Primary calibration of the volume of silicon spheres

Abstract

For direct density determination by so-called absolute procedures, the mass and the volume of a body must be determined. The paper gives an overview of dimensional measurements of silicon spheres used as density standards. Relative uncertainties for diameter measurements of less than 10−8 can only be achieved with interferometric procedures. After introducing optical interferometry the two main types of interferometers used are described in detail: plane-face interferometers and interferometers with spherical beam path. At present, uncertainties of 1 nm can be achieved for a diameter determination of silicon spheres, which corresponds to a relative volume uncertainty of ΔV/V = 3 × 10−8.

Realization of the kilogram by the XRCD method

“…The standard Comparison of interferometers used to measure the diameter of silicon spheres. Optical configurations used at PTB (a) and at NMIJ (b) [13,14].…”

“…Later, Zerodur cubes were similarly used as primary density standards to determine the density of silicon crystals by hydrostatic weighing and to determine the Avogadro constant with a relative standard uncertainty of 1.1 parts in 10 6 [11]. After the development of a polishing technique for manufacturing 1 kg Si spheres [12], it became possible to determine the density of a Si crystal by direct measurements of its diameter and mass thereby eliminating the need for hydrostatic weighing, leading to substantial reduction of uncertainty in the density measurement [13][14][15]. In order to further reduce the abovementioned uncertainty, an accurate evaluation of surface layers of the Si sphere became necessary.…”

Experimental Study of Volume Calibration of Mass Weight With Hydrostatic Weighing

“…Hydrostatic weighing method is one of traditional volume measuring methods with high measuring accuracy. With the development of Avogadro project [1][2][3], solid density standards are more used for the high repeatability and stability of density value, comparing with the liquid density standards. The volume of mass standard is needed to be measured in order to correct the air bouncy during the mass calibration process.…”

The Avogadro constant: determining the number of atoms in a single-crystal 28 Si sphere

“…The Avogadro constant N A is the number of atoms or molecules in a mole of a pure substance, for instance, the number of atoms (unbound, at rest and in their ground state) in 12 g of the carbon isotope 12 C. Therefore, N A expresses the mass of 12 C in kilograms according to M ( 12 C) = N A m( 12 C), where M ( 12 C) = 12 g mol −1 and m( 12 C) are the molar mass and atomic mass of 12 C, respectively. Many different measurements of the Avogadro constant, from that of Loschmidt to that of Perrin, supported the Maxwell and Boltzmann descriptions of matter in terms of atoms [1].…”