Solid density determination by the pressure-of-flotation method

Abstract

After a short overview of flotation methods and experiments, basic equations for the pressure-of-flotation method are given including a temperature and composition dependence of the liquid's thermal expansion and compressibility. Then, the pressure-of-flotation experiment of PTB is described. A new calibration procedure using doped silicon samples is presented. Now, density comparisons of silicon samples can be performed with an uncertainty less than 0.1 ppm for density differences up to 10 ppm, i.e. for practically all undoped silicon samples. Current applications of the method and an outlook to future developments are discussed. Relative uncertainties of the order of 10−9 seem to be possible and would allow new applications.

Volume determination of the Avogadro spheres of highly enriched28Si with a spherical Fizeau interferometer

“…This corresponds to a mean diameter of d AVO28−S5 = 93.7229717(11) mm (26) and d AVO28−S8 = 93.7222511(9) mm, (27) respectively. These results apply for a temperature of 20 • C and a pressure of 0 Pa.…”

“…Taking into account the correlations of the measurements, a density difference of the spheres of 0.000 089(97) kg/m 3 or 38(42) × 10 −9 , relatively, is yielded. These calculated densities of the whole spheres can be checked by a direct density comparison of the two spheres as can be performed with high precision by the pressure-of-flotation method [27,28]. In this method each of the silicon samples floats freely in a suitable liquid that has the same density as silicon.…”

In-Situ Liquid Density Measurement for Liquid Column Manometry

“…To bring the solid into the flotation state, it is possible to control either temperature 𝑡 or pressure 𝑝, the method then is called temperatureof-flotation (TFM) [12] or pressure-of-flotation method (PFM) [13], respectively.…”

Determination of the Avogadro constant and the redefinition of the kilogram

“…最好结果 [16] . [20] 或 浮 压 法 [21] 面度和表面粗糙度不能满足实验要求 [2,22] . 1987~1994 年间, 澳大利亚国家测量实验室的 Leistner 等人 [23] 研制出了新的单晶硅球加工技术, 利用该技术加工 出的单晶硅球近乎理想(球面度优于 50 nm, 表面粗 糙度 RMS 优于 0.2 nm), 完全满足现有实验精度要求.…”