Watt balance

The Watt balance, also known as the Kibble balance since 2017 (in honor of its inventor Bryan Kibble ), is an experimental setup that can be used to create a relationship between Planck's quantum of action and the unit of measurement, the kilogram . With a fixed kilogram, the Planck quantum of action could be determined and since May 20, 2019, when the Planck quantum of action was assigned a fixed numerical value, the unit of measure kilogram can be realized.

background

The kilogram was the only SI base unit that could not be implemented with the help of a measurement specification. Since 1889 it had been defined using the original kilogram stored in Paris . Comparative measurements between this prototype and national copies show a divergence of around 50  ppb over 100 years. For decades, physicists have therefore endeavored to improve the reproducibility of experiments with which the unit of mass can be traced back to natural constants to below 10 ppb. One approach is the Watt balance proposed in 1975 by B. P. Kibble at the British National Physical Laboratory (NPL). On May 20, 2019, the original kilogram was removed from the SI system and a numerical value for Planck's quantum of action was determined instead.

Measuring principle

The watt balance at NIST

Two experiments are carried out one after the other on a coil in a magnetic field, a weighing and a movement. During weighing, the current is measured that is necessary to compensate for the weight of the mass ; during movement, the induction voltage is measured, which is generated by a vertical movement at the speed : ${\displaystyle I}$ ${\displaystyle m}$ ${\displaystyle U}$ ${\displaystyle v}$

${\displaystyle I\propto mg}$

This contains the acceleration due to gravity, which can be measured very precisely through fall experiments, i.e. it can be traced back to the basic units of meters and seconds defined by natural constants. ${\displaystyle g}$

The interferometrically controlled movement with the speed induces a voltage ${\displaystyle v}$

${\displaystyle U\propto v,}$

which is measured without current. The constant of proportionality with magnetic induction and length of the coil wire can be reduced when multiplying the equations: ${\displaystyle B\,L}$ ${\displaystyle B}$ ${\displaystyle L}$

${\displaystyle U\,I=mgv}$

On both sides of this equation there is a power with the unit watt . This gave the process its name. A direct electrical power measurement would be falsified by the Joule heat . In order to get a measurement result for the mass, this equation is transformed into:

${\displaystyle m={\frac {U\,I}{g\,v}}}$

In it the tension is expressed as a fold of a Josephson tension ${\displaystyle U}$ ${\displaystyle n}$

${\displaystyle U_{\mathrm {J} }=f_{\mathrm {J} }{\frac {h}{2e}}}$

measured, which can be precisely adjusted via the microwave frequency . is Planck's quantum of action and the elementary charge . ${\displaystyle f_{\mathrm {J} }}$ ${\displaystyle h}$ ${\displaystyle e}$

The current is also determined by means of the quantum Hall effect via a voltage: ${\displaystyle I}$

${\displaystyle I={\frac {U'}{R}}={\frac {n'U_{\mathrm {J} }'}{rR_{\mathrm {K} }}}}$

There are and further dimensionless factors and is the von Klitzing constant . ${\displaystyle n'}$ ${\displaystyle r}$ ${\displaystyle R_{\mathrm {K} }=h/e^{2}}$

Of the natural constants occurring in both quantum effects and the latter can be abbreviated: ${\displaystyle h}$ ${\displaystyle e}$

${\displaystyle U\,I={\frac {nn'}{r}}f_{\mathrm {J} }\,f_{\mathrm {J} }'{\frac {h}{4}}}$

Experimental

The measurement takes place in a very complex setup in a high vacuum. Interfering magnetic fields must also be excluded at greater distances, as well as deformations and movements of the coil other than vertical.

At the International Bureau of Weights and Measures (BIPM) a model with a superconducting coil is currently being set up, which allows the simultaneous measurement of current and voltage without measurement errors due to a coil resistance. This reduces the demands on the constancy of the magnetic field and coil geometry.

Various alloys are discussed for the test mass in the Watt balance, for example a gold-platinum alloy. The material not only has to be resistant to abrasion and corrosion, as is usual for mass measuring standards, but also has to have the lowest possible magnetic susceptibility (magnetizability).

Alternative procedures

In addition to the Watt balance, work is being carried out on another method with which the kilogram can be realized on the basis of natural constants. In addition to the watt balance, there is the Avogadro project . In this process, the kilogram is realized as a multiple of the atomic mass of a certain nuclide . A large number of these atoms must be precisely determined for the connection to weighable masses. The approach of the Avogadro project is the indirect counting from the volume and the lattice constants of a single crystal, isotopically pure silicon sphere . The volume is determined by interferometry and the lattice constant by X-ray diffraction. The first of these balls manufactured for sale by PTB in Braunschweig bought Taiwan for one million euros at the beginning of 2018.

Individual evidence

1. ↑ Holger Dambeck: The puzzling shrinkage of the original kilogram. In: Der Spiegel . September 13, 2007.
2. ↑ Metrology: units of measurement will soon be carved in nature. Retrieved May 20, 2019 . 
3. ^ Z. Silvestri et al .: Volume magnetic susceptibility of gold-platinum alloys: possible materials to make mass standards for the watt balance experiment. Metrologia , 40/2003, pp. 172-176.
4. ↑ Ruth Hutsteiner: New original kilo for one million euros. At: Science.ORF.at. March 28, 2018. Retrieved March 28, 2018.

literature

• M. Stock: The watt balance: determination of the Planck constant and redefinition of the kilogram. Phil. Trans. R. Soc. A 369 (2011), pp. 3936-3953.
• RL Steiner et al .: Towards an electronic kilogram: an improved measurement of the Planck constant and electron mass. Metrologia, 42/2005, pp. 431-441.
• RL Steiner et al: Uncertainty Improvements of the NIST Electronic Kilogram. IEEE Trans. Instrum. Meas. 56 (2007), pp. 592-596.
• IA Robinson et al .: An initial measurement of Planck's constant using the NPL Mark II watt balance. Metrologia, 44/2007, pp. 427-440.
• AG Steele et al .: Reconciling Planck constant determinations via watt balance and enriched-silicon measurements at NRC Canada. Metrologia 49 (2012), pp. L8-L10.
• A. Eichenberger et al .: Determination of the Planck constant with the METAS watt balance. Metrologia 48 (2011), pp. 133-141.
• P. Pinot et al .: Theoretical analysis for the design of the French watt balance experiment force comparator. Rev Sci Instrum., 78/2007, PMID 17902975 .
• A. Picard et al: The BIPM watt balance: Improvements and developments. 2010 Conference on Precision Electromagnetic Measurements (CPEM), Daejeon, 2011, doi: 10.1109 / CPEM.2010.5543305 .

Web links

Commons : Watt Scales  - Collection of images, videos, and audio files

• The Watt scales at the Bureau International des Poids et Mesures (BIPM)
• The watt balance at NIST
• Lexicon of Physics: Watt-Waage Spektrum.de
• Alternative to the original kilogram Spektrum.de, September 14, 2005, with a schematic representation of a watt balance