Mass Measurement of 1-kg Silicon Spheres for Determination of the Avogadro and Planck Constants

For the accurate determination of the Avogadro and Planck constants by the X-ray crystal density method, the mass of 1-kg silicon spheres must be measured precisely. This paper describes the mass measurement method and the evaluation of its uncertainty at the National Metrology Institute of Japan (NMIJ). For the precise mass measurement, the amount of the physical adsorption of water vapor on the surface of the silicon spheres, which could be a relative amount of about 10^-8 of the total mass, was evaluated by comparison weighings both in nitrogen gas and in water vapor at a pressure of about 1200 Pa. In addition, we compare the results of seven 1-kg mass measurements conducted at the NMIJ and the International Bureau of Weights and Measures from 1996 to 2011 to confirm the reliability of our mass measurement.