Mass determination of silicon spheres used for the Avogadro project

The members of the International Avogadro Project are aiming at the redetermination of Avogadro's constant with a relative uncertainty of less than 2×10−8 in order to be qualified for the redefinition of the kilogram. Therefore, among other quantities, the volume of a sphere made of a silicon single crystal has to be determined very precisely with a diameter uncertainty of 0.3 nm. A special Fizeau interferometer with spherical reference faces has been developed at PTB providing the required precision in absolute interferometry and a generous coverage of the surface of the sphere at the same time. Due to the intrinsic imbalanced distribution of measurement positions given by the setup, an equalization has to be performed without introducing a numerical error. In this paper an appropriate procedure using point distributions on a sphere is described and characterized with regard to the number of points involved.

Section: Introductionmentioning

confidence: 99%

Influence of the distribution of measuring points on the mean diameter determination of the Avogadro project's silicon spheres

Bartl¹,

Nicolaus²

2009

“…To cover the sphere completely with measuring points, a set of about 20-40 segmentsdepending on the amount of overlap-is necessary. Since in the measurement data D, d 1 and d 2 represent only fractional orders of interference, an offset that corresponds to the integral orders of interference has to be added to get the actual diameter d. In the present case this offset can be derived from the mass and density measurements [12][13][14] of the sphere. During the measurement procedure for getting the whole topography the sphere is handled by a lifting and positioning mechanism.…”

Section: The Sphere Interferometermentioning

confidence: 99%

Interferometric determination of the topographies of absolute sphere radii using the sphere interferometer of PTB

Bartl

Krystek

Nicolaus

et al. 2010

This paper presents a method to reconstruct the absolute shape of a sphere-i.e. a topography of radii-using the sphere interferometer of PTB in combination with a stitching approach. The method allows for the reconstruction of absolute radii instead of the relative shape deviations which result from conventional sphericity measurements. The sphere interferometer was developed for the volume determination of spherical material measures-in particular the spheres of the Avogadro project-by precise diameter measurements with an uncertainty of 1 nm or less. In the scope of the present work a procedure has been implemented that extends the applicability of the interferometer to fields where not the volume or diameter but the direction-dependent radii are of interest. The results of the reconstruction were compared quantitatively to the independent results of sphericity measurements from CSIRO.

“…The density of AVO1 was measured in a project in order to determine the Avogadro constant by using a silicon single crystal. The mass was determined with a standard uncertainty of 19 µg [17,26] and the volume was calculated from more than 100 000 diameter values measured in the spherical interferometer of PTB [17,27]. This primary density standard has a standard uncertainty of 0.08 ppm.…”

Section: Applicationsmentioning

confidence: 99%

Solid density determination by the pressure-of-flotation method

Bettin¹,

Toth²

2006

After a short overview of flotation methods and experiments, basic equations for the pressure-of-flotation method are given including a temperature and composition dependence of the liquid's thermal expansion and compressibility. Then, the pressure-of-flotation experiment of PTB is described. A new calibration procedure using doped silicon samples is presented. Now, density comparisons of silicon samples can be performed with an uncertainty less than 0.1 ppm for density differences up to 10 ppm, i.e. for practically all undoped silicon samples. Current applications of the method and an outlook to future developments are discussed. Relative uncertainties of the order of 10−9 seem to be possible and would allow new applications.