The spacing of the {2 2 0} lattice planes of a 28Si crystal, used to determine the Avogadro constant by counting silicon atoms, was measured by combined x-ray and optical interferometry to a relative accuracy of 3.5 × 10−9. The result is d2 2 0 = (192 014 712.67 ± 0.67) am, at 20.0 °C and 0 Pa. This value is greater by (1.9464 ± 0.0067) × 10−6d2 2 0 than the spacing in natural Si, a difference which confirms quantum-mechanics calculations. This result is a key step towards a realization of the mass unit based on a conventional value of the Planck or the Avogadro constant.

A combined X-ray and optical interferometer capable of centimeter displacements has been made to measure the lattice parameter of Si crystals to within a 3 x 10(-9) relative uncertainty. This paper relates the results of test measurements carried out to assess the capabilities of the apparatus.

To determine the volume of solid density standards, manufactured as Si-crystal spheres, an optical interferometer is used to measure their diameter at the NMIJ. To support and complement these measurements, the effect of the Gouy phase has been studied analytically and numerically. In measurement, the sphere is placed between the end-mirrors of a Fizeau cavity and the distances between the cavity mirrors and the sphere are measured, as well as the cavity length. The present analysis outlines a model of the interferometer operation and quantifies the Gouy-phase correction in the diameter measurement.

No abstract