Evaluation of the long-term reproducibility of a realization of the kilogram by the XRCD method

Abstract The definition of the kilogram is presently based on the Planck constant h . It is therefore possible to establish a mass standard by realizing the kilogram using any method that relates h to mass. On the basis of this principle, we realized the kilogram by the x-ray crystal density (XRCD) method using a silicon sphere with a nominal mass of 1 kg. For the realization, the silicon core volume of the sphere excluding the surface layer was measured using a laser interferometer to determine the number of silicon atoms in the core. The mass of the silicon core m core was determined from the number of silicon atoms and the mass of a single silicon atom calculated from h . To evaluate the mass of the surface layer m SL , the surface of the sphere was characterized by x-ray photoelectron spectroscopy and ellipsometry. The sphere mass m sphere was determined from m core and m SL , and the standard uncertainty of the kilogram realization was estimated to be 23 μg. To statistically evaluate the long-term reproducibility of this realization, the realization result was compared with previous realization results in 2016 and 2019. The standard deviation of m sphere in the three realizations over five years was estimated to be as small as 2.4 μg, corresponding to 2.4 × 10 −9 in relative terms for 1 kg. This is only 10 % of the standard uncertainty of the kilogram realization. The standard deviations of m core and m SL over five years were also estimated to be 3.9 μg and 1.9 μg, respectively. On the basis of these statistical evaluations, the strategy for the kilogram realization by the XRCD method to establish the primary mass standard in the future is discussed.