Since 1889 the international prototype of the kilogram has served as the definition of the unit of mass in the International System of Units (SI). It is the last material artefact to define a base unit of the SI, and it influences several other base units. This situation is no longer acceptable in a time of ever increasing measurement precision.It is therefore planned to redefine the unit of mass by fixing the numerical value of the Planck constant. At the same time three other base units, the ampere, the kelvin and the mole, will be redefined. As a first step, the kilogram redefinition requires a highly accurate determination of the Planck constant in the present SI system, with a relative uncertainty of the order of 1 part in 108.The most promising experiment for this purpose, and for the future realization of the kilogram, is the watt balance. It compares mechanical and electrical power and makes use of two macroscopic quantum effects, thus creating a relationship between a macroscopic mass and the Planck constant.In this paper the background for the choice of the Planck constant for the kilogram redefinition is discussed and the role of the Planck constant in physics is briefly reviewed. The operating principle of watt balance experiments is explained and the existing experiments are reviewed. An overview is given of all presently available experimental determinations of the Planck constant, and it is shown that further investigation is needed before the redefinition of the kilogram can take place.

http://iopscience.iop.org/article/10.1088/0026-1394/50/1/R1/pdf

Watt balance experiments for the determination of the Planck constant and the redefinition of the kilogram

The redefinition of the SI unit of mass in terms of a fixed value of the Planck constant has been made possible by the Kibble balance, previously known as the watt balance. Once the new definition has been adopted, the Kibble balance technique will permit the realisation of the mass unit over a range from milligrams to kilograms. We describe the theory underlying the Kibble balance and practical techniques required to construct such an instrument to relate a macroscopic physical mass to the Planck constant with an uncertainty, which is achievable at present, in the region of 2 parts in 10^8. A number of Kibble balances have either been built or are under construction and we compare the principal features of these balances.

https://iopscience.iop.org/article/10.1088/0026-1394/53/5/A46/pdf

The watt or Kibble balance: a technique for implementing the new SI definition of the unit of mass.

The METAS watt balance project was initiated slightly more than a decade ago. Over this time, the apparatus has been through an uninterrupted series of upgrades that have improved its reliability to a point where continuous series of measurements can be taken fully automatically over periods of several months. A comprehensive analysis of possible systematic errors has now been completed and a large set of data has been analysed to calculate a value for the Planck constant h. This paper describes the watt balance in detail, explains the data acquisition and analysis thoroughly and presents the uncertainty budget. The value of the Planck constant determined with our apparatus is h = 6.626?069?1(20) ? 10?34?J?s with a relative standard uncertainty of 0.29 ? 10?6. This value differs from the 2006 CODATA adjustment by 0.024??W?W?1.

https://iopscience.iop.org/article/10.1088/0026-1394/48/3/007/pdf

Determination of the Planck constant with the METAS watt balance

We have measured Planck's constant and have obtained a value of 6.626?070?34(12)???10?34?J?s. To our knowledge this measurement of h has the lowest uncertainty reported to date. This result has been obtained from measurements of four masses of different material and nominal values varying from 1?kg to 250?g. The experimental procedures and the measurement uncertainties are described in detail.

https://iopscience.iop.org/article/10.1088/0026-1394/51/2/S5/pdf

A determination of Planck's constant using the NRC watt balance

Since 1889, the international prototype of the kilogram has served as the definition of the unit of mass in the International System of Units (SI). It is the last material artefact to define a base...

The watt balance: determination of the Planck constant and redefinition of the kilogram.

Since beginning the construction early in 2005, considerable progress has been made on the watt balance of the Bureau International des Poids et Mesures (BIPM). We have continued the development of a room-temperature version to test the feasibility of simultaneous force and velocity measurements. Preliminary measurements of the voltage-velocity ratio have been carried out with a reproducibility of the order of 1 part in 104. The coil suspension has been improved to reduce the undesired coil movement in the 5 degrees of freedom different from a perfectly vertical movement. Further work on the current source has reduced its long-term drift to a few parts in 109 per minute with a satisfactory short-term stability. A technique needed to separate the voltage induced in the coil from the voltage drop due to the current flow based on the use of a second noninductive coil has been tested. The second coil is now being integrated into the apparatus. Work has started on the geometrical and magnetic characterizations of a large precision solenoid that will become the reference for the magnetic field alignment. The collaboration with a university on the fabrication of our magnetic circuit is being continued. This paper briefly outlines the main ideas of the BIPM watt balance and reports the progress to date.

Progress on the BIPM watt balance

This report describes the first CCM key comparison of realizations of the kilogram definition based on the fixed numerical value of the Planck constant, which came into force on 20 May 2019. The objectives were to determine the level of agreement between realizations of the kilogram using Kibble and joule balances and the X-ray crystal density (XRCD) method and to provide input for the calculation of the first "consensus value" of the kilogram. The consensus value will serve as the basis for an internationally coordinated dissemination of the kilogram which will continue until sufficient agreement between realization experiments has been achieved.The comparison was organized by the BIPM and had seven participants. The BIPM, KRISS, NIST and NRC operated Kibble balances, the NIM used a joule balance and the NMIJ and the PTB participated using 28Si spheres, the masses of which were determined with the XRCD method. These realization methods were used to calibrate 1 kg mass standards under vacuum. The standards were sent (in air) to the BIPM where they were compared under vacuum with each other and with BIPM Pt-Ir working standards. The latter were calibrated (in air) traceable to the International Prototype of the Kilogram (IPK), the mass of which served as the definition of the kilogram until 20 May 2019.The results of the weighings at the BIPM together with the measurement results communicated by the participants allowed comparison of the values attributed to mass standards of 1 kg using the participating realization experiments. The level of agreement between mass determinations with the realization experiments and the BIPM as-maintained mass unit, traceable to the Planck constant through the mass of the International Prototype of the Kilogram can also be deduced.Main text To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Report on the CCM key comparison of kilogram realizations CCM.M-K8.2019

The International Bureau of Weights and Measures (BIPM) is developing a watt balance for the forthcoming redefinition of the kilogram. An improved version of the apparatus, based on a new closed magnetic circuit is now being assembled. The new apparatus will significantly reduce the type B uncertainty due to misalignment of the magnetic circuit as this work demonstrates. We present two techniques recently developed to accurately align the magnetic field of the circuit perpendicular to the direction defined by the local acceleration of gravity. Uncertainty below 30 μrad was achieved for both techniques which fulfils the requirements for the BIPM watt balance to enable a Planck constant determination at the 1 × 10−8 level.

https://iopscience.iop.org/article/10.1088/0026-1394/52/6/775/pdf

Alignment of the magnetic circuit of the BIPM watt balance

This report describes the second CCM key comparison of realizations of the kilogram definition based on the fixed numerical value of the Planck constant, which came into force on 20 May 2019. The objectives were to determine the level of agreement between realizations of the kilogram using Kibble and joule balances and the x-ray crystal density (XRCD) method and to provide input for the calculation of the second "consensus value" of the kilogram. The consensus value serves as the basis for an internationally coordinated dissemination of the kilogram and is updated after each new key comparison. Its use will continue until satisfactory agreement between realization experiments has been achieved. Another objective was the determination of the reproducibility of the realization experiments by comparing the new results with those of the first key comparison of kilogram realizations, CCM.M-K8.2019. The comparison was organized by the BIPM and had nine participants. The BIPM, LNE, METAS, NIST, NRC and UME operated Kibble balances, the NIM used a joule balance and the NMIJ and the PTB participated using 28Si spheres, the masses of which were determined with the XRCD method. These realization methods were used to calibrate 1 kg mass standards under vacuum or in air. The standards were sent to the BIPM where they were compared with each other and with BIPM Pt-Ir working standards. The latter were calibrated traceable to the International Prototype of the Kilogram (IPK), the mass of which served as the definition of the kilogram until 20 May 2019. The results of the weighings at the BIPM together with the measurement results communicated by the participants allowed comparison of the values attributed to 1 kg mass standards using the realization experiments of the participants. The level of agreement between mass determinations with the realization experiments and the BIPM as-maintained mass unit, traceable to the Planck constant through the mass of the International Prototype of the Kilogram, could also be deduced. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database https://www.bipm.org/kcdb/. The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Y. F. Lu

Papers

Progress on the BIPM watt balance

Report on the CCM key comparison of kilogram realizations CCM.M-K8.2019

Alignment of the magnetic circuit of the BIPM watt balance

Final report on the CCM key comparison of kilogram realizations CCM.M-K8.2021