Volume measurements of²⁸Si-enriched spheres using an improved optical interferometer for the determination of the Avogadro constant

Abstract

For the determination of the Avogadro constant by the x-ray crystal density method, an accurate volume measurement of 1 kg Si spheres is of primary importance. For this purpose, an optical interferometer was improved and used to measure the volumes of two 1 kg silicon spheres which were manufactured from a silicon crystal highly enriched in 28 Si. The apparent volumes of the spheres, which do not take into account the influence of the surface layers on the volume measurement by interferometry, were determined with a relative standard uncertainty of as small as 2.0 × 10 −8 . The surface of the spheres was characterized by using an improved spectroscopic ellipsometer. By considering the influence of the surface layers, the core volumes of the spheres, which exclude the surface layers, were determined. These results were used for the determination of the Avogadro constant in 2015 as a framework organized by the International Avogadro Coordination project. This paper provides details on the measurements, the improvements made to the apparatus, the data analysis and the uncertainty evaluation.

New Definitions of the Kilogram and the Mole: Paradigm Shift to the Definitions Based on Physical Constants

“…In a set of diameter measurements, the diameter is measured from 145 directions distributed near-uniformly on the sphere surface. 19 The set of diameter measurements is repeated, and between the sets, the for AVO28-S5c and 2.2 × 10 −8 for AVO28-S8c. 19 A different type of optical interferometer developed at the Physikalisch-Technische Bundesanstalt (PTB, Germany) was also used to measure the volume of AVO28-S5c…”

Determination of the Avogadro constant by the XRCD method using a28Si-enriched sphere

“…In a set of the diameter measurement, the diameter was measured from 145 directions distributed near-uniformly on the sphere surface [12,15]. The set of the diameter measurement was repeated 15 times.…”

“…The mean residual of the fitting was used as the uncertainty in the interferogram analysis [15]. Because this is a random uncertainty due to the noise in the interferogram, the uncertainty contributions from this source in 2015 and 2017 are not correlated.…”

“…In the volume measurements by interferometry in 2015 and 2017, the directions of the diameter measurement were determined based on 145 directions distributed nearly uniformly on the sphere surface [11,15]. In a set of the diameter measurement, the diameter was measured in the 145 directions, and the volume was determined from the average diameter.…”

“…In the sphere volume measurement by PTB in 2015, an optical interferometer with a spherical etalon was used [8,35]. The optical configuration and phase-shifting algorithm of the PTB interferometer were completely different from those of the NMIJ interferometer used in 2015 [8,15] and 2017 [11]. The uncertainty contributions of the sphere volume measurements by the two interferometers are therefore uncorrelated.…”