In 2011, a discrepancy between the values of the Planck constant measured by counting Si atoms and by comparing mechanical and electrical powers prompted a review, among others, of the measurement of the spacing of $^{28}$Si {220} lattice planes, eit
her to confirm the measured value and its uncertainty or to identify errors. This exercise confirmed the result of the previous measurement and yields the additional value $d_{220}=192014711.98(34)$ am having a reduced uncertainty.
In the watt balance experiments, separate measurements of the magnetic and electromotive forces in a coil in a magnetic field enable a virtual comparison between mechanical and electric powers to be carried out, which lead to an accurate measurement
of the Planck constant. This paper investigates the three-dimensional nature of the coil-field interaction and describes the balance operation by a continuous three-dimensional model.
The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate d
etermination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by counting the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, 6.02214084(18) x 10^23 mol^-1, is the most accurate input datum for a new definition of the kilogram.
