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The kilogram and the mole: Counting atoms

The Avogadro experiment and the watt balance are the pillars of the redefinition of the kilogram. They represent two independent possibilities of realizing the redefinition. Today, the unit "kilogram" is defined as the mass of the international prototype of the kilogram which is kept in a safe in Sèvres near Paris. International efforts are aimed at relating all base units, such as the second, the meter, the kilogram and the ampere, in future only to fundamental constants in order to create a system of units which is independent of artifacts. For this purpose, it is determined in the Avogadro experiment how many atoms are contained in almost perfect silicon spheres. The next possibility for a redefinition of the kilogram will present itself on the occasion of the General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM) in 2018. At the same time, the results of the Avogadro experiment must beconsistent with those of the watt balance. It is only then that a safe and exact redefinition of the unit of mass is guaranteed. The realization of the Avogadro experiment is based on the contributions of different working groups of PTB and of national and international partners.

Trailer zum Avogadro-ProjektTrailer zum Avogadro-Projekt

Was muss man tun, um die rundesten Kugeln der Welt zu „bauen“? Wie sehen die Arbeitsschritte dafür aus? Wie das Handling der Kugeln, die Lagerung, der Transport und einige der Messungen? Der Videoclip zeigt, wie die Kugeln zu handhaben sind, und macht die Vorteile dieser möglichen „Massenormale“ deutlich.


Den natürlich oxidierten Oberflächen der Siliziumkugeln im Avogadro-Projekt kommt eine besondere Bedeutung zu – während der Messungen, der Lagerung und dem Transport der Kugeln. Als eine mögliche Alternative wurde in einem Pilotprojekt, zusammen mit dem Fraunhofer Institut für Schicht- und Oberflächentechnik (IST), die Atomic Layer Deposition (ALD) untersucht.

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Beteiligte Arbeitsgruppen der PTB

Coordination of the project

Working Group 3.44 "Avogadro Constant" coordinates the research activities at PTB and the cooperation with institutes all over the world for the precise determination of the Avogadro constant. This is to create a foundation for the redefinition of the unit of mass "kilogram" on the basis of a fundamental constant.

Preparation of the spheres

The material of the spheres was manufactured in Russia by the Central Design Bureau of Machine Building in St. Petersburg and by the Institute of Chemistry of High-Purity Substances of the Russian Academy of Sciences in Nishni Novgorod. Then, single crystals without dislocations were drawn in the Leibniz-Institut für Kristallzüchtung (IKZ) in Berlin, and from these, the spheres were manufactured. WG 4.33 "X-ray Optics" prepares the samples of the 28Si crystal, and WG 5.56 "Manufacturing Technology" manufactures the spheres with as little a form deviation as possible.

Determination of the isotopic ratio and of the molar mass

The isotopic ratio and the molar mass are measured at PTB's Working Group 3.11 "Inorganic Analysis" by means of isotope dilution mass spectrometry (IDMS). (The relative atomic masses of the naturally occurring silicon isotopes 28Si, 29Si and 30Si are known with sufficient accuracy from other measurements.)

Working Group 3.11: Inorganic Analysis

Determination of the volume in the sphere interferometer

The volume of the silicon spheres is determined by WG 5.41



"Interferometry on Spheres" at 20 °C and in vacuum with the aid of a spherical Fizeau interferometer. In cooperation with WG 4.33 "X-ray Optics", this working group also performs numerical simulations for the interferometer. The temperature measurements of the volume and lattice parameter determinations are compared with one another and with the temperature realization of WG 7.42 "Applied Thermometry" with the aid of an electronic temperature reference point (20 °C) which has been developed by WG 3.43 "Solid State Density ".

Working Group 5.41: Interferometry on Spheres

Investigation of the sphere surfaces

On the surface of the spheres, an oxide layer and possibly other surface layers can be found which must be taken into account when determining the sphere volume and the sphere mass. The required knowledge of the thickness and of the structure of the surface layers on the spheres is determined by the following Working Groups with the methods indicated:

Working Group 4.33: "X-ray Optics" with X-ray Fluorescence Spectroscopy (XRF)

Working Group 5.13: "Layer Thickness and Crystalline Standards     

Method:  Spectral ellipsometry



Working Group 5.14: "3D Roughness Metrology"



Working Group 7.11: "X-ray Radiometry" with X-ray Reflectrometry (XRR) and X-ray Fluorescence Spectroscopy (XRF) at BESSY II

Density comparisons of the spheres and of material samples

WG 3.43 "Solid State Density" performs density comparisons of the spheres and of other samples. The density of the thermal oxide on silicon spheres has also been determined in this WG with the aid of density comparison measurements. Working Group 3.43: "Solid State Density"

Investigations of impurities of the sphere material

WG 3.14 "Optical Analysis" determines the contents of the main impurities boron, carbon, oxygen and nitrogen by means of low

temperature infrared spectroscopy. A result of the impurities is that the mass of the real silicon sphere differs slightly from the mass of a sphere which consists only of silicon atoms.

Working Group 3.14: Optical Analysis

Nationale und Internationale Partner

National and international partners

  • Dresden University: Measurement of the hydrogen concentration in the crystal by Deep Level Transient Spectroscopy (DLTS)
  • Halle-Wittenberg University: Measurement of the vacancy concentration in the crystal by positron annihilation experiments
  • Federal Institute of Metrology (METAS, Switzerland): Measurement of the surface layers of the Si spheres with X-ray photoelectron spectroscopy (XPS)
  • National Institute of Metrology (NIM, China), National Institute of Standards and Technology (NIST, USA) and National Research Council of Canada (NRC): Measurement of the molar mass of isotopically enriched silicon with IDMS
  • International Bureau of Weights and Measures (BIPM): Mass determinations of the silicon spheres in air and in vacuum and guarantee of the traceability to the international prototype of the kilogram
  • Istituto nazionale di ricerca metrologica (INRIM, Italy): Lattice parameter measurements at 20 °C and in vacuum with the aid of an X-ray scanning interferometer
  • NMIA: Diameter measurements of spheres at 20 °C and in vacuum with the aid of a Saunders interferometer
  • National Metrology Institute of Japan (NMIJ, Japan)

    o    Measurement of the mass of the spheres in air and in vacuum

      • Measurement of the diameters at 20 °C and in vacuum with an interferometer
      • Investigation of the oxide layer thickness with spectral ellipsometry
      • Investigation of the homogeneity of lattice distances in the 28Si crystal
    • National Institute of Metrology (NIM, China): Measurements in the fields of the molar mass, the volume, the surface layers and the mass