Measurement of the {2 2 0} lattice-plane spacing of a²⁸Si x-ray interferometer

Abstract

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.

Challenges in nanometrology: high precision measurement of position and size

“…One of the challenges is related to the precise determination of the Avogadro constant [8]. Within this task the lattice plane spacing of isotope enriched 28 Si material needs to be determined experimentally using a combination of an x-ray interferometer with a high precision optical interferometer [9] …”

A more fundamental International System of Units

“…The present definition of the meter as "the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second" demonstrates the scalability of an explicitly defined constant. At the small length scale, state-of-the-art x-ray interferometry measurements have determined the lattice spacing of isotopically enriched silicon-28 crystals 6 with an absolute uncertainty that is less than 10 −18 m (relative uncertainty of 5 parts in 10 9 ). At the large length scale, the lunar laser ranging experiment can measure the Earth-Moon distance with an absolute uncertainty approaching 1 mm (relative uncertainty less than 1 part in 10 11 ) by timing the roundtrip flight of a laser pulse from Earth to the Moon and back.…”

Accurate measurements of the Avogadro and Planck constants by counting silicon atoms

“…To eliminate the adverse influence of the refractive index of air and to achieve millikelvin temperature uniformity and stability, the experiment is carried out in a thermovacuum chamber. Continuous developments led to a measurement accuracy of 3.5 nm/m [21].…”