Mass Measurement of 1-kg Silicon Spheres for Determination of the Avogadro and Planck Constants

Abstract

For the accurate determination of the Avogadro and Planck constants by the X-ray crystal density method, the mass of 1-kg silicon spheres must be measured precisely. This paper describes the mass measurement method and the evaluation of its uncertainty at the National Metrology Institute of Japan (NMIJ). For the precise mass measurement, the amount of the physical adsorption of water vapor on the surface of the silicon spheres, which could be a relative amount of about 10 −8 of the total mass, was evaluated by comparison weighings both in nitrogen gas and in water vapor at a pressure of about 1200 Pa. In addition, we compare the results of seven 1-kg mass measurements conducted at the NMIJ and the International Bureau of Weights and Measures from 1996 to 2011 to confirm the reliability of our mass measurement.

Improved measurement results for the Avogadro constant using a28Si-enriched crystal

“…The thickness of PWL was estimated to be 0.39(9) nm and 0.43(9) nm for AVO28-S5c and AVO28-S8c, respectively. These results were obtained at NMIJ from the comparison weighings in nitrogen gas of about 1200 Pa and in water vapour of about 1200 Pa [42] for the two spheres using a stainless steel weight as a reference. The amount of PWL on the stainless steel weight was determined in advance by comparison weighings using artifacts with large surface area difference.…”

“…The data for the d CWL came from comparison weighings of the two spheres in nitrogen gas, at a pressure of ca.1200 Pa, and in water vapour, at a pressure of ca. 1200 Pa[42]. The density of the PWL was assumed to be 1.0 g/cm 3 4.…”

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

“…The thickness of the PWL was estimated to be 0.39(9) nm for AVO28-S5c and 0.43(9) nm for AVO28-S8c. These results were obtained by comparison weighings of the two spheres in nitrogen gas and in water vapour at pressures of about 1200 Pa at NMIJ [22]. The thickness of the CWL was estimated from the value reported by Mizushima [23] to be 0.28 (8) nm.…”

“…b Thickness of the CWL calculated using the data reported by Mizushima [23]. c Thickness of the PWL measured by comparison weighings of the two spheres in nitrogen gas and in water vapour at pressures of about 1200 Pa [22]. The density of the PWL was assumed to be 1.0 g cm −3 .…”

A numerical investigation of effective optical characteristics of dielectric mixture layer on Si sphere by FDTD method

“…Experiments [25][26][27][28][29] and numerical simulations [30][31][32][33] suggest that the effective optical characteristics of thin films and microscopic structures differ significantly from those of bulk materials. In terms of determining the mass using artefacts, several studies on measuring water sorption on Si spheres and mass standards using ellipsometry [21,34,35] have shown that the thickness of the water layer under ambient (air) conditions tends to be smaller than the values obtained using gravimetry [35][36][37] when the optical constants of bulk materials are used.…”