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

中国物理B ›› 2011, Vol. 20 ›› Issue (9): 90601-090601.doi: 10.1088/1674-1056/20/9/090601

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

张继涛, 吴学健, 李岩

State Key Laboratory of Precision Measurement Technology & Instruments, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, China

收稿日期:2011-01-04 修回日期:2011-04-07 出版日期:2011-09-15 发布日期:2011-09-15
基金资助:
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).

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

Zhang Ji-Tao(张继涛)^†, Wu Xue-Jian(吴学健), and Li Yan(李岩)

State Key Laboratory of Precision Measurement Technology & Instruments, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, China

Received:2011-01-04 Revised:2011-04-07 Online:2011-09-15 Published:2011-09-15
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

Key words: metrology, Avogadro constant, silicon sphere, spherical harmonics

中图分类号: (Metrology)

06.20.-f

06.20.Jr (Determination of fundamental constants) 06.30.Bp (Spatial dimensions)

张继涛, 吴学健, 李岩. Uncertainty reevaluation in determining the volume of a silicon sphere by spherical harmonics in an Avogadro project[J]. 中国物理B, 2011, 20(9): 90601-090601.

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[J]. Chin. Phys. B, 2011, 20(9): 90601-090601.

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

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

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