Logo of the Physikalisch-Technische Bundesanstalt

Mass determination of two new 28Si spheres in vacuum in preparation of the redefinition of the kilogram

  • Fundamentals of Metrology

A combined standard uncertainty (k = 1) of 6.1 µg (6.1 × 10−9 relative) was achieved for the mass determination in vacuum of two silicon spheres manufactured from a new 28Si crystal. By means of a Sartorius CCL1007 vacuum mass comparator, the necessary measurements were carried out in a pressure range from 3 × 10−3 Pa to 5 × 10−4 Pa.


This mass comparator is equipped with a vacuum transfer system which is compatible with the load lock of a combined XRF1/XPS2 system used to analyse the surface layers on the silicon spheres [1]. In order to minimize possible contaminations during the transfer between the mass comparator and the XRF/XPS apparatus and thus to ensure that the surface layers measured in the XRF/XPS apparatus are comparable to those located on the spheres during mass determination in the mass comparator, the spheres were transferred under vacuum conditions in a sealed container. In the course of the mass determinations, the two spheres specified as Si28kg01a and Si28kg01b were removed from the mass comparator in vacuum one and two times, respectively, transported into the XRF/XPS apparatus for surface analysis and then transferred back into the mass comparator for mass determination. Despite the additional handling required for transportation and the related additional surface contacts, a mass stability within ±1 µg (±1 × 10−9 relative) was achieved for both spheres (Figure 1). A pair of platinum-iridium sorption artefacts served as transfer standards for traceability of the silicon sphere mass in vacuum to the mass of a prototype of the kilogram in air [2-4]. These sorption artefacts are composed of a platinum-iridium cylinder and a stack of eight platinum-iridium discs. Both artefacts were made of the same material, adjusted to the same mass and have the same surface properties. Due to sorption effects, the mass difference between both artefacts changes during the air-vacuum transition. The change in the mass difference and the known surface difference were used to experimentally determine a sorption correction of 2.3 µg with a standard uncertainty of 1.2 µg for the transition of the platinum-iridium cylinder from vacuum (5 × 10-4 Pa) to air (relative air humidity 46 %, air temperature 20.9 °C).


The measurement results for the mass of the 28Si spheres take into account the corrections determined for the national prototypes of the kilogram by BIPM within the scope of the latest comparison measurements with the international prototype of the kilogram [5, 6]. A comparison measurement carried out in collaboration with the National Metrology Institute of Japan (NMIJ) in order to determine the mass of the Si28kg01a 28Si sphere showed that the results agreed within the standard uncertainty.

In combination with measurements carried out to determine the sphere volume and the mass of the surface layers as well as of the molar mass, the lattice spacing, the impurities and defects of the crystal, these measurements contributed to the Avogadro constant being determined – for the first time – by means of 28Si spheres with a relative standard uncertainty of 1.2 × 10-8 [1].


Figure 1: Mass stability of the Si28kg01b 28Si sphere in vacuum. The time is indicated on the x-axis in days, following the initial cleaning and surface inspection of the sphere in the mass laboratory. The y-axis shows the mass determined in milligram. The uncertainty ranges refer to the standard uncertainty (k = 1). Due to a malfunction of the mass comparator, the recipient had to be ventilated on the 28th day and then evacuated again. XRF/XPS measurements were carried out between the 24th and the 28th day, between the 45th and the 48th day and between the 52nd and the 54th day. After the initial XRF/XPS measurement, the surface was additionally checked and the sphere was cleaned (32nd day).


1X-ray fluorescence analysis
2X-ray photoelectron spectroscopy



[1]    Bartl, G.; Becker, P.; Beckhoff, B.; Bettin, H.; Beyer, E.; Borys, M.; Busch, I.; Cibik, L.; D'Agostino, G.; Darlatt, E.; Di Luzio, M.; Fujii, K.; Fujimoto, H .; Fujita, K.; Kolbe, M.; Krumrey, M.; Kuramoto, N.; Massa, E.; Mecke, M.; Mizushima, S.; Müller, M.; Narukawa, T.; Nicolaus, A.; Pramann, A.; Rauch, D.; Rienitz, O.; Sasso, C. P.; Stopic, A.;  Stosch, R.; Waseda, A.; Wundrack, S.; Zhang, L. and Zhang, X. W.: A new 28Si single crystal: Counting the atoms for the new kilogram definition. Metrologia 54 (2017), pp. 693-715
[2]    Picard, A.; Barat, P.; Borys, M.; Firlus, M. and Mizushima, S.: State-of-the art mass determination of 28Si spheres for the Avogadro project. Metrologia 48 (2011), pp. S112–9
[3]    Picard, A. Mass determinations of a 1 kg silicon sphere for the Avogadro project Metrologia 43 (2006), pp. 46–52
[4]    Davidson, S.; Brown, S. and Berry, J.: A report on the potential reduction in uncertainty from traceable comparisons of platinum–iridium and stainless steel kilogram mass standards in vacuum. NPL Report CMAM 88 (2004), National Physical Laboratory, Teddington, pp. 1–24
[5]    Stock, M.; Barat, P.; Davis, R. S.; Picard, A. and Milton, M. J. T.: Calibration campaign against the international prototype of the kilogram in anticipation of the redefinition of the kilogram, part I: comparison of the international prototype with its official copies. Metrologia 52 (2015), pp. 310–6
[6]    de Mirandés, E.; Barat, P.; Stock, M. and Milton, M. J. T.: Calibration campaign against the international prototype of the kilogram in anticipation of the redefinition of the kilogram, part II: evolution of the BIPM as-maintained mass unit from the 3rd periodic verification to 2014. Metrologia 53 (2016), pp. 1204–14


Contact person:

Dr. Michael Borys, Department 1.8, Working Group 1.81, E-Mail: Opens window for sending emailmichael.borys(at)ptb.de


Head of Press and Information Office

Dr. Dr. Jens Simon

Phone: +49 531 592-3005


Physikalisch-Technische Bundesanstalt
Bundesallee 100
38116 Braunschweig