Volume Determination in the Key Comparison for the Realization of the Mass CCM.M-K8.2019

For the first realization of the kilogram after its redefinition, the volume of two ²⁸Si spheres were determined. As part of a first international intercomparison for the realization of mass (CCM.M-K8.2019), national metrology institutes were called upon to determine the degree of agreement between the different representations of the kilogram. These are currently based on Kibble and Joule balances and on the X-ray crystal density method (XRCD). Discrepancies in mass between the different methods of representation are expected, since these also came to light in the determination of Planck's constant h, which is decisive for the new definition of the kilogram. Therefore, the first "consensus value" of the kilogram will be determined in the further course - as a basis for an internationally coordinated dissemination of the kilogram until sufficient agreement between the types of realization will be reached. Each contributing institute (seven participants in 2019/2020) realized the kilogram in its chosen manner and transferred the mass to two 1-kg mass standards (in vacuum). The International Bureau of Weights and Measures (BIPM), acting as a pilot laboratory, had the task of comparing these mass standards with each other and with the BIPM Pt-Ir working standards under vacuum. As additional information, these working standards were compared (in air) with the International Prototype of Kilogram (IPK, "le grand K"), whose mass served as the definition of the kilogram until May 20, 2019.

At PTB, the kilogram was represented by two spheres of highly enriched ²⁸Si according to XRCD, i.e. by determining the molar mass and the lattice parameter of the ²⁸Si crystals used, as well as by determining the volume of the sphere made from the respective crystal. In addition, an accurate surface characterization with XRF (x-ray fluorescence analysis) and XPS (x-ray photoelectron spectroscopy) performed in Department 1.1 is necessary - it is used, on the one hand, for optical phase correction for the interferometric diameter determination and, on the other hand, for correction of the surface layer masses at the transition to the transfer standards. The two spheres (ø ≈ 93.7 mm, m ≈ 1.000 kg) have already been used for the final measurement of Planck's constant h to establish its numerical value (CODATA 2018), as well as for a first international pilot study to determine the mass of the volume of an artifact of a single-crystal of silicon. One sphere, Avo28_S8c, is one of the two spheres from the Avogadro project that originally came from an Australian fabrication in 2008 but had to be decontaminated and repolished at PTB in 2010-2014 due to surface contamination caused by fabrication. The second sphere, ²⁸Sikg01a, originates from a newer crystal and was completely manufactured at PTB. The measurements were overshadowed by numerous external building measures and unexpected equipment failures (thermostatization and laser tubes), so that the tight schedule with the concatenation of the other quantities to be measured made high demands. While Avo28_S8c could only be measured in spherical interferometer 1, a time window remained for 28Sikg01a after the measurements in spherical interferometer 1 for a repeat measurement in spherical interferometer 1 as well as a measurement in spherical interferometer 2. The single interferometric measurements in sphere interferometer 1 as well as the measurement in sphere interferometer 2 differed from each other and from the previous measurements by only about 1/10 nm and therefore lay with their scatter within the relative measurement uncertainty of 9 x 10^-9 for the volume (k=1) given here for the comparison K8.