Determination of the Avogadro constant by the XRCD method using a 28Si-enriched sphere

Abstract

To determine the Avogadro constant NA by the x-ray crystal density method, the density of a 28Si-enriched crystal was determined by absolute measurements of the mass and volume of a 1 kg sphere manufactured from the crystal. The mass and volume were determined by an optical interferometer and a vacuum mass comparator, respectively. The sphere surface was characterized by x-ray photoelectron spectroscopy and spectroscopic ellipsometry to derive the mass and volume of the Si core of the sphere excluding the surface layers. From the mass and volume, the density of the Si core was determined with a relative standard uncertainty of 2.3 × 10−8. By combining the Si core density with the lattice constant and the molar mass of the sphere reported by the International Avogadro Coordination (IAC) project in 2015, a new value of 6.022 140 84(15) × 1023 mol−1 was obtained for NA with a relative standard uncertainty of 2.4 × 10−8. To make the NA value determined in this work usable for a future adjustment of the fundamental constants by the CODATA Task Group on Fundamental Constants, the correlation of the new NA value with the NA values determined in our previous works was examined. The correlation coefficients with the values of NA determined by IAC in 2011 and 2015 were estimated to be 0.07 and 0.28, respectively. The correlation of the new NA value with the NA value determined by IAC in 2017 using a different 28Si-enriched crystal was also examined, and the correlation coefficient was estimated to be 0.21.