The Measurement of the Silicon Lattice Parameter and the Count of Atoms to Realise the Kilogram

Abstract

X-ray interferometry established a link between atomic and macroscopic realisations of the metre. The possibility of measuring the silicon lattice parameter in terms of optical wavelengths opened the way to count atoms, to determine the Avogadro constant with unprecedented accuracy, and, nowadays, to realise the kilogram from the Planck constant. Also, it is a powerful tool in phase-contrast imaging by X-rays and, combined with optical interferometry, in linear and angular metrology with capabilities at the atomic scale. This review tells the history of the development of this fascinating technology at the Istituto Nazionale di Ricerca Metrologica in the last forty years. Eventually, it highlights its contribution to the redefinition of the International System of Units (SI).

Redefinition of SI Units and Its Implications

“…The results depict that the numerical and experimental determinations of the surface stress are challenging. Lattice strains and lattice parameter of measurements are underway to work out the problem of phase topography [4].…”

The kilogram: inertial or gravitational mass?

“…where m i ( 28 Si ball) is the ball's inertial mass and M (−) indicates the molar mass [4]. Since Si crystals are never perfect, mono-isotopic, and pure, ( 1) is corrected for the isotope abundances, impurities, and point defects (vacancies and interstitials).…”

“…Since the free-falling body and 28 Si ball ball have different compositions, (4) shows that the atom count and Kibble balance measure different quantities.…”

Defocused travelling fringes in a scanning triple-Laue X-ray interferometry setup

“…Detailed descriptions of the experimental apparatus are given elsewhere (Bergamin et al, 1993(Bergamin et al, , 2003Ferroglio et al, 2008;Massa et al, 2011Massa et al, , 2015Massa et al, , 2020. The analyser is displaced using a guide where an L-shaped carriage slides on a quasioptical rail.…”