The determination of the Avogadro constant-not simply a metrological problem

A new round in the determination of the Avogadro constant is under way at Physikalisch-Technische Bundesanstalt (PTB) and at other national metrology institutes perhaps as a step toward an alternative definition of the SI unit of mass. The required measurements of the relevant crystal data are currently hampered by an (unexpected and not yet totally identified) imperfection of the crystal lattice. The vacancy content in ultra-pure silicon crystals was investigated using positron annihilation, density comparators, and X-ray diffraction methods. The results obtained were compared with theoretically predicted lattice deformations around vacancies and defect densities generated during the crystal growth process. The investigations made allow the conclusion to be drawn that the relative amount of unoccupied regular lattice sites does not exceed 10^-8. The relative difference of 3×10 ^-6 in silicon molar volumes recently observed cannot, therefore, be explained by differences in vacancy concentrations. The surface structure of the silicon bodies was investigated by ellipsometry. As a result, the native oxide layer seems to be detrimental to the accurate measurement of the volume of the silicon spheres. New considerations concerning special surface preparations and treatments are discussed