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PTB Recipe for the New Kilogram

All under one roof: PTB has the know-how and has gathered all the technical components to redefine the unit of mass


It's a real pressure-cooker. In the international contest over the most accurate definition of the kilogram, researchers of the Physikalisch-Technische Bundesanstalt (PTB) now not only have the recipe in their pocket, they have also gathered all the components: They have set up a complex chain of many manufacturing and analytical steps in order to - by counting the atoms in a silicon sphere − accurately determine two constants of nature: the Avogadro constant and Planck’s constant. These are the pillars of a redefinition of the kilogram. The new skills and measurement methods which have been developed in the course of the past months and years − among other things, also within the scope of the international Avogadro project − must now prove themselves in practice: In March, PTB receives a crystal made of high-purity silicon-28, from which two spheres will be manufactured and then analyzed. The values determined thereby for the Avogadro constant and Planck's constant should have an unrivaled accuracy.

Sharp-sighted interferometer: The silicon sphere placed in the center is measured extremely accurately − an intermediate step on the path to a redefinition of the kilogram. (Photo: PTB)

Prof. Dr. Manfred Peters, former Vice-President of PTB, takes a critical look at the high-purity base material at the Leibniz-Institut für Kristallzüchtung (Leibniz Institute for Crystal Growth). From this material the staff members of the institute subsequently grow a flawless single-crystal.

"Our goal is to have PTB master the realization of the future kilogram completely autonomously", says Horst Bettin, head of PTB's kilogram project. To this end, PTB has goal-orientatedly developed new methods and improved already known methods. Some years ago, for example, the first silicon spheres for the experiment were polished in Australia by the – at that time – only expert worldwide. Today, the complete sphere production takes place at PTB and is so exact that the deviation from the ideal sphere shape is considerably less than 100 nanometers. With the sphere interferometer it is possible to determine the average diameter of the sphere accurately down to three diameters of an atom, and a UHV reflectometer determines the thickness of oxide layers on the sphere surface down to one nanometer.

However, Bettin's confidence is based not only on technology and the skills of PTB staff members, but also on the purity of the supplied material. In the Electrochemical Plant in Zelenogorsk, Russia, thousands of centrifuges were in operation for months in order to facilitate the more than 99.998 percent isotope purity of the silicon-28. "That was a master performance at the limit of what is technically possible", praised Manfred Peters, former Vice-President of PTB, who led the complex contractual negotiations with Russia and who heads the project with Russia. Also the subsequent cleaning of the highly explosive gaseous silicon tetrafluoride (28SiF4) and its conversion to silane (28SiH4), and subsequently to polycrystalline silicon was, according to Peters, "real pioneer work which earns the highest approval". The chemically complicated process especially developed for this project took place at the Institute of Chemistry of High-Purity Substances of the Russian Academy of Sciences in Nishniy Novgorod.

In the course of the coming months, another six-kilogram crystal will be supplied. From the Russian base material, the Leibniz-Institut für Kristallzüchtung (Leibniz Institute for Crystal Growth) in Berlin will in each case grow a flawless single-crystal whose inner structure is completely regular and without fractures. Both being free of impurities and having a regular structure are preconditions for the success of the experiment. In the end, PTB will have at its disposal a nearly perfect base material for four spheres.

From the round-bodied, cylindrical single-crystals, PTB produces crystal spheres that are rounder than anything else in the world. Each sphere is then measured individually according to all the rules of the art. The aim is to connect the coarse characteristics to the fine characteristics, that is, to produce the connection between the mass of the sphere and the mass of an atom. Thus, the researchers measure the mass and the volume of the 28Si sphere as well as the arrangement of the atoms in the crystal and the abundance of the three existing silicon isotopes, which yields the molar mass of the silicon used. Thus, they know how many moles of silicon are present in their sphere and how many atoms there are in one mole. The researchers have thus determined the Avogadro constant. The goal has been reached! And since the Avogadro constant is also linked to the Planck constant via a fixed physical relation, both can be determined in one fell swoop. Already at this point, PTB scientists miscount only twice every one hundred million atoms. The goal is to miscount only by one atom for every one hundred million atoms.

And why is this all being done? Doesn't everyone already know how heavy a kilogram is? Currently, all mass measurements in the world ultimately relate to a small cylinder made of a platinum-iridium alloy, which is kept secure in a safe at the International Bureau of Weights and Measures (BIPM) in Sèvres: the international prototype of the kilogram. Numerous countries have copies of the international prototype of the kilogram. With these copies and via further transfer standards, we teach weighing instruments how heavy a kilogram is. However, physical and chemical processes change things in the course of time. There are indications that the mass of the international prototype of the kilogram has also changed slightly. At worst, the international prototype of the kilogram could be destroyed or stolen all of a sudden. Then the definition would be lost for all time.

In order to evade the transient sword of Damocles, researchers are searching worldwide for a new definition. At the international General Conference on Weights and Measures, it was agreed upon to not only define the kilogram, but also three other physical units via natural constants in 2018, if possible - thus via physical quantities whose value can be neither influenced nor changes spatially or temporally. These units are the ampere, the mole, and the kelvin. For the definition of the kilogram, the Avogadro constant would actually be sufficient, but the mass metrologists also keep their "electrical colleagues" in mind: These want to define the unit of electric current, the ampere, also via a constant, namely the charge of the electron. And if the mass colleagues were to now add Planck's constant, the units of voltage and resistance would be simply derived therefrom. Since both – the Avogadro constant and Planck's constant – are interlinked, internationally it has been agreed to also define the kilogram via this constant, even though this is less vivid.

This will not change the dissemination of the unit: Also in the future we will tell our weighing instruments with the aid of weights – possibly also in the form of silicon spheres − how heavy a kilogram is. But these weights can be reproduced. Because the "mother" of all kilogram weights will no longer be a physical and, thus, destroyable object, but rather a defining constant in a mathematical formula which will defy all changes.

Technically speaking, in the contest over the redefinition of the kilogram there cannot, by the way, really be a "winner", because the kilogram will not be redefined until at least two scientific approaches and the experiments of three research groups come to consistent findings: namely to determine Planck's constant with sufficient accuracy. The experiments with the silicon-28 sphere are only one possible way to determine Planck's constant – it is the way that the PTB scientists are going. Several other institutes, particularly in the USA, Canada, France and Switzerland, are focusing on the watt balance. It allows the weight force of a mass to be compensated through electromagnetic force. In view of the progress made with both approaches, nothing should stand in the way of the redefinition of the kilogram at the end of 2018.


Dr. Horst Bettin, head of PTB Working Group “Avogadro Constant”,
Telephone: +49 (0)531 592-3330,
e-mail: horst.bettin(at)ptb.de

Dr. Roman Schwartz, Vice-President of PTB,
e-mail: roman.schwartz(at)ptb.de

Prof. Dr. Manfred Peters, former Vice-President of PTB,
e-mail: manfred.peters(at)ptb.de