Density comparisons of silicon samples by the pressure-of-flotation method at PTB

After a short review of the history of the flotation method, the flotation apparatus of the Physikalisch-Technische Bundesanstalt (PTB) and the measurement procedures are described in detail. A comprehensive description of the method used to achieve flotation by adjusting the hydrostatic pressure in the liquid is given, covering the heating by compression, surface effects and a calculation of the theoretical detection limit. Data evaluation of the single measurement is described as well as the least-squares fit for a group of samples using Lagrange multipliers to take constraints into account. Results of comparisons of density standards and samples measured to determine the molar volume of silicon and the Avogadro constant including the uncertainty budget and correlation coefficients are reported.