Absolute measurement of the density of silicon spheres to improve the primary density standard of NMIJ

Abstract

Abstract To improve the primary density standard of the National Metrology Institute of Japan (NMIJ), the absolute densities of two 1 kg silicon spheres, NMIJ-S4 and NMIJ-S5, were determined by measuring their masses and volumes. The volumes of the two spheres were measured by optical interferometry based on the primary length standard of NMIJ. For the accurate volume determination, the thicknesses of the surface layers on the spheres were determined by x-ray photoelectron spectroscopy (XPS). By combining the results of optical interferometry and XPS, the volumes of the two spheres at 20.000 °C and 0 Pa were determined with relative standard uncertainties of 3.0  ×  10−8 and 2.9  ×  10−8 for NMIJ-S4 and NMIJ-S5, respectively. From these results, the sphere volumes at 20.000 °C and 101.325 kPa were determined using the isothermal compressibility of silicon. The masses of the spheres in air were determined based on the national prototype of the kilogram of Japan. From the results of the volume and mass measurements, the densities of the two spheres at 20.000 °C and 101.325 kPa were determined with a relative standard uncertainty of 3.2  ×  10−8. The density difference between the two spheres was estimated taking into account the correlation between the densities of the two spheres. The pressure-of-floatation method was also used to determine the density difference between the two spheres. The density differences determined by the two different methods agree with each other within their uncertainties.