international research effort to
accurately determine the Avogadro constant by counting the atoms in an
isotopically enriched silicon crystal. The surfaces of two 28Si-enriched
spheres were decontaminated and reworked in order to produce an outer surface
without metal contamination and improved sphericity. New measurements were then
made on these two reconditioned spheres using improved methods and apparatuses.
When combined with other recently refined parameter measurements, the Avogadro
constant derived from these new results has a value of $N_A = 6.022 140 76(12)
\times 10^{23}$ mol$^{-1}$. The X-ray crystal density method has thus achieved
the target relative standard uncertainty of $2.0 \times 10^{-8}$ necessary for
the realization of the definition of the new kilogram.
