The correlation of the $N_A$ measurements by counting $^{28}$Si atoms

TL;DR

This paper reports an improved measurement of the Avogadro constant by counting $^{28}$Si atoms in isotopically enriched silicon spheres, with enhanced precision and correlation analysis for better accuracy.

Contribution

It introduces refined measurement techniques for silicon sphere properties and provides a correlation estimate to improve the accuracy of Avogadro constant determination.

Findings

Reduced uncertainty in molar mass, lattice parameter, mass, and volume measurements.

Enhanced sphere surface quality through etching and repolishing.

Estimated correlations improve the reliability of the measurements.

Abstract

An additional value of the Avogadro constant was obtained by counting the atoms in isotopically enriched Si spheres. With respect to the previous determination, the spheres were etched and repolished to eliminate metal contaminations and to improve the roundness. In addition, all the input quantities -- molar mass, lattice parameter, mass, and volume -- were remeasured aiming at a smaller uncertainty. In order to make the values given Refs.\ 1 and 2 usable for a least squares adjustment, we report about the estimate of their correlation.