Volume determination of the Avogadro spheres of highly enriched 28Si with a spherical Fizeau interferometer

Within the scope of the efforts concerning the redefinition of the SI base unit 'kilogram' the final results of the international research project aiming at the redetermination of the Avogadro constant are ready to be announced. Among other quantities the volume of two spheres which are made of a highly enriched 28Si single crystal had to be determined. For this purpose a special Fizeau interferometer for the measurement of the spheres' diameters has been developed at PTB. This paper reports the final results of the volumes, the uncertainties and also the latest findings regarding systematic corrections including the effects of surface layers on the pure silicon core. The results are confirmed by density comparison measurements.

[1]  Michael Krystek,et al.  Interferometric determination of the topographies of absolute sphere radii using the sphere interferometer of PTB , 2010 .

[2]  Naoki Kuramoto,et al.  Present State of the avogadro constant determination from silicon Crystals with natural isotopic compositions , 2005, IEEE Transactions on Instrumentation and Measurement.

[3]  J. A. Gaunt The Triplets of Helium , 1929 .

[4]  G. Bartl,et al.  Influence of the distribution of measuring points on the mean diameter determination of the Avogadro project's silicon spheres , 2009 .

[5]  E. Palik Handbook of Optical Constants of Solids , 1997 .

[6]  Michael Borys,et al.  State-of-the-art mass determination of 28Si spheres for the Avogadro project , 2011 .

[7]  Arnold Nicolaus,et al.  The coefficient of thermal expansion of highly enriched 28Si , 2009 .

[8]  H. Böhme,et al.  Phase-determination of Fizeau interferences by phase-shifting interferometry , 1989 .

[9]  Sphericity analysis of solid density standards , 1998 .

[10]  Kenichi Fujii,et al.  Density Comparison of Isotopically Purified Silicon Single Crystals by the Pressure-of-Flotation Method , 2011, IEEE Transactions on Instrumentation and Measurement.

[11]  K. Fujii,et al.  Density comparison measurements of silicon crystals by a pressure-of-flotation method at NMIJ , 2004 .

[12]  Yasushi Azuma,et al.  Surface layer determination for the Si spheres of the Avogadro project , 2011 .

[13]  Nava,et al.  Optical properties of polycrystalline nickel silicides. , 1990, Physical review. B, Condensed matter.

[14]  Ralf D. Geckeler,et al.  Improving the Measurement of the Diameter of Si Spheres , 2007, IEEE Transactions on Instrumentation and Measurement.

[15]  R. Nicolaus,et al.  Aperture correction for a sphere interferometer , 2009 .

[16]  Yasushi Azuma,et al.  Counting the atoms in a 28Si crystal for a new kilogram definition , 2011 .

[17]  P. De Bièvre,et al.  Large-scale production of highly enriched 28Si for the precise determination of the Avogadro constant , 2006 .

[18]  O. Heavens Handbook of Optical Constants of Solids II , 1992 .

[19]  U. Kuetgens,et al.  Present Status of the a Vogadro Constant Determination from Silicon Crystals with Natural Isotopic Composition , 2004, 2004 Conference on Precision Electromagnetic Measurements.

[20]  Ludwig Bergmann,et al.  Optics: Of Waves and Particles , 1999 .

[21]  Gerhard Bönsch,et al.  Absolute volume determination of a silicon sphere with the spherical interferometer of PTB , 2005 .

[22]  Horst Bettin,et al.  Solid density determination by the pressure-of-flotation method , 2006 .