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

作　　者：张继涛 吴学健 李岩 

机构地区：[1]State Key Laboratory of Precision Measurement Technology & Instruments,Department of Precision Instruments and Mechanology,Tsinghua University

出　　处：《Chinese Physics B》2011年第9期152-158,共7页中国物理B（英文版）

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

摘　　要：To determine the Avogadro constant with a target relative uncertainty of 2 x 10-s, 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.To determine the Avogadro constant with a target relative uncertainty of 2 x 10-s, 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.

关 键 词：METROLOGY Avogadro constant silicon sphere spherical harmonics 

分 类 号：TN304.12[电子电信—物理电子学]