Uncertainty reevaluation in determining the volume of a silicon sphere by spherical harmonics in an Avogadro project

doi:10.1088/1674-1056/20/9/090601

Abstract To determine the Avogadro constant with a target relative uncertainty of 2 × 10^-8, the uncertainty component of the silicon sphere's volume introduced by the spherical harmonics method, which is usually used in determining the sphere's volume, is reevaluated. By means of representing the shape of the silicon sphere by an ellipsoid with Gaussian white noise in its diameters, the uncertainty of the current mapping methods based on the spherical harmonics theory can be estimated theoretically. It is evidenced that the uncertainty component attributed to the current mapping method is underestimated. To eliminate this effect as much as possible, the number of mapping points should be increased to more than before. Moreover, a new mapping method is proposed to accomplish the equal-area mapping with large number points on the silicon sphere.

Keywords: metrology Avogadro constant silicon sphere spherical harmonics

Received: 04 January 2011
Revised: 07 April 2011
Accepted manuscript online:

PACS:	06.20.-f	(Metrology)
	06.20.Jr	(Determination of fundamental constants)
	06.30.Bp	(Spatial dimensions)

Fund: Project supported by the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2006BAF06B06) and Tsinghua University Initiative Scientific Research Program, China (Grant No. 2009THZ06057).

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Zhang Ji-Tao(张继涛), Wu Xue-Jian(吴学健), and Li Yan(李岩) Uncertainty reevaluation in determining the volume of a silicon sphere by spherical harmonics in an Avogadro project 2011 Chin. Phys. B 20 090601

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Uncertainty reevaluation in determining the volume of a silicon sphere by spherical harmonics in an Avogadro project

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